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Medical_Surgical_Nursing	NCLEX_Hotspot_Question_Example_Digoxin_Practice_Question_Pharmacology.txt	hey everyone is stares red sterner sorry and calm and in this video I want to be going over our weekly NCLEX question and don't forget to check out our other free resources to help you study for in clicks so let's get started a 55 year old male patient is ordered by the physician to take digoxin which is also called blue moccasin 0.25 milligrams by mouth daily prior to administering this medication you will assess what area on the diagram okay this question is one of those hotspot type questions that you may encounter on the NCLEX exam and for this particular question we need to click in the area that we're going to assess prior to giving the medication call dioxin also known as an awesome so the first thing that should be popping in your head is what is digoxin well digoxin is a cardiac medication and acts on the heart is part of the cardiac glycosides family and digoxin is really an interesting drug because it has this positive inotropic effect on the heart so what does that mean it means that it's going to cause each heart contraction to be stronger so when your heart beat and it squeezes that blood out that contraction is going to be stronger so that blood can get out of that heart muscle and go to the body and go and do its job however on the flip side the Jobson also has this negative quantitative effect which is going to slow that heart rate down so you have a slower heart rate that stronger contraction and this is a great drug for allowing the heart to beat more efficiently this medication is also used in patients with particular types of heart failure and again what is heart failure we learned in our in click review lectures that heart failure is when that heart muscle has become weak and when the heart becomes weak it cannot pump efficiently so that blood will stay in the heart it can backflow to the lungs causing respiratory issues or in extremities and things like that and what digoxin will hopefully do is it will slow that heart rate down which decreases the demands on the heart but it will also cause that weak muscle to contract stronger so you hopefully get decreased amounts of blood pooling in that heart it's also used in treatment sometimes of a condition called atrial fibrillation which is one of those arrhythmia where the heart rate is beating you're a Euler is not being regularly have decreased blood flow and digoxin can slow that irregular fast heart rate down and help it beat more efficiently now as the nurse prior to giving the dachshund you always want to assess the apical pulse for one full minute and in adults you want to make sure it's at least sixty beats or greater now next question you want to ask yourself is where is this apical pulse located that is the whole thing whenever you're looking at that diagram that's what we're trying to find so the apical pulse is located also where the point of maximal impulse is so it will be located at the apex of the heart now whenever you're looking at the heart is flipped upside down the base is up at the top and the apex is at the bottom and this is going to be the same listening area for where you will assess the mitral valve so let's backtrack and talk about all the places that we assess on the chest whenever we're listening to heart film because when we're listening to heart sounds what are we doing we're listening to the closure of those four valves so we're listening to loved-up s1 and s2 so what are those four valves were listening to first kind of Alves we're listening to are called the semilunar valve and that includes your aortic valve and your pulmonic valve and whenever these close that is s2 what you will be hearing that's the dub part of love dub then we listen to the atrioventricular valves which are the tricuspid and the mitral valves and when they close you hear s1 which is the love part now whenever you're assessing your patient I like to use this mnemonic because it helps you go in the order of how they are on the chest all patients take medicine in the first letter of each word correlates with that heart valve so let's look at where each heart valve is located because we are theme for where the mitral valve is located because this is where we're going to listen to our applicable pulse okay so the aortic cause all for aortic is found on the right side of the sternal border in the second intercostal space which is right here the next is the pulmonic valve and this is found left of the sternal border in the second intercostal space then you will go down a little bit and you will go to the left of the sternal border in the fourth intercostal space and this is where you will find the tricuspid valve and then you will go down just a little bit to the fifth intercostal space and you will go to the midco Vick Euler line which is the middle of where the clavicle is and this is where you'll find your mouth troll valve also also your apical pull so you will listen there for one full minute and count that make sure it's at least sixty beats or minutes and this is where it is located therefore whenever you're taking the exam you will click within this area to determine what the apical pulse would be before you administer digoxin okay so that wraps up this NCLEX review question of the week and don't forget to check out our other NCLEX review questions and our other resources as well thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Carotid_Artery_Assessment_Jugular_Venous_Distention_Neck_Assessment_Nursing.txt	hey everyone its ears register nurse are en comm and in this video I'm going to be going over how to assess the neck specifically the carotid artery and looking at those neck vessels now this is typically done during the cardiac part whenever you're assessing a patient either from head to toe or you're just wanting to do a cardiac focus assessment and this is really important on those middle-aged or older adults who have a history of cardiac disease because what we're going to be doing whenever we're doing this assessment we are going to auscultate the carotid for brewery's which I'll go over that here in a second and we're going to palpate and we're going to fill on the carotid artery we want to know how the contour feels or the amplitude and we're going to grade it and then next we're going to assess those neck vessels for any bulging looking for fluid overload things like that so let's get started so first what we're going to do is we're going to auscultate the carotid artery and what we're listening for are breweries and that's what I talked about beginning the video and this is where you have a turbulence of blood flow and it will sound like a blowing or swishing sound and this is indicated of atherosclerosis narrowing and what you want to do is you want to use the bell of your stethoscope and we're going to listen in three different places to get a really good assessment we're going to listen at the angle of the jaw so find the jaw we're going to go right below it so we're going to go in there and then we're going to go mid cervical area which your cervical areas your neck and we're just going to go in the middle of it so we're going to go about right there and then we're going to go at the base of the neck and the key whenever you're doing this is you want to press lightly with the Bell of your stethoscope and whenever you're doing that you're just pressing lightly because you don't want to create a false bruit or compromised circulation by narrowing the arteries and what you want to do whenever you do this you want to have the patient take a breath and have them exhale and hold it for a second while you're listening so you're not hearing breath sounds and it won't mess with the sounds that you're hearing so we're going to listen real fast okay so first let's go at the angle of the jaw okay take a breath for me and exhale I take a breath for me and exhale again okay again okay and that sounded great and then you're just going to compare sides and repeat on the other side now let's palpate the carotid artery now whenever you're doing this you want to again compare sides like how you are whenever you're listening but what you're going to do is you're going to palpate lightly and what you want to use is your index finger and your middle finger finger do not use your thumb and avoid putting too much pressure on the carotid sinus which is up in this area because this has sensitive baroreceptors and especially in the older patients you're elderly patients you cause an vagal stimulation which will slow the heart rate down so do not do that it's generally good to palpate in the lower half of the neck to avoid that carotid sinus area and what you want to do is you want to locate the trachea and the sternocleidomastoid muscle and in that middle of that groove is where you will find that carotid artery and what you're looking for what you're actually feeling for is the amplitude and the contour you want it to feel smooth and rapid have a rapid upstroke and a slower down stroke and you want to grade it and a normal grading is two plus if it's really hard and bounding it would be three or four and if it's you can barely feel it it's diminished okay now what we're going to do is we are going to assess the vessels in the neck and we're particularly paying attention to those jugular veins and we're looking for increased central venous pressure and to do that what we're going to do is have the patient lay back supine on their back at a 45 degree angle and sometimes it helps to get an extra little light so you can shine it on the neck so you can see the vessels very good and what we're going to do first we're going to look for the sterno mastoid muscle which runs right here and we're looking for the external jugular which overlays this muscle and normally what you will see is that it's slightly flat again you might need your light or you may not even see anything at all which is okay and if you do see that this is bulging or very very large this is usually present in patients with congestive heart failure who have increased central venous pressure but here it's not some flat and you want it to look like that okay so that is how you assess the neck for your head-to-toe assessment now be sure to check out my other nursing assessment videos a link should be popping up so you can access that and thank you so much for watching
Medical_Surgical_Nursing	ACE_Inhibitors_vs_ARBs_Mechanism_of_Action_RAAS_Nursing_NCLEX_Pharmacology.txt	hey everyone its air threats Turner sorry end comm and today we're going to compare some medications we're going to look at ace inhibitors and ARBs and as always whenever you get done watching this YouTube video you can access the free quizzes that will test you on these two medications so let's get started in our previous lectures we went in depth over ace inhibitors and ARBs but now let's do a quick review so we can see the similarities and the differences so when you take an exam you can easily differentiate between these two medications so we have ace inhibitors a stands for angiotensin converting enzyme ARB stands for angiotensin 2 receptor blockers now these medications affect rass they do it in different ways however they both achieve the same results now what is wrath well rice is the renin-angiotensin-aldosterone system but what does this system do well it manages our blood pressure specifically whenever it drops and the whole goal of Wrath is to get angiotensin 2 on board because it is a major active vasoconstrictors if we can vaso constrict other things we can increase our blood pressure we increase blood pressure we maintain tissue perfusion so what happens with rafts is that whenever the blood pressure drops the kidneys some cells in the kidneys will sense this and they will release renin when marooning goes into the circulation it is going to stimulate a substance that is in the liver called angiotensinogen and angiotensinogen is going to turn into angiotensin 1 well we got to get to angiotensin 2 so to do that ace will help us out that is angiotensin converting enzyme it's going to convert angiotensin 1 into angiotensin 2 so we're there we have this major vasoconstrictor present but it has to bind to some receptors because then we can get things going so one type of receptor that this angiotensin 2 is going to bind to is called an angiotensin ii receptor site type 1 and whenever angiotensin ii binds with those type 1 receptors it is going to lead to the results we need it's going to cause vasoconstriction of our smooth vessels so when we constrict vessels that is going to clamp down and is that that is going to help increase blood pressure increase our systemic vascular resistance in addition we are going to trigger the release of a substance called aldosterone by the adrenal cortex and the whole reason for this is to help increase blood volume because if we can increase blood volume we constrict our vessels we are definitely going to increase blood pressure and maintain tissue perfusion and to do this is this aldosterone will cause the kidneys to keep sodium in water but excrete potassium now let's look at how these two medications affect rats because remember they do it in different ways but they achieve the same results and really what they're targeting is this angiotensin 2 so let's look at ace inhibitors what ACE inhibitors are going to do is they are going to inhibit ACE hence their name so they inhibit this part of rass they prevent angiotensin 1 from turning into angiotensin 2 so we don't have angiotensin 2 being able to do its job now ARBs what it's going to do is it's going to inactivate the angiotensin ii receptor sites type 1 so we will have the conversion of angiotensin 1 to angiotensin 2 you have a snoo in its job but what we're going to prevent is as angiotensin 2 being able to bind with these type 1 receptors so you don't get the effects of angiotensin 2 so as you can see they're both affecting angiotensin ii ace inhibitors is just preventing this ace ARBs it's preventing the activation of these receptor sites either way they are affecting how Angie to works therefore with both of these medications what they're going to achieve is that they're going to cause vasodilation instead of vasoconstriction so that's going to decrease systemic vascular resistance and decrease the blood pressure and it's going to make it a little bit easier on the heart to pump and here in a moment where we talk about what these drugs are used for you'll see why they're beneficial on some patients in addition they're both going to decrease that secretion of aldosterone which again was to help increase our blood volume so instead of keeping sodium and water we're going to excrete it but they will cause the kidneys to keep potassium so we really have to watch out for hyperkalemia in these patients who take these drugs now some other things you want to remember to help you differentiate between them is how their generic name is what is it specifically in with with ACE inhibitors the generics are going to end with pril like lisinopril with ARDS the generics will end with Soren like losartan so when you're looking at the meds and you're trying to turn exist an ace or ARB look at the ending of those generic names it'll really help you and another thing I want to point out is with ace inhibitors some patients not all can develop this persistent nagging dry cough and the reason for that is because of how this ACE inhibitor is influencing this ACE enzyme that is converting angiotensin 1 into angiotensin 2 over here with ARBs a dry persistent nagging cough is not likely and a lot of times if a patient does develop this dry persistent cough with an ace the physician may put them on an ARB because that will help clear that up so the reason for that is because ace normally will inactivate a substance called Brady Kannan Brady Kannan is an inflammatory substance and what it will do is a little break it down so don't and activate it but if we're blocking this by throwing on an ACE inhibitor we're not going to be in debating this Brady cotton so it can increase and it can cause this coughing another thing with ace inhibitors that you want to watch out for as the nurse is something that can happen called angio edema this is where you have swelling of the deep tissues and it can present up swelling of the face the tongue the lips and it can cause a difficulty breathing and if that happens that's a medical emergency it's less likely to happen with an ARB so there's a low chance of it happening but you always just want to monitor for that as well now let's wrap up this review and let's talk about what these medications are used for and look at our nursing interventions and our patient education together so water ace and ARBs used to treat well we've already learned that they help lower the blood pressure so they're great in helping patients who have hypertension managing that blood pressure keeping it low in addition patients who have heart failure this is where the heart muscle is damaged and it can't really pump so it's not really maintaining cardiac output plus blood can backflow go into the lungs lead to pulmonary edema and how ace and ARBs will work is that they can help decrease the after load in the preload on the heart making it easier to pump and get blood out to maintain cardiac output in addition ace and arts can be used after a patient has a myocardial infarction again just helping the heart pump easier after it's been damaged and these medications can help decrease the progression of diabetic nephropathy in those patients who have type 2 diabetes now what is diabetic nephropathy well this is kidney disease caused by diabetes and whenever a patient has kidney disease those little nephrons and the kidneys are affected because that's a functional unit of the kidney that doesn't work and they really lose the ability to filter the blood very well so protein will start to leak into the urine well if you have high blood pressure you're increasing the amount of protein that's going into the urine well if we throw an ace and Arbonne that can help lower the blood pressure which will decrease now a protein that's going into the urine hints slowing down our kidney disease so these medications have like that renal protective mechanism now what are some patient education and things you want to watch out for eisenerz well we've learned that this meant these medications can increase the potassium level with the way that it affects aldosterone because aldosterone is not really going to be released so now the kidneys are going to start keeping potassium so there's a risk for hyperkalemia therefore you want to monitor the potassium levels but you want to tell the patient to avoid consuming a diet really high in potassium so watch those salt substitutes that have potassium and those foods that are high in potassium like spinach avocados bananas etc because I can increase our potassium levels in addition you want to talk to the patient about how to prevent a condition called rebound hypertension this is where the blood pressure will get so high it'll be hard to actually bring the blood pressure down and this tends to happen when a patient just abruptly quits taking their ace or their arm so educate the patient about the importance of never just quit taking the medication because sometimes patient let's say they're started on an ACE inhibitor they develop that dry nagging persistent cough it's driving them crazy and it's driving everyone else around them crazy because they keep coughing so they may just quit taking the medication but instead of doing that they need to talk to their doctor and their doctor can switch them to something else where they won't have that dry cough so just let them know that that can happen if they just abruptly quit taking it in addition they need to make sure they're monitoring their blood pressure at home they need to get a device they need to write down the recordings of what their blood pressure is daily doing this is best because we want to make sure that these medications are in fact managing their blood pressure or are they still hypertensive or is it too much they're hypotensive so definitely communicate that to them and lifestyle changes that they need to do if they're taking these medications to help lower the blood pressure let them know that anti hypertensive medications are not cure for high blood pressure they need to manage their diet by eating healthy exercising or quit smoking if they're smoking to help with that as well so we want to monitor the potassium level as we discussed over here because of hyperkalemia but we also want to look at the liver enzymes making sure the liver is not being affected and renal function because in some patients who are dependent on the RAF's because let's say they have severe heart failure with severe heart failure or their cardiac output isn't that great so they depend on this rafts to maintain cardiac output for them so if we give them an ace and an ARB which affects Rask that's really going to cause some kidney issues so we want to be making sure we monitor the BU in the creatinine what's the renal out there urinary output is at least 30 CC's an hour are they having any abnormal swelling going on in their body where they're retaining fluid and lastly you want to talk to the patient about this cough that can happen with these ACE inhibitors and if they can't tolerate it what should they do and remember they can be switched to arms which doesn't have that dry persistent cough now one thing you really want to watch out for if you're working with patients who have heart failure and they're on an ACE inhibitor let's say that all of a sudden they get this coffee well you want to further investigate this call if you don't want to just write it off oh it's that coffee that you get with ace inhibitors because with heart failure they their heart will be weak the blood will back up into the lungs or they'll get pulmonary edema so they'll start getting a call but this coffee will be like a wet COFF you'll hear crackles if you listen to their lungs they'll have difficulty breathing with just any movement like movie from the bedside chair to the bed they get really winded so you want to make sure that is this just that Koff that you get with ace inhibitors which is dry it's not gonna be have crackles or wet or is this heart failure exacerbation so make sure you look at that in addition educate the patient about this angioedema that's more likely to happen with the ACE inhibitors but can happen with ARBs it's less likely it's rare to but educate them about the swelling of the face the mouth the lips difficulty breathing and let them know that's a medical emergency and that they should seek attention immediately okay so that wraps up this review over ace inhibitors versus ARBs thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Neurogenic_Shock_Nursing_NCLEX_Distributive_Treatment_Interventions_Signs_and_Symptoms.txt	hey everyone it's Sarah threads sterner sari ends all calm and in this video we're going to continue our series on shock by talking about neurogenic shock and as always after you watch this youtube video you can access the free quiz that will test you on this condition so let's get started neurogenic shock occurs when the sympathetic nervous system loses the ability to stimulate nerve impulses now when this happens it's going to lead to major hemodynamic changes in our patient now why is that well one of the reasons is due to the massive vasodilation that is occurring so what's happening is that our vessels are going to be relaxed they're going to be wide and in the end what this leads to is decreased tissue perfusion so the male of oxygen that can go to those cells that make up our tissues and organs is very limited which is why we're going to see signs and symptoms of shock now neurogenic shock is occurring due to a nervous system issue hence why we call it neurogenic and it's occurring due to an issue with a division of the autonomic nervous system which is the sympathetic nervous system so we're having issues with that now you can also hear neurogenic shock sometimes being referred to as vasogenic shock they're the same thing now neurogenic shock is a form of distributive shock and in this series we talked about two other types of shock that are also considered a distributive form of shock and do you remember what they were they were in a phylactery and septic so in these three types of shock we have this major vasodilation occurring it's occurring for different reasons like with anaphylactic it's due to an allergen with septic it was some type of infection and with neurogenic it's a nervous system issue specifically our sympathetic nervous system what's happening is that this sympathetic nervous system has lost the ability to regulate the diameter of our vessels so they're just relaxed and that is lee - the vasodilation so distributive forms of shock affect how those small vessels work and it's for different reasons depending on the type of shock so what can cause neurogenic shock and which patients are at risk for it well any patient that has had a spinal cord injury and we're talking about at certain locations so if they've had like a cervical spine injury or an upper thoracic injury above t6 they're at risk for neurogenic shock in addition patients who have received spinal anesthesia or they're taking drugs that affect the autonomic or sympathetic nervous system that can lead to neurogenic shock now it's all about the pathophysiology of neurogenic shock in simplify what is occurring in this condition okay so we've established that this is occurring because we have an issue with our sympathetic nervous system it's lost the ability to stimulate nerve impulses and this is a big problem because we're gonna have major hemodynamic changes because the sympathetic nervous system plays a huge role with our blood pressure especially and how it regulates the diameter of those vessels so let's do a quick review okay the sympathetic nervous system arises out of the autonomic nervous system so what is that autonomic nervous system do it controls those functions that we can't consciously control like our heart rate or blood pressure or digestion just to name a few and you can take the autonomic nervous system and divided into two systems you have the parasympathetic system which is that rest and digest system it allows you to just chill it decreases your heart rate it allows you to digest food now the sympathetic nervous system is that system that keeps you alive especially when you're in danger and it does a lot of functions like it dilates your pupils for better vision so you can see the danger it increases your heart rate and it increases blood pressure now one way it does that by increasing your blood pressure is that the sympathetic nervous system plays a role in controlling vasomotor tone so what does that fancy word mean well what the sympathetic nervous system does is it regulates the diameter of our vessels and how it does this is that these sympathetic nerve fibers that are coming out of that sympathetic nervous system branch out and hang out on the layer of the vessels and these neurotransmitters are going to be released called epinephrine and norepinephrine and remember what those do those are big like vasopressor type agents they're gonna cause vasoconstriction and they will do that at a rate whenever they're needed by the sympathetic nervous system when it's stimulated so if you have a high rate of those firing you're gonna be having vasoconstriction but if you have a low rate or if it's not being fired at all what's that vessel going to do is just gonna relax it's going to dilate and that is what is happening here in this condition so with this major vasodilation this is going to affect the resistance in our vessels if our vessel is nice and open and relaxed that's going to decrease the resistance inside of it so we're gonna have a decrease in our systemic vascular resistance which is going to cause us a lot of problems and affect our cardiac output so let me try to illustrate it this way so maybe it'll stick in your head a little bit better if we take a water hose and let's say the water hose is our vessel and we narrow that water hose we just increased the resistance that that water must flow against and that's gonna really increase the pressure of how about water is flowing through out there you narrow that water hose and on the other end you're just gonna see that water shooting out at a very high speed it has a lot of pressure on it but if we take that water hose and we want it that water doesn't have a lot of resistance it has to go through does it that water if it's so wide could actually just pull in that vessel and maybe not even flow forward if it's so why that's really the same thing that's happening here these vessels have wound up so much because they've lost resistance that it's going to decrease the blood pressure so you're gonna see hypotension and you're gonna see where there can be venous pulling a blood in this peripheral area in these extremities so back to the systemic vascular resistance because we've lowered that resistance so much that's gonna decrease cardiac afterload and afterload is the melt of resistance so that ventricle must overcome to pop open that aortic valve to get that blood out of the heart well if it's not meeting a lot of resistance because we have this massive vasodilation it's gonna be easier for that ventricle to squeeze that blood out of itself and open up that your teeth out so we've dropped cardiac afterload now with our venous pulling because there's not much resistance getting that blood back to the heart that's going to cause some other issues first it's going to decrease the amount of blood that's going to return to this heart that's going to cause a problem because it's not gonna leave the heart a lot of blood to pump and the heart maintains our cardiac output which is the amount of blood that the heart pumps per minute for not pumping a lot of blood per minute there's not a lot of blood that's rich in oxygen going to those cells that make up our tissues and organs so the blood here is just gonna be pulling hanging out now this is gonna decrease cardiac preload so because you have a decrease of venous blood returned preload is where those ventricles is the amount of those ventricles stretch once they have filled at the end of a sleeve you don't have a lot of blood flowing back to them they're not really feeling very much so preload and afterload play a role with cardiac output it plays a role with the stroke volume so cardiac output equals heart rate times stroke volume if we're decreasing those things or decrease in cardiac output another big thing to remember about this Venus pulling a blood in these extremities is that whenever that happens we have blood just hanging out what does that increase the chance of we want blood constantly going throughout the body it can increase the chance of a deep vein thrombosis for me so when we talk about nursing interventions keep that in mind another thing that is going to play a role with this whole hypothermia thing that we're going to experience a little bit later on is that whenever blood is pulling here in the extremities and the peripheral area it's not returning back to the body so here's all the blood hanging out and whenever it's hanging out here it's going to be causing the body to lose a lot of heat so heat is gonna be leaving the body and you can feel on the extremities that they will be warm and dry but the body itself will be cold because you have this venous point and that's even going to play big role with the body cooling off more because it's just hanging out there another thing that's going to affect our cardiac output is our heart rate because we remember cardiac output is heart rate times stroke volume so these patients can experience bradycardia where your heart rate is less than 60 now why are they experiencing a slow heart rate well remember we talked about the parasympathetic and the sympathetic nervous system parasympathetic system keeps your heart rate nice and slow helps you rest the sympathetic nervous system is going to increase the heart rate well if we don't have the sympathetic nervous system being able to work the way it should who's gonna take over and just keep doing what it does the parasympathetic system and it's going to be unopposed by the sympathetic nervous system that normally keeps your heart rate up so it will take over and we can see bradycardia and lastly another big thing that's going to be occurring is hypothermia and this is from where our hypothalamus is really not working very well it can't regulate our temperature so we will have a low temperature rate and the big thing I want you to take away with this because it's different than the other types of shock is that because had the vaso constriction those extremities felt cold and clammy and the other ones right well because we have this Venus point of blood here and it's not really it's not returning to the heart the extremities can be warm and dry but the body will be cold and the overall core body temperature can be low hypothermia so keeping all that pathophysiology in mind let's sum up our signs and symptoms that we're gonna see in this patient now remember whenever we talked about the other types of shock and those early stages that sympathetic nervous system really could take over to try to save her life at first right by causing vasoconstriction by regulating the diameter of those vessels by secreting epinephrine and norepinephrine and it can do that and help us out a little bit they here in this type of sha remember that sympathetic nervous system just can't do that so that's why some of these signs and symptoms are a little bit different compared to those other types of shock so you'll want to remember those differences so of course we're going to have the hypotension the low blood pressure and that's because you have the massive vasodilation going on and you have the decrease of Simek vascular resistance the bradycardia was from where we have an unopposed parasympathetic nervous system it's really the one taking over because the sympathetic nervous system isn't there to increase the heart rate so you can have that the hypothermia where we're having where we can't regulate our temperature or body is cooling off because it's just pulled in our peripheral area and it's just cooling and it's not returning back to the body so they can have warm dry extremities but the body itself is cold and that core body temperature can become hypothermic and another thing that can be seen is if your patient has hemodynamic monitoring through like a pulmonary artery catheter they would have low filling pressures in the heart like a low pulmonary artery wedge pressure and that is occurring because we have that massive vasodilation so again was blood returning to the heart very well know you have decreased systemic vascular resistance there's no resistance really pushing it there so your D Senor preload and really the filling pressures in the heart so that would be low now one thing I just want to hit on quickly was that neurogenic shock and spinal shock are two different conditions spinal shock you're going to have signs and symptoms associated with sensation with motor and with reflexes and neurogenic shock you're really just seeing these hemodynamic changes in your patient now let's wrap up this lecture and let's talk about nursing interventions and treatments for a patient in neurogenic shock okay so first of all let's talk about the goal what's our goal for this patient well it's to manage the patient's ABCs and we're talking about airway breathing circulation and spine so big thing what we want to do is we want to protect the patient's spine they most likely have had some type of injury that's the big cause of neurogenic shock and again it was the cervical area or the upper thoracic above t6 and we want to keep the spine and mobilize we don't want to cause any more damage and decrease profusion to the spine so some ways that we can do this is have the patient wearing a cervical collar and log-rolling the patient during transport or using a backboard that can really help keep the spine immobilized another important thing that we're going to be doing of course is assessing and managing the airway and the airway can be affected with these patients depending on the location of the injury so they may need intubation and mechanical ventilation if respiratory failure is present and of course because our patient is in shock we want to maintain tissue perfusion this is where we're maintaining circulation so patients who have had like spinal injuries we want to make sure that that spine is being perfused along with the other organs so a goal is to maintain the map the mean arterial pressure to be between 85 to 90 millimeters of mercury this will help maintain perfusion to the organs especially the spine now how are to do this one way is through the administration of IV fluids this can be crystalloids and what this is going to do is it's going to fill those dilated vessels and increase the venous return to the heart which will increase cardiac preload and help play a role in increase in our stroke volume which will help increase our cardiac output however whenever giving patients with neurogenic shock IV fluids we have to use this with caution because we don't have an issue with fluid loss they normally have a normal fluid volume so we want to make sure we're not sending them into fluid volume overload and if your patient started having difficulty breathing you are hearing crackles when you listen to their lung sounds they're getting swollen with edema or if they have hemodynamic monitoring and you can see that they have an high central venous pressure CVP or a high pulmonary artery wedge pressure which again represents the filling pressures in the heart you want to suspect about this patient it's probably in fluid volume overload now how about if the fluids are not working to maintain tissue perfusion well those opressors can be used and what these drugs will do is they will cause vasoconstriction and we need some vasoconstriction in these patients because we have major vasodilation sympathetic nervous system is not controlling or vasomotor tone and our vessels are just really relaxed so we need to throw on something that will help them contract constrict so whenever we do this this is going to increase systemic vascular resistance where we were once a decrease and when we increase assuming vascular resistance that's going to increase blood pressure and in the long run we can increase cardiac output and another type of drug that can be used it's also a vasopressor but has positive inotropic effect is dopamine dopamine will vaso constrict and increase the heart rate so when you throw all that together we're going to increase our tissue perfusion now what about bradycardia if your patient has a really low heart rate can be done well atropine can be given and this drug will increase the heart rate and how it does this is it blocks the parasympathetic effects on the heart and remember the parasympathetic system was being unopposed so it's just keeping the heart nice and slow so this medication will help combat that but if the bradycardia is really severe the patient may need temporary pacing and some more nursing interventions for this patient would be around the hypothermia that the patient can be experiencing so of course we want to be monitoring their body temperature very closely and be using warming devices as ordered by the physician to help keep the patient warm and we don't want to rewarm them too fast you want to do it at a moderate rate and consider fully placement because some patients lose their bladder function and we don't want them to retain urine so we want to drain that out plus we need to keep track of their urinary output and make sure it's at least 30 CC's per hour because in shock remember the kidneys can be affected if they're not being perfused very well we have a low urinary output that tells us our kidneys are really struggling and we're possibly in renal failure territory and we want to prevent deep vein thrombosis a DVT because remember these patients are at risk for this because of that massive vasodilation allowing that blood to pool so we want to make sure that we're putting in our plan of care that we're going to perform range of motion exercises daily with these patients applying compression stockings and ministering anticoagulants per than the order and we want to make sure that we avoid allowing the patient to cross their legs which can impede blood flow or placing a pillow under the knees because this will compromise circulation okay so that wraps up this review over neurogenic shock thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Pneumothorax_Nursing_Pathophysiology_Interventions_Open_vs_Closed_vs_Tension_Pneumothorax.txt	hey everyone it's Sarah register nurse rn.com and in this video I'm going to be doing an inlex review over pumo thorax this video is part of an inlex review series over the respiratory system so what I'm going to be doing in this video is I'm going to be talking about the patho the different types of pneumothorax the signs and symptoms and the nursing interventions and I highly recommend that after you watch this video you also check out my video on chest tube care because chest tubes and pneumothorax go hand in hand so you can learn those nursing interventions and a card should be popping up so you can access that video after you watch this and as always over here on the side and in the description below you can access the quiz and the notes so let's get started first let's start out talking about what is a pneumothorax what is the definition of it well in a nutshell what it is is it's the collapsing of a lung due to air accumulating in the plor space which the plor space is the space between the V iseral and the paral plura and it's also called the intra plur space now before we dive into our patho signs and symptoms of nursing interventions let me go over some key points with you so you can remember and keep these in the back of your mind as we're discussing this stuff okay a pneumothorax can be partial or total um collapsing of a lung and it usually affects one lung causes of pneumothorax include it can happen spontan ously without any warning it can be caused by trauma to the chest like blunt trauma or a penetrating trauma for instance if a PA patient was in a car wreck that airbag hitting the chest can cause it or CPR or um a gunshot wound or a stabbing can cause air to go into that space other things lung disease a medical procedure like a central line placement a lot of times after a patient has a central line place like say a pick line the uh you'll need to get a chest x-ray to make sure and there is an anuma thorax and everything's good or mechanical ventilation with um positive in expiratory pressure where um barot trauma can happen and we'll really be talking about this with tension Nemo thorax and how are pneumothorax how is it diagnosed it's diagnosed usually with a chest x-ray an ultrasound or a CT scan small pneumothorax you can have small large they vary in size small ones tend to resolve on their own without treatment however if it's large and they will need treatment like a chest tube placement which will help drain that air out of the intor space or needle decompression where they stick a needle into that space and um aspirate the air and um again we'll really be hitting on that with the tension pneumothorax which is a medical emergency and that is one of the treatments for it now let's look at the path of physiology of a pneumothorax but first let's look at our lung Anatomy because it goes hand in hand okay here you have some lungs and what you see in red is the chest wall and attached to the chest wall is your paral plura and then you have in the white areas that is the intl space and then next the green is your visceral plural which attaches to the lung and what happens in this intor space you have small amounts of Cirrus fluid so as you breathe in and breathe out that fluid allows your lungs to Glide over one another without any pain and it creates a negative pressure and your lungs love negative pressure if anything is added into this space like with the pneumothorax your lungs collapse they do not like that so they thrive on negative pressure and this negative pressure acts like suction to keep your lungs inflated so in order to keep your lungs inflated you need that negative pressure now when air enters into the space it can happen again through like an object piercing through this chest wall we we would get an open numo thorax and all the air from outside is entering into this space causing pressure to push on that lung and collapse it or um a layer the visceral plora ruptures and whenever ruptures it releases Air that you're breathing in into that inor space which that is like a closed pneumothorax or barot trauma like with mechanical ventilation that can happen as well now as this air builds in this space what happens is that it decreases the ability of the lungs to recoil on that affected side so what happens is that lung gets pushed away from that chest wall and it leads to collapse and remember your lungs like negative pressure so they don't have that you're going to have some major problems now let's talk about the different types of pneumothorax what I'm going to hit on is things you need to know for your nursing lecture exam and inlex because they ask about specific um types of pneumothorax like spontaneous open uh closed or attention so let me go over those with you first let's talk about closed pneumothorax what is this this is where air leaks into to the intl space without an outside WB so the key thing with this is that your chest wall which is here in red and your plora are going to remain intact it's the opposite of what happens in an open pneumothorax which we'll go over here in a second so what can cause this one thing that can cause this is a rib fracture say that the person falls downstairs and breaks the rib you get a sharp bony prominence off of that broken rib it goes in it pierces through tears through that viscera plora of the lung so you have a tear and every time time that person breaths in and breathe out air is going to escape through that tear into this space which should not happen so what happens is that this space gets bigger and bigger as it just fills with air think about it like you're blowing up a balloon as you blow into the balloon it gets bigger and bigger and so that's what's going to happen because remember your lungs like negative pressure this is adding pressure to it so it's going to cause the lung to collapse another thing another common cause of a closed pneumothorax is what's called a spontaneous pneumothorax and this is where you have a defect in the avolar wall and the visceral plora and this causes what happens is that you develop a pulmonary blood and this is like a sack like blister that develops on the visceral layer of the lungs and um what can happen is that this BLB can rupture no warning sign that's why it's really called spontaneous because there wasn't an injury that caused it it just happened without warning and that blister ruptures and it releases Air into the interp space and these blbs can develop over time patients can have multiple one multiple blbs and um they may not rupture immediately once they develop however um some things that can increase a pulmonary blood to rupture is like changes in air pressure if the patient um changes maybe altitude or something like that or there is or the patient takes a sudden deep breath or they smoke now um spontaneous pneumothorax is categorized by primary or secondary and let me go over those with you real fast um you can have a primary spontaneous pneumothorax and this tends to occur in people without lung disease they tend tend to be young less than the age of 30 and tall and thin however you can have a secondary pneumothorax and this occurs in people with lung disease like COPD asthma cystic fibrosis things like that now let's look at open pneumothorax what is this this is where there is an opening in the chest wall that causes a passage between the outside air and the interpur space so as you can see see in this illustration here you have the chest wall which is in red and you have your prodl let's say that this patient was stabbed it's a big Stab Wound and what it's done is it's allowing it's create this opening to allow inhaled and exhaled air to pass back and forth so your plur space is getting all this air in and out and as it passes in and out you could hear a sucking sound this um open Doo thorx is sometimes referred to as a sucking chest swing because what's happening is that your body is shunting air through the chest wall instead of the trachea which is what it does during normal circumstances when you don't have a big gaping wound on your chest and it will create that sucking sound and the intor pressure pressure will become equal with the outside pressure which will lead to lung collapse because remember your lungs thrive in negative pressure now inlex inlex tip thing you need to know about open pneumothorax may see it on your nursing lecture exam or the inlex okay a nursing intervention say you have a patient come in they have a big open wound they have this what are you going to do nursing intervention would be to place a sterile occlusive dressing and tape it on three sides leaving the fourth side untaped because this is going to allow exhaled air to leave the opening but seal back over it when the patient's inhaling hence it's going to be hence it's going to help prevent a tension numo thorax so what what is a tension pneumothorax a tension pneumothorax happens when an opening to the interpolar space creates a one wave valve which leads air to collect in that intol space But it cannot Escape so it just keeps building and building and building and this is a medical emergency that patient needs treatment immediately and attention in thorax can happen um as a complication of a pneumothorax such as an open or close so as you can see from this drawing here pressure is just building and building and building and as that pressure builds this leads to increased thoracic pressure and you get compression on that unaffected lung and the heart which is not good and you will get a medianum shift where your heart your trachea your esophagus and V vessels are going to shift to the unaffected side and this is going to cause major compression on your other lung and decrease Venus return because your Vena is being compressed so what's going to happen you're going to see these certain signs and symptoms in this patient and I would remember this what's going to happen is the patient's going to try to compensate because they are air hungry because they have limited amount of breathing room so they're going to become tpic they're going to try to breathe and breathe but it's not going to work they're going to be hypoxic then um they're going to have compression on that vnea which drains the blood from your body to your heart to get reoxygenated well what's going to happen is that your heart's going to become tpic you're going I mean tartic you're going to increase your heart rate because it's noticing that you're not getting blood to all those organs and tissues that you need but there's nothing to pump because of that compression on those great vessels so you're going to have Tac cardic they're going to be Tac cardic but they're going to have hypotension because it's going to reduce your cardiac output and pretty much much your patient is going into shock and the patient can also have jugular Venus distension now a late sign of um this is tracheal deviation that's going to happen L later on whenever things are really really bad so if you see that not good it's very late now one thing I want to touch on you need to watch patients who are on mechanical ventilation with pee that positive in expiratory pressure because they are at risk for developing this due to what's called barot trauma which um over time all that pre extra pressure on that lungs is going to lead up lead to buildup of air in the inl space from rupture of the visceral plora now if this happens they will need treatment that the physician will do will be needle decompression well they'll insert a needle in and aspirate that extra air that has built and helped relieve all that tension that is going on now let's look at the major signs and symptoms that a patient could have when they have a pneumothorax and to help you remember it um remember the pneumonic collapse because a pneumothorax is a collapse lung so um each letter will correlate with the sign and symptom Okay C for chest pain patient may complain of chest pain all of a sudden that is sharp and could be worse on inspiration also another C for cyanosis just where they're not getting oxygenated good you can see blue around the lips the skin tone could turn a bluish color next o for avert tacac cardia and tpen that is where the body is trying to compensate for that low oxygen level that's going on the heart's trying to pump faster to get blood to the body because it has low oxygen level and the body's causing the respiratory system to increase in respiration so you can take more oxygen in L for low blood pressure the other L for low spo2 if you have them on an spo2 monitor you may notice that it would be less than 90% a for absent breath sounds on the affected side if they have a collapse lung you're not going to hear breath sounds on that side that has a collapse lung compared to the other side so you'd want to compare the sides see um how they're sounding next p for pushing of the trachea to the unaffected side remember that was in attention pneumothorax but remember if your patient has a Neo thorax or a chest tube they are at risk for attention pneumothorax so if you see that um it could be developing into that but remember that's a late sign next s for subq osma this is where um carbon do oxide can escape into the skin so you may see these little bulging areas maybe in the face the neck the lung I mean the abdomen and whenever you feel it it's like a crunchy feeling to it and this is known as subq osma another s for sucking sound and remember that was in the open pneumothorax where you have that Passage through the chest wall that is allowing air to go in and out of the lungs through that opening of the chest e for expand expansion of the chest will be unequal so wherever you have the collapse lung remember it's not inflating and deflating fully like compared to the healthy lung on the other side so you'll have unequal chest rise and fall and then D for dmia of course they're going to have difficulty breathing because they only probably have one lung that's working appropriately now let's look at the nursing interventions what are you going to do for this patient as the nurse who have who has a pneumothorax um you're going to of course be monitoring the breath sounds um what do they sound like on this side compared to the other side and you're going to be watching The Rise and the fall of the chest you're going to be monitoring their Vital Signs especially their blood pressure their heart rate their respiratory rate and their oxygen saturation uh assessing for that subq osma administering oxygen as ordered by The Physician um it's best whenever a patient has a respiratory issue to keep them in uh the head of the bed in Fowler's position to decrease that effort of breathing and remember whenever we talked about open pneumothorax what you're going to do with the dressing by um using a sterile clusive dressing placing it over the opening taping it on three sides and leaving one side untape so um it'll allow the air to escape and prevent attention pneumothorax and then another biggie is maintaining that chest tube drainage system if it is placed by The Physician and that's why I really recommend that you watch that video on chest tubes because it'll really help you understand how to care for them but let me go over some highlights with you um a patient with a pneumothorax you would want to make sure while you're maintaining the drain that you're assessing for leaks in the system the chest two drain drain system and make sure it's working appropriately how to troubleshoot it a lot of inlex questions and nursing exam questions like to ask you well the drain came out what are you going to do or the system's broken what do you want to do because this stuff does happen in real life and they want you to be prepared for it next um with a numo thorax just from where we've talked about the anatomy and phys the pathopysiology of it we're removing the chest tube is removing air from the interpolar space so you may have intermittent bubbling in that water seal chamber as the air is escaping but excessive bubbling in the water s chamber represents a leak somewhere in your system so you want to investigate it and figure out where it is also as the patient breathes in and breathes out the water SE seal Cham chamber will fluctuate up and down however um a lot of questions like to ask you you've noticed that it's quit fluctuating up and down in the water sell chamber what could it be um either it's a kink somewhere in the system or that lung has re-expanded so you want to assess those breath sounds and see what it sounds like okay so that is about pneumothorax now go to my website register nurse rn.com and take the free review quiz and be sure to check out the other videos in this series and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Tuberculosis_TB_Symptoms_Treatment_Causes_Nursing_NCLEX_Review.txt	this is cereth registered nurse orion coleman in this video i'm going to be going over tuberculosis in this video is part of an ink lex review series over the respiratory system and as always at the end of this youtube video you can access the free quiz that will test you on this condition so let's get started tuberculosis is a contagious bacterial infection caused by Mycobacterium tuberculosis and tuberculosis tinge to mainly affect the lungs specifically it resides in those upper part of the lungs so the apex and here in a moment you will know why but it's not just limited to the lungs once it gets in the body it can spread to the lymphatic system and it can travel to the brain the joins to live or the spine in the kidneys so remember that because a lot of times whenever people think of TV they think of oh it just affects the lungs but it can affect other areas of the body as well now let's talk about this bacterium Mycobacterium tuberculosis number one it is an acid fast bacteria which means whenever you collect sputum on this patient which you're going to be doing a lot for patients who you're testing for tuberculosis you will send it to the lab and they will do a special test where they're going to do an acid fast staining procedure and if this is indeed Mycobacterium tuberculosis it will stain a bright red color in addition this bacteria is aerobic which means that it absolutely loves oxygen so it needs lots of oxygen in order to thrive and grow which is why this bacteria likes to reside in those upper parts of the lobe the apex compared to the base because this is where you have the higher amount of oxygen now how is tuberculosis spread to other people because it's contagious well if you have a person like our little man here on the board if they have active tuberculosis which means that they're having signs and symptoms associated with the infection they've had a positive sputum culture for this bacteria their chest x-rays I'm normal and they've had like a positive skin test or blood test so they have active tuberculosis so anytime that this person creates an action that's going to make droplets that harbors this bacteria such as yelling coughing talking laughing when they expelled that out of through their nose on their mouth they're putting this bacteria into the atmosphere the air for others to come along and breathe in when they breathe it in it'll go down into their airway and this bacteria loves oxygen so it'll hang out in the lungs and depending on if this patient has a strong immune system what's going on with them they can develop active tuberculosis now why is this why is this airborne rather than like droplet well this bacteria is very small so it can suspend itself in the air instead of with like droplets those bacterial viruses are large they don't stay in the air very long at all and they fall onto the surfaces or wherever it can fall so as a nurse providing care to this patient what are you gonna wear well first of all there are airborne precautions what goes along with that you'll want to wear a respirator anytime providing care around that patient at all not a surgical mask because a respirator like an in 95 mask is special in that it will help filter out this small bacteria so you won't breathe it in in addition on top of that they will need special ventilation in the room and a negative pressure room to help prevent spreading that bacteria and you want to keep that door closed another thing is looking at your risk factors whenever you're getting these patients they're presenting maybe with signs of tuberculosis you want to look at those risk factors which we're going to go over here in a moment because winter bar closest the patient has to be in contact with others for a specific amount of time which is why patients who are in long term health care facilities they're inmates and Prisons homeless shelters where people are living in tight quarters with each other their risk for majorly spreading to it to other residents or other people who live there so now let's look at those risk factors and I would remember these factors for tests because test questions can't arise from this material so to help us remember the risk factors for someone developing tuberculosis let's remember the pneumonic TB risk TB sands fruits of our closest so RT of course what I just talked about is tight living quarters and these are your patients who are living close proximity together they are in long contact which just gives them time to be over exposed to this bacteria hanging out into the air and they can contract it next be below or at the poverty line and these are people who don't have great access to health care because they just can't afford it such as people who are homeless our refugees also immigrants who are coming from countries where they're high cases of tuberculosis next either immune system issues example a person who has HIV whenever a person has HIV they have a weak immune system so that makes them more susceptible to tuberculosis or they're taking immunosuppressant drugs which suppresses the immune system so anytime you see a test question says patient has HIV or taking these type of drugs think okay risk for tuberculosis yes for substance abusers these include people who use IV drugs or are alcoholics and last K for kids kids less than the age of five their immune system isn't fully developed it's weak so they are definitely at risk for tuberculosis especially if they're residing in a house with someone who has active TB so as a nurse we need to really assess for those risk factors and how do we do it well we ask specific questions on mission and your documentation the paper work that you're doing whenever you're admitting a new patient is going to have questions similar to this and if you have a patient who's coming in for respiratory issues you want to be thinking in this realm you know it's rare to have tuberculosis patients here in the US but you do have them I have provided care for patients who do have active tuberculosis so you want make sure you're thinking about it because it can happen still so you want to ask your patient have you traveled outside of the US or lived outside of the US if so where was it and how long are they from one of those countries that have high rates of tuberculosis next where do you live where's home for you are they from a long-term care facility like a nursing home are they an inmate and a prison which you'll usually be tipped off for that because they'll have a guard with them or do you live in a homeless shelter also do they use drugs if so what type of drugs because we're looking for really IV drug use because that not only puts them at risk for DeMarre closest but at risk for HIV and having HIV dramatically increases the chance of them having tuberculosis because of the weak immune system then you want to ask them were you born here in the u.s or were you born in another country as a child because in some countries they give the vaccine to prevent tuberculosis because they have high rates of tuberculosis called the BCG vaccine also known as the BAC sillas comment Gaye ran vaccine and this prevents tuberculosis but the thing you want to remember with this vaccine and I would remember this that if your patient has had this vaccine as a child they whenever you if you give them one of those skin tuberculin test the PPD test they will have a false positive because they've already been exposed to the Mycobacterium tuberculosis their immune system recognizes it because they had a vaccine so they're gonna have a false positive so it's best for them to have like a blood test which we're gonna go over the testing here in a moment and a chest x-ray to rule that out in addition you want to ask them about their signs and symptoms because when active tuberculosis presents they will have these specific signs and symptoms which are coughing that lasts for three weeks or more so ask them okay your coughing how long has this been happening also ask him what does their sputum look like are they coughing up blood do they have a fever night sweats fatigue unintentional weight loss chills a loss of appetite they just don't feel like eating or they're having chest pain or pain with breathing or coughing all can be related to an active tuberculosis infection and of course you also want to ask them have you had a TB skin test if so when was it and do you remember the results and you'll want to try to access those results if possible now let's talk about latent tuberculosis infections versus active tuberculosis infections and I would remember the differences between the two for testing purposes okay not everyone who actually inhales that Mycobacterium tuberculosis is going to develop a full-blown case of active TB because what happens is that when many people breathe this in our immune system recognizes it and it's strong enough to take care of it so what it does is it says hey this should not be here we are going to fix this so the army of our immune system comes in and it surrounds that bacteria and it encapsulates it now this person at this point has latent tuberculosis infection but the body is keeping it dormant now what can happen is that this bacteria can become active again why would it do that well when the immune system becomes weak or let's say the person gets HIV so it can become active again and it can turn into active tuberculosis which is what happens with a lot of these cases that we see many cases were person and held this wild back their immune system had it under control for a while but then the mean system broke down and this germ got out and was able to infect and cause an active infection so let's look at the differences between the two how how's your patient going to present so first with latent TB person has Justin held it their immune system is keeping it under control and most people are not going to develop an active infection they need that weakening of the immune system or something to make that germ come back alive so are they going to be contagious no the immune system has it under control will they have signs and symptoms no they're not going to they're going to have an abnormal chest x-ray no their chest x-ray is going to be normal because it's not causing any problems how's their sputum is it gonna have that Mycobacterium tuberculosis in it no it's going to be negative so they're not really going to know the only how they will know is whenever they go and get a skin test done the PPD tuberculin skin test or the blood test they will test positive for it and that is because their immune system have seen this bacteria before it's created this response to it so when we inject that the PPD in their forearm or they get a blood test we will see that their body reacts to it now do patients who have latent tuberculosis still need treatment yes they do because it'll prevent them from having a possible active infection in the future now according to CDC gov people who do not receive treatment about five to ten percent of them will actually develop an active TB infection so they still need treatment those medications now let's look at active tuberculosis are they contagious absolutely they have this bacteria in here that our immune system just can't deal with so it's flourishing and can't infect others are they going to have signs and symptoms absolutely they'll have those signs and symptoms that we just went over their chest x-ray is going to look abnormal they're gonna have a positive sputum culture because that bacteria is in there which is why it's contagious because they're putting it out when they call flyff breathe yell and one thing that these two will share is that this person of course will also have a positive tuberculin skin test and a positive blood test and with this active TB because it is in the system not being controlled by the immunes so it can easily spread via the lymphatic system and effect those other structures other than the lungs like the brain the joins the liver the kidneys and etc now let's talk about the testing that can be used to help diagnose a patient with tuberculosis because as a nurse you're going to play an important role in administering some of these tests and interpreting some of the results so first let's talk about the PPD skin test this has a lot of names it's also called the man to test TB skin test tuberculin skin test you may see it abbreviated TST all of us the same thing it just has a lot of names now what is this okay this is where a patient is injected with purified protein derivative with a tuberculin needles a special needle on the inner part of the forearm and as a nursing student and I know as a nurse you have had this type of tests done and after injection it will look very similar to this picture right here it will be nice and raised up after they have injected that into the forearm now whenever you give this test to a patient you have to tell them that they have to come back and you have to assess the site or someone else who's qualified the site within 48 to 72 hours and anything over 72 hours they'll have to repeat it and what you're assessing for is in duration of that injection site which is is it hard and raised up and you're gonna measure it in millimeters we're not looking at the redness we're looking at the in duration so how do we interpret results and I would remember this for testing purposes because the results are based on certain criteria based on those risk factors we just went over which is why wanting to cover those with you so you're measuring the site if it measures 15 millimeters or more that is positive in every one if it measures 10 millimeters or more that is positive in a person who's an immigrant an IV drug user works or is living and those tight living quarter areas or a child less than four if the size is five millimeters or more that is positive in a person who has HIV or if the person's been in contact with another person who has active tuberculosis they've had an organ transplant or their immune system is suppressed say that they're taking drugs that suppress it so that would be considered positive now just remember that just because a patient has a positive result doesn't mean that they have active tuberculosis they could have latent or they could have active so you need to get a chest x-ray and a speedom culture to help dipper differentiate between that because this test does not do that another type of test is a blood test where instead of injecting the PPD in the forearm they will just draw blood and it look at the immune systems reaction to this Mycobacterium tuberculosis and they'll put that in these three special tubes so these tests are called interferon gamma release assays and IG are a lot easier to say and there's two types that are on the market currently you have the quan chi faire on TB gold the QFT test or the t spot test now the benefits over this blood test over the PPD test is that the patient doesn't have to return to have the results read in addition it's great for patients who have had that BCG vaccine the BAC sillas comment gay ran vaccine so they won't get a false positive with this and this test is becoming a little bit more popular than the PPD test now one thing this test doesn't do as long along with the PPD test is it does not tell if the patient has latent TB or active t v-- they will need a chest x-ray and the sputum culture to help differentiate that another thing that can be ordered is of course a sputum culture and we about that a little bit already where they can do and AFB smear and acid-fast box a little smear and they do that special stain and what color will it stain if it is this bacteria that bright red color and they can obtain the sputum through either the patient coughing it up or if the patient can't do that they can do a bronchoscopy where they can go in and collect sputum now as a nurse who's going to be collecting those sputum cultures you need to know that you will collect the sputum on three you'll collect three different collection specimens on three different days and it is best to collect it in the morning before the patient has breakfast because they've just got up and I was where there's a lot of those respiratory secretions from after they just got up from sleep and of course a chest x-ray can be ordered they can look at the imaging for that and look for specific findings that's found in tuberculosis here you can see a normal chest x-ray you can see the right and the left lung it's nice and clear however this patient has pulmonary tuberculosis and you can see the chest cavity in the lungs and you can see interstitial infiltrates on both of the lungs due to a TB infection now let's talk about nursing interventions and treatment for tuberculosis okay you have a patient who has active TB they're the ones with those signs and symptoms and they're contagious what are you going to do you want to put them in airborne precautions which entails what again following standard precautions plus always wearing a respirator while providing care to that patient in that patients room so that in ninety five masks and the patient will need to be in a negative pressure room that door stays closed all the time and if it does open it we'll let you know because it will start beeping also you need to ask yourself okay how about this patient has to leave the room to go down for testing a lot of times testing can be done in the room at the bedside but sometimes they have to go down to have a special procedure if they do have to leave the room for that you'll want to put a surgical mask on them so remember that now most patients with active tuberculosis unless they're having complications are treated as an outpatient at their home because treatment for this takes about six months to a year to treat they're gonna be on like four different medications and treatment would just be way too expensive for them to be in the hospital for that long so you want to provide some education pieces to the patient to educate them so if they have active t v-- they're being treated at home they will have to remain in isolation this means they can have absolutely no visitors they can't go to school they can't work they can't go to public outings the only place they can go if they have to is to medical appointments and whenever they do that they need to wear a surgical mask because they're contagious and can spread this to other people also if they live in a home with other people they have to keep a separate room and stay away from those people so they don't spread it especially if you have little children in the house and doors and windows need to stay closed at all times now the patient is coughing sneezing they always need to do that in a paper towel and dispose of that immediately by flushing it or keeping it in an air-tight baggie and disposing of that and when can this person come out of this isolation well whenever they have been on their medications for at least three weeks their mutant cultures will hopefully start to become negative and they will need three negative cultures and their signs and symptoms need to be improving in order for them to meet criteria to be out of isolation and be able to live a normal life again and another thing I want to point out so you're just familiar with it is dot directly observed therapy and this is when a person will actually come out to the person's house who has TB and they will give them their medications and actually watch them swallow the medications and observe them for any signs and symptoms of complications or answer any other questions and this is usually like a public health nurse or someone who's specially trained in doing this and this helps increase compliance with these medications because these patients have to be on these anywhere from 6 to 12 months and they're taking them at different times and it can get confusing or they can just forget to take them which is leading to an increase in drug-resistant TB so the CDC recommends that all patients with tuberculosis are on this dot program to help prevent non-compliance and prevent so much drug-resistant TB now let's switch gears and let's talk about the medications used to treat tuberculosis we're gonna talk about five different drugs but we're really going to concentrate on four of them because they are the ones that are mainline in treating tuberculosis so to help us remember those four drugs let's remember the word Peri Peri means surrounding around and what happens with TB is that normally our body will surround that germ and encapsulate it well our body's really not doing that so we have to have these medications onboard to surround and kill these bacteria so that's how I like to remember it so pee here as in amide which has bactericidal effects which is a fancy way of just saying it kills the bacteria now you need to watch this drug in patients who are diabetic have kidney problems or gal because Pierce in imide increases uric acid levels and we learned in our gout video that's the whole reason for a gout attack is whenever a patient's uric acid levels are increasing so the doctor is gonna be monitoring those uric acid levels you as a nurse need to be looking for signs and symptoms of a gout attack happening it usually likes to start in the big toe the great big toe and it'll be red and warm patient will have limited mobility and it'll be extremely painful in addition this drug can cause liver and kidney problems so be monitoring that as well looking for jaundice look at their urinary output and GI upset is common with this so a ministering that with food will help decrease that efore ethambutol and what this drug does is it stops RNA synthesis so it's bacteriostatic which means that it prevents the bacteria from reproducing now with this drug it can inflame the optic nerve so as the nurse be thinking about vision and educating your patients to immediately report if they have any vision changes like their visions become blurred or they have a change in how they perceive color and they will need regular check-ups it can also cause peripheral neuropathy and this is where you have damage to those peripheral nerves so be asking your patients are you feeling any numbness or burning in your extremities because this can happen and if you do have a patient report numbness burning in their extremities or vision changes you want to notify the physician immediately about this are for rifampin and this drug works to stop RNA polymerase and what that does is it kills the bacteria now there's some things you want to educate your patient on because there's one thing that they're probably going to notice and it can really make them scared if you don't tell them about it one thing is that it can turn their body fluids Orange and their tears their sweat their urine will be orange and you'll want to reassure them about that and tell them if they do wear contact lenses especially those soft kind it will permanently stain those so they'll want to switch and we're hard lenses in addition educate your patients who are on hormonal like birth control that it will be less effective so they want to use backup methods and watch going out in the Sun because they can sunburn easily it makes the skin more sensitive and absolutely no alcohol while taking this medication really with all these drugs for tuberculosis your patients want to avoid alcohol because the liver can be affected with almost all these drugs so no alcohol and teach them about signs and symptoms of liver issues like jaundice having issues bleeding I for isoniazid also I&H and what this drug does is it kills bacteria and stops its growth but one thing that this drug can also do is decrease vitamin b6 levels so what a patients who take this are going to be on supplements and you'll want to assess your patients for that peripheral neuropathy that can happen during low vitamin b6 levels like ask them are you having tingling in your extremities you feel excessively tired depression which can all point to that that Baumann b6 is low and again monitor liver function and for neurotoxicity and lastly streptomycin now this drug isn't as commonly used as those other four I went over because of its side effects but it is used in some patients and I want you to remember the big thing with that one thing is is salt protein synthesis and it kills bacteria but a big side effect of this that you want to watch out for is their hearing so you want to monitor the hearing and ask the patients are you having any issues with hearing for instance are you having ringing in the ears because this drug is odo toxic and it affects cranial nerve eight so always ask your patients who are taking streptomycin if they are having any hearing issues okay so that wraps up this video over tuberculosis thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Pneumonia_Symptoms_Pathophysiology_Nursing_Respiratory_Disorders_NCLEX_Lecture_Part_1.txt	hey everyone its sales red sterner sorry and calm and in this video I want to be doing an ink Lex review over pneumonia this video is part of an interview series over respiratory disorders so be sure to check out the other videos in this series this video will be part one of pneumonia in part two I'm going to be covering the nursing interventions and the medication specifically antibiotics use and treating ammonia and I'm going to give you a clever mnemonic on how to remember that in this video I'm going to be hitting on the pathophysiology of pneumonia the definition the risk factors how's diagnosed and the signs and symptoms so as always over here on the side and in the description below you can access the quiz and the notes so let's get started first let's start out talking about the definition of pneumonia what is it in a nutshell it is a lower respiratory tract infection that causes inflammation of the alveoli stacks and remember the alveolar sacs are responsible for gas exchange and here on your diagram the purple areas that look like little grape sacks is where the gas exchange occurs and what they do is they in play in deflate and they transport through a capillary wall carbon dioxide out so you can exhale it because this is a waste product of metabolism and then it's going to take that fresh oxygen that you just inhaled and how that transported through the body and the heart will help play a role in that as well now the key players in pneumonia one key player are germs this has attacked the system which is called cause inflammation of that sac and this germ can be a bacteria a virus or a fungi or a fungus I'm very rare but it can happen with the fungus also the big thing that plays a part in pneumonia is your lung Parekh einem which I like to call the trio for gas exchange is your Abiola your ovular ducts and your bronchioles now let's talk about normal gas exchange and what's happening and then compare it to whenever one has the Monia and what's going on with them okay normal gas exchange occurs whenever you take in oxygen up through your upper respiratory system through the nose down through those sinuses beyond through the linux then it's going to hit the lower respiratory system which will include your trachea then the trachea will branch off at the quarry and up into your right bronchus and your left bronchus so your primary bronchi then it enters into the lungs of the hilum which also your pulmonary artery your pulmonary vein from the heart enter in at the hilum as well into the lungs because the heart again plays a big role in gas exchange and then it breaks off into your secondary bronchi your tertiary bronchi to the bronchioles to the alveolar ducts and then then into these a viola or sacs now the a viola lower sax here's one blown up so you can see it looks like normally has capillary setting on it from your pulmonary arteries and your pulmonary veins and remember the pulmonary artery from the heart takes uh Knox jaded blood to the lungs to become oxygenated and then the pulmonary vein takes that oxygenated blood back to the heart it's going to go through the aorta and be pumped through the system so you can get some oxygen to your body so that's what's happening constantly these stacks are inflating and deflating carbon dioxide is leaving these sacs you're going to exhale that out car oxygen is coming into the SAC being transom transported onto red blood cells and carried throughout the system so let's look at this up close so here's an a viola and here you have a capillary running this capillary is coming from the heart so it's pulmonary artery and it's an oxygen a that's why they're blue and these cells are exhausted and tired so they're getting rid of that waste buildup of carbon dioxide and putting that into this alveoli so you can get rid of that through exhaling then also at the same time oxygen that you just freshly inhaled is going through this capillary wall and attaching attaching to these exhausted red blood cells and they'll revived and ready to go back through the system so they red and they go through the heart through the pulmonary vein and do their dog now with pneumonia what's going on here okay well what's happened normally your respiratory system can normally fight off these germs that you're coming into contact every day on a daily basis through you know filtering out through your nose but certain conditions can increase your ability of developing pneumonia and decrease your ability of your body's ability to UM fight off these germs so what happens say you get a bacterial body can't fight it off what happened is that this a viola sex or so type a viola psyche and it gets inflamed and when it gets inflamed what happens is that things start to pull in there so it starts to become full of fluid this one's nice and um spread out it opens and closes this one has become bogged down with fluid then your body has since that there's inflammation going on so it seems its army of white blood cells to come and fight that infection that's there so it starts to fill with red white blood cells and then you have your red blood cells that are normally they're already getting stuck there and they start forming along with that bacteria so that's just way too much for the alveoli sac to implant to inflate and deflate so what happens is that you don't have the ability of those cells to rid itself of carbon dioxide so you're going to have the buildup of carbon dioxide then you can't get that fresh oxygen to the system so guess what you're going to have hypoxemia low oxygen in the blood because that oxygen can't get through that capillary wall to be transported so you're going to get conditions called rest or acidosis which we'll go over a little bit more here in a second but I wanted to cover that with you so you can see that now there are certain things that will increase a patient's chances of developing pneumonia so let's look at those risk factors okay a prior infect Shen's such as influenza a cold a lot of times patients will get that and they will develop pneumonia because there's they've got this infection that's decreased their ability to filter out these germs and bacteria so they develop this along with whatever they have else going on also if they have a weak immune system infants and elderly are definitely at risk for developing pneumonia an HIV or if they're taking medications and that are autoimmune to suppress the immune system they're at risk for developing this because their body's not working like it should because it's suppressed another thing is if they're in mobile they're in bed they've had a stroke that has made them where they're not allowed where they can't move or they've had some type of change in neuro status like dementia and these patients are really a lot at risk for aspiration where and they may aspirate their stomach contents or food they eat into the lungs which increases pneumonia or they have a lung problem underlying issue like COPD or pneumonia as a nurse taking care of patients and had a lot of patients come in with pneumonia especially during the wintertime fall time and they have COPD and they got pneumonia or they'll post up from surgery a lot of times we talked about this in the incentive spirometer in CLECs review video we want to teach our patients before surgery how to use that incentive spirometer after surgery because these patients usually are in pain especially if they've had abdominal surgery chest surgery they don't want to call debrief take deep breaths so their risk for developing this plus their system has just went through a major surgery and has stress out their bodies so the ramune system isn't working as strong as it should now let's talk about respiratory acidosis I talked a little bit about this at the beginning now let's look at a little bit more in depth specifically those ABG values now if you're not familiar with respiratory acidosis I had a whole Inc Lex lecture on that a cart should be popping up so you can access that comes with the quiz and everything so you can watch that familiarize yourself with this condition but what happened in pneumonia as we learn those sacks are not being able to inflate and deflate so the alveoli aren't being able because they're so inflamed they're so congested they're not allowing those cells to release the carbon dioxide into the respiratory system so you can exhale it so what's going to happen is that your body is going to be keeping carbon dioxide and we don't like that because it's a waste product and we want rid of it in turn the fresh oxygen that we just have taken in through inhalation isn't going to get through that capillary wall to go to the heart so it can be transported through the system so you're going to have low oxygen in the blood and the patient's going to be experiencing hypoxia so your arterial blood gases your ABG's are going to reflect this so we're going to have high carbon dioxide and low oxygen in the blood so typical AVG's RPO po2 is going to probably be about less than 90 millimeters of mercury our blood pH because carbon dioxide when we keep too much of that it's a waste it's an acid and our blood is going to become acetic so our blood pH is going to drop it's going to run less than 7.35 and our pco2 which is our carbon dioxide measurement is going to be high because we are retaining carbon dioxide so greater than 45 now your body tries to balance itself out so the lungs and the kidneys in these acid baths acid-base imbalance try to help each other out so what will happen because you also look at your bicarb and to compensate the kidneys will try to keep or conserve the hco3 which is your bicarb to increase that Bloods pH because it's so low right now it's acidic and a normal blood pH is 7.35 to 7.45 so you may see a bicarb if it's trying to help compensate and be greater than 26 now let's look at the causes we talked about how bacteria can cause it viruses and guy so let's talk a little bit more about those and then we'll talk about the types of pneumonia okay so bacterium most pneumonia infections are bacteria it's the most common especially in your community acquired types of pneumonia I'm streptococcus pneumoniae is the most common type of bacteria that infects a person to cause them to have bacterial of pneumonia another type of pneumonia is caused by an atypical bacterium and it causes what's called as walking pneumonia we've all heard it and it's caused by that type of bacteria my coat mycoplasma pneumoniae and walking pneumonia how it's different the symptoms tend to be a little bit more milder then straight-up pneumonia and hence why they call it walking because it doesn't seem to be a severe to confound them to bed require hospitalization and that is what that but that bacteria is what causes that then you have the viruses some viruses that can cause pneumonia like influenza or RSV which is a lot in your pediatric patients and then fungi like I said this is the least common it tends to affect people who have weakened immune system and they get it from just normal outside like plants or animals that healthy people who have strong immune systems can fight off normally but because they're awake immune system normally something that a person wouldn't get they just get it okay now let's talk about the types okay there's two types that I would be familiar with with their definition okay you have community-acquired and this is the most occurring and this is where the person has got that germs bacteria water they've got outside of the healthcare set setting hence why they call it community they were acquired at somewhere in the community another type is hospital-acquired and a lot of patients who are on mechanical ventilation aren't risk for this the person has contracted this pneumonia germs somewhere within the hospital setting now this tends to be your worst type of pneumonia because the bacteria tends to be really strong and tends to be resistant to antibiotics and the criteria for putting this as hospital-acquired I would remember this is if the patient has developed it 48 hours to 72 hours after admission it would be classified as hospital-acquired pneumonia so how is pneumonia diagnosed a lot of times it will be picked up whenever your auscultate een with the stethoscope the doctor may be listening and they may hear coarse crackles rhonchi which is a type of wheezy or bronchial breath sounds which are normal breath sounds if hurt in the tracheal area but they're not normal if you hear them over the peripheral one field because it can represent lung consolidation and I have a whole video series on with audio clips where you can listen to normal breath sounds and abnormal breath sounds and a card should be popping up so you can access that and the patient along with these sounds may have these other signs and symptoms but this will usually lead to the doctor ordering a chest x-ray which is a great way to diagnose pneumonia because they will be able to look at the lung field see where it's at and show infiltrates if they have any and a sputum culture a lot of times these patients have very productive coughs or coughing at all different color types stuff and you can send that sputum off and they can culture it to identify the type of bacteria or fungus that is causing the problem and which is great because whenever they pick medication therapy if it's a bacteria they can pick if it's a grand positive or gram-negative what type of antibiotic they should use which we'll be covering in part two okay so what are the signs and symptoms of pneumonia to help you remember this remember the pneumonic pneumonia we're talking about pneumonia so just remember each letter in each letter will correspond with the sign and symptom so here are the typical signs and symptoms of pneumonia P productive cough or pleuritic pain this type of pain is chest pain that the patient experiences whenever they're coughing or breathing it feels like chest pain in for neuro changes this is especially common in elderly patients they probably won't even have a fever but you'll notice that they're all of a sudden confused they have an increased respiratory rate and they're just really tired so that's how they can present with that eve for elevated labs such as as you've seen with the carbon dioxide the pco2 and increase white blood cells because your body is trying to fight infection so those will be increased you for unusual breast healed again you may hear these coarse crackles rhonchi or those bronchial breath sounds within the peripheral lung fields M for mild to high fever the bacteria if this is a bacterial cause of pneumonia these patients can run really high temperatures sometimes greater than 104 degrees Fahrenheit Oh for oxygen saturation will be to decrease a lot of times it will be less than 90% and they will need supplementary oxygen in for nausea and vomiting these people absolutely just feel horrible they don't feel like eating they feel sick to their stomach I for increased heart rate and respiratory rate they'll beat a kapeniak and tachycardic because of the infection going on in the body and the hypoxemia because the heart the lungs is trying to increase that respiratory rate to blow off that carbon dioxide they have and get some more oxygen in but it's not working because it's all inflamed those Abiola sacs and then a the last part of it they'll be aching all over they'll feel horrible and they'll have activity intolerance with shortness of breath just simply moving from the bed to the chair will make them very winded okay so that is part one of pneumonia be sure to check out part two and don't forget to take that quiz in clicks review quiz on pneumonia and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	ARDS_Acute_Respiratory_Distress_Syndrome_Nursing_Pathophysiology_Treatment.txt	hey everyone say earth register nurse are in.com and in this video I want to be going over a cute respiratory distress syndrome also called a RDS in this video is part of an Inc Lex review series over the respiratory system and as always I've ended this YouTube video you can access the free quiz that will test you on this condition so let's get started a RDS is a type of respiratory failure that occurs when the capillary membrane that surrounds the alveoli sacs starts to leak fluid and whenever it leaks flu and fluid will actually enter into this sac well we know that's a problem because why well let's review our anatomy and physiology of our lungs a little bit so what part of the lungs is really that functional unit it's the alveolar sacs this is where gas exchange occurs so if we took a sack and we blew it one up and we looked at it up close this is sort of similar what it would look like okay so here on the sack overlaying those sacks are like capillaries and those capillaries are bringing blood from the heart because all the blood goes to the heart must pass through the ones to get oxygenated so you have blood coming from the pulmonary artery and the blood coming from the pulmonary artery is like the used up blood the body is just used as came back to the heart to get reoxygenate 'add and to rid itself of carbon dioxide so here it comes down through the pulmonary artery and the oxygen that this person just breathes it in is going to cross over into that capillary and he's going to oxygenate the blood now what's going to leave the blood is that build up that carbon dioxide and it's going to cross over into that in that alveoli sac and carbon dioxide is going to be exhaled by the person so you have this beautiful intake of oxygen and outtake of carbon dioxide and then the blood is going to go back through the pulmonary vein it's going to be pumped by the heart and it's going to go throughout the body and replenish your organs your brain your kidneys everything we need to function but we have a problem with a RDS what's happening is that this capillary membrane which is represented here in the purple isn't working correctly it's starting to leak fluid from this capillary bed so flu it's starting to leak where it shouldn't go and it can collect in this sac so you're gonna have decreased gas exchange and what's gonna happen is a sac will become so filled with fluid you're gonna have a problem with that sac being able to stay open so it's going to collapse and we don't want our alveoli sacs to collapse because when that happens when that person tries to take in air with oxygen in it it's not going to work because that sac is collapse it's not working so you're going to get a decrease in oxygen in the blood the fancy term is hypoxemia so you have low oxygen in the blood and what's that going to do to your organs can your brain your kidneys your gut everything we need to live work without oxygen in it No so organs are going to suffer and the patient can die so the patient when they're in really severe a RDS they're gonna need respiratory assistance of some kind and usually it's like mechanical ventilation with peep positive end expiratory pressure what what's that going to do well that peep as you're gonna learn later on your nursing interventions is going to help open up these sacs that have collapse which is going to improve our gas exchange and help the patient so first let's talk about some quick facts about a RDS okay the onset is fast this happens suddenly and usually when you're going to see this condition is impatience here really are already hospitalized they're there for something else let's say a severe burns or sepsis which is one of the most common causes of a RDS so they're hospitalized with another condition and they develop this so as a nurse you've really got to listen to those respiratory sounds look at your patients respiratory system and what happens is that usually develops due to some systemic inflammation that's occurring in the body so we know that all the blood in our body has to go through the lungs to get oxygenated we just learned that so if you have some type of complication going on the body that's making that immune system send off those inflammatory cells well that's gonna be a really present in the blood so we have sepsis somewhere and so the blood that's going through the body normally eventually is gonna come to the heart in this area for this gas exchange to happen so it can go back and do its shock well if those inflammatory cells are here in this blood what's it gonna do it can damage this capillary membrane and cause it to leak fluid so you can have direct injury that causes a RDS or you can have indirect which we're going to cover those here in a moment so be keeping that in mind now the mortality rate with a RDS is relatively high so patients who have this is a very serious condition they're treated in the intensive care unit now let's talk about what causes that capillary membrane that surrounds our V live site to leak and then we'll talk about the pathophysiology and the phases of a RDS okay so any event that leads to major systemic inflammation in the body can cause this condition and this is usually from indirect sources so the source is not in the lungs it's somewhere else throughout the body and what happens is that the immune system with your inflammatory cells is producing a lot of those and of course they're in the blood so once the blood is passing through the lungs because we learned it has to do that they can damage that capillary membrane causing leakage of fluid so some conditions that can cause that our sepsis and remember sepsis was the most common cause of a RDS and if a patient sepsis is being caused by a gram-negative bacteria the patient has a very poor prognosis because it's going to be really hard to treat in addition burns can cause uh severe burns the body you have major inflammation going on with that so you can definitely see why that can happen in addition blood transfusions where they've had multiple transfusions inflammation of the pancreas pancreatitis hints that inflammation going on with the pancreas and drug overdose now another way a person can develop a RDS is through direct causes so the source is what our lungs it's coming from the lungs and it has been directly damaged that capillary membrane and what can cause this is like pneumonia patient gets pneumonia in those lungs and can damage that membrane aspiration a lot of patients who have difficulty swallowing they can aspirate food gastric secretions which we know that gastric secretions what's the role of it digest so if it gets inside of our delicate lungs that can definitely damage that capillary membrane along with an inhalation injury we talked in depth about that in our burn series how inhaling any toxic substances like smoke powders anything like that get in there damage the membrane near drowning events or some type of embolism now let's talk about the pathophysiology of a RTS how does this happen now as I go through these phases this is the absolute worst case scenario not all patients will even go through these phases some patients recover faster than others but if they do hit this last phase their prognosis is very important they're gonna have a lot of lung damage so there's three phases we're gonna talk about that exudative then the proliferative and then the fibrotic first let's talk about the exudative phase okay this happens about 24 hours after injury and remember it can be direct or an indirect injury regardless there's gonna be damage to that capillary membrane so when you have damage to that membrane fluid is going to start to leak into the SAC and that fluid is protein rich now what's one thing we have been talking about with protein protein regulates water that oncotic pressure so if you have this fluid that's leaking with a lot of protein in it it's going to draw more water to it which isn't good so at first this fluid is going to enter into the inner stitching which is like that space that is in between the sac and that capillary membrane so whenever you're listening to lung sounds in the early part of this they may sound normal or a little bit diminished you're not going to start hearing I'm normal lung sounds until that fluid starts going into this alveolar sac so that's where it's going to go after the inner stitching and then that's where this patient is going to have pulmonary edema so you can hear those crackles with that now one thing with acute respiratory distress syndrome is that the physician has to determine is this a RDS or is this heart related like heart failure while we're getting the pulmonary edema we're going to talk about it in our nursing interventions but they will probably look at a pulmonary artery wedge pressure and whatever that reading is can help us know is this a RDS so keep that in mind in addition from everything that's going on there cells in there that produce surfactant and they're going to become overwhelmed and become damaged so we're going to have decrease amounts of surfactant being produced now what does serve a couldn't do it helps decrease surface tension so in other words it helps the SAC stay stable so it doesn't collapse whenever a person exhales and we're not having that with this so what's going to happen you have decrease amounts of surfactant it equals an unstable alveolar sac that's going to collapse and they're gonna develop a condition called act electus so with act electus the person's not going to be able to move that oxygen in because that sac is collapsed so where aux agem level is going to fall hypoxemia now to make things even worse if it couldn't get any worse something's going to develop that is made up of dead cells and proteins called a highland membrane and this membrane is going to affect how the lungs work it's going to make the lungs less elastic so the lungs are going to be stiff and you're gonna have decreased lung compliance so really how the lung can stretch and whenever the person breathes in and out so what's gonna happen you're gonna have what's called a VQ mismatch a ventilation and perfusion mismatch where the ventilation the ability to ventilate isn't going to match the body's ability to perfuse so with all this going on the fluid buildup in the alveoli sacs the decreased surfactant the hilum membrane that's developing it's all going to lead to the IV la sac collapsing it's not gonna work also you're gonna have to see a decrease in lung compliance which is going to throw us into a VQ mismatch and whenever you're looking at your patient as the nurse because of all this path though that's going on there is a hallmark sign and symptom that you want to remember and it's called refractory hypoxemia so as the nurse you can give them high amounts of oxygen concentration of oxygen it's not going to increase their oxygen level and the reason is is because what's going on our lung is getting stiff our sacs are collapsed that oxygen cannot flow down through that fact to go into that capillary and replenish the body so there's no way you can get that oxygen back up because of what's going on so when you look at ABG's what are you gonna see well in the very early stages in order for the body to try to compensate it has low oxygen so what do you think your body wants to do whenever it has low oxygen and wants to increase your breathing so they're gonna have an increased respiratory rate but as we've just learned it's not gonna help so we're still gonna have a low Oh to level so we're breathing hard we're breathing hard well oxygen it can't get in but carbon dioxide is still crossing over so as we're breathing out that fast breathing why are we going to be blowing off carbon dioxide so our co2 level will drop and blood pH level will increase so we're going to enter into respiratory alkalosis at first now as this patient progresses to those different phases we have the continued development of this Highland membrane it's going to make it even more hard for co2 to cross over we're going to start actually increasing in our co2 levels along with the patient's respiratory muscles are just going to get wore out so you're gonna see an increase of carbon dioxide so then they can enter into respiratory acidosis later on the next phase is the proliferative phase and this occurs about 14 days after injury and just like the word proliferative it's talking about growing and reproducing that's what's happening in this phase the body is trying to repair structures so you have these cells that are being reproduced quickly to do this and you're going to have the resorption of that fluid that was in that sac but here's the thing it's not going to be reproduced and restructured like it should be what's gonna happen is that this lung tissue that's being created is gonna be very dense and fibrous so you're going to have even more decreased lung compliance in the hypoxemia is going to get worse so after that phase about three weeks after injury some patients enter into the fibrotic phase and this is where you have fibrosis of lung tissue does it work right and pretty much what the patient can have is just dead space in the lungs that just doesn't work you don't have gas exchange so patients who do enter into this fibrotic phase are gonna have major lung damage and their prognosis is very poor and like I said at the beginning not all patients will enter into this this is like worst case scenario so to help us remember all that pathophysiology we just talked about and so you can recall this easily on his house let's remember this new morning AR D s that's what we're talking about so the first that a is act electus so let me write that up here this is what's developing and why was that developing well we have fluid in that in that Ivo livestock we have decreased surfactant cells which is decreasing our surface tension and our sac is collapsing so we have that our is for refractory hypoxemia so the patient is developing that and remember that was a hallmark sign and symptom you can give them high amounts of oxygen concentration but it's not going to increase their or their oxygen level and then D they have decreased lung compliance and we have that high limb membrane that's starting to develop and the fibrosis of the lung tissue decreased surfactant collapse sacs so our lung compliance ability of our lungs of stretch and fill with air it's totally decreased so our lungs are getting stiff they're getting hard and then the S is surfactant is cells are gonna be damaged so you're gonna have decrease surfactant which really ties in with the collapse lung and everything going on so more signs and symptoms are you gonna see as the nurse with this condition well very early on these signs and symptoms are going to be really barely noticeable they're going to be very subtle so when you listen to lung sounds they may sound normal you may hear like a random crackle here and there but that's because that fluid because I kept Larry membrane is damaged the fluids really just in the inner stitching but as it moves into that sack that's where you're gonna start seeing a lot of problems you can start seeing difficulty breathing on the patient's part they're gonna be really air hungry because their body is saying we need oxygen and they're gonna be wanting air they're gonna have that increased respiratory rate that we talked about low oxygen level their SATs are going to be low arterial oxygen level is going to be low and you can see respiratory alkalosis in the beginning and then as it progresses this pulmonary edema seen worse and worse getting decreased lung compliance that surfactant is gone we have collapsed sacs all throughout the lung fields they're gonna be full-blown respiratory failure they're gonna have that refractory hypoxemia which is that hallmark sign in symptom of art so remember that in your memory I'm gonna have cyanosis why is that tissues aren't being perfused so they're gonna be blue there's no oxygen to perfuse mental status changes tired fatigued confused why the brain is being deprived of oxygen increased heart rate that heart is stressed out from the low oxygen so it's beating harder and faster chest retractions literally this looks like the skin is just pulled over the ribs you can see the ribs and the body is just trying to get air in from where it's not getting the oxygen you will start to hear crackles throughout not just randomly throughout and that's the pulmonary edema and a chest x-ray which can be done to look at RTS will have a wideout appearance to it where the patient will have bilateral infiltrates throughout the lungs they'll talk about some nursing interventions for patients with a RDS so a big goal of course is maintaining that airway and respiratory function of these patients because it's significantly compromised so a goal is to have that PA o2 which is the arterial level for oxygen at least 60 millimeters of mercury or greater that's where we want them and their oxygen saturation to be at least 90 percent or greater so usually how that is accomplished most patients will be on mechanical ventilation with peep again that was positive in expert ory pressure and the pea pressures are going to be high for these patients they can be titrated anywhere between 10 to 20 centimeters of water and it'll be titrated based on how the patients responding how everything looks and why does it have to be so high well what we just learned in the path of everything that's going on with the lungs those lungs are collapsed so we've got to get those open so the reason why is there's decreased lung compliance that elasticity of along the ability of it to stretch it's become stiff so it's really not happening in addition there's fluid edema in those sacks so we're working against that and there's decreased surfactant being produced so we don't have that surface tension being maintained we have a very unstable sac so we have collapse so they need that high pressure to help open up those alveoli sacs that are collapse especially during exhalation and with our pressure our goal or end result hopefully will have improved gas exchange increase that oxygen level and keep those sacs clear of fluid but because this pressure is so high you have to watch out for complications related to this because it can increase intra thoracic pressure which can compress the heart and decrease cardiac output so you got to watch those blood pressures these patients are going to have sophisticated monitoring hemodynamic monitoring you'll be looking at that so they do have hypotension starts to develop that decreased cardiac output the physician can prescribe them like colloid solutions crystalloids IV solutions to help with that also like inotropic cardiac drugs like dobutamine to help with the hearts ability to contract properly to help prevent this in addition the patient can develop hyperinflation of the lungs because of this high pressure that is being exerted on it so the patient is at risk for a pneumothorax where the whole lung just can collapse in addition to like sub-q emphysema be watching out for that where air is actually escaping the lungs there's like a hole in the lung and it's going into the tissues and you can fill it you've ever felt it before it's like crunchy like Rice Krispies or something just in the skin it feels very weird now prone positioning let's talk about positioning positioning can't help with respiratory function there's various types of positioning but I want to hit on the prone positioning this is where you move them from their back to their belly so they're actually laying on their belly here in nursing that's a little bit weird pit innovational on their belly but it's actually been shown to increase their oxygen without having to increase the oxygen concentration and why is that well it helps improve ventilation and perfusion and it helps improve air flow because you no longer if you're laying back having the heart lay back in compressing up posterior parts of the lung so you're really not getting air flow whenever they're like that when you flip them over you don't have the heart compressing that instead it's gonna really lay up against the sternum in addition it's going to help move secretions to other areas that normally couldn't be free some from secretions because of this supine position and it's going to help improve that act elect assist another thing is that a pulmonary artery wedge pressure reading may be obtained and this is where the physician can rule out if this is cardiac related because we have a weak heart like heart failure that's causing fluid to back up into the lungs and this is what we're seen this respiratory distress with this pulmonary edema or it's a capillary membrane issue in this sac that's causing fluid to leak so what this does is it measures the left arterial pressure so pulmonary catheter is inserted with a balloon and it's wedged in the pulmonary arterial branch and here's the following readings if the reading is less than 18 millimeters of mercury it's a RDS if it's greater than it's a cardiac issue so just try to remember that number in addition as the nurse you want to monitor other body systems making sure they're being perfused right that they're getting enough oxygen so with renal why are you gonna look at you're gonna look at the urinary output if you have really bad urinary output those kidneys aren't working you got a problem how are they mental status wise are they confused they tired brains not being perfused look at your blood pressure heart rate in addition and there we talked a little bit about fluids and like dobutamine for the decreased cardiac output but they can also be ordered corticosteroids that's going to be for that inflammation because what was a big reason person develops a RDS is that systemic inflammation core Coast over can help decrease that inflammation also antibiotics why would antibiotics be given if patient has subsets want to treat that infection in addition GI drugs can be ordered a lot of times patients with everything that's going on they can develop stress ulcers so some drugs to help prevent that in addition as a nurse you want to be watching out because this patient is going to be able to move they can have what a they're at risk for pressure injuries pressure ulcers so watch out for that so when you're think about your plan of care you want to include that they're at risk for ventilator acquired infections being on the ventilator puts them at major risk for that and nutrition problems they can't eat so you want to watch those wait those electrolytes and make sure they're getting proper nutrition okay so that wraps up this lecture over a RDS thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	NCLEX_Pharmacology_Review_Question_on_Medication_Beta_Blockers_Weekly_NCLEX_Series.txt	hey everyone it's sth register nurse rn.com and in this video we're going to be going over our weekly inlex practice question and don't forget to check out the other practice questions in this series so let's see what our question says a patient who has a health history of uncontrolled hypertension coronary artery disease and diabetes militis is prescribed to take propanolol you have provided the patient with education about this new medication which statement by the patient indicates your teaching was effective a I will take this medication every morning with grapefruit juice B if I miss a dose it is important that I double the next dose to prevent potential side effects C it is important that I monitor my blood glucose level very closely while taking this medication or D I will immediately stop taking this medication if I experience cold hands or feet so for this particular question it is wanting to know which statement by the patient is correct about this medication propano wal that they're going to be taking so we're looking at the correct statement so out of all these three are going to be wrong and one is going to be correct so before we do that let's analyze this scenario now as you read the scenario some things should be be jumping out at you for instance the patient's health history and they have a history of uncontrolled hypertension which is high blood pressure they also have coronary artery disease and diabetes malius now let's talk about that drug propanolol that's what they're prescribed now let's think back to pharmacology this is the generic name of the drug generic names tend to have the same letters for the ending and and the ending for this is ool which drugs end an ool these are our beta blockers so propanolol is a beta blocker now it falls under the non selective category there's several groups of beta blockers you have ones that act on just that heart tissue specifically their beta 1 receptor blockers and then you have these which act on both the beta 1 and beta 2 receptors now let's backrack and talk about what beta blockers do let's review in our pharmacology because it's going to make sense when we're throwing in that this patient has diabetes mtis because whenever you have diabetes malius and you're taking a beta blocker you have to watch out for some certain things that can happen Okay so what do beta blockers do in a nutshell beta blockers block your sympathetic nervous nous system what does your sympathetic nervous system do it is responsible for that fight ORF flight response so whenever you're stressed or in danger that system kicks in it increases your heart rate so you get tacac cardia you get Bronco dilation so you're going to breathe deeper so you can run away and get out of there now non selective which is propanalol it blocks beta receptors one and two remember now where are beta 1 receptors they're mainly in your heart so whenever you take this drug it acts on those neurotransmitters specifically norepinephrine and epinephrine so those will be blocked and in the heart and what will happen is that you will get a slower heart rate instead of that tacac cardia now think about diabetes malius whenever these patients have hypoglycemia what are those classic signs and symptoms one of the most classic sign and symptom is tacac cardia their heart rate goes up I've had a lot of patients tell me my heart rate's increase we might need to check my sugar I feel like it's down now if they're taking a beta blocker that is blocking that response they're not going to have that classic Tac of cardia so they may later on their sugar will drop so much and it may be too late before they can treat it before they can treat it appropriately Now Beta two receptors where are these mainly located they are located in various places number one your lungs you have two lungs that's how I remember beta 2 they can also be in the skeletal muscle acts in the liver one thing I want to concentrate on is that liver and the muscle now what these beta receptors do they increase a process called glycogenolysis what is that big old word what it means is that whenever a patient has hypoglycemia the body tries to correct that so it will do glycogenolysis which is going to break down glycogen to glucose which is going to increase that blood sugar however this is being blocked in this patient this process it's slowing it down so when this diabetic has hypoglycemia they're not going to be able to increase that blood sugar naturally with that process so you have this double-edged sword you have where they're not going to be able to notice their blood glucose because they don't have that tack of cardia going on and they don't have that process of increasing that blood sugar naturally themselves so those two things are going to be blocked now let's look at our options you probably are already figuring out the option based on what we just discuss with that and looking at these but let's break them down and discuss why they're wrong okay option A I will take the medication every morning with grapefruit juice okay big thing that jumps out at me grapefruit juice why would a patient want to take medication with grapefruit juice all the time one thing that's was always drilled in my head in nursing school is never take grapefruit juice okay with beta blockers specifically you don't want to take medic this type of medication or various medications with great fruit juice cuz grapefruit juice contains chemicals that can slow the absorption of the medication so the patient wouldn't want to take their beta blockers with grapefruit juice they need to be educated to actually avoid that and to take it strictly with water so this is wrong option b says if I miss a dose it is important that I double the next dose to prevent potential side effects if a patient misses a dose of their beta blockers they don't need to double the dose they need to take it as soon as they remember unless that next dose is due because these medications as we talked about with the beta blockers um they decrease your heart rate they do a lot of things to your heart and if you're taking double the dose they are at high risk of a cardiac event going into um some lethal Rhythm so that is incorrect option C it's talking about monitoring your blood glucose levels very closely and I just discussed why that is our answer because the way the beta 1 and the beta 2 receptors work with the maintaining the blood glucose and the patient is already diabetic taking insulin probably that's what we assume and um so they have to monitor their blood sugar especially with these non-selective beta blockers so that is our answer now let's look and see why D is wrong this patient says that they're going to stop Tak their beta blocker immediately if they experience cold hands and feet well this is a normal side effect with these non-selective beta blockers because remember they're not just acting on that cardiac tissue they're acting on other areas and a lot of patients I've had actually report my hands are so cold since I started taking this drug my feet so this is actually a side effect that can happen and another thing that makes this statement wrong is that you would never just immediately stop taking a beta blocker they need to be tapered off of this because if they just all of a sudden quit taking that medication they can go have cardiac death or something worse can happen so that answer is wrong for that reason okay so that wraps up this inlex practice question be sure to check out our other inlex lectures and quizzes and nursing skill videos thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Thiazide_Diuretics_Pharmacology_Nursing_NCLEX_Review_Mechanism_of_Action_Side_Effects.txt	hey everyone in cereth register nurse RN calm and today we're going to talk about thiazide diuretics and as always after you watch this youtube video you can access the free quiz that will test you on this medication so let's get started as we've been reviewing these medications in this pharmacology series we have been remembering the word nurse because each letter of that word helps us remember those important concepts we need to know for exams so first we're going to talk about the name specifically the family name of the drug because this tells us how the drug works on the body and we're dealing with the thiazide family specifically those thiazide diuretics well thiazide tells us that this medication works in the early part of the distal convoluted tubule that's found within this nephron and what this drug is going to do it's going to affect a co transporter that's found within this early part of the dct and this transporter is called the sodium chloride co-transporter and it is considered a cyanide sensitive transporter so hence why this drug works so well and what it's going to do is it's going to prevent this transporter from being able to do its job and just as its name says is that this transporter transports sodium and chloride from the filtrate to go back into the blood to be reabsorbed by the body well for stopping this process of this sodium chloride going back into the body that means it's gonna stay in this filtrate which eventually turns into urine when it exits the body so if we have sodium chloride stained in this filtrate it's going to result in increased sodium in the filtrate which is going to draw water to it because water loves sodium so more water will stay in this filtrate will not be reabsorbed back into the body less of it will be and this is going to cause the person to have increased urination because we have more fluid in the urine so we're getting those diuretic effects that this drug does and this will help slightly decrease our blood volume you because we're moving it now thiazide diuretics are not as potent or as powerful as loot diuretics like furosemide and the reason for that is because each type of diuretic that you have is going to affect different structures within this nephron which is going to alter how sodium is reabsorbed back into the body because if we keep it in the filtrate that means water is going to stay there and that's going to help provide that diuresis effect so for example loop diuretics we learn work in the loop of Henle and specifically this thick ascending line' and this thick ascending limb is responsible for about 25 percent of sodium reabsorption so we throw on a lube diuretic we're not going to be reabsorbing all that said he was going to stay in the filtrate that's a high percentage of sodium so it's going to have a stronger effect by keeping water in it compared to this distal convoluted tubule where it only accounts for about five to seven percent of sodium reabsorption so you can see the percentage differences and while loop diuretics are a lot more effective than a thiazide diuretic but the thiazide diuretic does provide a nice diuresis effect not as strong as a loop diuretic and another thing about thiazide is that they're less effective in patients who have a compromised GFR a go merrill ER filtration rate meaning that this glomerulus of this nephron is not very effective in filtering the blood and with loop diuretics they are good in patients who have this compromised GFR like they have renal failure let's say you have a patient with renal failure who has fluid volume overload well we can give them a loop diuretic and that can help remove that fluid but with a thigh we wouldn't want to do that because their GFR is compromised in some examples of thiazide diuretics are like hydrochlorothiazide in DAP amide clora thiazide Mottola zone and chlorothalonil unfortunately we can't go by their ending like with some of the other drugs generic names but some do in in thiazide now let's talk about how these thiazide diuretics work on this nephron to cause diuresis but to do that let's review the basic anatomy and physiology of this nephron here's an illustration of a nephron if we took a nephron and stretched it out it would look something similar to this also you can see how the nephron sets within the kidneys and these structures work within the kidneys to allow them to function and without them working properly the kidney fails to do its job and there are millions of these little nephron structures within each kidney and they function to filter the blood and manage the amount of water ions and waste in the blood and either it's going to cause some ions and water to be reabsorbed back into the blood so you can use them or it's going to make it where the ions and specifically waste and water will stay in the filtrate so it'll be excreted as urine so these little structures are always tweaking this filtrate that's created by the glomerulus until it's where your body needs it to be and if it's not you excrete it as urine and the nephron is divided into several parts and each part has its own unique role for tweaking this filtrate which is why certain diuretics work on certain areas of the nephron and the parts of the nephron include the afferent and efferent arteriole the afferent arteriole delivers blood via the renal artery to the nephron so it can be filtered the afferent arteriole takes blood away from the nephron after it has been filtered so when the nephron receives blood through the afferent arteriole it's going to go through the glomerulus and this is going to filter the blood and create the filtrate which will eventually exit the body as urine and the filtrate is going to contain ions which are like electrolytes water and waste and it's gonna drip down into Bowman's capsule which will collect the filtrate as it drips down from that mara less then the filtrate is going to start its journey of being tweaked and by the other parts of the nephron to the point where the body is satisfied with it and what it doesn't want it's going to be excreted as urine so the first stop is the proximal convoluted tubule and this area is going to reabsorb water ions etc and the parts that we've talked about up to this point hang out in the renal cortex of the kidney and this provides like an isotonic environment where the sodium concentration is equal in the inside hence the nephron and that filtrate compared to the outside however as this filtrate starts progressing going down into the loop of Henle it's going to enter into a hypertonic environment because it's in the renal medulla and this is very necessary for water re-absorption by that descending limb of the loop of Henle and the collecting duct so once it leaves the proximal convoluted tubule it's going to go down into the loop of Henle and then loop of Henle has the descending and a sending limb so it's tweaked there as well and remember I talked about how that thick ascending limb is responsible for about 25% of sodium reabsorption so the filtrate is going to go up and again it's going to enter back into the isotonic environment and it's going to go into the distal convoluted tubule and this is the structure that we care about for this lecture for the thiazide because this is where the thiazide diuretics works specifically in that early part and some functions of this distal convoluted tubule is to of course reabsorb sodium and chloride but it also plays a role in reabsorbing calcium and i want you to remember that because one of the side effects of thiazide diuretics is that it can increase calcium levels and also it plays a role with secretion of potassium into the filtrate then it leaves the DCT and it's making its journey to the collecting ducts and this is the last part of the nephron where the filtrate is finally tweaked ions and water will be it reabsorbed and the last part of the collecting duct is found in that renal medulla and this will play one last role with that water reabsorption then it will exit the body through the renal pelvis and you will have urine which will go to the ureters and be urinated out now let's go a little bit more in depth to how these thighs I diuretics work in this distal convoluted tubule and tie it in with why we're gonna see these certain electrolyte imbalances for these patients and these are some important concepts you want to remember for your exams because it'll tie in with your nursing interventions and your patient teaching so we've already established that the distal convoluted tubule is going to play a role in us reabsorbing sodium and chloride and calcium and the secretion of potassium ions as well into the back into this filtrate so the distal convoluted tubule when we throw a thiazide and it's going to affect this code transport the sodium chloride co-transporter it's going to prevent it from allowing these sodium and chloride ions from leaving the filtrate and going back into the blood and hanging out in the blood and keeping those levels nice and stable so because we're not going to be receiving that sodium we are going to potentially lower the sodium levels in the blood leading to hyponatremia so that's one electrolyte imbalance you want to watch out for now because we're inhibiting this co-transporter it's going to alter how these other channels and transporters can work within this distal convoluted tubule to deal with other ions to be reabsorbed and one ion reabsorption that's going to be affected will be calcium because it is affected by a particular channel known as the t RP v v channel and because we inhibit this sodium chloride coat transporter it's actually going to inhale how this channel works so it helps the body reabsorb calcium back into the blood well for enhancing how this channel works we're going to be reabsorbing more calcium in the blood which can lead to hypercalcemia increasing our calcium levels in the blood a normal calcium level is about eight point five to ten point five milligrams per deciliter now this can actually be beneficial and we're going into a little bit for what this drug is used for but patients who have recurrent renal stones that are composed of calcium can actually benefit from this because if we are increasing calcium reabsorption from the filtrate to go back into the blood that's leaving less calcium and that filtrate which leaves less calcium that can help create a renal stone also patients who have low calcium levels we can possibly throw in a thiazide to help increase the reabsorption of calcium in the blood which can hopefully help increase their bone density so it can be beneficial in some instances but as a nurse you want to watch that calcium level also thiazide diuretics can cause hypokalemia and that was similar to our loop diuretics they also can lower the potassium level so they share that and why is that same like with loop diuretics as this filtrate travels through this distal convoluted tubule here we in the early part we prevented that sodium from being reabsorbed so more is hanging out in the filtrate well it's journeying down through rest of this to be oh well it's high in sodium and these channels are influenced by aldosterone and we've learned that aldosterone causes the body to keep water and sodium in exchange for potassium so if we have a lot of sodium in the filtrate traveling down through these aldosterone influence channels that's really going to cause the body to secrete potassium into that filtrate which is going to lower our potassium levels and also going with that potassium hydrogen ions so we can lower our potassium levels in normal potassium levels about 3.5 to 5 milli equivalents per liter and the patient could possibly experience metabolic alkalosis due to the loss of those hydrogen ions so remember that and patients may have to take potassium supplements you'll want to be watching that potassium level for sure especially if they're on other medications which we'll talk about here in a moment and educate them about foods that are rich in potassium and they want to definitely keep those in their diet those are diuretics can also alter the blood sugar and this is important to know for your patients who are diabetic thiazide diuretics can increase the blood glucose level the reason for why they do that is not truly understood but we want to educate our patients to monitor their glucose glucose level closely because their insulin or their oral diabetic medications may have to be tweaked based on if they're getting this hyperglycemia and thiazide diuretics can increase uric acid levels which can lead to gout attacks and the reason for this is that these drugs alter how the proximal convoluted tubule deals with your ate and it actually increases how urate is reabsorbed which can increase your gas levels and lead to gaol attacks so you may need to monitor those uric acid levels and high uric acid levels for a male tends to be anywhere anything greater than seven and four females greater than six so if you see a uric acid level of 15 that is not good that means that they have high uric acid levels so what if eyes I diabetics use four which is the second part of our word of nurse well they can be used to treat hypertension high blood pressure and they're usually about the first line for helping a patient treat their high blood pressure and what it's going to do it's going to decrease that sodium and water out of the blood which can help lower the blood pressure in addition they can be ordered for patients who have heart failure this is where the heart is weak to pump blood it becomes overwhelmed and blood starts backing up into the lungs and to the body and the patient is really just miserable so what these medications can do is they can be prescribed a lot of times with ACE inhibitors and we talked all about ACE inhibitors and this can help actually increase the function of the heart and help the patient feel better also as we've talked about thiazide diuretics can be used in the treatment of renal calculi which are those renal stones that are composed of calcium now let's wrap up this review and let's talk about nursing responsibilities the side effects and education pieces for the patient who may be taking a thigh-high diuretic so whenever you have a patient taking a thiazide you really want to be watching out for signs and symptoms of dehydration because we're increasing your their urination and how much fluid is being removed from their blood volumes so some things as a nurse you can watch out for is you can look at their vital signs how is their blood pressure if it's hypotensive low that's the salts less than 90 that probably means that we've removed a little bit too much fluid volume from their blood also the heart rate will be increased as well we're tachycardic from where the heart's trying to compensate for that loss of fluid volume then we can also look at their eyes and O's you want to make sure you are strictly measuring that and the patient can help you with that they're alert and oriented and whenever they go to use the bathroom to urinate you definitely want to make sure you were measuring that because you want to look to see how much they're taking in versus how much they're putting out they're really not putting out anything at all the renal function could be compromised so we want to make sure that we are digressing them but not too much and we can look at their daily weights where we weigh them every day at the same time using the same scale this tells us their fluids status and really tells us how effective this medication is working because if they're gaining weight instead of losing weight we made not very effective with this diuretic they may need something else anyone to teach the patient to weigh themselves a lot of patients with heart failure may be on these medications and we want to teach them to weigh themselves every day and to write it down to keep track because if they've gained more than like three pounds in one day that could mean that they're retaining fluid and they may be having heart failure exacerbation and will need to go to their doctor to get treatment also as a nurse we want to monitor their labs because as we've learned these drugs cause electrolyte imbalances so the physician will order the labs we will get those results and we will look at them you always want to look into results especially before you give their medications because electrolyte imbalances can induce like toxicity of other drugs so we've learned that the I sides cause a lot of hypo a lot of hyper conditions so let's talk about the hypo we know that it can lower the calcium and potassium levels causing hypokalemia and if your patient is on digoxin and their potassium level goes too low it can increase the risk of digoxin toxicity so always look at that potassium level and be educating your patient to be consuming foods that are rich in potassium like bananas avocados strawberries potatoes etc because that will help keep that level high in a normal digital I just want to throw this in there is about 0.5 to 2 nanograms per milliliter the other hypo condition you can cost is hyponatremia where that sodium level is too low and that was another thing that lube diuretics did as well it can lower it too low so if you had a patient who's taking lithium that's not good because when sodium levels drop if a patient's taking lithium it can increase the risk of lithium toxicity so a normal lithium level is about 0.5 to 1.2 millimoles per liter so remember these two drugs if we go into these hypo conditions either hyponatremia or hypokalemia with those it can cause toxicity those are some important concepts no exams love to ask about the hyper conditions that these drugs can cause our hyper hyper Cal C Mia the high calcium level hyperuricemia the high uric acid level and hyperglycemia again teach your diabetic patients to monitor their blood glucose really closely while taking a thigh and some other little miscellaneous things you want to remember is that whenever you give a patient any type of diuretic they can get up and use the bathroom on their own you need to make sure they have easy access to it because you don't want them to fall and get hurt and avoid giving doses of diuretics at night because we want our patients to sleep at night we don't want them up using the bathroom all the time so make sure you're not doing that and orthostatic hypotension this is where the when the patients maybe they've been sitting or lying down they get up they can fall they become dizzy you want to teach them to change position slowly because we're altering the fluid status in their body and as a nurse you want to make sure that this medication is being effective is it doing its job how do their lungs sound is their blood pressure coming down maybe they're getting this drug for hypertension how is their weights are they gaining weight or losing weight so we play a huge role with that as well okay so that wraps up this review over thighs I diuretics thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Respiratory_Acidosis_Acid_Base_Balance_Made_Easy_NCLEX_Review_ABGs_Made_Easy_for_Nurses.txt	hey everyone it's Sarah with register nurse rn.com and in this video I'm going to be going over respiratory acidosis I'm actually doing a series on acid and base imbalances so if you're studying that right now be sure to check out those videos now in the previous video I went over respiratory alkalosis and showed you the differences how it affects the body what to remember for the inlex exam in your nursing lecture exam so be sure to check out that video so in this video what I'm going to do is I am going to simp simplify the pathophysiology with what's going on in respiratory acidosis I'm going to give you a pneumonic on how to remember the causes and we're going to go over signs and symptoms nursing interventions and then I'm going to take it a step further and work a arterial blood gas problem with a patient that's in respiratory acidosis and show you how to set the problem up using the Tic Tac Toe method and how you can determine if it's compensated not compensated and things like that now after this video be sure to go to my website register nurse ran.com and take the free quiz that will test your knowledge on respiratory alkalosis and respiratory acidosis a card should be popping up or a link in the description below and you can access that free quiz so let's get started with the pathophysiology because in order to truly understand what's going on in the body during respiratory acidosis you have to know what is being affected in the lungs then the cause is will make sense it'll literally be like Common Sense it'll click in your brain so let's simplify this okay whenever you breathe you take in oxygen through your either your nose or your mouth so the oxygen enters in through there the ferx area then it goes down through the Linx which is your throat down through the trachea which branches off into the bronchus which then branches off into the bronchials and then to the avolar Sachs now the avolar sax is where everything the gas exchanges are happening and what happens is that oxygen enters in and carbon dioxide comes out because carbon dioxide is that buildup of whatever your body has left over and you're going to breathe that out so the carbon dioxide will go backwards of how the oxygen entered and it will exit through your nose or through your mouth now in those avolar sacs what's happening is oxygen is going into those sacks carbon dioxide's coming out Oxygen's attaching to the red blood cells the red blood cells are transporting it throughout your body to your organs to your tissues and giving it fresh supply of oxygen but when youever you have something that's interrupting the breathing either you have depressed respirations where um maybe you gave them an opioid they have too much drugs involved or something like that it causes depressed breathing they're not expelling the CO2 so anything that's affecting the the body's ability to breathe normally because in an adult normal respirations are 12 to 20 breaths per minute so if it's less than 12 they're not breathing appropriately so they're not expelling the CO2 and we'll go over the causes a lot more in depth and your diaphragm which is below your lungs plays a role in this as well so if you have anything that affects the diaphragm which in neuromuscular dis diseases which we'll go over here in a second that can affect because whenever you breathe in diaphragm goes up helps squeeze that air out squeeze that carbon dioxide out and then it relaxes so if you have anything affecting that that can cause problems so whenever you have the buildup of the CO2 this causes your blood pH to become acidic and here are some key Concepts that you need to remember for this disease process that your teachers will probably ask you on exams or on the inlex so let's look at these key Concepts okay overall respiratory acidosis is the buildup of carbon dioxide in the blood and it's mainly due to Brady penia which Brady means slow penia deals with respiration so you're having really slow respirations where you're not getting rid of that carbon dioxide and what happens carbon dioxide's in your body there's too much of it and your body's like oh we do not like this so your blood pH because of that carbon dioxide causes the blood to become very acid it and it will become a pH of less than 7.35 and you remember you have a lot of Co carbon dioxide CO2 hanging around so the levels are going to increase so anything greater than 45 now whenever this happens in the body remember your body loves homeostasis it loves to keep everything nice and equal so it'll use other systems of the body to try to regulate this out so the kidneys will act actually start to release bicarbonate hc3 and you will start to see these levels rise and the reason that they're trying to rise is to help decrease that pH help to increase that pH level to make it normal because right now it's decreased and they want to increase it so by releasing the bicarb it will help hopefully increase it and any levels greater than 26 if you see that in a blood gas that's what your body trying to do is trying to compensate with that now you want to memorize these live values you seriously just want to commit these to memory so you can understand what's going on because whenever you're solving blood gas levels or anything like that you're going to have to refer back into your memory hey what's normal what's acidotic what's not so let's go over it real fast a normal pH level is 7.35 to 7.45 a normal P2 level your carbon dioxide level is 35 to 45 how I remember these two remember the fives at the end 7.35 to 7.45 and then again P2 is 35 to 45 you see the three and the five and the four and the five and then the hc3 which is your B carb the normal is 22 to 26 and then I just have this little chart this helps me remember it if it's if it's an acid or not an acid and for pH anything acid right here anything less than 7.35 is an acid anything greater than 7 .45 is a base alkalic um pco2 is the opposite so the high number anything greater than 45 is acidotic and anything less than 3 35 is um alkalotic and bicarb anything less than 22 is acidotic and anything greater than 26 is alkalotic so just try to remember that cuz that's going to help us whenever we try to solve our blood gases and I'm going to show you how to do that using the Tic Tac Toe method okay so let's go over the causes of respiratory acidosis okay remember this pneumonic the word depressed depress breathing because that is one of the big reasons why your body is becoming acidotic why you're having that buildup of CO2 so remember the word depress and each word will correlate with what's what the cause is okay first drugs any drugs such as opiates which are morphine fitel questions like to throw that out at you say the patient overdosed on morphine or Fenty or something like that or any sedative such as versed that's a lot of times given during moderate SED sedation will cause respiratory depression and remember when the patient is breathing less than 12 breaths per minute they're just barely breathing and they're not expelling that CO2 that CO2 is building up so that can cause respiratory acidosis so you want to watch patients with that also the other D diseases of the neuromuscular system I talked about this at the beginning this is the myasthenia gravis or gillium bra syndrome and this is weakness of the voluntary muscles like the diaphragm which helps to squeeze that carbon dioxide out and in these syndromes they're not working properly so they can't expel that carbon dioxide it's hanging around in there okay e edema anytime you get extra fluid in these lungs like in pulmonary edema um especially with congestive heart failure patients that fluid is hanging around those sacks and remember in the avolar Sachs we talked about how there's a gas exchange between oxygen and carbon dioxide it messes up those Sachs those Sachs can't open and close properly so it just starts to retain the CO2 so that can cause it next pneumonia almost the same concept as the fluid with pneumonia you have that excessive mucus production around those sacks which is and your sacks are filled with pus and fluid and they're not able to even properly inflate and deflate so you have that buildup of that carbon dioxide that your body is trying to get rid of so pneumonia can cause it and the rest next one the r respiratory center of the brain is damaged okay in your brain you have the medulla and the ponds area that is responsible for your respiratory center now if you have any traumatic brain injury or you have a stroke that affect that affects that area that can affect the way that the patient breathes how they take breaths so they can develop respiratory acidosis okay e for imali and this can block the pulmonary artery or the branches of the lungs depending on where the imali left the body this can be a fat emili air emilii um it can go into the branches and block off so if you have something blocking off that Branch whenever you're trying to get that oxygen into that AV AR Sac it can't go so if it can't go carbon dioxide can't go and carbon dioxide is just going to stay and hang out in the blood so that can cause problems so anything blocking in the lungs can cause those issues and the other s spasms of the bronchial tubes this is asthma whenever a patient has an asthma attack these bronchial tubes start spasming which is blocking again just like the Emi the gas exchange the and what is going to happen is at that patient whenever they're having that they're not taking those nice deep breaths and they're building up that CO2 okay and the last s this is another this is another important s um this what is happening with this is that you have the sac elasticity of the avolar sac is damaged and what's happened is that this Sac is damaged either because of a disease process called chronic obstructive pulmonary disease COPD or empyema and what happens is whenever this sack is damaged it's usually due to smoking so that's why healthc care providers really encourage patients to quit smoking because they take in the smoke the smoke goes through the lungs and it damages those sacks and what happens is that the sack becomes damaged and it doesn't properly deflate so whenever it doesn't properly deflate it retains CO2 that's why you'll hear patients who are COPD patients their CO2 retain because that sack is not deflating properly and it's keeping all that carbon dioxide now let's look at the signs and symptoms the nursing interventions and work an arterial blood gas problem and show you what a patient with respiratory acidosis would look like okay how does your patient present and look whenever they're in respiratory acidosis normally this is going to start to happen gradually and you'll start to see a neuro decline neuro changes all of a sudden they'll become confused maybe not answer your questions appropriately and they'll just KN off and fall asleep I remember I um had a patient one time he was starting to go into this and he we would be talking and all of a sudden he would literally fall asleep right in front of my face and we checked his ABG levels and sure enough he was in respiratory acidosis so really watch your neuro part um also the patient may say I just have a headache and then they're confused and they're drowsy that should send a red flag too and of course respiratory depression they're going to have a really slow respiratory rate less than 12 breaths per minute so make sure as a nurse you're counting those respirations appropriately and monitoring those and have low blood pressure as well okay so what do you typically do for a patient who is in respiratory acidosis um of course you'll contact the doctor they'll give you a lot of orders on what to do but typically this is what's going to happen you're going to administer oxygen and if the patient is alert enough you're going to encourage coughing and deep breathing helping them take those full deep breaths in and out cuz remember we want them to expel that carbon dioxide that's buil up so we want them to be taking normal breaths at a rate of at least 12 to 20 breasts per minute and if the patient has been having asthma attacks COPD or empyema a respiratory treatment might be good so get respiratory therapy involved to give them a treatment help with that Bronco dilators because remember in asthma you have Bronco constriction and that'll help open them up and so they can breathe proper properly and have that gas exchange go so they can expel that carbon dioxide and also if your patient is in this a lot of times um narcotics will cause this morphine fentel even lur tabs things like that anything that's an opiate or a sedative like Valium things like that can cause respiratory depression so you'll want to hold those medications don't want to give those because it will make it worse now remember this this is very very very important watch potassium levels with respiratory acidosis we talked about this in the hyperemia fluid and electrolyte series um because this will cause an increase of your pottassium levels anything greater than 1.5 so you want to watch that whenever you get hyperemia involved you start you need to watch for any EKG changes that's associated with hyperemia which are tall p waves the flat p waves or a prolonged QRS and PR interval so watch for any of that now if the patient has pneumonia you'll be giving um antibiotics encourage incentive spirometer usage so they can Brea in pop those sacks open which have the mucus and the PFF in them so you can help gas exchange and um if it's really really bad um if it the CO2 level whenever you draw your blood gas if it's greater than 50 the doctor May order the patient to have endot tracheal intubation so um prepare the patient for this or if they're in respiratory distress so that is the nursing interventions for that now let's work a problem that will show you how to do a blood gas problem on a nursing exam or the inlex because this is what nursing professors love to ask you whenever they're going over acid base imbalances they're going to throw some ABG values out out at you and they're going to give you some options and you have to decide what it is so I like to do the ABG I mean the Tic Tac Toe method whenever I'm solving ABG problems I have several two videos on where I go in depth on how to use the Tic Tac Toe method setting up your problem and solving that a card should pop up a links should be in the description as well so you can watch that video on how to do that okay so here's what the problem says patient has the following abgs a p CO2 level of 48 a pH of 7. 25 a by carb H3 level of 27 what condition is presenting so we've got to go back to our chart that you have hopefully memorized and you got to remember what's acidotic what's alkalotic and you're going to set up your Tic Tac Toe remember as a child we would play tic tac toe so just set it up with your lines name one column base one normal and I mean one acid one normal and one base now we are going to plug these values in um to whether it's an acid or a base so let's take it one by one okay p248 okay we're thinking back to our table we know that 35 to 45 is a normal P2 level and anything greater than 45 is acidotic so we're going to put P A2 here cuz it's an acid and then we're going to look at our pH okay we know that a normal pH is 7.35 to 7.45 anything less than 7.35 is an acid so we're going to put pH under acid okay we got a tic TCT toe right here is our Tic-Tac toe three in a row so we know that we are dealing with a respiratory problem that right there tells us in our tic-tac-toe another reason tic tac toe is great is because you're trying to figure out if you're dealing with a respiratory metabolic problem that's the whole issue with these abgs for a lot of students okay now we're going to look at our by carb and the the last part whenever after you get your tic tac toe the one that's in the other column you're going to be looking at that and you're going to be saying to yourself okay is this the body based on this value is this compensating fully is it partially compensating or is it not compensating at all so let's look at it our buy carb is 27 so we know a normal by carb is 22 to 26 and it's abnormal it's 27 according to that our chart it is basic so we're going to put it over here so remember at the beginning of this lecture we talked about how whenever there's a buildup of CO2 in the lungs the kidneys are going to try to fix this by releasing bicarb hc3 so the levels are going to increase abnormally why because it wants to bring that PH down and this is what we're seeing so the body is trying to compensate so we got some compensation going on here so we know we have respiratory acidosis and it's compensated but is it fully or partially compensated so this is where you've got to think okay it's 27 now what's the purpose of bicarb trying to increase the purpose is because it wants to bring that pH back to a normal level right now our is not normal it is still acidic so it's just partially compensated so if it would fully compensated the pH would be back to normal so this is respiratory acidosis partially compensated okay so that is about respiratory acidosis now be sure to take that quiz to test your knowledge on the difference between respiratory alkalosis and acidosis and thank you so much for watching and be sure to to check out my other teaching tutorials and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Lung_Sounds_Abnormal_Crackles_Rales_Wheezes_Rhonchi_Stridor_Pleural_Friction_Rub_Breath_Sounds.txt	hey everyone this is Sarah with register nurse rn.com in this video I'm going to let you listen to six abnormal lung sounds which will include wheezes Strider crackles and plor friction rub this will be part of a review series of the lungs also be sure to check out the video on normal lung sounds as well as a lecture and skills demonstration which is part of this series so let's get started [Music] [Music] m for okay thank you so much for watching remember you can go to our channel to find more videos on nursing skills inlex prep and more so please subscribe and share this video with others
Medical_Surgical_Nursing	Loop_Diuretics_Pharmacology_Nursing_Mechanism_of_Action_Furosemide.txt	hey everyone it's sarah red sterner sorry and calm and today we're going to talk about Luke diuretics and as always when you get done watching this YouTube video you can access the free quiz that will test you on this medication so let's get started as we've been going through this pharmacology series we have been remembering the word nurse which helps us determine those important concepts that we need to know about these drugs that we are studying and again in stands for name because this tells us how the drug works on the body what family of drugs is a part of you tells us what it is used for what is it tree are tells us the responsibilities of the nurse and this is where a lot of test questions will come from to determine if you know how to care for a patient who is taking this drug S stands for side effects and then e stands for the education pieces for the patient about this medication so let's start with a name we are dealing with loop diuretics loop tells us that this medication is going to influence how the loop of Henle works within this nephron and specifically loop diuretics effect the thick ascending limb of the loop of Henle diuretics tells us that this medication is going to somehow increase the urinary output by affecting how sodium is reabsorbed back into the blood it's actually going to inhibit that process from occurring so you have more sodium within this nephron and if you have more sodium you're going to keep water within that nephron instead of it going back into the blood so these medications can help remove extra fluid volume from a patient who's like in fluid volume overload now loop diuretics are the most powerful of all the diuretics and will be also talking about thiazide x' and potassium sparing diuretics and our next videos and to help you recognize if you're dealing with a loop diuretic or a thiazide or a potassium sparing diuretic always look at the end of the generic name loop diuretics tend in ni de or my m ID and some examples are like you met an AI furosemide and tore some ID with exception of ethic rinic acid which doesn't end in night or mine so what loop diuretics do again is they effect this thick ascending limb of the loop of Henle and particularly what it's going to do is it's going to inhibit a special protein coat transporter from doing its job and this cotransporter is the sodium potassium chloride transporter and what it does just like its name says it does is it's going to help transport some specific ions from the filtrate to go back into the interstitium into the blood and those ions will be one sodium one potassium and two chloride and then we'll take that from the filtrate and in a sense push it back to go back into the interstitium which will go into the blood however if we inhibit this ion transport specifically the transport of sodium we're going to alter some things because it's going to change the tone isset II of this medulla inner stitch them because this area is very hyper tonic so if we decrease its tone isset II it's going to alter how specific parts of this nephron are able to reabsorb water back into the body instead more water will stay in this filtrate and hence will be urinated out which hits our goal of increasing urinary output however to truly understand this whole process we've got to go back and we have to review the anatomy and physiology of this nephron here on the right we have an illustration of a nephron and if we took one and we stretched it out it would look something similar to this and how its structures are set up and here on the Left we have how that nephron actually sets within the kidney and you want to take note of this because some parts of the nephron are found in the cortex which is like an isotonic environment compared to some of them being found in the medulla which is a hypertonic environment and this helps you understand how these nephrons work with the way that they will tweak the water and the ions so these nephrons are structures within the kidneys that allow them to function and without them actually working properly the kidneys won't be able to do their job and there are millions of these nephron units in each kidney and they function to manage the water ions and waste that will be reabsorbed by the body or excreted as urine and the nephron can be divided into several parts each part of the nephron has its own unique role for tweaking the filtrate that is created by the glomerulus until it's just what the body needs and what it doesn't need it will be excreted as urine and these parts include the afferent arteriole and the efferent arteriole and the afferent arteriole is going to take blood via the renal artery and deliver it to the nephron so it can be filtered and the every arteriole will take that blood that's been filtered and send it back to the body so blood enters into the nephron via the afferent arteriole and it's going to be filtered by the glomerulus and the glomerulus will create the filtrate which will eventually exit the body as urine and in this filtrate or ions which are like electrolytes like potassium sodium magnesium etc water and waste and this will drip down into Bowman's capsule now it's going to encounter its first to be aware the tweaking of what will be needed by the body or excreted by the body via the urine is going to occur so it goes through the proximal convoluted tubule and remember that this area so far is setting in that renal cortex which is an isotonic environment then that filtrate is going to go down into the descending loop of Henle so this is like that first structure of the loop of Henle and this is found in the medulla and again it's hypertonic so it's very salty compared to the isotonic and in the cortex where the salt content was equal on the inside of the nephron compared to the outside but here in the medulla that is different so really salty on the outside which is going to play a role in the way that water is reabsorbed so the filtrate goes down this ascending lute limb of the loop of Henle and what I want you to remember about this descending limb is that it is permeable to water but it's not permeable to ions which means water can leave this land that ions cannot so because it's so salty here hypertonic water is going to leave this descending limb which is going to concentrate that filtrate and make it really concentrated with sodium and all those other ions then the filtrate is going to go up through the ascending limb of the loop of Henle and it's going to hit the thick ascending limb and this is where loop diuretics work remember they block that co-transporter the sodium potassium chloride co-transporter and I thought filtrate hits this thick ascending limb it's really concentrated so normally those ions are going to be transported specifically that sodium that'll help keep that renal medulla hypertonic however whenever we're throwing in a loop diuretic that's not gonna work very well so then the filtrate will go up through the distal convoluted tubule it has left that hypertonic environment now it's back in the cortex where it's isotonic again it's going to be tweaked depending on what the body needs and then the filtrate is gonna go down through the collecting duct and some of this area enters again into the medulla where you're gonna have some more water reabsorption by the body and then the filtrate will go through the renal pelvis and then eventually will be urinated out so we've just seen how filtrate is created by this nephron and how it flows through the nephron and event exits the body as urine however since we're talking about loop diuretics we have to dive a little bit deeper into this loop of Henle and how loop diuretics affect the loop of Henle to cause diuresis to increase urinary output and one thing it's going to do it's going to affect how the body is going to reabsorb sodium so keep that in mind because if we're not reabsorbing sodium it's staying in the nephron that means water is gonna stay in there and it's going to exit the body hence increasing our urination so we said that in the proximal convoluted tubule the filtrate is there it's in that nice isotonic environment but then once it goes down into the loop of Henle it's gonna go into the medulla which is hypertonic it's really salty and there's two parts of that loop of Henle we have the descending limb in the ACE ending limb and they're really different and what they're permeable to what they allow to leave the nephron and go back into the interstitium and into the blood so filtrate comes down from the proximal convoluted tubule hits this descending limb of the loop of Henle and remember that was permeable only to water not ions and since its hit this really salty environment the waters like hey we're leaving we like salt so the water leaves the filtrate and this loop of Henle is actually responsible for about 15 to 20 percent of water reabsorption so it reabsorbs a lot of water so now waters left and the filtrate is really concentrated with these ions which is great because once it hits this ascending limb the ascending limb deals with that because remember this thick part of this sending limb is permeable to ions those electrolytes but not water so hits this ending limb and you have all these little Co transporters simipour channels that are going to help allow ions to leave this filtrate go through the cell hit the inter stitch and go to the blood and they're all working together beautiful to do their job and one of those code transporters was the sodium potassium chloride co-transporter so it takes one sodium one potassium two chloride takes it puts it back into the blood now the cool thing about the loop of Henle it's responsible for about 25 percent of the sodium reabsorption which it's gonna play a role in keeping this renal medulla hypertonic keeps it salty so we can play a role with reabsorbing water because also you're collecting doug's once it hits this hypertonic environment water is going to be removed right before it leaves so if we throw in something like a loop diuretic that's going to inhibit this co-transporter from transporting especially the sodium the potassium and chloride we're going to alter the tone isset ii of this environment which is going to decrease how much water is able to be reabsorbed through the collecting duct and from this loop of Henle so if the water is not leaving this nephron it's staying in there because we have lots of sodium still in here and remember sodium water love each other the water is going to stay in this nephron it's not going to be reabsorbed through the body so it's gonna leave the body as urine and we've hit our goal we have increased urinary output now let's talk about what loop diuretics are used for what do they treat well we've already established with how luke diuretics effect this nephron is that they're gonna increase a patient's ability to urinate so they're gonna be putting out a lot more urine well if you're putting out a lot more urine that's dropping your fluid volume in your blood now why would we want to draw up a patient's fluid volume well patients who are in fluid volume overload where they have way too much fluid hanging out in the blood and this can occur in patients who have heart failure where the heart is just so weak it just can't pump blood forward and you have different types like systolic dysfunction or diastolic dysfunction but the blood can backflow go into the lungs leading to pulmonary edema literally it's like the patient is drowning in their own fluid and the fluid can leak and go into the lower extremities where you have swelling there as edema so we throw on this loop diuretic that is going to tell the blood once it's being filtered by this nephron hey we're not going to be sending too much water back to you because we're going to tell this nephron not to reabsorb this water because we're going to alter the sodium content in our nephron and around in this medulla we're not gonna make it as hypertonic so guess what you're not gonna have some fluid coming back to the body instead this patients going to urinate it out also patients who have liver impairment where they get the side effect of ascites where they have a lot of swelling in the abdomen that can help with that patient the pulmonary edema as we just talked about and hypertension leave diuretics aren't as helpful with hypertension compared to like thiazide but sometimes they're prescribed for that to help lower the blood pressure and that would come from lowering the fluid volume which will lower the pressure same concept you lower the amount of water that's going through a water hose you're gonna lower the pressure and it also treats hypercalcemia which is where you have a high calcium level in the blood but how can loop diuretics treat a high calcium level in the blood well we've learned that loop diuretics really manipulate how ions are going to be transported back into the blood from this filtrate because we're inhibiting this sodium potassium chloride transporter and that will throw things off so normally the filtrate will flow down through here remember once it passes this distal limb it's going to be really concentrated in ions so we're not only talking about like sodium potassium chloride we're also talking about calcium and magnesium they're positively charged so they're going to go up in this thick ascending limb where we're having normally if we don't have a loop diuretic we will have sodium one sodium one potassium and two chloride being transported over also working as well doing its ion exchanges like the sodium potassium pump you can have potassium chloride symporters and calcium channels and all of this together is creating this like positive potential this concentrate electrical gradient that can normally take this calcium and this magnesium and force it out of this filtrate to go back into the interstitium and be reabsorbed into the blood but if we inhibit this co-transporter that's going to throw those things off and we'll lose that positive potential so the calcium and the magnesium will stay in the filtrate will not go and be reabsorbed and that can lower our calcium levels and our magnesium levels more so our calcium levels so that's why we can use this to treat high calcium levels and I'll talk about the responsibilities of the nurse and the side effects associated with Luke diuretics we're going to mesh the two so with patients taking loop diuretics thread a huge risk for dehydration so we want to monitor their fluid status and make sure they're not becoming dehydrated how can we do that well we can look at their vital signs and see where's their blood pressure is that systolic less than 90 we've probably diurese them a little bit too much how's their heart rate are they tachycardic where it's above a hundred that can be signs of dehydration along with excessive thirst being lethargic and we want to make sure we are strictly measuring their intake and output because we don't want the patient just consuming all this fluid and it's really undermining the effectiveness of this drug or we don't want them to be just putting out so much where they have this major negative loss of fluid compared to how much they've been taking in so for me and you want to make sure that you give them a urinal and you measure it every time you into that urinal and women that you put the tool that height in the toilet so you can collect the urine and if they have the Foley you can just look and see how much urine was put out of the Foley plus we want to make sure that they're putting out enough here and and that we're not sending them into like renal failure and we're going to be collecting the weights daily at the same time using the same scale and we're looking and seeing how much their weight is fluctuating because Wayne a patient is a great indicator of their fluid volume status and how much weight they're losing because if they're gaining 3 pounds in like a 24-hour period that's not good that means they're retaining too much fluid so we will look at that and compare that and we want to monitor their labs patients who are going to be on live directs especially there's IV forms they're gonna be getting daily basic metabolic panels where we can look at their electrolytes and the renal status so one thing you're really going to look at is the potassium if you can't remember anything else about live diuretics remember that loop diuretics can lower the potassium level it can cause hypokalemia a normal potassium level is 3 point 5 to 5 milli equivalents per liter and it's very common if your patients on long term loop diuretics or those IV routes they're going to be receiving some type of potassium supplementation to help replace that potassium level and I want to point out this with digoxin this is the big thing you need to know we cover this in the digoxin video that we went over in this pharmacology series but if your patient is on digoxin and they're taking a loop diuretic you always always want to look at that potassium level before you minister their next dose of digoxin because it can increase digoxin toxicity so they're on digoxin taking a loop what are you gonna look at there potassium level we don't want them to have hypokalemia now why can they have a low potassium level well what's happening is that remember we're not having these ions being transported across so they're going back into the blood so one ion that's really gonna be concentrated in this filtrate will be sodium so once the filtrate goes up it's gonna hit the distal convoluted tubule and in this tube you'll especially the distal part it uses a transporter that is influenced by aldosterone to reabsorb sodium and one thing that we have learned about aldosterone in our lectures is that it will cause the body to keep sodium but excrete potassium so we have a high amount of sodium here it's influenced by this aldosterone so it's really going to enhance how the aldosterone is gonna work so you'll be keeping reabsorbing the sodium but you're going to be excreting potassium now only are you going to excrete potassium which is going to lower the level you're going to excrete hydrogen ions so the patient can also have metabolic alkalosis as well with these loop diuretics so that is another side effect so it can also draw up your magnesium level which we talked about over here with how it's affecting how calcium magnesium are being reabsorbed and of course it can drop your sodium level because we're keeping sodium in the snare on and excreting it out another thing that I want you to remember is that loop diuretics can increase uric acid levels so watch out for signs and symptoms of gout and why is it increasing uric acid levels well the proximal convoluted tubule is being affected with how is dealing with urea and urate is a waste and what this medication can do unfortunately is cause the body to increase its absorption of urate which in turn will increase uric acid levels so that's another thing you have to watch out for and another thing I want you to remember is that loop diuretics can cause inner ear damage with a condition called odo toxicity and as a nurse how can you prevent this from happening one way is slowly and ministry IV routes of loop diuretics so when a patient is ordered like IV lasix or all some I'd you want to give it slowly because we don't want to cause inner ear damage and as a nurse you're going to be looking at the effectiveness of this drug you're going to be looking at their weights are they losing weight meaning they're losing fluid you're gonna see how much urine they're putting out look at their eyes and O's you're gonna listen to their lungs do they sound clear or you hear crackles where there's still fluid in there and look at their edema they're swelling has their legs swelling went down they they're not pitting as much and even the patient's starting to feel better a lot of patients will report wow I feel so much better since I've had this fluid removed and one thing you want to keep in mind as the nurse is when to give this loop diuretic because as I pointed out they're very powerful and they work pretty fast so if you if the dose is order dry before bedtime that's probably not the best time to give it to the patient because they're gonna be up throughout the night urinating which is going to affect their sleep and if they're trying to get to the bathroom in the dark that can increase the risk of falling Plus let's say a dose is due but they have to go for a procedure you want to make sure that you call that department and make sure that patient is going to have access to the bathroom because they will have to urinate after taking this medication now let's wrap up this lecture and let's talk about the education pieces for the patient so we definitely want to teach them to watch out for signs and symptoms of dehydration because they're going to be urinating a lot we don't want to deplete their fluid volume so you want to teach them to watch out for excessive thirst where they're not urinating at all or they're really tired and to monitor their blood pressure and heart rate at home if there are really hypotensive where that systolic is less than 90 and all that together they'll want to report to their physician and teaching them about following a healthy diet and eating foods that are rich in potassium because we're wasting potassium and foods that are rich from potassium are like potatoes avocados bananas spinach etc so they definitely don't want to restrict that and they want to change positions slowly when they're getting up from a sitting or lying down position because we're changing the fluid volume status in the patient they can have orthostatic hypotension and we don't want to get up and fall so encourage that and to weigh themselves daily and to record it because as a nurse that's performer nursing interventions we are weighing them we want to see their fluid status so they need to do that as well and to monitor their weights and make sure that they're not gaining like no more than 3 pounds per day because that could be a sign that they're retaining fluid okay so that wraps up this review over loop diuretics thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Costovertebral_Angle_Tenderness_Exam_CVA_Percussion_Assessment_Test.txt	hey everyone is fair thread sterner sorry and.com and in this video I want to show you how to check for cost over to Beryl tenderness also known as CVA tenderness this is found in patients who may have a kidney infection because what has happened is that the kidney becomes inflamed from the infection and then when you take your hand put on the bat and thump or percuss it will cause the patient tenderness so let me show you how to do that okay so what you want to do is you want to find the last rib posts király and that is the 12th rib so if you fill in between the ribs be about right here and then you're going to find the spine and underneath the 12th rib and between the spine is that cost over to Beryl angle and about right here is where your left kidney is located and over here is where your right kidney is located so what we're going to do is we're going to take our hand and we're just going to put it over here we're going to make a fist and we're going to thump our hand and we're going to ask the patient if those have any pain okay do you have any pain with that okay and then we're going to do it to the other side you have any pain okay and if they had pain that would indicate a possible kidney infection thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Endocarditis_Nursing_Pathophysiology_Treatment_Infective_Endocarditis_Lecture.txt	hey everyone it's sarah thread sterner sorry and calm and in this video I'm going to be going over an insect's review of endocarditis this video is part of an inkless review series over the cardiovascular system so be sure to watch this series if you're studying for ink Lex and what I want to do in this video is I'm going to cover the path of in the carditis the different types the signs and symptoms and the nursing interventions and then after you watch this lecture be sure to go to my website register nurse orient calm and take the free ink Lex quiz that will test your knowledge on this material and a card should be popping up so you can access that so let's get started first let's start out talking about what is in the card itis it is inflammation of the in the Cardian layer of the heart in the Karndean layer is a membrane that lying inside of your chambers of your heart and it's found over your heart valves as well now in the cord itis can affect several things it can affect your heart valves you have four heart valves you have your tricuspid valve your bicuspid valve also called mitral valve your pulmonic valve and your aortic valves these can all be affected it can also affect your cord a tune in D it can cause it to rupture and these are just fibrous cords that attach your vow to the papillary muscle of the heart and also your intraventricular septum which is just this little area that separates your ventricles can be affected as well but it's most likely and in the core dies to affect your heart valves now how is it treated it is treated typically if you get infective in the car dose which we're going to talk about the different types with antibiotics however it's tricky if you get infected part itis on your heart valves because your heart valves do not have a blood supply going to them so if you get some type of pathogen on that valve and you're hot your body's not going to recognize that and send those white blood cells there it may say hey we do have an infection but I can't get these white blood cells to get to that infection to kill it and whenever the patient does take antibiotics they have to take them for a long period of time to help get rid of that infection because it's hard to get there because no blood supply so what are the different types of endocarditis you have infective endocarditis which is called ie and then you have non effective in the carditis first let's talk about the infective kind okay this is where bacteria viruses fungus any type of thing gets into your bloodstream how would it enter into your bloodstream well through invasive procedures like dental work I have seen this patient gets infected in the carditis turns out a month ago they had all their teeth pulled because they were getting fitted for dentures and they develop this so what happens implantable devices like pacemakers ICDs a central line placement or IV drug use big big thing and what happens is that that pathogen attaches to that valve now people with healthy valves can develop this but if you have a defective valve you're more likely to get infected in the carditis and we'll talk about the pathogenesis here in a second of how it happens and what classifies as unhealthy valves what happens what causes a patient to get unhealthy heart valves well whenever you have a heart valve problem like especially mitral valve prolapse or they've had a valve replacement also romatic heart disease they had strep infection when and wasn't treated appropriately attack the heart valves mess up the heart valves cause defects on it or congenital heart defects and what happens is that they develop this infect it they the heart valve gets messed up it can become leaky regurgitate it can become Sonos which is narrow send them into heart failure which we talked about in our heart failure failure in CLECs review series or it can even cause an embolism so let's look at the pathogenesis of how this actually happens okay let's take the tricuspid valve say that this patient as it's I'll have Ematic fever so they already have a defective heart valve well about a month ago they had dental work done had several teeth pooled and all of a sudden they are developing some fevers really high fevers feeling really sick go into the doctor tell the doctor their history and the doctor orders a transesophageal echocardiogram to look at those heart valves well how did this pathogen possibly form on their heart valve well let's look at the pathogenesis of how a heart valve develops into ie infective endocarditis well what happens is that whenever that heart valve becomes effective platelets and fiber doones start to stick to those endothelial cells on the heart valve and it forms a little thrombus and right now which will go over the second type we have non infective in the car dies because just this little sterile thrombus but when the patient had their dental work done they introduced a lot of bacteria into their blood system so the blood just nicely jetting down through that tricuspid valve from the H from the right atrium down through the tricuspid down through the right ventricle and now pathogens in that blood and it decides to stick onto that thrombus which was just a beautiful sight for that thrombus for that pathogen to just start growing so the pathogen sticks to thrombus and grows and then as it grows and gets big it sends off an inflammatory response in your body but your body can't get to it because there is no blood supply coming to that heart valve so those white blood cells can't get there and it grows and it can break off and I'm cause an embolism it can cause your heart valve sleek narrowing and send them into heart failure so that's what happens now with infective carditis you can have two types of it that effects two different groups of people and I would remember this first type is a qie and this affects people with healthy heart valves they don't have anything wrong with their heart valves but whenever they get a bacteria on there that's growing this has a very high death rate with it and the hallmark thing of this is that the signs and symptoms that the patient is going to have is going to be very sudden and very very severe however on the flip side you have sub acute infective endocarditis and this affects patients with a pre-existing condition like they had rheumatic fever which was in our one example I just went over or they have a mitral valve prolapse they already have something wrong with their heart valve and the signs and symptoms it's the hallmark of this is that they tend to be subtle and they have a slower onset it'll take weeks to months to develop signs and symptoms and one thing you want to remember is that IV drug users are at risk for both types both q and both subacute they can develop either one now let's look at the second type of into carditis non infective in the cart itis this is where we're talking about the pathogenesis or maybe there's trauma to the heart valve or the patients in a hyper coagulated state where they're at risk for forming clots clot six to that heart valve and they form a sterile thrombus on that valve now it isn't pathogenic yet has it become infected because there's nothing growing on it but it has increased the patient's chances of developing ie and they could possibly throw off a piece of that small thrombus they have form now let's look at the signs and symptoms of infective endocarditis now remember with nonlin infective in the cart itis we have a sterile thrombus that has formed on the valve it hasn't become pathogenic yet here it has so this is where we're going to start seeing some signs and symptoms and help you remember that remember the mnemonic pathogens because pathogens is what is causing our problem they've got in attached to that thrombus and have started an infection so let's remember that okay p4 petechiae as a nurse who's taking care of patients with endocarditis infective endocarditis I have seen this they will have tiny purplish red spots on the skin and this is from emboli breaking off a with for anorexia and one because they just don't feel good they're sick they have an infection so they have a loss of appetite but also because they're in spleen will be enlarged your spleen is responsible help for helping you fight infection your sling and summer car closer will enlarge splenomegaly and push on that stomach so they won't feel hungry t4 tired and weak h4 high fever these patients are going to have very high fevers that's going to be one of the reasons that they have came to you for help because you know they feel bad they don't know what's going on they have a really high fever so you need to investigate it more and they may have signs and symptoms of heart failure because that valve is messed up it's leaky and they could have signs of left-sided heart failure which we talked about in our in CLECs review series if you're interested in that Accord should be popping up and you can access that playlist um another thing anytime whenever you're studying bring clicks on your nursing lecture exams and you see names of something that's either someone's name who discovered it or it's a weird name remember it because it's probably going to be on your test oh for ostlers nose what are these these are tender red lesions that you can find on the hands or the feet g4 fingernail changes the jam finger and this is where on the nail beds if you look you'll see small small dark lines and again this is from emboli it looks like wood splinters I have seen that before e4 in B'Elanna in the Mladic event again we'll talk about that a little bit more in our nursing inventions but they can throw emboli and to the spleen to the kidneys the central nervous system the lungs things like that from where it's breaking off a writ read Miam where this is a non tender nodular lesions that can be found on the palms of the hands or the soles of the feet and these are known as Janeway Lee remember that don't get ostlers nose and Janeway lesions confused Janeway lesions are non-tender red modulars found on the palms and the soles of your feet Oscar's nodes were tinder red lesions found on your hands and feet so remember one cinder one's not tender okay next for in night sweats again fight an infection they're gonna have night sweats and another in four new cardiac murmur and again you might hear some mitral valve murmurs because the valve is messed up so you're listening to their heart and we go I hear a murmur and you see in their health history there is no mention of a murmur and they said I've never been told I have a murmur you might want to have that investigated more because there could be something going on especially if they're showing all these other signs and symptoms and s the last part of it splenomegaly and this again is just where the spleen is enlarged spleen helps you fight infection and has got bigger and then another thing these spots called Roth spots and this is where when you look into the eyes you can see bursts of blood vessels in the retina x' with white centers so it's a roth spots now how is infant infective endocarditis diagnosed a lot of times you'll get blood cultures to see what if anything is growing in the blood because that helps them determine what type of antibiotics they should use they'll also what a great test is is a te eye transesophageal echocardiogram this is a little bit different than a thoracic echocardiogram where they just do an ultrasound over the chest this is where they will stick a probe down through the esophagus look at the back of the heart and they can actually see those heart valves opening closing and see if they see any vegetation is growing and they can tell you where the vegetation is located about how big it is now let's look at the nursing interventions first what you want to do is you want to monitor the patient for any embolic and then such as because each different have different signs and symptoms so as the nurse be aware of where it possibly could be originating from for instance a spleen embolism if the patient starts all of a sudden complaining of radiating abdominal pain that goes from their back to their shoulder it could be the spleen an embolism has broke from that vegetation went there or renal they're complaining of flank pain in the groin and there's pus and blood in the urine or a central nervous one with the brain there's changes in their neuro status all of a sudden they become confused and they can't speak to you properly or pulmonary they're complaining of chest pain shortness of breath this via or you know so their oxygen saturations are plummeting okay another thing you want to monitor them for are signs and symptoms of heart failure some things you want to look for is fluid overload are they getting swelling in their legs in their belly their arms their hands are their lungs congested with crackles how's that sounding next another thing you may be doing if the doctor orders is collecting blood cultures and again this is just the type what type of bacteria is growing in the blood so they can treat it properly with specific antibiotics because specific antibiotics target certain bacterias and the patient will be started on IV antibiotics and they'll probably be ordered to get a central line place a PICC line most commonly and some antibiotics they typically order vancomycin or Rocephin and these patients will need this for a long period of time sometimes up to four weeks so they will go home to get this go home with home health or be administering it to themselves so education pieces remember this you want to educate the patient how to administer their antibiotics how to hang the bag things like that how to connect it to their central line and how to care for their central line how to flush it how to monitor for signs and symptoms of infection and stress the importance of completing all antibiotics stopping antibiotics in the middle of treatment can increase resistance another thing is they need to inform all other healthcare practitioners who provide care to them especially their dentists about their history of infective endocarditis because if they're going to have any more procedures done that are invasive they will need to be prepped with a prophylactic antibiotic to prevent reoccurrence of the endocarditis again and they need to practice good oral hygiene because a lot of times this bacteria gets in your mouth and can reinfect you so that is about in the carditis now go to my website register nurse are in home and take the free quiz and be sure to check out my other in clicks review series on the cardiovascular system and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Partially_Compensated_vs_Fully_Compensated_Uncompensated_ABGs_Interpretation_Tic_Tac_Toe_Method.txt	hey everyone it's Sarah threads to nurse Orion dock home and in this video we're gonna be going over partially versus fully compensated arterial blood gas practice problems now after you watch this YouTube video don't forget to access the free quiz that will give you more ABG practice problems so let's get started now in our previous video on how to solve ABG practice problems we use the tic-tac-toe method but sometimes whenever you use the tic-tac-toe method you may notice that you don't get a tic-tac-toe where you get those three in a row and when that happens you have to further analyze these values that you are given and you have to ask yourself am i dealing with partial or full compensation and is this a respiratory or metabolic problem so in this video we're going to tackle those issues now before you even attempt to answer abd problems you have to commit some normal lab values to your memory so let's go over those first is blood pH a normal blood pH is 7.35 to 7.45 anything less than seven point three five is considered acidotic anything greater than seven point four or five is considered alcoholic so basic next is paco2 this is the partial pressure of carbon dioxide so it represents our respiratory system and remember that a normal PA co2 is anywhere between 35 to 45 now these numbers are flipped whenever if you set up a table like this anything greater than 45 is considered an acid anything less than 35 is considered alkalotic so remember that as well the last thing I want you to remember is the by card the hco3 this represents metabolic cancer renal system in normal values for bicarb is 22 to 26 anything less than 22 is considered an acid and anything greater than 26 is considered alkalotic now whenever we're dealing with ABG problems and we have compensation going on especially full compensation we have to look at that blood pH to help us determine if we have a respiratory or metabolic problem now I said that a normal blood pH is 7.35 to 7.45 now let's further analyze it the absolute normal for a blood pH is 7 point four zero so that's like right in the middle of 7.35 to 7.45 and if we had some full compensation going on meaning our pH is back to normal so some system either the respiratory system or the metabolic system has helped put us back to normal and you're gonna see with these ABG's is that the respiratory and the renal system metabolic system is always trying to balance that blood pH out it will either increase the bicarb lower the bicarb increase the carbon dioxide or learned about the carbon dioxide to help get that blood pH back to normal and depending on what side of the spectrum innocence that this value of blood pH is falling from that absolute normal can tell us is it a little bit more on the acidotic side or is that blood pH a little bit more on the alcoholic side so let's go over this the absolute normal with 7.40 and 7.35 to 7.45 is our normal so any value of a blood pH that's normal that get falls between 7.35 to 7.45 and any blood pH that falls between 7.4 zero to seven point four or five is on alkalotic side now it's still normal but it's falling either more on the acidotic or alcoholic side so let's go reverse few practice problems okay the first problem I want to go over is something where we don't have any compensation going on and then we're going to add on partial compensation full compensation and you can see how these values are changing and how we're getting our answers using the tic-tac-toe method and looking at those normal values that we've commit to memory so our problem is our pH is seven point two to our paco2 is 49 and our bicarb is 24 so have our tic-tac-toe set up and we have acid over here normal over here alcoholic here if you're not familiar with that how to do the tic-tac-toe method I'm going to show you okay so we're gonna look at each of these values and we're gonna put them in the column that they go and we're looking for a tic-tac-toe and again as I said the being in the lecture if we have some type of especially full compensation going on we're not going to get a tic-tac-toe because our pH will be normal okay so pH is 7.2 - what's the normal value 7.35 to 7.45 so it's less than 7.3 bucks so we know it's acid on it so we're gonna put our pH here our paco2 which represents the respiratory system is 49 normal PA co2 is 35 to 45 since it's 49 it's greater than 45 it's on the acidotic side so we're gonna put it over here oh we have a tic-tac-toe right here but we're not done yet let's mess with our bicarb our bicarb is 24 what's a normal bicarb 22 to 26 this is normal it's falling with a normal range so we'll put that here well looking at this we know that we have acidosis going on and we have respiratory acidosis because paco2 represents respiratory so we have respiratory acidosis now do we have compensation going on that's the next thing you ask yourself and the answer is no and how do I know that we don't have compensation going on well our blood pH is abnormal still it hasn't been corrected it's not falling within its normal range and the system that helps balance everything out either the rest or E or the metabolic system it's still normal our bicarb isn't trying to throw itself in an abnormal range to help combat this acidotic so it could if it was going to come and say it would start increasing itself to make things a little bit more alkalotic but it's not doing that so this is uncompensated so we have respiratory acidosis uncompensated now look at that same problem again but let's change about you let's change our bicarb instead of being 24 let's make it 28 so we know that we still have respiratory acidosis going on because our blood pH is low and our PA co2 is high putting it on acidotic side however our bicarb now is not normal it's 28 so it is greater than 26 so it's on the alcoholic side so we'll put it over here now next thing we want to ask ourselves do we have compensation going on yes we do now is it full compensation or partial compensation it is partial compensation how do I know that well it would be only full compensation if our blood pH was normal once a blood pH is normal either the respiratory or the metabolic system has helped balance that blood pH out and got it normal however it's not normal here it's still abnormal so it's partially compensated we have the metabolic system trying to increase our bicarb to help balance out these acidotic conditions because by trying to make it more basic the blood will hopefully push that blood pH a little bit higher to make it normal so we have respiratory acidosis that is partially compensated now let's look at our next problem okay our blood pH is 7.4 to our paco2 is 32 and our bicarb is 18 so what we're going to do is we're going to plug it into our tic-tac-toe so our blood pH what's a normal blood pH 7.35 to 7.45 and this falls within normal range so our pH is normal now right now you should be thinking compensation full compensation because we have got our blood pH back to normal but let's look at those other values ok pco2 which represents the respiratory system is 32 normal range is 35 to 45 it's on that low side so it's alkalotic so we'll pin it under here and our bicarb is 18 normal bicarb is 22 to 26 it's less than 22 so it's on the acidotic side now this is when you've set up your tic tac toe and you look and you're like I don't have a tic tac toe but we know that we have full compensation going on because our blood pH is back to normal however we have to determine is this wrestle Tory or metabolic problem and to help us do that we have to further look at this blood pH so even though our blood pH is within range at 7.4 - what side of the spectrum is it falling on that on that acidotic side or is it on the alcoholic side and it falls on the alcoholic side so what's happened is that our bicarb has decreased and it's trying to make things a little bit more acidic in that blood to bring the high alcoholic blood back down so our bicarb is out of whack because it's been trying to do that and it's achieved it because we have full compensation but it's still a little bit that blood pH on the alcoholic side and it's originated from a respiratory issue so it's respiratory alkalosis with full compensation now let's look at our next problem our blood pH is 7.37 our paco2 is 33 and our bicarb is 17 so let's plug it in our pH falls within normal range it falls within 7.35 to 7.45 so we'll be put it here and you should already be thinking ooh compensation our pH is normal we probably have full compensation but let's look at our other values our paco2 is 33 normal is 35 to 45 it falls less than 35 so it's on the alcoholic side so we put it here and again that represents the Vittori system and their bicarb is 17 so it's less than 22 so it's on the acidotic side and bicarb again represented the metabolic part so we see that we have full compensation going on we don't have a tic tac toe so we had to look further at our blood pH and it's normal so we have full compensation but is this respiratory or metabolic so we have to look at blood pH closely a normal blood pH the absolute normal is seven point four zero ours is seven point three seven so it's on the acidotic side so we have metabolic acidosis going on that is fully compensated and how I got slowly compensated is because that respiratory system tried to decrease the carbon dioxide and whenever it does that it's making things more alkalotic to help push that blood pH higher into that normal range and it did but it's still on acidotic side but it finally got it to normal and achieve what it was supposed to do now let's say that this was seven point two seven instead so that changes things a little bit here our blood pH is now seven point two seven so it's not normal anymore it fell less than seven point three five so it's on the acidotic side so let's move it over here now this has changed things a little bit do we have full compensation going on anymore nope we have partial compensation and I want you to see that because we have our tic-tac-toe so we have metabolic acidosis and we have partial compensation the paco2 has taken itself out of normal range to make things more alkalotic but it hasn't corrected it yet by making that blood pH become normal so this would be metabolic acidosis partially compensated okay so that wraps this video over partially versus fully compensated ABG's thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Ventricular_Septal_Defect_Nursing_NCLEX_Pediatric_Congenital_Heart_Defects.txt	hey everyone it's sarah thread sterner sorry and calm and in this video i want to be going over ventricular septal defects in this video is part of an ink lex review series over pediatric nursing and as always after you watch this youtube video you can access the free quiz i will test you on this condition so let's get started what is this condition also called VSD it is a congenital heart defect that occurs when a hole forms in the ventricular septum so there should never be a hole in the septum that separates your ventricles and we're talking about the right ventricle and the left ventricle and here in this drawing you can see a big gaping hole in between those ventricles and what's that going to do it's going to alter blood flow it's going to create this left to right shunt of blood so blood in the left side of the heart is going to be shunted it's going to flow to the right side of the heart now when that happens we're gonna have issues especially if this is a large hole in the heart it's gonna cause increase lung blood flow because you're going to have all this blood from the left side shunting over here to the right side plus you have all this blood already entering in through your inferior and superior vena cava and it's going to be shot up through the pulmonary artery to the lungs and the lungs cannot handle all that blood volume it's gonna affect them and in turn it's going to affect the heart and when we talk about the pathophysiology of this condition you will see why we all let's talk about some quick facts about VSDs okay according to cdc.gov one in every 240 babies born in the United States each year will have a ventricular septal defect and there's various types of VSDs there's four different types that we're gonna talk about and patients can have multiple holes within this septum they don't have to just have one and they can have various sizes like small moderate or large and these holes can affect different layers of the septum so the first time we're going to talk about is called membrane and these holes are found in the upper section of that septum so about right in this area and they tend to be found close to the tricuspid valve which is found over here on the right side of the heart in between the right atrium and the right ventricle or over where the aortic valve is on the left side of the heart coming off of the left ventricle and when these holes get close to these valves they can damage them so they can have issues with their valves a lot of patients with v SCS especially larger ones they can have what's called aortic valve regurgitation where that valve is not closing properly and blood is really back flowing from that Valve hence regurgitation another type is a muscular of VSD and these are holes that are found in this lower section of the septum now one thing to remember about these muscular VSDs is that if they are small they tend to have a high probability of closing on their own so self closure another type is outlet VSD these are also called Conal or sub arterial vsts and just as the name says outlet these holes are going to be found close to structures where blood is leaving the heart so those structures would include like the pulmonic valve and the aortic valve because that's where blood leaves the heart it leaves the right side over here through the pulmonic valve to go to the lungs and then it leads through the aortic valve the blood to go through the body and these vsts tend to be rare but I can't occur the last the fourth type is an inlet VSD and it's really the opposite of the outlet because it's found near structures where blood is entering into the heart so it would be failed where the tricuspid valve is or the bicuspid bicuspids also known as the mitral valve now as I said before small VSDs a lot of times they are monitored and they tend to close all by ourselves within that first year of so the physician nurse they may hear a heart murmur they monitor that with an echocardiogram which is like an ultrasound of the heart and they can look at that but with large VSDs they will definitely need to be monitored and they will usually be started on medications because what happens with this condition is you get heart failure so that we started on medications to help with the contraction of the heart make it stronger but slower like digoxin diuretics to help with all this fluid that is backing up within the lungs and ACE inhibitors to help lower that pressure and lower the workload on the heart let me tell you more about those in our nursing interventions also they will need repair usually to close that large hole in that septum now let's talk about the pathophysiology of a ventricular septal defect and as I'm talking about this path oh and the complications that arise from these defects what I'm talking about are these large holes that exist in this septum because the large holes allow more blood to be shunted from the left side to that right side rather than a small one so to understand VSDs you first have to understand the normal blood flow of the heart so I'm going to quickly review that and then I want to show you what's going on with a VSD and you'll see the difference okay so with normal blood flow of the heart everything starts on the right side of the heart and the goal of the right side is to get an oxygenated blood to the lungs so it's going to take it right to the lungs so blood enters in through your superior and inferior vena cava it flows down into the right atrium then it goes down through the tricuspid valve which opens up and allows it to flow down to the right ventricle and normally a normal heart without a hole there is no connection between the right and left ventricle so the right ventricle will contract it will shoot the blood up through the pulmonic valve through the pulmonary artery which is going to take it right to the lungs and the is gonna do its job and oxygenate that blood so now the blood is oxygenated it's going to enter in through the left side of the heart so the blood has left the lungs to go through the left side of the heart through the pulmonary vein it's gonna flow down through the left atrium then down through the bicuspid also called the mitral valve into the left ventricle and the left ventricle is very strong because it has to be strong in order to pump that fresh oxygenated blood up through the body into the system so it has to generate a lot of pressure there's more pressure on the left side of the heart than there is the right side of the heart so that blood is pumped up through the aortic valve then through the aorta and all through your body now let's what about the blood flow in a patient who has a large VSD so a large hole in this septum so blood is going to enter into the heart just like it normally would in a heart without a hole in the septum it's going to flow down through the right atrium the right ventricle but now we have a connection between our right ventricle and our left ventricle and that is where our issue is going to cause problems now we just learned that the pressure in the left side of the heart is a lot more than the pressure on the right side of the heart so that is why we have a left-to-right shunt because that left side needs more pressure in it to get that oxygenated blood to the body compared to the right side the right side just has to get it to the lungs so we have all this blood that's already really been on the right side of the heart in a sense recyling and coming over to the right ventricle then you have all this blood that's coming from the circulation that's exhausted needs to be oxygenated in the right ventricle so you have like extra blood volume that this right ventricle has to pump that it's not really creative to pump that much blood to the lungs so the right ventricle over time is going to enlarge so it's pumping all this extra blood to the lungs now the lungs definitely cannot handle this increase blood flow and over time what's going to happen you're gonna have pressure increasing and the arteries that feed the lungs are going to become damaged and they're actually going to narrow so you're going to get a condition called pulmonary hypertension and this is going to cause that infant that child a lot of issues a lot of breathing issues and it's going to cause issues on their heart because the right ventricle is already exhausted from having to pump extra blood volume now when this pulmonary hypertension occurs we have narrowing of arteries this heart this heart has to pump even harder to squeeze that blood to the lungs so it's like the same concept with a water hose you narrow that water hose in order for that water to get it through the water hose to the other end it's really going to increase its exertion and it's pressure to get that water through that narrow little hose and that's what's happening so that's going to cause even more problems and that's going to stress the heart out and we're going to get heart failure so you hear you have this infant who has heart failure and the parent usually will notice signs and symptoms about one to three months after birth and they'll have difficulty feeding because it takes a lot of energy to eat that because they have to suck on that bottle and their energy is expiring because their heart can't keep up because it's so weak so they don't finish those feedings and it burns a lot of energy having to breathe having to pump this heart so they're burning extra calories they're not feeding to take in that caloric intake so they start to lose weight and their growth is affected in addition they can start to get a lot of lung infections because you are getting all this congestion where fluid is back flowing into the lungs from where this heart is weak the heart failure and they're at risk for more infections in addition they can start to have dysrhythmias where atrial fibrillation where their heart electrical activity is not working right and they're at risk for valve issues like I said earlier regurgitation of those valves and they can have endocarditis they're at risk for developing infection within the heart because the lining in the heart can be disrupted because of what's going on and bacteria can stick in there and cause infection now what if this VSD is never repaired and they have this continuous left/right shunting the overflow of the blood going to the lungs stressing the lungs out stressing the ventricle out all this what's gonna happen well this is left untreated the patient can develop what's called eisenmenger's syndrome and this is where you have a reversal of that shunting so what's going to happen due to that extensive pulmonary hypertension that has happened what will happen is that you will actually have a reversal of shunting of blood that will go right to left so instead of going left to right this blood will actually start to now flow into the left ventricle so you won't have the shunting anymore of this the oxygenated blood going into the right ventricle but you'll have the unex ajaita blood going into the left ventricle and that's going to cause some issues what's going to happen is now you're going to have this uh NOSSA genital blood that didn't make it to the lungs to get oxygenated go back into circulation and the patient will start having cyanosis bluish tinting color of the skin low oxygen in the body because it didn't get oxygenated it's going back through circulation and you can start to see clubbing of the fingers and things like that and this condition is irreversible they will usually need a heart or lung transplant so really patients need to get treatment for this so that does not occur when else talking about signs and symptoms of a VSD okay when are you going to start to see signs and symptoms in the pediatric patient in that infant who has like a VSC like a large VSD because those are really the ones that cause our signs and well you're not really gonna see it immediately on birth you may hear like a heart murmur but that infant is going to start showing those signs and symptoms of the heart failure pulmonary hypertension about one to three months after birth now why is that okay well in utero when the baby is in there moments belly and that pressure in the right side and the left side is equal because their lungs aren't working yet but once they are born they start breathing on their own things are going to start changing in the heart the pressure specifically the pressure on the right side of the heart is going to start to decrease so if they do have this large gaping hole in their septum as that pressure starts to decrease over time which is about two to three weeks you're going to start seeing this shunting of blood because the pressure will be decreasing on the right side compared to the high pressure in the left side so around one to three months once that pressure has stabilized its decreased on the right side that left side will start shunting that blood over to the right side and that's going to increase that blood volume going to the lungs Linda pulmonary hypertension heart failure and the parent may bring their baby in for those checkups report and baby's not feeding right they get really tired fatigued easily the weights aren't really looking good for that child based on its age and they could start having frequent lung infections all pointing to a sign that hey this baby may have a congenital heart defect we need to do an echocardiogram and see what's going on so to help us remember the signs and the symptoms let's remember the word hole hole in the ventricles that is what is going on so what we're gonna do is sum up everything we went over and that's our signs and symptoms so eight is heart failure we talked about why there is heart failure going on and the pulmonary hypertension so the signs and symptoms you're gonna see is they're gonna have difficulty breathing with all the fluid congestion from where that heart is weak in there and fluids backing up they're gonna fatigue with ease especially with any activity feeding swelling in the hands the extremities where the fluid is building up crackles and the lungs from the congestion of fluid and they can have sweating with any type of activity like a lot of parents report while they're feeding they may get really sweaty be cold and clammy Oh for often experiences lung infections and that goes back to the congested lungs from where they have all that fluid in there and l4 a low growth weight loss of weight and that ties back to their heart and breathing burning a lot of energy to maintain life for that child that can burn a lot of energy they're not eating like they should because they're just exhausted from where their little heart is just exhausted and they can't stay awake to continue and they're just exhausting next is Eve for extra heart sounds and a heart murmur may be detected in VSD you may hear it at birth it really depends because why are you even hearing a heart murmur what's it from well what it's from is that you have this flow of blood from the left ventricle to the right ventricle so you're hearing that turbulent gradient of that blood crossing over during systole and depending on the pressure changes that's occurring in that infant you may or may not detect it because remember the pressure changes over the next two to three weeks now the term of the murmur is holosystolic or pin systolic murmur and this means that you're usually going to hear it starting at s1 and it'll extend into s2 and it can be found in the left lower sternal border and what's interesting is that smaller VSD so small holes can actually produce a louder murmur than compared to a large one and think about it if you blow through a really small hole you can actually hear the noise it's a lot louder than if you blow through a big large hole so that's where that's from now let's talk about nursing interventions and treatments for a patient with a ESD a big thing that is done is that of course the VST will be monitored and medications will be ordered especially for those large ones because the doctor wants to prevent that patient from developing heart failure pulmonary hypertension and going into the Eisenmenger syndrome which is irreversible so they can give them medications and of course surgical repair so as a nurse you want to be familiar with some of these meds one man they can get is called digoxin and what does the Johnson do well it helps the heart contract stronger and it slows it down which is perfect for this infants heart because it's exhausted and it's been really just pumping away and it's weak so digoxin can make it stronger but pump slower but you have to watch this drug and it's a great drug but if it gets where it's not in therapeutic range it can cause toxicity and death so what you have to do is you have to before you give it you monitor and record the apical pulse for one full minute and depending on what that pulse is you may or may not give the medication and you'll always follow the physicians parameters for that but the guidelines are usually this to hold the medication if the infant's heart rate is less than 90 to 110 beats per minute or for children if the heart rate is less than 70 or for adults if the heart rate is less than 60 also what potassium levels a low potassium level hypokalemia can increase digoxin toxicity so a lot of times these patients may be on diuretics like lasix that wastes potassium so you've really got to monitor those potassium levels make sure they're getting enough potassium because it can lead to digoxin toxicity normal level your therapeutic level is 0.5 to 2 nanograms per milliliter we'll be measuring that also in your infants you want to watch that heart rhythm one early signs and symptoms of ditch talks the city in an infant is a dysrhythmia so watching that heart rhythm that EKG also watching for vomiting and the antidote for detox digoxin is digi buying other meds that can be prescribed or like diuretics and what diuretics do is that they will help pull fluid extra fluid that's build up from the body and the patient will urinate it out but you have to watch because it can throw off electrolytes and if they're on digoxin what do you want to monitor potassium levels because you can have digital sisse T so we will be monitoring their eyes and O's making sure their renal function is good they're not taking in too much and not really putting out you want to monitor that and monitor their weights because that indicates if they're retaining fluid because again their risk for heart failure with this condition another drugs they can prescribe are ACE inhibitors and what these will do is lower the blood pressure when you lower the blood pressure that's going to lower the pressure in this left ventricle which is great right because if we lower the pressure in the left ventricle what's gonna happen we're going to decrease that shunting of that blood from left to right so we can get more blood flowing up through the body which is where we need it instead of going back to the lungs and congesting those lungs and stressing them out so another thing nursing wise we won't be thinking about their nutrition because one of the big signs and symptoms that they're going to have is their growth can be affected because they are just so exhausted they don't feel like eating so sometimes they need supplements they may have to have a feeding tube you want to educate the parent about the importance of getting proper nutrition as a nurse you're gonna be doing calorie counts you're going to be weighing them measuring them seeing where they're at next you wanna be thinking about as the nurse is risk for infection their risk for lung infections because the pulmonary hypertension going on the congested lungs so they need to make sure that they're getting those preventive vaccines to prevent any type of respiratory infection their risk for and stay away from people who are sick and the endocarditis sometimes they have to be prescribed antibiotic to prevent and the in dakar tightest and treatment surgery for the really large bsts they can have surgery where a patch is actually placed over this hole and the tissue from the heart will actually grow over the patch and keep that patch in place and sometimes a heart calf can be performed where they can go in and close the hole that way okay so that wraps up this review over VSD thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Respiratory_Alkalosis_Acid_Base_Balance_Made_Easy_NCLEX_Review_ABGs_Made_Easy_for_Nurses.txt	hey everyone it's sarah with registered nurse orient comm and in this video i'm going to be going over respiratory alkalosis right now I'm doing a series on acid and base imbalances so if you're studying this in school be sure to check out those videos now in the previous video I went over respiratory acidosis because there are some differences in these two conditions so in this video what I want to do for you is I want to highlight the things you need to know for NCLEX and for your nursing lecture exam so I'm going to be going over the key concepts so what I'm going to do is I'm going to simplify the path though because if you can understand the pathophysiology you can understand the causes and why the patient has those signs and symptoms and what are the nursing interventions for the patient why are you doing those it all makes sense then I'm going to follow it up and work a arterial blood gas problem for you with a patient who is in respiratory alkalosis and show you how to set it up and I'm going to use a tic-tac-toe method now after this video be sure to go to my website registered nurse Orion comp and take the free quiz that's going to test your knowledge on respiratory alkalosis and respiratory acidosis a card should be popping up or a link in the description below so you can get that free quiz okay first let's look at the pathophysiology of this and simplify it okay whenever you have respiratory alkalosis the problem is in the lungs specifically in these little a vor sacs but first let's talk about what's going on when you're breathing in air and expelling air okay what happens is that you take oxygen in through your nose or in through your mouth and it travels down to your fear necks then down through your lyrics which is your throat then down through the trachea which brought which branches off into the bronchus your rotten left bronchus then that branches off into your bronchioles and then that branches off into your a vor sacs now in that sac is where gas exchange is happening so you just took in all this fresh fresh oxygen and that's going to go across that sac and attach to a red blood cell which a red blood cell is going to transport it through your ball buddy and supply your muscles your tissues all that with that nice oxygen but your body is trying to get rid of the carbon dioxide that's built up in its body so the carbon dioxide will go across that Abiola our sacs membrane and it will travel the opposite direction of what oxygen did and you will expel it out through your nose and through your mouth now a normal adult breathes 12 to 20 beats per minute and I mean breaths per minute and that is a good amount of breathing to get rid of this oxygen this carbon dioxide so anytime you have something that's messing with how much you're breathing or anything like that it's going to affect how much carbon dioxide you are getting rid of so here these are key concepts you want to remember you are expelling way too much carbon dioxide and you're doing this due to taka Pina tacky means fast pina deals with respiration and you're probably breathing more than 20 breaths per minute so you're just going hyperventilating and what you're doing is you are just pushing all that carbon dioxide out and your body does not like that so whenever you're getting rid of all that carbon dioxide what happens is that your pH in your blood starts to increase you're starting to make your blood alkalotic basic and any value greater than 7 point 4 or 5 it's alkalotic but your paco2 which measures your carbon dioxide levels start to decrease and the reason they're decreasing is because you're blowing it all all out of your lungs it's going away so the level will be less than 35 now the body doesn't like this and remember as we always talk about the body loves to be in a homeostatic environment likes everything to be normal so it will try to use other organs of the body to help fix problems that's going on so the kidneys start to play a role in this and what the kidneys will do to try to compensate is that it will cause the kidneys to start getting rid of all this bicarbonate to just flush it out of the body so you're going to be urinating all this bicarbonate out which is hco3 and the body hopes by doing this it will decrease that pH which is alkalotic right now because remember your ph is high it wants to get it down so it thinks by getting rid of all that bicarbonate it will help do that so you want to memorize these lab values commit these to memory because whenever in nursing school they love to give you blood gas analysis problems and ask you is this pressed for alkalosis acidosis is a compensator partially compensated things like that so commit these to memory and I'm going to go over them with you real fast okay a normal blood pH is 7.35 to 7.45 a normal paco2 which it measures your carbon dioxide levels is thirty five to forty five and a normal bicarb which is measured in hco3 is twenty two to twenty six and you need to know which values or acidotic and which are alkalotic so I have this little table to help you remember anything less than seven point three five in a pH is an acid and anything greater than seven point four five is basic alkalotic okay for paco2 measuring your carbon dioxide levels it's the opposite the lower number I mean the higher number is actually acidotic so anything greater than forty five is an acid and anything let greater than thirty or thirty-five is basic anything less than thirty-five is basic and any four bicarb anything less than twenty-two is an acid and anything greater than twenty-six is a base so it's alkalotic okay so let's look at those causes of respiratory alkalosis okay so we've established that you're breathing too much you're breathing way too fast you're hyperventilating you're having tachypnea so let's remember the pneumonic tachypnea because that is a big cause for why you're having respiratory alkalosis so each letter will correlate with a cause okay so T T stands for temperature increase in the body aka fever what happens is whenever you have a fever this is increasing the metabolic needs of your body and to compensate for that your lungs your respiratory center tries to increase the respiratory rate so what you're going to be doing why you have a fever you're going to be hyperventilating you're going to be breathing way too fast and you're going to be getting rid of that carbon dioxide so that can cause a fever a four aspirin toxicity remember this this a lot of tests like to ask about this they might give you a scenario that a patient who ingested a whole bottle of aspirin and what condition are they at risk for so remember this and why this causes rest for a local OSIS is because whenever and you have too much aspirin on board in the body it causes the body to go in hyperventilation mode because it simulates that respiratory center in your brain the medulla and the pons to breathe faster it also causes a fever which we just learned that fever causes respiratory alkalosis it causes a lot of bad things to the body also increases your fat ass or decreases your potassium levels and makes you go into metabolic acidosis so that can cause respiratory alkalosis mc4 controlled mechanical ventilation patients who are intubated are definitely at risk for respiratory alkalosis remember this this is another test question that in clicks and professors like to hit on they'll say that the patient has these following blood gases and the blood gases will be respiratory alkalosis and they'll say which patient below would you expect to maybe have be at risk for having these type of blood gases so remember this I'm the reason that these patients are at risk for this is because and they have a machine that's controlling how much they're breathing how much controls the rate of their breathing and what can happen is that you can hyperventilate the patient and cause them to take in too much oxygen and deeply too much oco-2 so you're hyperventilating then we have a fast respiratory rate so you really have to monitor these patients um h4 hyperventilation which is the whole basis for this and this is where just where you have the excessive respirations and you're expelling the co2 so just hyperventilate can cause it and why war hysteria the H I mean the Y and hysteria this is where you have anxiety of patients coming into an anxiety attack one of the hallmark signs of an anxiety attack is that they SAR just hyperventilating and they're getting very worked up and again the sleeps of the rapper rapid breathing they have the hyperventilation and they're just expending all that co2 so that's going to throw off their levels pain P for pain and whenever patients in pain they're hurting they're breathing Pass have increased increased respiratory rates so again you're expelling the co2 a pregnancy can cause this especially if a woman is in the third trimester of pregnancy because you have the fetus that has moved up up underneath that diaphragm and the respiratory tract has changed in the way that it's settled because you have this fetus up there and that can lead to respiratory alkalosis and pneumonia okay in for neurological injuries any injuries to the head that hurts the respiratory center again the medulla or the pons area like with a head injury or a stroke can cause the patient to go into respiratory alkalosis me4 embolism and and edema in the lungs and then a for asthma due to hyperventilation because whenever a patient has asthma attack they are hyperventilating sometimes and this can cause them to blow off too much co2 okay so now let's talk about how these patients are going to look what you're going to do for the patient as the nurse and then let's work a arterial blood gas problem with a patient in respiratory alkalosis okay so how are these patients going to look to you as the nurse whenever they're in respiratory alkalosis okay one of the most classic signs if you can't remember any of the other signs and symptoms is this the patient is going to have a very fast respiratory rate they are going to really just be breathing in and out hard a rate greater than 20 but sometimes you're going to see it up in the 40s just really hyperventilating this in turn is going to cause them to be confused they're going to be tired for breathing that fast their heart rates also going to be increased because I mean they're really using some energy so their heart rates going to be high now other signs and symptoms that you really really want to remember are these the following um technique any EKG changes muscle cramps and positive Chbosky sign does Shabbat skis ring a bell remember in the fluid electrolyte series where we're talking about calcium whenever you have low calcium levels you can have tetany muscle cramps and the positive to vote ski sign that's where you stimulate the Meseta muscle at the jaw line tap that and either the nose will twitch or the lips will twitch if the calcium level is low and whenever you have respiratory alkalosis this affects your calcium and potassium levels and it decreases them so they will exhibit signs if they're really bad alkalotic of hypocalcemia and hypokalemia now remember in respiratory acidosis it actually increased the potassium levels so remember that because a lot of test questions like to hit on that so in alkalosis it decreases calcium and potassium levels but in acidosis it increases your potassium level okay so what are you going to do for this patient who is in respiratory alkalosis okay you want to teach them breathing techniques if they're having an anxiety attack something like that you want to have them slow their breathing down hold their breath get that breathing to slow down or rebreathing in the paper bag that helps them whenever they're blowing off that co2 to inhale that co2 again hopefully to get those levels back up watch the potassium and calcium levels and for those signs and symptoms of low potassium and calcium levels and also and remember this this is a big one if the patient is on mechanical ventilation because remember that was a cause a respiratory alkalosis make sure that the settings are appropriate and they're not hyper ventilating so you'll want to watch out for that now let's solve a or Tyrael blood gas problem that many professors on your exam and on the ink Lex will ask you to solve they'll give you the scenario of these blood gases and say which of the following is a patient in and is it compensated fully compensated or not compensated okay so I like to whenever I solve any blood gas problems to use the tic-tac-toe method I have a video the card should be popping up our link in the description below where I actually have two videos where I work the tic-tac-toe method with you show you how to set up the problem and everything like that so be sure to check out that video because this really makes it easy solving blood gases okay so first thing we want to do is we want to look at our readings and we set up our tic-tac-toe remember as a child we would set this up there were lines and you're going to label one column acid the middle column normal and the next column base which is four alkalotic conditions okay so we're going to look at the paco2 and it says it's 25 so we remember back from our memorization of our chart that a normal PA co2 level is 35 to 45 so this is not normal there 25 so we know that they are alcoholics because anything less than 35 is alcoholic so we're going to put paco2 over here under our basic okay next pH 7.5 we know that a normal pH is 7.35 to 7.45 anything greater than seven point four or five is basic so our pH is basic and we have tic-tac-toe right here so we know that we are dealing with respiratory alkalosis and that's one thing with these ABG problems you don't know if you're dealing with metabolic or respiratory out of respiratory issues so the tic-tac-toe method helps you because when you get attacked tic-tac-toe you know that whatever your issue is is the one that you have a tic-tac-toe with so we have respiratory alkalosis now we need to decide if this is compensated partially compensate or not compensated so we're going to look at our bicarb now remember at the beginning of the lecture I talked about the kidneys will excrete the bicarb to get to help bring that pH level down so we're going to look at the bicarb level to see if this is what the body's trying to do to compensate because if the bicarb level is messed up then the body's trying to compensate so our bicarb level is 17 a normal bicarb level is 22 to 26 so it's not normal so the body is trying to compensate and anything less than 22 is acidotic so our hco3 is acidotic so the body is trying to compensate but is it fully compensated or is it partially compensated now this is where you're going to look back at your pH now the whole reason that the kidneys is excreting all that bicarb is to help bring this pH back down to normal because it's really high so we look at our pH our pH it's still abnormal so it hasn't fully compensated yet so this will be respiratory alkalosis partially compensated it would be fully compensated if our pH was normal but it's not okay so that is a little bit about respiratory alkalosis now be sure to go to my website register nurse Orion comm and take the free quiz to test your knowledge on rest for alkalosis and acidosis and be sure to check out my other teaching tutorials and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Mean_Arterial_Pressure_MAP_Calculation_Formula_Explained_Nursing.txt	this is a registered nurse RN calm and in this video I want to go over how to calculate the mean arterial pressure the math and if you would like some extra practice problems you can access the free quiz at the end of this YouTube video so let's get started first let's start out talking about what is the mean arterial pressure the map it is the pressure in our arteries during one cardiac cycle and it tells us how well our vital organs are being perfused like our renal system and brain and with the brain we learned in our video about increased intracranial pressure the mean arterial pressure is very important in allowing us to maintain that cerebral perfusion pressure so how do we calculate mean arterial pressure well to do that we have to remember this formula so I would commit this to your memory it says the mean arterial pressure is equal to the diastolic blood pressure which is that bottom number times 2 plus the systolic blood pressure which is the top number divided by 3 and to calculate your map what you need to know is you need to know the person's blood pressure and here our blood pressure is 102 over 70 so let's set our problem up and work it okay so we're diastolic is 70 so 70 times 2 equals 140 and then we're going to take 140 and add that to the systolic blood pressure so 140 plus 102 equals to 42 then we're gonna take 242 divide it by 3 so 2 42 divided by 3 equals 80 point 6 repeating we're gonna round that up so our map is 81 and how do we interpret that that is within normal limits so our map is good okay so that is how you calculate the mean arterial pressure and don't forget to take that free quiz for extra practice problems thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Urinary_Tract_Infection_Nursing_NCLEX_UTI_Symptoms_Treatment_Cystitis_Pyelonephritis_Urethritis.txt	hey everyone is fairs registered are sorry and calm and in this video I'm going to be doing an in cooked review over a urinary tract infection in this video is part of an in clicks review series over the renal system and don't forget the free quiz that you can access at the end of this video so let's get started so what is a urinary tract infection it is an infection film within the urinary system so what structures are included in the urinary system well we have two kidneys we have a right kidney in the left kidney and coming out of the kidneys which help drain the urine are your ureters and the ureter is attached to the bladder and then the urine comes out of the urethra now you can have a urinary tract infection in the lower part or the upper part or both and typically what happens is that a UTI census start in the lower part of the system and can my greatest way upward so with the lower you can have an infection of just the urethra which would be considered urethritis or the bladder called cystitis now with the upper system the ureters can be infected and typically if they're infected you probably either have a lower urinary tract infection or an upper or both and it's called ureter Ida then you can also have where the kidneys are infected and it's referred to as pyelonephritis and if the kidneys get infected this is not good because the kidneys if you look here they are connected to our circulation so if they get infected that infection whatever present can easily migrate into that circulation go to the heart and then we can get septic shock and the patient can die so we really really got to be careful and assess appropriately to make sure not spread to the kidney now urinary tract infections tend to affect women more than men why well really the reason why is the female anatomy in a woman the urethra tends to be shorter than the males we throw so it makes it easier for bacteria to migrate up through that urethra and make its way to the bladder another thing is the close proximity between the rectum and the urethra making it easier for bacteria just to migrate over there especially if the woman is hot is not wiping properly like from front to back and fed they're wiping back to front or wearing tight underwear things like that just make it easier for specifically a coli to travel to that your referent and in fact the woman with a urinary tract infection now let's look at how urine flows and the defense system set in place in your urinary tract that really helps prevent urinary tract infections because here in a second when we go over the causes and it will make more sense and widest if it causes causey and the patient's increased risk of UTI because you're seeing a breakdown in these defense systems so first how does urine normally slow okay we know that their kidneys filter our blood and the nephron plays a huge role in this and it creates a substance called filtrate which will lead and the nephron as urine so urine will be produced and it will leave at the renal papilla from that nestling it will go down through the minor major tail acts out through the renal pelvis down through the ureters and your ureters connect to your bladder and what's neat about the ureters is that you have these one-way valves that prevent urine from in the bladder and back climbing into those ureter so we don't want that to happen because if that happens we have a higher risk of urinary tract infection that you're in in a sense of saying stagnant and that's a good medium for bacterial growth and does one-way valves are called your toe vesicle valves and then the urine sessions in the bladder which is stored and once your bladder becomes really full you'll feel that urge to void and you will void down through the urethra exits there now let's look at our defense system okay the first defense system is really the physiology of how urine drains out of the kidneys because it's raised in a downward motion it doesn't back slow because if we have backflow of urine we have beautiful conditions for a urinary tract infection so what structures really help us keep that urine flowing downward because if they get messed up then we're going to have that increased risk of urine back flowing so the first thing which we sort of talked about are those your your toe vesicle valve and in one condition that we're going to talk about and these valves are messed up there causing reflux of urine to go back flow into the ureters into the kidney so some conditions can cause issues with those vows another thing are the muscles of the bladder your bladder help help squeeze out that year and completely we don't want to have urinary retention which is one of the reasons a person can get urinary tract infection however over time like with patients who have diabetes or in patients who are immobile who are able to get up and go to the bathroom so they have a distended bladder over time those muscles become weak which can lead to the bladder muscles not working properly another thing that helps keep that your employment downward is the pressure created by the urine in the bladder all that urine in there creates pressure which in a sense sucks that bladder it sucks that urine down through the system with the pressure through the ureters and helps the person get rid of the urine now another defense system is really the urine itself urine typically is sterile and it has these antiseptic properties to it that helps prevent germs from sticking to the lining like the lining of the bladder wall and what way the role in that is the pH of the urine and we like acidic urine and the urea concentration however with some conditions like diabetes we can have issues where the urine has changed because remember with diabetes one of the reasons we can find out person s IVs is when we check their urine there's leaking glucose in their urine and normally in the nephron specifically the proximal convoluted tubule 100% of the glucose is normally reabsorbed however with diabetes glucose there's too much and so it's leaking into that urine and that provides a beautiful medium for bacteria to grow and for them to just flourish where normally if they had a better pH they wouldn't have that now also your urine I mean your bladder the lining within the bladder has your immune system cells which helps fight bacteria so bacteria do tend to get in there the immune system will see that and attack that however whenever you have a person who has a suppressed immune system and they are at risk for having bacteria to continue to grow to that immune systems not attacking that germ now another defense system this is specifically in mouth is the prostate gland the prostate gland secretes this fluid that has my antimicrobial properties to it and it helps Coster your refre so a bacteria gets in there that fluid from the prostate gland is in there it can help kill that bacteria however whenever you have an enlarged prostate it is not secreting fluid properly and it's squeezing that your refre shut so you're going to have backflow of urine and you're not going to have that antimicrobial fluids help ward off that infection and in a defense system specifically in women and is the normal flora found in the vagina now this is really due to about kiri called black Toback Phillip and it helps keep the environment acidic because the vagina and the urethra are close together and whenever though lactobacillus is there if I chance from the rectum ecoli did migrate upward and that like Toback Scylla can help fight that infection due to the acidic condition because the bacteria will not live so that is another defense system that the body has now let's look at the causes of urinary tract infection most common types of urinary tract infection tends to be bacterial and the most common bacteria tends to be a coli which has probably came from the GI system so for testing purposes I would try to remember these causes because test questions like to ask you out of all the patients which patient is most at risk for urinary tract infection okay so to help us remember let's remember the pneumonic hard to avoid because it's UTIs and they have difficulty pain okay the first one is H for hormone changes and this can be with pregnancy menopause birth control why what is what is this do and it changes that normal flora in the body and what can happen remember whenever we're talking about one of those defense systems and is that lactobacillus and wherever you throw off the hormones that flora changes down there and bacteria can get in there and cause an infection so anytime you're messing with hormones your risk another one is a antibiotics again this just changes that normal flora kills all the good bacteria our for renal stones and what happens is that those renal stones get in there and they prevent that urine from draining and what could happen is that a stone can form and it can form within the kidney and you can have it maybe in the K lacks of the kidney or stuck in the pelvis of the kidney or the upper part of the ureter and what happens is that that urine will not drain out of that kidney it will stay stagnant in there and this can lead to a urinary tract infection d for diabetes and with diabetics they tend to have compromised circulation they have decreased immune system response so bacteria gets in there they they don't attack it as efficiently as they should and they tend to have if it's not controlled diabetes they can have glucose in the urine which is great environment for bacteria to grow and they tend to have that urinary retention because the nerves aren't working properly to let them know hey I need to empty my bladder those muscles become weak due to those that overextended bladder overtime so they are at risk for diabetes another thing are toiletries t4 toiletries and this is because tool trees like taking excessive bubble bath using that soap over time is coming in contact with the urethra can cause irritation also powders perfume tampons Senate or not scented and especially scented and sanitary pads over woman during this ministration if she's having a lot of recurrent UTIs you don't let her know not to use scented tampons or sanitary pads and to avoid tampons because that can cause urinary tract infection increase our risk okay oh for obstructive prostatic hypertrophy and this is seen and males typically who have BPH and what happens with this is that they get urinary retention and what happens is that that prostate enlarges and it squeezes or compresses the urethra urine can't get out so you get urinary retention and also that prostate gland isn't able to secrete that antimicrobial fluid properly so you lose the fighting power of that fluid to fight off infection as well next vesicle ureteral reflex also called vur and this tends to happen in the pediatric population it's a congenital defect and what's happening is that urine is back flowing from that bladder to the kidneys because of a valve defect remember we have those one-way valves called euro vesicular valves and they are not closing properly and they are allowing your in to back up to the through those your returns and into the kidneys and you these kids will have recurrent constant infections and when they go in they look and they see that they have issues with their vows next Oh for over extended bladder and this is where the bladder is not in feed whenever it needs to be empty patients who are at risk for this our patients who are in mobile they can't get up they can't move so they just sat there with the over extended bladder this weakens those bladder muscles which will lead to urinary retention so whenever they do get a void they keep some that urine in there another person at risk for that are nurses and because we tend not to go to the bathroom when we need to because we're going to get this done we're going to get that done and we tend to some nurse o struggle with over extended bladder so always into your bladder next I we have several of those the first is indwelling catheter like a Foley catheter and if you've ever worked in a hospital for any time you're always hearing get that Foley catheter out because that is just an endurance way for bacteria to get in and causing urinary tract infection so we want to remove those Foley's as soon as possible the other eye invasive procedures intercourse sexual intercourse and especially spermicide there use and women are definitely at risk for this just because of that short urethra so voiding after sex is very important and another thing is Rd for decreased immune system and that immune system just isn't able to fight off infection and they are really at risk for developing your viral and your fungal of origins of the urinary tract infection now let's look at how a urinary tract infection is diagnosed because as a nurse you need to be familiar with tests the physician may order because you're going to be playing a role in collecting some of these specimens okay so the biggest thing that's order to help diagnose a UTI is a urinalysis also called a UA and it's going to check for white blood cells and bacteria and your role as the nurse is to collect this via the clean cache method so you're going to either be doing this or the patient so you'll want to educate them how to do this and this method helps us prevent contaminating that specimen which could give us a false positive okay so when you're collecting a UA it's best to collect when the bladder has been full for about two to three hours so the urine is concentrated not diluted and what the patient will do or you'll do is that you will why with an antiseptic wipe so you will clean the area then you will have the patient void a small amount in the toilet and then they will stop in and midstream they're going to void until it's halfway full in that cup and they'll want to hold the cup at least a few inches away from the urethra so and it doesn't get contaminated now sometimes patients have Foley catheters so how would you collect a your analysis from a Foley well on the Foley and close to where the Foley is inserted just a little bit down the tubing is an access port and on this port you can clean the poor with an antiseptic cleanser then use a needleless syringe and it will just screw on the access port and you can withdraw some urine that you need and put it in the cup and sometimes there's not urine freely draining from there so you can clamp the tubing to collect some of the urine however you never ever want to collect the specimen from the collection bag because sometimes there's a bacteria present in there and it's not a good indicator if the patient has a urinary tract infection so always use the accessport another test order is called a urine culture and sometimes a lot of times a UA and a urine culture will be ordered together and this will assess the type of bacteria if it's caused by bacteria that is growing in the urine so they can order antibiotics appropriately to treat the specific bacteria however it depends on your lab but it takes about two days to receive that result back now typical question that likes to pop out the law is falling patient is order to start IV antibiotic therapy or Pio antibiotic therapy who has a UTI and the physician has also ordered ordered or urine culture and how will you proceed with following Alexei's orders so and you want to remember you want to collect your urine culture first before you even give that antibiotic because giving that antibiotic if you gave the antibiotics first it would start fighting the infection and you wouldn't be able to properly culture that urine so always do the urine culture first then give the antibiotic okay another test is called as a sauce Katti and that's where they insert a scope and they go down and they look inside the bladder and the urethra and this is ordered most commonly for people who have this crea current and urinary tract infections they want to see what's going on is there a structure issue in there a blockage something like that okay now let's look at our signs and symptoms of UTI what is the patient going to report to you okay and patient may have pain when voiding and can be described as like a burning sensation whenever the stream starts when they're boarding they may also have a persistent need to avoid like this really intense urge they've got to go pee but whenever they do pee it's just really small amounts or there's nothing that comes out at all that's because that bladder is irritated not your we throw it's really inflamed the urine will be odorous and this is definitely something that you will be able to smell and you will know it's there it's not just a faint smell it's right in your face there the urine will appear dark and cloudy you won't be that nice light yellow color also and during your assessment they will have pain with what's called the cost over tee ball angle and this is known as CVA ten Ernest and this is most commonly associated with a kidney infection and this is how you would assess for CVA tenderness so what you will do is that you will find where the last rib on the back is which is your 12th rib and you will find the spine and you're going to go at the angle and the angle is below the 12th rib and in between the spine and this is about where your left kidney is located and about where your right kidney is located so then you're going to take your hand you're just going to place it over there and you're going to stomp the area with your fist you're going to make this fist and then you're just going to thump it and we're wondering if the patient has pain whenever we do this the high pressure but pain is what we're looking for so like that and then go to the other side and test it and they have pain that could indicate again a kidney infection another thing your patient can report are spasms or like cramping like feeling of the bladder and the urethra and this can be very very painful to a patient who has a UTI and also they will have a fever and on that urinalysis they can have increased white blood cells now one thing I really want to point out because this is another thing that tests love to ask about urinary tract infection okay in your geriatric population they can not have these typical signs and symptoms like a fever and the persistent need to boy and maybe even any pain with pain and what they tend to experience is all of a sudden they were who they were alert and oriented but now they're confused they don't know where they are they're really agitated and they are falling a lot I don't know how many times as a nurse I've had patients who were admitted with this and they really didn't know what it was a doctor suspected urinary tract infection because all of a sudden they had mental status changes but really as turns out had a urinary tract infection got treated for it and came back to normal so really really watch this in your patients and who are elderly not just for testing purposes but in the hospital because you will definitely encounter this now let's look at the nursing intervention that you're going to do for a patient with a urinary tract infection and as I go through this information be sure to really pay attention to those education pieces because include because the in place exam and your nursing lecture exams like to ask questions about how you're going to educate the patient some things you should watch out for and being like that so as the nurse what we're really doing is that we are going to do the following we're going to assess that patient for signs and symptoms of a urinary tract infection because really all patients are at risk for this mister immune system suppressed they have diabetes things like that so we want to catch this early so they can get treatment fast before it spreads to the kidneys and eventually the systemic circulation we want to maintain dirt and monitor their fluid status look at those eyes and O's and making sure that their urine output is at least an 30 CC's an hour that they're putting out that good amount of urine because if they're not chances are they could be going into renal failure maybe the UTI has progressed that far also we're going to help them control their pain because with the UTI patients will have excruciating pain especially those spasms and cramping pain so we'll help them with not only formal logical medicine medicines but norm pharmacological techniques as well which we'll go over in a second and we'll administer medications purposes or like the pain relievers but also the antibiotics and we're going to really be educating our patients like and how to prevent this from happening again and how to take treatment how to take those antibiotics how to and monitor yourself for urinary tract infection things like that we're going to be monitoring them for complications again it's went and they're becoming SiC maybe treatment smart working we want to make sure that they're not entering into that and we're going to collect and monitor their labs like that your analysis that you're in culture and if anything comes back abnormal like there's white blood cells or bacteria present in that you a we need to let the physician know so they can order treatment now typically whenever a patient has a Foley catheter the physician will order you to remove it if a urinary tract infection is present always check with the position if they want you to remove that because you'll need an order for that because again Foley catheter is a great entrance for bacteria and some things I see is that whenever a patient has a Foley catheter and they develop a urinary tract infection they made for a complain of the need to void even though they have this catheter that's draining the urine so if it's not pink somewhere the tubing is not kink somewhere the bladder may be irritated irritating the urethra may be irritating they may have an infection another thing remember with the urine culture you want to collect that first and then start the antibiotics always remember that we'll be encouraging at least two and a half to three liters of fluid per day as long as they don't have any contraindications whatever the physician orders and why why do we want them to take in this much fluid well number one we want the urinary system to be flushing itself getting that bacteria out there on antibiotics it's fighting it but we want it out and we want to keep the urine diluted a lot of times and antibiotics that's typically prescribed for urinary tract infection is a group of drugs called solanum eyes bactrim is I'm a popular one and the thing with bactrim is that if the urine is concentrated they can develop what's called crystal urea where they develop these little crystals in their urine and this will not happen if the urine is diluted it decreases the chances so you want to really tell them to consume a lot of food and let the patient know that this can possibly happen so this is an incentive why you need to consume good amounts of fluid and some other things that I want to point out about the back trim is that with antibiotics we really want to try to give these at the same time every day so tell the patient taste this at the same time every day why because we want to keep that blood level constant so that antibiotic can keep working we don't want those blood levels to dip of the antibiotics and because it won't fight as fast then we I'm wanting to always take all the antibiotics don't just quit taking them because urinary tract infection you think it's gone because this increases the resistance of the bacteria to the antibiotics always take all the antibiotics another thing we're going to be doing is encouraging the patient to avoid every two to three hours helping them go every 2-3 hours keep that system flush we don't want to have an overextended bladder keeping that urine in there with the pain and non-pharmacological what we could do is a warm fist bath help that urethra is really inflamed that can help an ease that or heating pad another thing I'm physicians sometimes ordered a drug called perineum also called Panozzo priding sometimes your staff and what this is is this is like analgesic it will help coat the bladder and the urethra and it will provide release decrease that burning urine the spasms things like that but one thing you have to watch with this and it's a normal side effect is the orange colored urine and it's almost the same color is what this marker looks like it can be a little reddish tint but this pencil arm patients whenever they go to void in the commode because it's just this really bright orange so that is a normal side effect if you see that as a nurse know that it's normal okay some education pieces for your patients and preventing urinary tract infections again they you take all those antibiotics female patients need to wipe from front to back very crucial if they wipe from back to front they'll introduce that bacteria in the rectum to the urethra an after sexual intercourse it's a very important to void to clear out that urethra and they also need to avoid wearing any tight underwear and it's best to wear loose cotton underwear void bubble bath perfume sprays powders this irritates the urethra and your administration a boy tampons and be sure to change those sanitary pads all since and to avoid caffeine and alcohol because these products actually irritate the bladder and the urethra and to void every two to three hours again just to keep that urinary system flush okay so that wraps up this lecture on UTIs thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Lung_Anatomy_and_Physiology_Gas_Exchange_in_the_Lungs_Respiration_Transport_Alveoli_Nursing.txt	hey everyone it's sarth register nurse rn.com and in this video I'm going to be going over lung anatomy and the physiology of gas exchange this video is part of an inlex review series over respiratory disorders so be sure to check out those other videos in this series and as always over here on the side and in the description below you can access the quiz and the notes that go along with this lecture so let's get started first let's start out talking about the role of the lungs what do the lungs do the lungs remove carbon dioxide from our body and it does this by exhaling and carbon dioxide is a waste product from metabolism and it replenishes the body with fresh oxygen and it does this by whenever we inhale whenever we breathe in we're taking in oxygen it's going to go down through our lungs and here in a second you'll see how that oxygen is transported to those red blood cells to replenish your body and another thing to remember is that your heart and lungs work together to make this gas exchange happen because what your heart does is it drains all that un all that used up blood that your body has used which is unoxygenated it pumps it to the lungs which will take it through the pulmonary artery to the lungs to get oxygenated then the pulmonary vein will drain that oxygenated blood back from the lungs and it will pump that fresh blood that your body needs with oxygen in it so your heart and your lungs go together now let's look at the anatomy of the lungs up close Okay air that you inhale with oxygen will enter in through your nose and through your mouth and it will go down through your upper respiratory system which will include your nasal cavities down through your Linex and here's your thyroid cartilage and then your there's your CID cartilage and then it we'll enter down through the lower respiratory system which includes your trachea and the trachea will Branch off into the broncus at the Carina this cartilage triangular area and you will have your primary bronchi which is your right and left broncus and the broncus enter into the lungs at the Highland also what enters into your lungs at the Highland are your pulmonary arteries and your pulmonary veins which are from the heart because remember the heart and the lungs work together so the p AR artery will deliver blood to the lungs to get oxygenated because it carries unoxygenated blood then gas exchange will occur in the avolar Sachs in the avioli and it will drain that fresh oxygenated blood back through the pulmonary artery and the heart will pump that oxygenated blood through the aorta and it will go to the tissues in the body and replenish it with fresh oxygen then your primary bronch ey will further Branch off into the the lungs into low bar bronchi which are also known as secondary bronchi then it goes even further into tertiary bronchi also known as segmental bronchi and then the segmental will go into even smaller little Airways known as bronchials and um to connect the bronchioles to the avolar Sachs you will have avolar ducts and then you will have the avolar Sachs which are the purple little sack areas in the lung and then this inside this are avioli and this is where gas exchange occurs now let's talk a little bit about the lung itself here you have the right lung and you have the left lung the right lung is made up of three loes you have the right upper the right middle and the right lower then you have the left upper and the left lower so notice the left lung only has two loes where the right lung has three loes then your lung is made up of two layers with some C fluid in the middle of it here the area in the red is your visceral layer visceral is surrounding the lung lungs a vital organ visceral VI remember that visceral attaches to the vital organ itself that is how I remember it and then um you'll have the little area of serus fluid in between that and then you'll have the plural layer which will um be surrounded around the lungs around where the thoracic cavity is and what that little Cirrus fluid does is allows the lungs to Glide on each other as you breathe in and breathe out to prevent any friction okay now let's talk about what is going on with the body physically whenever we are inhaling and exhaling because what there are a lot of things that are going into play while we're doing these simple tasks your lungs are working your heart your diaphragm and your accessory muscles to get this simple inhalation and exhalation done so what happens is that you breathe in oxygen through your nose through this whole system that we went over and what happens to allow you to do this is that your diaphragm will contract and right now when it's curved up like this it's in the relaxed position but it contracts and it lowers and whenever it lowers down this creates a negative pressure which allows you to suck in that oxygen and fill those lungs so oxygen travels everywhere it hits those avolar sacks and this is where the gas exchange occurs then carbon dioxide will enter in and you need it's time for exhaling so what happens is that this diaphragm will relax it creates this you already have this high pressure in your lungs which will allow you to force that air out which will include the carbon dioxide and the water so what has happen happening on that microscopic level between the carbon dioxide and oxygen so let's take a look okay so what's happening is you're breathing in you're breathing out and during this whole time these little sacks right here your aviol sacks are inflating and deflating because you're having the constant transport of carbon dioxide out and oxygen in so on each sack that you have you have capillaries and these capillaries are originating from the pulmonary vein in the pulmonary artery and remember your pulmonary artery is taking unox oated blood from the heart to get replenished so it can take it back through the pulmonary vein to the heart to the aorta and replenish the body so what happens let's look at it right here this is just like an individual avioli blown up so you can see it and you have the little capillary here so you have what's came from the heart the unoxygenated cells that are releasing their B their waste product of CO2 into the respiratory system so you can breath Bree it out and it can leave and then it's also taking in the oxygen that you just breathed in and attaching itself to these red blood cells so they're turning red and they're going back through the pulmonary vein to the heart so what's happening is carbon dioxide and oxygen is transporting across this thin little capillary wall and you have this constant exchange of carbon dioxide oxygen carbon dioxide oxygen think of it as like an assembly line and but all these little red blood cells lined up these ones are the exhausted ones who are getting rid of their waste product of CO2 and then the Oxygen's coming and attaching to them and making them feel better and they're going to go back and do their job so that is what happens in a nutshell with gas exchange whenever you're breathing in and breathing out in these avolar sacks okay that was about lung anatomy and the physiology of gas exchange be sure to check out my other respiratory videos and thank you so much for watching and please consider subscribing to the YouTube channel
Medical_Surgical_Nursing	Menstrual_Cycle_Phases_Female_Reproductive_System_Follicular_Luteal_Proliferative_Secretory.txt	hey everyone it's sarah thread sterner sorry and calm and in this video I'm going to be going over the reproductive cycles specifically the woman's menstrual cycle this video will be part of an in klux review series for maternity so if you're studying this section be sure to check out my other videos in this series and as always in the description below or at the end of the video you can access the quiz to review your knowledge on this material so let's get started okay behind me I have the whole menstrual cycle laid out for you and what I want to do is I'm going to walk you through it by cycle day so you can understand what is going on now as a nursing student what you specifically want to pay attention to during this lecture because it's things ass on your exam are the following you want to pay attention to each phase what is happening in that phase and when that phase is occurring specifically those cycle days then you want to pay attention to hormones because tests Club to ask about the hormones like the role of the hormone what it's doing to the body so first let's look at what's going on okay a typical woman's menstrual cycle is 28 days so here we have our timeline 1 to 28 and mid cycle is when ovulation occurs so that is day 14 now the whole roll the whole goal of a reproductive cycle is to reproduce so what the body is doing it's taking your ovaries and your uterus they are working together in case an egg is fertilized and you have the development of a baby that is the whole goal and if that doesn't happen then the cycle will start all over again which monthly cycles women have monthly cycles so that is what why all this is happening and what is going on so what happens is that you will have ovary changes and changes in the uterus and E Faye's each each stage has three phases the ovary will have three phases the follicular ovulation and luteal and then your uterine will have three phases the minstrel the proliferative and the secrete Ettore now some of these phases overlap with each other with a like with a follicular will overlap with the minstrel and proliferative and then ovulation will happen and then the luteal and the secrete Ettore will overlap together because as you're going to see these phases are actually helping each other what's happened with the changes that are going on in the ovaries is actually helping the uterus get prepared for that potential baby that may be formed so let's start with ovarian changes okay we have follicular follicular faith' happen cycle days 1 through 13 and the whole goal of the follicular stage is to prepare a follicle to be released a mature egg let the name help you for each stage so follicular follicle that is the big goal of the ovary it wants to mature a follicle in the egg to be released so it can be fertilized and implant in the endometrium so what happens what is a follicle ok you have two ovaries you have your right ovary and your left ovary and you have little fluid-filled sacs in each ovary lots of them a woman is born with lot of them and they contain little immature eggs and what happens is that your body will release hormones to cause some of those follicles to mature and then you'll release it during ovulation so the body is doing that during the cycle so how does it do it okay your hypothalamus it will release gonna tropen gonadotropin-releasing hormone which will cause your anterior pituitary gland to release follicle stimulating hormone also called FSH and luteinizing hormone LH and these two hormones play a huge role in getting that egg developed and released so what happens is whenever your ovary senses the anterior pituitary gland releasing FSH it starts to stimulate those follicles to grow now several follicles will start to grow but only one will mature into what's called a graphing follicle crabbin follicle is the mature follicle that will release the egg and all those other follicles will die they will not release an egg now as this follicle grows and gets bigger and more mature you will notice if you're charting hormones that estrogen will start start increasing because that follicle is releasing estrogen and whenever estrogen is released it's slowly going as that egg maturing you will have a negative feedback loop from your hypothalamus to the ovary which is going to cause a little dip in FSH and luteinizing hormone because it's signaling to your body the estrogen rises is that that egg is maturing so your body doesn't really need all the FSH and LH right now because that egg is doing its job so you'll have a slight dip but then as that egg matures and it's ready it's ripe it's ready to come out you will have that massive peak of estrogen because it's signaling that egg is ready whenever you have that massive peak of estrogen you will have a positive feedback loop which is going to cause your anterior pituitary gland to release a massive amount of luteinizing hormone called the LH surge LH plays a huge role in getting that egg out of that graph and follicle to go into the fallopian tubes to possibly get fertilized so LH is rolled is the cause the egg to be released to mature and it does this whenever you get that huge surge it's going to break that wall of that graph and follicle that has that much egg and that eggs want to come out of there and then it's going to call that follicle that released that egg that grass and follicle to turn into a very important structure called the corpus luteum now here in the luteal phase you will see what the corpus luteum does it plays a role in secreting progestogen progesterone and estrogen and what those hormones do is it's going to make your body your endometrium specifically receptive for potential implantation of a fertilized ovum so that's what it's going to do now after you had this LH surge about 24 to 36 hours after that surge the egg will be released so you have the surge then a little bit later the egg will be relief now the most fertile days for a woman are about the last five days of the follicular phase and in 24 hours after ovulation so about cycle days 9 through 16 depending on when the woman ovulate and everything because this stuff is not clear cut and dry every woman varies so about 9 to 16 days of the cycle is whenever she is fertile because remember and your LH surge happens 24 to 36 hours and then the eggs release so typically the LH surge can happen days 11 through 13 and then you have the release of the egg and sperm if a sperm is present it can live in the reproductive tract in ideal conditions up to five days so it can be there and hanging out until that egg is released now corresponding with your follicular phase remember we got some uterine changes going on and the first phase of the uterine cycle is the menstrual phase and this is cycle days one through six this is when the woman will have bleeding and she is shedding a layer of the endometrium and this layer is called the stratum function Alice of the endometrium and what's happened is that lot last cycle pregnancy did not occur so the protest region and estrogen levels dropped that caused the body to cycle all this back over so hypothalamus releases gonadotropin-releasing hormone then causes the anterior pituitary gland to release FSH LH which is going to start stimulating those follicles and the menstrual phase is happening during the follicular phase all this is working hand-in-hand so after about 1 to 6 days we will go into the proliferative phase and this is cycle days 7 through 14 so here in the menstrual phase she shed the layer now the goal is to rebuild the stratum function Alice in case the egg is fertilized and it needs a place to implant so it can grow which is in the endometrium so it will start rebuilding how does it rebuild it rebuilds with due to estrogen being secreted and where as estrogen being secreted from that growing follicle that's fixing to release the egg because it knows hey a mature egg is coming we've got to get ready we've got to rebuild this layer in case it implants so it's working hand in hand and also that estrogen will cause you know the layer to rebuild but it also will affect the cervical mucus will cause the cervical mucus to thin become more sperm friendly which a sperm does present at the thin mucus will allow it to migrate easier easier to the fallopian tubes for potential implantation okay so we've had our LH surge we're now on day 14 and this is the ovulation phase of the ovarian space so we have ovulation the egg is released after LH surge now the ovum it's now called an ovum it's released into the - neil cavity then it's swept into the fallopian tube with the help of the fimbriae the fimbriae have cilia on them and these will cilia act like little fingers and move in a wave type motion and whenever that ovum is released from that ovary into the peritoneal cavity the fimbriae cilia get that ovum and sweep it in to the fallopian tube so it can get fertilized and the egg will only live for 24 hours and then it disintegrates now a woman if she's charting her basal body temperatures she may notice a dip in basal body temperature and then around ovulation and increase 0.4 to 1 degrees Fahrenheit now if sperm is present to fertilize the most common site of fertilization I would remember this is the em and put em Pugh lobe of the fallopian tube the ampulla is most commonly where the sperm and the egg will meet up and fertilization will occur now so let's move to day 15 through 28 rest of our cycle we're in the second half of our cycle we just did the first half we had our midway point of ovulation now we're in the last part of it okay it's called the luteal phase and this is cycle days 15 through 28 it also corresponds with the uterine phase phase changes which is the secrete Ettore which is 15 through 28 as well and again you're going to see they're working hand-in-hand because the whole goal of this whole face is to prepare the endometrium for potential implantation of this hopefully fertilized ovum but if it doesn't there isn't any fertilization of that ovum what will happen is that our cycle will restart again and we'll come all the way back over here and I'll just repeat itself ok so what's happening here is that our corpus luteum has formed remember it's formed from that follicle that released the egg and this is going to act as a temporary endocrine structure that is going to help support pregnancy it is very very interesting how it works so I'm the endocrine what is going to release is a lot of progesterone which is going to play a role in this credit or e phase of the endometrium which um it will cause the endometrium to be receptive for implantation of that fertilized ovum and it stimulates estrogen production which are your two main hormones that keep pregnancy viable and going good so your corpus luteum will stay in place for 14 days and if there was no pregnancy at all and it will disintegrate and turn into the corpus albicans now what will happen is because your corpus luteum is secreting progestogen and estrogen that's its goal and you have no FSH and LH because that negative feedback loop it's suppressed that because we don't want that if we have that or menstrual cycles going to start over and if we have a fertilized ovum we don't want that because we need progesterone and estrogen so if it dies you're going to have a major drop in progesterone and estrogen and the cycle is going to start all over LH and FSH is going to come back now let's say that fertilization did occur well the corpus luteum will stay in place because it has a very important job of keeping that progesterone and estrogen in the system so that fertilized egg can implant into the endometrium so what will happen what causes it to stay in place is that the embryo will start to release HCG which is human chorionic gonna troponin which is what pregnancy tests pick up and this prevents the corpus luteum from dying so it will stay in place and the corpus luteum will stay in place until the placenta takes over and your placenta produces massive amounts of progesterone and estrogen to keep the pregnancy and it will take over the placenta will take over at about 8 time and then your corpus luteum has done its job and it will die so that is the menstrual cycle now be sure to go to my website registered nurse or en comm and take the free quiz that will test your knowledge on this material and don't forget to check out my other videos in this series and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Patent_Ductus_Arteriosus_Nursing_Lecture_Pediatric_NCLEX_Review.txt	this is cereth register nurse re and calm and in this video i'm going to be going over patent ductus arteriosus in this video is part of an ink lex review series over pediatric nursing and as always after you watch this youtube video you can access the free quiz that will test you on this condition so let's get started what is patent ductus arteriosus also known as PDA it is a congenital heart defect where the ductus arteriosus does not close after birth like it should and what's going to happen is this is going to lead to increased pulmonary blood flow so you're gonna have a lot more blood going to the lungs then it should and this is going to lead to some complications and in a moment you're gonna see why we're seeing these certain complications in this patient now to really remember these congenital heart defects for pediatric nursing exams let the name of the condition help you because it gives you some clues and you can take those clues and plug it in with the normal blood flow to the heart those complication signs and symptoms treatments it really makes sense so we're talking about hay tent ductus arteriosus what is patient mean in the medical field it means something has failed to close what's failed to close this ductus arteriosus structure now the let next thing is what is the ductus arteriosus well it is a vessel that connects the aorta to the pulmonary artery in a fetus so a baby in the womb needs this structure it's very important for their circulation but as adults we don't need it and what's the purpose of this structure what it does is it carries blood that on the right side of that fetuses heart to the rest of the body so you have blood that comes in through the superior and inferior vena cava goes through the right atrium tricuspid valve right ventricle up through the pulmonary artery the pulmonic valve and then it's going to go through this neat little ductus arteriosus and go through the rest of the body and the reason is doing that inside of just gonna go through the lungs is because the lungs are not working in that fetus they're not functional yet but when it's born the lungs will become functional and that's going to change the blood flow for the baby so instead of having blood being shunted in various areas you're now going to start to have the normal blood flow after birth which is why it's so crucial for this ductus arteriosus to clamp off and close itself because if it doesn't what's going to happen okay what's going to happen is you're gonna have the normal blood flow going in through the right side of the heart the oxygenated blood it now needs to get to the lungs because the baby doesn't have the placenta anymore to give it like it did when it was in its mother's womb so Bloods in the right side it's going to be going to the lungs getting oxygenated it's going to enter back through the heart through that pulmonary vein into the left side it's gonna be shot up through the eighth order through the rest of the heart but if we have this ductus arteriosus that's still open what's gonna happen is that this blood that's in this aorta it's going to allow blood to pour down through the pulmonary artery so you have blood that's minasan oxygenated through the lungs and it's going down to this ductus arteriosus through that pulmonary artery and you have all this extra blood going to the lungs and this really stresses the lungs out over time because it's going to create a really high pressure and that pressure is going to damage the integrity of those arteries that feed the lungs so over time those arteries are going to narrow so you're gonna get pulmonary hypertension and why is that an issue well that's going to cause a bunch of respiratory issues for that patient decrease oxygenation at risk for more lung infections in addition it's going to make it harder on this heart because if you have this narrow artery where you're trying to get blood to the lungs to get oxygenated that causes a lot of resistance on the heart and it's going to get fired overtime and the patient can enter into heart failure because it's like the same concept if you take a water hose you make a really small opening that water has to really push to get through the opening it's like the same concept with the blood so you're gonna see heart failure in addition that high pressure in the lungs because what you're having is this left right shunt and you have blood from the left side of the heart being shunted to the right side of the heart you have the increased pressure that's going to damage the lining of the structures inside the plumbing of your heart which can increase the risk of any bacteria that may be present in the blood to stick inside the heart causing endocarditis now let's talk about the signs and symptoms of a patent ductus arteriosus okay the signs and symptoms really vary and they vary depending on the size of this opening if a patient has a large PDA it's gonna cause signs and symptoms and those complications that we talked about because you have a lot of blood escaping from that a order into that pulmonary artery and you have an increased pulmonary blood flow now if it's really small and it's not really allowing a lot of blood to escape in there you're not gonna have a lot of pulmonary blood flow so the patient could be asymptomatic a lot of times they close on their own but with the large PDAs they will need repair of some type and we'll talk a little bit about that in our treatments later on now PDAs are most common in premature infants and to help us remember all those signs and symptoms let's remember the pneumonic call and this will have signs and symptoms thrown in there with that pathophysiology that we were talking about earlier so the first C is cardiac this is definitely going to cause some cardiac issues and when you're assessing this patient listening to heart sounds you may hear something unique and remember this this is like a hallmark thing of this condition it's called a continuous machinery like heart murmur continuous and meaning that you're gonna hear it during diastole and systole it's gonna be continuous and you can hear it at the left upper sternal order and why is that well if you have a large PDA what's happening is a lot of blood is escaping and it's causing this turbulent blood flow pressure going on and when you listen here you can hear that turbulence at that left upper sternal border this machinery sounding like in addition they can have in the carditis and we talked about that so they're at risk for that plus they can have an increase heart rate number one because of the pulmonary issues going on they have low oxygen levels the heart has to work harder plus it has to work harder to pump the blood through those narrow arteries going to the heart in addition they can have what's called a wide pulse pressure now what is a pulse pressure well this is where you take the systolic blood pressure and you subtract it from the diastolic blood pressure and you get a number and that number represents the force that is needed for the heart to contract so in these patients these babies it's going to be high and according to open Journal of Pediatrics this is defined as a difference between systolic and diastolic blood pressure of greater than 15 to 25 millimeters of mercury in premature infants and greater than 25 millimeters of mercury in term infants so why is there a wide pulse pressure well it's highs back to diastolic pressure it's the one causing us the problem it's going to draw because remember diastolic pressure is the pressure of blood in the arteries when the heart is filling when it's resting in between its beats so if you have blood that's escaping into this pulmonary artery during that time that's going to lower the pressure that is all it pressure so whenever you have a lower diastolic pressure you subtract it from the systolic pressure you're going to get a higher number in addition you can have heart failure which we talked about fat so it's not normal for a newborn baby to have heart failure and this can bruising it with lung congestion where the fluids backing up into the lungs so they can have crackles they can have difficulty breathing next pay for activity and tolerance these infants are to fatigue very easily and it's time back to what's going on with the lungs with the heart and any type of activity like eating crying feeding can cause them to fatigue and they can actually have sweating diaphoresis with it as well next is L for lung we're gonna have a lot of lung issues because that pulmonary hypertension in the lungs from the increased blood flow it's narrowing those arteries that are feeding the lungs increasing the pressure there so our lung functions really going to decrease they're gonna have issues with that so they can be at risk for more infections and they're gonna have problems feeding so a baby who's trying to nurse or suck on a bottle if they're having respiratory issues it's really gonna be difficult for them which ties to the next L these infants a lot of times have loss of weight because number one they're burning a lot of calories to breathe and they're not able to get enough caloric intake because they're having trouble feeding so a lot of these patients are at risk for failure to thrive now let's talk about the treatment for pdas what can be done to close this extra vessel that is allowing extra blood to escape into the pulmonary artery it's increasing lung blood flow well a medication can be given and the med what it can do it can cause this vessel to clamp off and it'll close a toughie medication use is called indomethacin I would remember that pdaa indomethacin put those two together and it is a prostaglandin inhibitor however what to remember about this is that it's usually only used in premature infants that's where it's really going to be successful sometimes it can be used in the really young infants who are like a few days old but it's not gonna work for older infants children or adults another treatment is invasive where they can do a heart catheterization where they go up with a catheter through a blood vessel they insert a device that will actually close the structure off or they can perform surgery where they go in and actually tie the vessel off okay so that wraps this review over PDA thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Arterial_Ulcers_vs_Venous_Ulcers_Nursing_Characteristics_for_PVD_Peripheral_Vascular_Disease.txt	hey everyone it's sarah thread sterner sorry and calm and in this video we're going to compare an arterial ulcer versus a venous ulcer and I want to get on those main concepts you need to know for exams about these types of ulcers so let's get started when you're studying arterial and venous ulcers you want to be able to identify where these ulcers tend to be located and how they appear because that's where exams love to ask you about so first let's talk about arterial ulcers with arterial ulcers there's an issue with the peripheral arteries being able to supply the extremities and the signs and symptoms of an arterial ulcers tends to be found in that lower extremity below the knee cap and we have an issue with blood flow so that rich oxygenated blood being able to get to those extremities perfuse it and give those extremities the oxygen it needs and that blood flows being blogs so that's how our signs and symptoms are going to look something that would be related to ischemia so arterial ulcers tend to be located on the ends of the toes the top of the feet are the dorsum of the feet in the lateral malleolus region so the lateral ankle region which is the outside part of your ankle and how these ulcers appear they tend to have very little drainage and very little tissue granulation where you have healing of new tissue and that's because there's compromised blood flow going to that ulcer in that extremity so it can't really drain and it can't really heal so they tend to be pale and very lot pink or they can even be in severe cases necrotic or black and how they look they tend to be very deep and they have this punched-out appearance where it literally looks like someone just took like maybe their thumb and just punched out that area which gives it this noticeable wound edge and margin that gives it a round appearance and here's an example of an arterial ulcer notice it's located on that lateral malleolus ankle area it literally looks like someone maybe took their thumb and just punched out that area it's nice and and the womb bed is Pell doesn't have a lot of drainage and the skin surrounding it is really dry and scaly now let's compare that to a venous ulcer also called a venous stasis ulcer with venous ulcers you have an issue with the venous system so those veins are either damaged or the valves of the veins are ever stretched and they can't help drain the blood back to the heart so you get blood pulling being stagnant typically in those lower extremities and this is going to cause problems because you're going to get a lot of swelling so they tend to be located on the medial parts of the lower legs below the knees and the medial malleolus region so the inside of that ankle region compared to arterial that was on the lateral this is the medial and they tend to appear swollen the skin will be tight you'll have a lot of edema and there will be drainage in granulation present and the reason is because we actually have blood flow going to these wounds we don't have an issue with it being perfused we just have an issue with the veins being able to take the blood flow back so that's why compression is really helpful with these venous wounds like a new naboo will help compress that area and get the blood to return and help with healing because they have the zinc oxide in them now the base of the wound will be deep pink and red because again we have the granulation present because we don't have a perfusion perfusion issue and the edges of the wound they will not be nice and round they're gonna be irregular and the depth of the wound tends to be shallow and here is an example of a venous stasis ulcer you can tell by where it's located that medial part of the leg almost to the lateral malleolus area it's definitely uneven there's a lot of swelling look at how tight that skin is they also have that brown pigmentation of the skin which is very common with venous stasis ulcers the wound edges are irregular and look at the base of the wound it's a nice deep red okay so that wraps up this review over arterial ulcers versus venous ulcers
Medical_Surgical_Nursing	Pneumonia_Treatment_Nursing_Interventions_Antibiotics_Medication_NCLEX_Respiratory_Part_2.txt	hey everyone it's Sarah with register nurse rn.com and in this video I'm going to be going over part two of an inlex review over pneumonia what I want to be covering are the nursing interventions and the medications used to treat pneumonia now be sure to watch part one because that builds upon this video I discuss the patho the risk factors the different types and the signs and symptoms of pneumonia and as always over here on the side or in the description below you can access the notes and the quiz that go along with this lecture so let's get started first let's talk about nursing interventions what are you going to do for this patient as the nurse okay first thing you want to do is you want to monitor that respiratory system because with pneumonia our respiratory system is what is having trouble so what you're going to do is you're going to be osculating those lung sounds typically with pneumonia we learned this in part one you could expect to hear maybe some coarse crackles or wheezing also known as wron ey or bronchial breast sounds which are normal breast sounds if heard in the tracheal area but if H in the peripheral lung Fields this could represent lung consolidation so you want to be listening to that you want to see if they're improving or if they're getting worse another thing is you want to monitor those bottle signs how is that respiratory rate are they tpen um what's that oxygen saturation is it less than 95% or 90 where do we want them also you want to not only look at that but you want to see how their skin color is are they CTIC one thing that um if a patient is not getting good oxygen supply the first thing that you will notice I have seen it many times as a nurse is where they start to turn blue is in their lips the pink color of their lips all of a sudden you'll start seeing the lips start turn lightly purple purple and then they'll start to turn blue and then you give them more oxygen and then they'll turn a nice rosy red R color again so assess those lips and especially the skin to see if they're getting enough oxygen because that's a Telltale sign also monitor their arterial blood gas results Physicians will order this it'll come up in your computer you need to report if anything is getting too abnormal are they retaining way too much carbon dioxide and they're super hypoxic where they have low oxygen in the blood they may need to be placed on bypass or mechanical ventilation so you always want to look at their arterial blood gases and compare it with the previous ones that they had also your job if ordered is to collect a sputum culture a lot of times if a patient's admitted with pneumonia there will be an order set that says collect sputum culture and um you'll give them something to cough and spit their sput them in you'll send it off so they can see what is causing this pneumonia also as the nurse you'll be watching the respiratory system but you'll need to assess when they need suction a lot of times times you may have to do it naso tracheally go in through the nose down through the trachea and um suction them especially if um all of a sudden there's just so much mucus so much going on they can't breathe and you need to go in there and get it out really fast so they can breathe and um assess their need for Respiratory breathing treatments a lot of places have respiratory therapists that will administer those but as the nurse it's your responsibility to um make sure if the patient needs one that you call them if the breathing treatment is ordered as needed a lot of times with patients with pneumonia they will be scheduled so the respiratory therapist will be on the floor routinely giving your patient whatever the doctor's ordered a lot of times what will be ordered is like Bronco dilators sometimes chest percussion therapy may be ordered but respiratory therapy will do that for you and another thing you want to do is educating educating the patient about the following incentive spirometer usage I did a whole inlex review on incentiv perometer you can access it in a card above if you want to watch how to use an incen perometer and what to expect what kind of test questions you may be tested on with an is but with an incus prometer this helps the patient um deep breathe and um what will hopefully happen it'll pop open those sacks get that air moving get that mucus out so we can help them get better they'll want to use that 10 times every 1 to two hours while wake another thing is that they want you want to keep them hydrated um they'll be running a fever so that causes dehydration and respiratory Alone um causes a person to lose about 300 to 400 milliliters of water per day and this will help keep the secretions thin because if they come de become dehydrated those mucus that mucus will become thick and hard to cough and get up however ever patients with contraindications like heart failure renal failure you would not want to give them this much fluid so you need it's based on per patient what's going on with him so always assess that another thing is if you have a patient who's immobile you want to um make sure you're turning them frequently to keep secretions moving and have their head of the bed up at least 30° especially why eating because um there risk for a aspiration aspirating their GI contents or food that they're eating into the lungs which can cause pneumonia in itself but make the pneumonia a lot worse another thing big thing is make sure that they are aware and they are up to date with their vaccines they're getting the annual flu shot because as we learned in part one viruses can cause pneumonia a lot of times a patient will have the flu um it's hurt their immune system it's made them more susceptible to the germs in the environment and they developed pneumonia also for patients who are 65 or older or from 19 to 64 with risk factors like they live in a long-term care facility they have um issues where they're more susceptible catching pneumonia there's a vaccine called pneumax where they can get that every five years to help prevent from some forms of pneumonia so let them know that also for your patients who smoke um help them um figure out ways to quit smoking because this increases the chances of reoccurring pneumonia um also educate them about avoiding sick people and especially during um Peak seasons of flu going out and crowds will increase their chances and the importance of hand hyene always washing the hands using hand sanitizer while they're out in the public especially before they eat and another thing we will be doing as the nurse is administering medications whatever the doctor ordered um this typically includes antipyretics keep the fever down flu IV fluids to keep them hydrated um if it's a viral cause they will not be ordered antibiotics because antibiotics are for bacterial forms of pneumonia but you may be giving antivirals like Tamiflu or something like that now let me talk more in depth about the antibiotics that are used to treat pneumonia the categories of the category of drugs there are various antibiotics that are used to treat pneumonia and the drug use depends on the type of bacteria that is causing the infection if the patient can tolerate it or if they're allergic to it or something like that so here are the drug categories that are typically used to treat various cases of bacterial pneumonia and to help you remember those I have developed this pneumonic to help you remember them and each letter the beginning of the word correlates with its drug category so remember various medications frequently treat pneumonia C okay the first one is vom myosin this isn't a drug category it's the name of a drug specifically and it's the only one out of these um but vom myosin is used to treat severe cases because it's one of the antibiotics left that can treat resistant bacteria however um it's rare but this drug can cause what's called ODOT toxicity where it can cause hearing loss so monitor your patients listen to your patients if your patient starts complaining of I'm hearing this loud ringing in my ears all of a sudden or roaring or something like that it could be um the beginning of hearing loss caused by this medication so remember that inlex purposes nursing lectures that's a big one that always stands out okay next drug the M for micro Lids some drugs included in this are like zpack Zithromax this is a narrow spectrum antibiotic and and it treats mainly gram positive and it's used in patients who have a penisin penicillin allergy so if they're allergic to penicillin chances are they'll be prescribed this medication another drug use are called are called tetracyclin and a popular one um is called doxic cyclin and this is a broad a broad spectrum antibiotic treats both gram positive and gram negative has a broader range however um this is not for pregnant patients because it can cause um fetal retardation of growth can discolor teeth and it's not for children less than eight because of discoloration of teeth also it can increase the your patient chances of getting a sunburn outside it makes the skin very photosensitive so educate them about that also educate your patients who are taking birth control ask them if they're on doxcycline they're young or um within childbearing age ask them if they're on birth control because this can decrease the effect of of birth control and they need to use another method to prevent pregnancy also when taking this medication do not take milk products or anti acids while taking the medication because it can ab affect the absorption of the tetracycline antibiotic okay another one is called fluoroquinolones Popular one use is called Levaquin this is a broadspectrum antibiotic as well treats both gram positive and gram negative it is used um to treat severe infections just like the fom myosin and um especially those resistant forms however this drug has a lot of black box warnings from the FDA on it because it can cause some really nasty side effects so watch the following um any type of infections like SEI this is a gastrointestinal infection where um pretty much this antibiotic has just killed every um your normal flora of your gut and has allowed clostridium bacteria Titan Bay the patient um will have profuse diara frequent frequent um episodes of it and it will have a horrific smell so if your patient starts having that may want to let the physician know so they can send it off for a sample if they're taking this medication because it could be what has caused it another thing that has been um seen with this drug is tendon rupture of the tendons say a patient's been taking this all of a sudden their tendon ruptures happen and young healthy people there on this drug has been linked to that and QT interval prolonged as well another drug category called sephos sporin um some drugs that fall into this are like klex or rosin um there's different generations of sephos sporin you have uh one and two three and four generations three and four tend to be broadspectrum where they target gram positive and gram negative compared to the first and second Generations um however if a patient is allergic to penicillin and um they may be allergic to seos sporns as well there's been a relationship between that so monitor your patient if they are prescribed this and the physician wants to prescribe this to them all even though they may be allergic to penicillin you want to watch that because they may be allergic to this as well and the last drug is penicillin um popular ones penicillin G this is a narrow Spectrum drug so your only narrow spectrums out of this is your microids and your penicillin and the early generations of your seos sporin and then everything else third fourth generations and everything else would be broad spectrum and you want to monitor them if they're if they say they're allergic to sethos sporin probably won't be prescribed like with the sepor p penicilin they may go ahead and prescribe them like a microid just in case but sometimes they'll still prescribe it because they don't know if it's a true penicillin allergy so watch that and um this also decreases the effectiveness of birth control so um make sure you assess if your patient is on birth control medicine so that is part two of pneumonia specifically the nursing interventions and medications be sure to watch part watch part one and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	MeteredDose_Inhaler_MDI_Demonstration_Without_Spacer_Nursing_Open_Closed_Mouth_Technique.txt	hey everyone its era thread sterner sorry and calm and in this video I'm gonna demonstrate for you how to use a metered dose inhaler using both the open mouth and closed mouth technique so what is a metered dose inhaler this is an inhaler used to deliver a set amount of medication into the patient's lung and the medications include like bronchodilators like albuterol a brand name for that is like ventolin or pro air along with corticosteroids such as fluticasone which is known as flovent and patients who have respiratory diseases like asthma COPD may be prescribed these inhalers now these inhalers can also be used and be ordered as a combination where there's one inhaler but there's two different types of drugs in them like symbicort which would contain a bronchodilator and a corticosteroids so you want to keep that in mind and always look at what your patients going to be taking another thing is is that you want to teach the patient proper technique when using these inhalers because if they don't use them correctly what will happen is that not a lot of the medication will get down into their lungs it'll just stay in their mouth and that is a big issue with some of these medications like corticosteroids so whenever you are teaching the patient how to use an inhaler try to get a spacer this is what it looks like and it attaches onto the inhaler and they inhale through that which I will be demonstrating in the next video how to use but if and then hey if a spacer is not available you can use the open or closed now technique and always go by whatever the physician has prescribed for the patient while the patients will tell you what they've been using and you need to make sure that they're doing it right now why would you want to use a spacer well the spacer is going to be easier to use than that open mouth the closed mouth technique because whenever you're using this inhaler with those techniques you have to simultaneously press the inhaler down and inhale at the same time which takes a lot of practice so if you have a really young patient or a patient who's older who has issues with holding the inhaler that can be troublesome also then hailer in the chamber is going to allow this in a sense lead time for them to inhale the inhaler substance so they don't have to press it down simultaneously and it's going to decrease the amount of medication that's going to be left in the mouth which with corticosteroids we don't want that because it can cause mouth irritation like thrush so what we're going to do first is we're going to perform hand hygiene and we're going to perform the patient's five rites we're going to make sure that we have the right patient the right drug the right dose we're doing that at the right time and the right rap and you always want to look at what you're giving because whenever you're doing these inhalers or some things you want to keep in mind okay say you were going to be giving a bronchodilator inhaler and a corticosteroid inhaler so you have two inhalers it's very important you know which one you need to give first the first one you want to give is the bronchodilator because it's going to open up those lungs and die like that then you need to wait five minutes and then administer the corticosteroid because then the corticosteroid can get in there and do it straw by decreasing the inflammation now say you were giving two puffs of a bronchodilator and that was it or two puffs of the corticosteroids and that was if you would first do a puff of the bronchodilator and say they need another Ronco dilator puff you would wait one minute and then give the other ones so if you're giving the same medication just two different doses you're gonna wait one minute but if you were going to give a bronchodilator then a corticosteroid you would wait five minutes because we need five minutes for the bronchodilator to do its job and then another thing you need to remember is that after the patient uses then hailer after doing a corticosteroid they need to rinse they need to gargle and rinse their mouth with water and then spit that water out because the corticosteroid whenever he comes into contact with those mucous membranes and the mouth it can cause thrush so it's very important you get your patient to do that next what you want to do is you want to prime then hailer so you're going to prime the inhaler if it's the first time you're ever using that if the patient hasn't use it in a week or more has dropped it or recently cleaned it so before you do that just make sure that your inhaler is in de it's not expired so to do that what you're going to do is you're just going to gently pop this canister off and it will tell you the expiration date this is 2020 so we're in date and the dose that we're using in this inhaler the reason here is a demo dose it's a teaching dose that doesn't like contain medication also never administer medications to a patient if you don't have proper credentials or if you've not been trained and always follow your Hospital protocols so another thing whenever you're going to go priming you want to check expiration date but you also want to make sure that there's enough doses in this inhaler because they only contain so many puffs so a lot of inhalers have a counter on them and it'll tell you how many's last like 2010 however many so look there to make sure you have enough and if it doesn't say it like this one doesn't the box will tell you how many sprays are in each inhaler and this one has 200 sprays so you'll need to pay attention to how many sprays the patient's doing a day and calculate that out for instance say that the patient is doing two puffs twice a day so how many puffs is admin today four and there's only 200 puffs in this box how many days is this inhaler going to last if they do it every day just 50 days so you want to keep track of that now two problem inhaler what we're going to do is we're going to remove the cap and then just hold with your thumb at the bottom and your two fingers at the top and gently give it a shake and depending on the manufacturer is how many sprays you're gonna spray to prime it because each and hailers difference always read the instructions with this one it's four so what we're going to do is just do four sprays now that our inhaler is prime let me demonstrate for you the open mouth technique I'm going to tell you about it and then I will show you how to do it or so what you're gonna do is you're gonna have your patient set up and you're gonna have them hold the inhaler in between their thumb and their two fingers and give it a good shake for about eight to ten seconds just to mix up that medication and really good then they're going to measure out two fingers with between their mouth and then hailer and make sure that inhaler is pointed at their mouth and what they want to do is they want to breathe in and then breathe out through their mouth until they no longer can and then after that simultaneously they want to hit the inhaler down and breathe in slowly through the mouth of the stuff that's coming out of the inhaler and then they'll want to hold their breath for 10 to 12 seconds and breathe out slowly if they need another puff of that same medication they can do it in one minute so let me show you how to do that then after that retype the inhaler and if it was a corticosteroid be sure to gargle and rinse the mouth with water and spit and perform hand hygiene and document now let me demonstrate the closed mouth technique so what you want to do is hold inhaler in between the thumb and the fingers and give it a good shake for about eight to ten seconds to get the medication mix well and you'll have the patient take a breath in and then out through their mouth until they can no longer exhale and then put the mouthpiece of the inhaler in between the tea keeping the tongue flat on the lips sealed around it and they will simultaneously hit then hellar button and breathe in until they no longer can breathe in and then hold it for about ten seconds and then exhale slowly and that will look something like this and after that recap inhaler and again if they were using a corticosteroid have the patient gargle and rinse the mouth and spit with water and perform hand hygiene and document and if they needed to use the same medication again how when would they do it they would do it in a minute but if they were going to be using say this was a bronchodilator and they needed to use the corticosteroid how long would they wait five minutes okay so that wraps up this video on how to use a metered dose inhaler using the open and closed mouth technique thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Incentive_Spirometry_Spirometer_NCLEX_Review_for_Nursing_with_Demonstration.txt	hey everyone it's Sarah register nurse rn.com and in this video I want to do a quick inlex review over the incentive spirometer and as always over here on the side or in the down in the description below you can access the resources that goes along with this video so let's get started first let's talk about the learning objectives of what I want you to learn from this lecture I want you to learn what an incos prometer is how to use it so you can educate your patient which I'm going to do a demonstration and walk you step by step on how to do that and then at the end I'm going to go over an inlex style question of what you could expect to be asked in your nursing lecture exam or on the inlex about an Inc spherometer so first let's talk about the definition of what an Inc spirometer is also known as an is the definition is that it's a device that encourages slow long deep breaths to help pop open the avioli Sachs which helps move secretions and keeps the sacks working because the biggest problem with a lot of patients who need to use an incin spirometer is that these Sachs have become deflated which we'll go over the cause here in a second so we want to prevent that or help treat that to help get those Sachs improving their function so it's used with helping with the prevention or if a patient's experience experiencing this with a condition called acasis and a lot of patients who are going for surgery or after surgery especially like thoracic or chest or abdominal we want to encourage them to use this device it's a little device that seems like it wouldn't have a significance to it but it really does and it really works another reason um we would use this device is to help patients with breathing disorders such as COPD because this helps increase their lung function had a lot of patent Pat who have severe COPD but and they regularly use their incin prometer every day and they report that they have they can breathe better and they can tolerate more activities compared to whenever they're not using their incentive spherometer regularly also if a patient has pneumonia one of the first things I would like to do whenever my patient has pneumonia is get them in Sim spirometer and educate them how to use that because what's going on with pneumonia you have nasty PFF infection going on in these aviol sacs and the bronchioles and we want to help move that out keep that lung function going and pop those open so the Big Goal with this incentive spirometer is to inflate get those aviol sacks working back and to keep that patient regularly deep breathing now let's talk about lung anatomy and specifically what is happening in the lungs whenever a patient is experiencing AC lecis because this is one of the main reasons we want to educate a patient to use inim spirometer so what happens is whenever you're breathing you have air that you've breathed in go down through your trachea down through your broncus into your right and left broni which branch off into that and then you have your bronchials and then it flows down into your avolar sacs and this in those sacks is where the gas exchange occurs and these Sachs are constantly infl fting and deflating as the air flows in and flows out but what can happen as you see with this little avolar Sac he's pitiful he is collapsed what's happened is that in these bronchioles some fluid or a mucus plug or maybe a tumor can get in there and the air as you see with the blue arrow is trying to flow into there and it can't it's stopped by that blockage so that sack becomes deflated now what you want it to look like is this nice and inflated the air exchange is just passing through really nicely now acusis the definition is that you have a lung or part of it part of it has collapsed and those AOL AR sacs are unable to inflate and deflate and perform the gas exchange and again like I said earlier this is very common after surgery especially after abdominal or th thorax surgery so as the nurse we want to educate our patients before they're going for surgery cuz they are at risk for this now let's talk about your role as a nurse with an incentive spherometer okay big role is that we're going to educate our patient how to use it and stress to them the importance because a lot of times patients see this little device and they're like what in the world is that going to do for me but like I said at the beginning it's it looks insignificant but is a very important device so we need to educate them how to use it also monitoring we need to monitor the lung sounds and make sure we're having Improvement for instance if you're educating your patient how to use this device for pneumonia monitor those breath sounds like at the beginning of the shift they sounded really bad but you encourage them to use in Sim perometer throughout the day and was their Improvement do those lungs sound better next observe the patient meeting their goal and make sure they're using it right um because a lot of times whenever patients want to use this device they either want to use it really fast which I'll demonstrate for you or they just want to blow into it and they use it incorrectly and they're not getting the full usage out of it so it's important You observe that they're using it right and that they're meeting the goal that the physician has ordered for it to be and how are goals figured out because as you can see on the inim perometer we'll go over the layout of it there's little areas that are measured in milliliters of how much the patient should pull whenever they're sucking in and it's based on a patient's height and their age so just for comparison for instance a a male patient who's 5'8 who's age 30 should pull about 3,150 milliliters compared to a female who's the same height the same age will pull about 2900 so it varies based on patients age and their hype now let's let me demonstrate for you how to use an incentive spirometer and go over an inlex question with you okay here we have a basic incentive spirometer every hospital is different on what they carry but generally this is the most popular and it will come in a little plastic bag and it'll come with the mouthpiece with the flexible tubing and the device and what you want to do as a nurse is you want to connect your mouthpiece tubing to the port of where it plugs in so you'll just push that on there like so and um let's go over the parts of it here you have the mouthpiece and it moves it's flexible and you have right here this little yellow marker and this is where you set how much what the patient's goal should be should they do about 2,000 um 1,500 wherever they go this will just help the patient know hey this is my goal where I need to get then you have the yellow pist and this thing will osculate up and down as the patient breathes in and breathes out and you have your hand rail where the patient will hold it while they are breathing in and you could put this this is just a bed rail holder where you could put it on the bed if you wanted to and then over here is another very important part you have a face that is frowning a happy face and then another face that's frowning then you have in the middle this yellow indicator and whenever the patient breathes in they don't want to breathe in too fast or too slow just perfect and this will um go up and just stay right in there as the patient breathes and this is how where the patient wants to stay to get the best um usage out of this and then on the back some have this some don't there's a little oxygen Port if your patients on um oxygen you can plug it in here so they can get it while they're breathing now let me demonstrate how to use this okay first let's go over some wrong ways to use in sinometer a lot of times if patients haven't been educated properly they will do what they think you're supposed to do naturally with it by blowing into the device rather than actually inhaling from the device another wrong way patients may try to use in Sim prometer is by quickly inhaling and exhaling off the device like this now let's look at the right way to use in s perometer okay first what what you want to do is you want to set the goal for the patient with the yellow marker so they know where they need to get whenever using this incentiv spomer then you're going to have the patient set up and exhale completely then have them seal their mouth around the mouth piece tightly and they will inhale slowly and deeply making sure to keep the yellow indicator on the side within normal range they don't want that little yellow piece to go too high or too low and as they do this the Piston will rise up and have the patient keep inhaling as deep as possible until they can't inhale anymore and then they'll need to hold their breath for 6 seconds and then exhale slowly and allow the Piston to fall before repeating again and record the amount that they were able to get on thenc perometer and they will perform this at least 10 times every hour or two while awake so this is what it looks like in action okay here's a typical inlex question you may see on exam the inlex about inin spirometer a lot of these questions like to ask you about patient teaching or um How You observe the patient using it and are they doing it correctly so let's look at this question you're providing preop teaching to a patient who will be having abdominal surgery after discussing with the patient how to use an incentive spherometer you ask the patient to demonstrate how to use the device what action by by the patient demonstrates the patient understood your teaching a the patient inhales quickly and rapidly B the patient inhales and then exhales into the mouthpiece C the patient inhales slowly until they're unable any longer and holds breath for 6 seconds and then exhales or D the patient slowly inhales and exhales multiple times and then hold holds breath for 2 seconds so whenever you're looking at this question you got to say okay how do you properly use an incentive spirometer and delete from there so let's look at option A A the patient inhales quickly and rapidly no we can mark this off because whenever you're using an Inus prometer as you just seen you do it slowly over time you don't do it quickly B the patient inhales and then exhales into the mouthpiece no the patient inhales into the mouthpiece but does not exhale into the mouthpiece so that is wrong okay C the patient inhales slowly until they're unable any longer and holds breath for 6 seconds and then exhales and this is right C is our answer because as you've seen with the demonstration you have the patient do it until they can no longer do it anymore because they're inhaling they're putting all that pressure on those avolar sacs and then after they hold their breath for 6 seconds and then exhale now let's look and see why D is wrong D the patient slowly inhales and exhales multiple times and then holds breath for two seconds no this is wrong because the patient is isn't going to inhale exhale inhale exhale and then hold breath and anywayss they hold it for 6 seconds instead of two so our answer is C okay that's a review over the incentive spomer now be sure to go and check out my other videos in this lung series for the inlex revieww and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Renal_NCLEX_Review_Question_on_Acute_Kidney_Injury_Stages.txt	hey everyone is stares Westerners are n.com and in this video I want to be going over a weekly NCLEX question and don't forget to check out our other free resources to help you study for in clicks so let's get started a 36 year old male patient is diagnosed with acute kidney injury the patient's 24 hour urine output is four and a half liters faithfulness stage at Aki what complications and assessment findings may present in this patient select all that apply a water intoxication be hypotension C low urine specific gravity D hypokalemia e GS are greater than 90 milliliters per minute f normal B you in and creatinine levels or G profound confusion due to a 30 Nia so from our scenario we know that our patient has acute kidney injury Aki also known as acute renal failure and one thing that should be jumping out at you in the scenario is that patients 24-hour urinary output which is four and a half liters so now you should be thinking to questions like what is the normal urinary output and what are their stages of acute kidney injury okay so a normal urinary output is one to two liters per day that's what a normal adult should be putting out now those stages let's go over that because if we can determine what stage this patient is in whenever we're going over these signs and symptoms and findings we'll know if this is the correct answer okay so for stages you have the first stage which is the initiation stage and this is where there have been a cause of injury to the kidney remem remember from a renal series we talked about pre renal causes intra renal causes and post renal causes to win signs and symptoms appear so when the signs and symptoms appear there in another stage and they can either go through the awkward or the diaeresis stage not all patients go from an issue Alaric they may skip all glory can go straight to diuresis so you really always want to be watching that urinary output so we know they're not in the initiation stage okay the auger is what is that well one of the best ways to determine if they're in there in this stage or diuresis for recovery is to ask yourself what is their urinary output well it's for enough leaders and what does the urinary output be in the augering stage it should be less than four hundred milliliters per day so less than 400 milliliters per day now our patient is having four and a half so we can write them out of being in this stage but let's review this page because if we see signs and symptoms that should be going in the augur aquino we can eliminate those from over here so we'll put a little bit about dollar on blurred stage okay their urinary output is very minimal and why is that well that Blom aerialist that part of the nephron that filters the blood is damaged and it's not filtering the way it should so the familiar filtration rate that GFR is going to be severely decreased and a normal GFR if greater than ninety milliliters per minute so that is the amount of blood that wall Meireles is filtering so it's not filtering the blood like it should so all the wastes all the water all those electrolytes are staying and accumulating in the blood and not being excreted through the kidneys to be voided out so GFR is going to be decreased what's going to happen to our waist level specifically that'd be you and in creatinine they're just going to stay in the blood because our goal memory list isn't filtering it so they're going to dramatically increase and when we get that what's going to happen patients want to have acidotic conditions they're going to get confused and they're going to have issues like that so we're gonna have a confuse patient who's not filtering a lot of blood because they're not filtering a lot of blood what's going to happen to that water in the blood it's just going to stay there it's not going to be filtered through the kidneys so you're going to get fluid volume overload which can lead to hypertension edema swelling which can lead to pulmonary problems like pulmonary edema and heart failure things like that so fluid volume is going to be increased and we're going to have high / tension okay electrolytes electrolytes going to be all out of whack and specifically we're looking at the potassium levels what's going to happen to this we're going to have high firk Alenia because glomerulus isn't filtering that potassium out we're also going to have hyper false potamia which is going to decrease our calcium level hypokalemia and we're going to have high magnesium levels called hypermagnesemia so we're going to be dealing with a lot of high electrolyte except for the calcium now how is our urine specific gravity going to be is already I'm going to be really concentrated or is it going to be diluted well it's going to be very concentrated so the urine specific gravity is going to be high and whenever you do see the urine put out by these patients that they put any out very dark colored and very concentrated looking okay now let's go to the diaeresis stage what is the urine area out there going to be in the diaeresis stage okay to help me remember this always think of giving patients diuretics whenever you get patients i redick's what do they do they your na a lot so this is what happens in this stage they're putting out a lot of urine and remember one a few liters is the normal amount and these patients who are in this stage can fit out anywhere from three to six liters per day so I think it's confident to say our patient is probably in the diaeresis stage because they're putting out a lot of urine now let's talk about the diaeresis stage okay what is going on well this is where Al Gore mare Ulis is starting to function again so where GFR is going to start improving it's going to start increasing but it's going to be I'm normal still so remember a normal one was greater than 90 milliliters per minute so it's increasing but it's still not there so our kidneys have got that ability to filter the blood again so it's going to start removing a lot of waste from the blood specifically urea and creatinine but it doesn't have the ability yet to concentrate the urine so we're not going to get electrolyte balances yet so what's going to start happening two or bú in in creatinine they're going to start coming down but they're still going to be on normal but they're going to come down now because I go Mary Liz is starting to filter again it's removing specifically a lot of your reality that blood into that filtrate now this is going to cause osmotic diuresis because that high amount of urea is going to cause water to pull from the blood into the kidneys and that is where you're going to see this high amount of urine being lost so they're peeing a lot what's going to happen to their fluid volume they're urinating it up it's going to decrease so they're going to get hypose tension now what's going to happen to our electrolyte levels well we can concentrate our urine yes and we're putting out a lot of fluids well one thing that's going to happen is our potassium levels going to drop so they're at risk for hypokalemia and what's not happening to their urine specific gravity so you're going to be really concentrated or is going to be diluted let me really diluted so it's going to be low because of all that water being pulled from the body into the nephron okay so we're getting somewhere we have a lot of our combinations and our signs and symptoms now why are they not in recovery cuz some people may think they're into the recovery stage well the recovery stage is when the urinary output is normal they have recovered and everything's back to normal so the GFR is going to be normal which is going to allow us to maintain or be you in and creatinine level which will be normal our fluid volume status should be normal and our electrolytes will be normal and you'll be able to maintain itself here this patient isn't maintaining because they're at four and a half liters or voiding Matt within a 24-hour period so they're in the diaeresis age now let's start eliminating our option okay a water intoxication are they going to have this no if anything they're going to be fluid volume depleted they're not going to be water intoxicated so this is not one of our answers so they're going to have hypotension yes because remember their depleted fluid volume they're urinating all their fluid in their blood out so they can have hypotension so B is an answer C low urinary specific gravity yes it's going to be low because that urine is really diluted it's not concentrated like how it was here inaugural stage hypokalemia yes because they are urinating all that fluid out in one of those main electrolytes that can be in trouble whenever a patient is urinating a lot is potassium that's why whenever we give like loop diuretics like lasix we're always watching those potassium levels because it's getting wasted so yes hypokalemia are they going to have a GFR greater than ninety milliliters per minute no member of their GFR is increasing but it's still going to be on normal they've got the ability to filter the blood but it's not going to be normal yet that would be in the recovery stage if they make it they're depending on the degree of damage that was done to the kidney so that's not one of our answers are they going to have a normal B you in and creatinine no they won't that's in the recovery stage but the bu and creatinine will start decreasing but it won't be and it won't be normal yet and G profound confusion due to a co a vo t Mia that is that buildup of those waste products in the blood and actually in the diaeresis stage because I'd be you in sorry because the glomerulus is starting to filter again they're actually you're going to see them become more alert and oriented compared to the alert stage where they're really going to have that confusion so no that is not an answer so our answer is B C and D okay so that wraps up this weekly inquest practice question and don't forget to check out the other questions in this series thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	How_to_Interpret_Heart_Rhythms_on_EKG_Strips_How_to_tell_the_difference_between_Afib_Aflutter.txt	hey everyone it's sarah with registered nurse RN comm and today i'm going to go over EKG rhythms specifically atrial fibrillation and a flutter many people have a hard time differentiating between those two rhythms along with normal sinus rhythm so today i'm going to go over the differences between the rhythms show you on the board what each rhythm looks like what you need to look for the p-waves the are waves and give you five easy steps on how to analyze these rhythms here in a second I'm going to go over those five steps and these five steps are steps that you need to use whenever you analyze any type of rhythm so it can help you differentiate between other types of rhythms such as v-fib v-tach sinus tach and every other type of rhythm that's out there but first before you watch this video if you're relatively new to analyzing EKGs or you need a refresher please check out my other videos on how to analyze the PQRS and how to count the ventricular and atrial rate because it will help give you a foundation and before you watch this video so you won't be that confused and also another important thing after you watch this video be sure to go to our website registered nurse Orion calm and take the quiz on testing your ability to analyze these atrial dysrhythmias so let's get started so the first thing we're going to do is go over those five steps okay the first step whenever you're looking at a rhythm you'll want to look to see if there's any P waves present remember this is the atrial contraction of the heart and if there are P waves how many P waves are there in a six second strip now I was talking to you about the other video on how to count your atrial rate in six seconds and what you do is you count the little boxes that are on your EKG strip and you count until you hit 30 and however many appeared in the 30 in between those 30 boxes you take that and multiply that by 10 and then you have your atrial rate next are the P waves regular this is where you want to use your calipers and if you don't have calipers you can use a piece of paper and you'll measure out to see if each atrial contraction which is your p-waves is regular next number three are your are waves regular this is part of the QRS complex where you have the spike and you want to measure out with either your calipers or a piece of paper if the are waves are regular for how many our waves are in six seconds you're going to do this the same way that you calculated your P waves and next number five if you do have P waves what is the length of your PR interval this is very important whenever you are looking for a heart block and the width of your QRS complex this is where you would count the little squares in between the spike and it tells you how wide or narrow your QRS complex is this is very important because in tachycardias your complex tends to be narrow but in v-tach your complex used it tends to be wide so that helps you analyze those rhythms so now let's go over what a normal rhythm looks like and compare it with atrial fibrillation and atrial flutter right here you have normal sinus rhythm now we're going to apply those five rules or five steps to analyzing this rhythm and this is what you normally get with normal sinus rhythms okay first we're going to look to see if there's P waves present and remember either from the video that you watch on the PQRS wave where I explained it or you just know your P waves present before your QRS complexes and right here in green you can see our P waves so yes we do have P waves now next step is to count how many P waves are present if within six seconds and remember you want to count these itty-bitty squares thirty of them and in between however many thirty are is what your atrial rate is and here our atrial rate is 70 beats per minute we got seven of these p-waves and we times that by 10 and we got 70 so our atrial rate is 70 beats per minute I remember a normal rate is 60 to 100 okay next we're going to see our p-waves regular are they happening at exactly the same time here you can use calipers but right here I'm going to use a piece of paper and how you do that is you get your piece of paper and you mark where the p-wave began which is right here and then you mark where the other p-wave started okay so we have an estimate where it is now we're going to compare the other ones together and we just move our piece of paper and see they're presenting exactly where I marked it so it looks like our p-waves are definitely regular okay next we're going to ask ourselves are our our waves regular this is memory have Q R st so we're looking at our waves these are the tops which are the spikes and we're going to see if these are regular using the same method that we did with the P waves I'm going to mark on our piece of paper and compare them and they are definitely regular so yes and next we're going to count how many of these are waves are in normal sinus are in this rhythm and we have 7 1 2 3 4 5 6 7 so our ventricular rate is 70 beats per minute and we just want to make sure that we don't have a heart block going on or anything so we would count from the beginning because we want to look at our PR interval at the beginning of the P way to the beginning of the QRS and our interval is less than 0.1 2 seconds which is normal I mean it's 0.12 and you want your interval between 0.12 to 0.20 seconds so that's a normal PR again a normal PR interval is zero point one two to zero point two zero seconds and then QRS complex it's very narrow and it's definitely less than 0.1 two seconds okay let's go over our next rhythm atrial fib okay now since we cover normal sinus rhythm which is a normal rhythm most of us are in let's cover atrial fibrillation and atrial flutter but first let's talk about what's going on in the heart whenever you're having these two rhythms what's happening whenever these atrial dysrhythmias are happening is that the foci in the heart are sending various multiple signals to the atrium which is causing them to quiver and when they quiver blood is just pulling in there and it's not shooting through the valves to get through the heart so whenever blood is pulling that is not good that means that a thrombi or a thrombus could be forming and that really puts your patient at risk for strokes and a pulmonary embolism anything like that so whenever this is happening especially at a fast rate we have to get it under control so let's go over atrial fibrillation now using the five steps that we went over we're going to look at this rhythm and whenever you look at this rhythm all you can see majorly are your QRS is and your T waves and in between that you see these little squiggly lines some people may interpret those as P waves those are not P waves they're called fiblet or e waves which are called F waves so those are that now you can't count your pick if you don't have P waves you can't count your P waves so the next step would be how many P waves are there there's none so you'd put unable to determine now number two or second step is are the P waves regular again we don't have any P waves account so that would be unable determine step three our waves now we do have our waves but have you do you notice anything different these are waves are different looking than our other ones a normal sinus rhythm so we want to see if they're regular again you'll want to use your calipers or a piece of paper like I am here we're going to measure out our waves and what we're going to do is we're going to mark on our paper where the first two are and compare them with the others and look they are not matching up at all so it's very safe to say that our our waves are irregular so in afib we have no P waves we can't count the atrial rate and RR waves are irregular so let's keep going step 4 what is the rate of the our waves we can count those because they are present and we're counting them in the six seconds and remember the six seconds you count 30 square small squares and you multiply that about 10 and here we have 80 but because it varies I don't know if you've ever been in a clinical setting and you've seen a patient in atrial fib but you'll notice that their heart rate is constantly fluctuating one minute it'll be 80 next minute will be 86 the next minute and it might be 90 then go back down to 80s it's always fluctuating so here the rates in the 80s and then next you would count your PR interval but we can't count our PR interval because we don't have any P waves but we can count our QRS complex and it's definitely less than 0.1 - it's very narrow so that is the hallmark with the afib so let's go over those again with afib you're not going to have any P waves while you're seeing or F waves okay no P waves and you want can't be able to count the atrial rate and your R waves will be irregular because you have various times that those atrium are quivering and then you have the P Q the QRS wave contracting and you're seeing those are waves so they will be irregular now let's move on to a flutter because there is a big difference between a fib and a flutter and you'll be able to see on this diagram okay for a flutter right here you probably already noticed something different in between your T waves and your PQRS is you have what's called sawtooth appearance of an F wave these are actually very beautiful to see on a real patient who's in a flutter and most of the time your patients will be in afib but there are occasions where you'll see patients in atrial flutter and it's very noticeable and the reason it is is because you have these sawtooth appearances of the F waves now in a theme you do not have the sawtooth appearance of these so that is a huge thing that you will have so let's go through our five steps step number five are there any P waves no there's no P waves only F waves so we can't count the atrial rate step two we want to look at our our waves and we do have our waves and are they regular and we're going to measure them out and typically in a flutter you're our waves will be regular there are some times where they're not regular but here they are definitely regular so they measure right next you'll want to count your ventricular rate and to do that you'll count your are waves and we have one two three four five six seven this is a little bit longer than a six second strip but the rate is 70s and with a flutter it will typically say the same because you don't have the fluctuation like you do in a fib because your are waves are regular here in a flutter so it's the 70s 71 72 and next you would try to count your PR interval but you can't hear because you don't have any P waves and your QRS complex is narrow it's zero point it's less than zero point one two so that's normal so again your atrial flutter will have the sawtooth appearance but it will not have any P waves and your R waves will typically be regular so let's go over real fast again the difference between atrial fib and a flatter a fib you will have no P waves and your R waves will typically be irregular okay in a flutter you will have the sawtooth appearance of your f waves and there will be no P waves and your our waves will be regular so now let's test your knowledge and take a quick quiz a quiz question 1 let's analyze and see what this rhythm is ok using the easy 5 steps let's start ok is there any P waves there are no P waves I just see some T waves and QRS so no P waves question 2 are the P waves regular we don't happy way so we don't know set 5 are waves we do have our waves and are they regular so using either the piece of paper or your calipers let's measure out our ways and see if they're regular and let's see they are definitely not regular so no are our waves are not regular so we know we have no P waves and are our waves are unregulated are in 6 seconds let's count them we look like we have a rate of probably 140 to 150 s so pretty fast that is our rate for our waves and what is the length of our PR interval that's last step we don't have any P waves so we can't count that and the width of our QRS complex is less they're pretty narrow so it's less than 1 point 2 so the hallmark according to what we just learned this is atrial fibrillation it wouldn't be a flutter because we don't have the sawtooth appearance like we did in the other one and it's definitely not normal sinus rhythm because we do not have P waves in this rhythm and our waves are irregular so let's go to the next rhythm okay our second question we have this rhythm here now using our five steps we're going to see are there any P waves no P waves are there and we can't count the atrial rate because there's no P wave so we'll move to step three which are are the are waves regular and we'll measure them out to see if they are and they are most definitely regular so we know that we have no P waves and are our waves are regular how many are waves do we have in six seconds we'll count them out two three four seven we have seven and six seconds and remember the strip was a little longer than six seconds and we can't count the length of our PR interval and the width of our complex is less than one is about 0.12 seconds so we know that we have this sawtooth appearance for our F ways we know that there's no P waves and our our waves are regular so we know that this is atrial flutter now let's move to our next one okay our next rhythm is this let's start with our five steps are there any P waves yes finally we have P waves okay what let's count and see how many P we have in six seconds one two three so we have seven so 7 times 10 is 70 so we have an atrial rate of 70 next let's see if our P waves are regular you're going to use your calipers are a piece of paper and our P waves are definitely regular next we're going to see how our our waves look are they regular as well I'm going to mark those out our our our waves are regular so yes so we have P waves we have an atrial rate of 70 we have our waves and let's count our ventricular rate 1 2 3 4 5 6 7 7 times 10 is 70 so we have a ventricular rate of 70 and the length of our PR interval looks like it's about 0.12 seconds we're measuring from the P wave to the beginning of the QRS to see how long it is you want to do that to make sure you don't have a heart block and the width of our QRS complex is normal at 0.12 as well so here this meets all the signs of normal sinus rhythm so that is our answer to that now to our very last one okay we have this last rhythm as our very last question now let's analyze in it use the the five-step rules first we're gonna look for P waves do we have any P waves all I see our QRS is some T waves and just these little squiggly lines known as F wave so no P waves so since we don't have P waves we can't count the atrial rate and we can't see if they're regular so next we're going to move on to our our waves and we definitely have our waves and let's see if they are regular and it definitely looks like that our our waves are not regular so we have no P waves and our our waves are unregulated in tricular rate using the six second rule it's about the 80s so we have a ventricular rate of 80s and we're going to see if we can't counter PR interval because we don't have a P way and our QRS complex is normal so it's about 0.12 seconds so we know from what we've learned that this must be atrial fibrillation because we don't have any sawtooth appearances and we have no P waves and RR waves or not regular so that is answer to that one so that's the difference between atrial fib and atrial flutter and I hope you found this useful and be sure to go to our website registered nurse RN comm to take that quiz on how well you can differentiate between those rhythms yourself and be sure to check out our other teaching tutorials and subscribe to our youtube channel thank you so much for watching
Medical_Surgical_Nursing	Digoxin_Nursing_Pharmacology_NCLEX_Cardiac_Glycosides.txt	hey everyone it's sarah thread sterner sorry and calm and today we're gonna talk about digoxin and this video is part of an in clicks review series over pharmacology and as always after you watch this YouTube video you can access the free quiz that will test you on this medication so let's get started when studying these drugs for exams or even administering them to a patient you always want to make sure that you are familiar with the drug so to help yourself do that anytime you come across a drug name you want to ask yourself the following five questions number one what's the name of the drug specifically that family name what drug category does this drug fall into because that's going to tell you a lot about how that drug works next you want to ask yourself what is this drug used for and that's going to tell you why you're giving this medication to the patient they have some type of condition that the physician feels like the patient would benefit from this drug then you want to ask yourself what are your responsibilities as a nurse when dealing with this drug what are you watching for monitoring for then you want to ask yourself what are those side effects the common side effects that may be seen with this drug and then lastly you want to ask yourself those education pieces that you need to provide to that patient so if they do go home on this drug they will know how to take it properly so to help us remember all those questions let's remember the word nurse because whenever we're administering medications we have to think as a nurse so first let's talk about the name so we're dealing with the drug digoxin and this drug is part of the cardiac glycoside family and these drugs help the heart pump more efficiently by inhibiting the normal function of the sodium and potassium pump now this pump is found on the cell membrane of our cells that make up our muscle fibers and muscle fibers play a huge role in how strong your heart is able to contract so if we alter that pump we're going to alter the contractility of this heart muscle now another thing the dachshund does is it alters how fast or how slow your heart beat so it's going to alter the rate and it can alter how fast these impulses are sent through the electrical conduction system of the heart now there's three things I just described are the inner trophic Crona trophic and drama trophic actions of the heart and digoxin either effects that in a positive or negative way so let's talk about how it affects the heart and you want to remember these actions because tests love to ask about that when referring to digoxin so digoxin causes a positive inotropic effect on the heart and what this means is that it causes the heart to squeeze or contract harder so it increases cardiac contractility which in the end is going to increase stroke volume another thing it does is it has a negative chrono trophic effect on the heart which causes the heart to be at a slower rate it also causes a negative drama trophic effect which is going to cause impulses to be sent slower through the AV node now when we take all these actions and combine them together what's the result for our patient's heart the heart is gonna squeeze more blood out so more blood is going to leave the heart so whenever we're doing that we're increasing stroke volume and stroke volume is the mail of blood that is leaving this ventricle with each beat and when we increase that we're going to increase cardiac output we want good cardiac output because if we don't have a high enough cardiac output your organs aren't being perfused and the patient can die and remember cardiac output is calculated by taking the heart rate times the stroke volume and stroke volume one of the big things that affect stroke volume was contractility and digoxin increases contractility so we will get increased cardiac output now let's talk about what it's used for digoxin is used to treat heart failure cardiogenic shock or dysrhythmias like atrial fibrillation or a flutter and why we would want to throw on digoxin in some of these patients is because with these conditions there's issues with the heart pumping and emptying correctly either like with heart failure or cardiogenic shock there's failure of this heart as a pump those muscle fibers aren't contracting like a lot of times in my cardio infarction happens these cells die that play a role in how our heart contracts so the heart just doesn't pump very well or the electrical conduction system like an afib a flutter is just discharging impulses way too fast and it's altering how the heart is able to empty now let's talk about responsibilities what's our responsibility as the nurse well we did we really want to monitor for toxicity because patients can become toxic with this drug so what are those early signs and symptoms that hey your patient may be experiencing digoxin toxicity well they're going to be GI related like nausea vomiting and erection they can also report vision changes so if your patient reports like double vision blurred vision or especially that the color of their vision like they're seen yellowish greenish halos in their vision that is a warning sign and it can also cause cause dis arrhythmias which tends to be a little bit later now digoxin has a therapeutic range that you need to remember so commit this to memory that's another one of those lovely test questions the range is 0.5 to 2 nanograms per milliliter anything greater than 2 is considered toxic so let's say you have a scenario and the didge level is high what are you going to do what's your nursing action you're gonna hold the dose notify the MD now what is the antidote for digoxin what can reverse it it's easy to remember it's called digibind now what can cause digoxin toxicity well electrolyte imbalances can and this is another part that you definitely want to remember a big electrolyte imbalance that can cause ditch toxicity is a low potassium level called hypokalemia and this is where that level drops less than 3.5 now whatever a patient for a cardiac reason especially like heart failure or something like that where fluid is backing up in the heart going to the lung causing a lot of edema the patient may also be on a diuretic to help remove that extra fluid so if a patient is on a diuretic you have to watch those ones that wastes potassium through the urine we're talking about like loop diuretics specifically like furosemide lasix that's a popular one because it can lower the potassium level if they're on digoxin as well they're at risk for having a low potassium level so you want to monitor that very closely other electrolyte imbalances is like a low magnesium level with hypomagnesemia and this is a level less than 1.5 or a high calcium level hypercalcemia and this is where that level gets higher than 10.2 now which patients are at most risk for digoxin toxicity because they have altered liver and renal function usually it's decrease well our elderly population because these systems aren't working as great as they should and this is where this drug is really removed from the body we have to watch them on digoxin another big takeaway about the responsibilities of a nurse is whenever we're administering this medication we want to measure the apical pulse if you don't know how to do that I have a whole video on how to do that and you're gonna do this for one full minute and you will hold the dose of didge if it is less than sixty beats per minute in an adult less than 70 beats per minute in a child or less than 90 to 110 beats in an infant next is side-effects what other side effects came this patient have with this drug they can have fatigue diarrhea or thrombocytopenia and then the last part of our questions was education pieces what are we going to teach this patient who's going to be taking digoxin well of course we want to teach them how to recognize those signs and symptoms of toxicity and especially those early signs and symptoms that were related to the GI system the nausea the vomiting and anorexia also that they need to keep their appointments for when they need drug levels drawn or we're going to monitor their electrolytes or their liver or renal function and just let the patient know that they're really important to keep so we can make sure they're not getting digoxin toxicity and if they are on drugs that are wasting the potassium like those diuretics the importance of consuming foods that are rich in potassium which would be like potatoes port tomatoes oranges avocado spinach bananas things like that to keep that level high because remember hypokalemia can cause digoxin toxicity and how to measure their pulse how to count their heart rate before they take their drug every time and when to call the doctor if their pulse rate is too low and talked to them about those parameters that we went over with this drug okay so that wraps up this review over digoxin thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Coronary_Artery_Disease_CAD_Anatomy_Nursing_Heart_Disease_Pathophysiology_Treatment_Part_1.txt	hey everyone it's sarah with registerednessrn.com and in this video i'm going to be going over coronary artery disease this will be part one of this video now this video is part of an nclex review series over the cardiovascular system so if you're studying this be sure to check out my other videos that are part of this series and a playlist should be popping up so you can access all those videos so what i'm going to do in this video like i said it's part one i'm going to be covering the definition of cad i'm going to be covering the patho the signs and symptoms the risk factors and how it is diagnosed and then in part two i'm going to cover the nursing interventions and the medications used to treat this disease so be sure you check out part two after you watch this video now after this lecture be sure to go to my website registernursern.com and take the free nclex review quiz that will test you on coronary artery disease and a card should be popping up so you can access that quiz so let's get started first let's start out talking about what is coronary artery disease well in a nutshell this is what it is um it's where your coronary arteries that deliver a constant blood supply to your heart muscle these arteries that set on top of the heart because your heart in order for those that muscle to work properly it has to have a constant fresh nice oxygenated blood going to it it starts to develop these fatty plaques which will cause blockages or restrict blood flow to the heart and these fatty plaques are caused by a condition called atherosclerosis and this occurs in the artery wall and it happens over time and like i said it limits the blood supply to the heart muscle and it can if it gets so bad it can eventually stop blood from flowing to certain parts of your heart and cause your heart tissue muscle to die as these plaques what is dangerous about these plaques can not only grow mess up blood flow but it can also they can also rupture there's certain blacks more vulnerable than others and they can rupture their contents form a thrombus and we go into myocardial infarction also atherosclerosis can lead to um hypertension because again atherosclerosis really means a lot of people determine hardening of the arteries so people can have high blood pressure get chest pain myocardial infarction and heart failure now let's look at the anatomy of the heart i want to cover the main arteries that feed your heart muscle there's a lot of different arteries that these branch off into but i want to go over the main ones and then i want to go over the pathophysiology with you of how this actually happens in the artery okay here we have an anterior view of the heart and you have the aorta which branches off into your left coronary artery and your right coronary artery now remember from our heart blood flow videos and everything we learned that the aorta has been supplied with rich oxygenated blood from the lungs it just went got pumped through the heart got oxygenated now it's going to go through the body and replenish the body so let's talk about the left coronary arteries first okay your left coronary artery comes out of your aorta out of your aorta goes to the left side because remember this is the left side of the heart this is the right side of the heart and it branches off into some other arteries now you can't we can't see the left coronary artery here because it's going to be on the other side of the heart the posterior view so that's why it's outlined a little bit differently but then it branches off into the left circumflex artery remember circum means around so this artery actually comes around the heart and it provides blood to the left atrium and to the side and the back of the left ventricle so knowing where your ventricles and atrium set in the heart really help you to know what these arteries are feeding so again it feeds the left atrium because remember your left atrium is up here and the side and the back of your left ventricle and then go down through here we branch off into the led which is the left anterior descending artery and this provides blood to the front and the bottom of the left ventricle and the front of the septum then we come over here to our right coronary artery and comes from the aorta and it branches off into the right marginal artery and this supplies blood to the branches of the right ventricle and then you have the posterior descending artery and all these arteries the main job of the right coronary artery is to provide blood to your right atrium your right ventricle and to the bottom of the left ventricle in the back of the septum now let me cover what's called collateral circulation because this is really neat what happens okay a lot of times whenever a person has chronic ischemia chronic blockage the body the heart will actually try to reroute circulation around that blockage so it can get blood to that heart muscle so let me demonstrate this okay say that we have a blockage right here okay what's happening we're not getting any blood flow at all here and the body's like oh no we've got to fix this so what happens is it starts to develop these little tiny blood vessels that will just like branch off and we'll go around that blockage over to the other side so it can somehow get blood flow there so that is what is called collateral circulation so if you ever hear that that's what it is it's just the rerouting with tiny blood vessels to go around that blockage so they can get some blood supply to that heart tissue now let's look at the pathophysiology of how this actually develops now there are certain risk factors that will increase a patient's chance of developing coronary artery disease like smoking a family history of it diabetes things like that high cholesterol so um more other patients are more susceptible to this so this is how it starts out first you have a nice healthy artery and normally going through your artery is blood and in that blood you have red blood cells and you have what's called ldl which is low density lipoprotein which is your bad cholesterol and you also have hdl which is your high density lipoprotein but what happens is that over time say patient has one of those risk factors there's damage to that artery the ldl starts to stick to that artery wall and it starts to grow over time and as it grows notice that it is limiting the blood flow that would normally go to the heart this one's nice and open this one's narrowing so the patient a lot of times it's asymptomatic doesn't have symptoms but as they start doing activity they notice that they become really short of breath and they're starting to get some chest pain but when they rest then the chest pain goes away and what's happening is that whenever you're doing activity your heart rate's increasing you're increasing that workload on the heart that blood flow is really being limited that's going there but when you rest relax straightens it out and they get relieved of chest pain but what can happen and then that's stable angina so whenever they're having chest pain on activity but it goes away stable angina they really need to go to the physician let them look at that out look at that and run some tests which we'll go over those tests a little bit later but what can happen to these fatty plaques is that they can rupture some plaques are more more vulnerable than others and what happens right here as you can see this plaque has ruptured it's spilled its contents into the blood the artery wall is messed up and the body's like oh no the artery wall is messed up we've got to do something about this so he thinks it's going to help but in reality it's going to cause more problems so right now the patient um starts to form a thrombus your body sends all those nice clotting things to your artery wall to repair it and as that thrombus gets bigger and bigger and grows it's going to completely stop blood flow and your patient's going to enter into acute coronary syndrome and they're going to have some unstable angina where their chest is literally it's completely unrelieved by rest it's severe it's hurting nitroglycerin's not helping and and the blood flow is going to stop as that thrombus right here completely blocks it you're going to get a myocardial infarction where your heart muscle is going to die or become damaged and so that is how that develops over time with the pathophysiology and how it grows now let's look at the risk factors what increases a patient's chance of having atherosclerosis of the arteries one thing is smoking smoking causes a lot of vasoconstriction damages those arteries increases the chances of those plaques forming being obese or overweight having a high cholesterol level having a sedentary lifestyle diabetes or family history so if you're given a test question and it throws out all these patients with these certain histories pay attention and look for these certain signs and symptoms especially if you're doing a medical health history and they tell you all these things because that increases their chances of developing this okay how do these patients usually present what are their signs and symptoms like i said earlier typically in the early stages of coronary artery disease they're going to be asymptomatic until that plaque starts growing more and more and they may notice that they have some chest pain with activity it's like a heaviness on their chest and it may they may have some shortness of breath with this and have fatigue but it will go away whenever they rest this is considered stable angina and it is not a medical emergency but it needs to be evaluated so if a patient's having this they need to go to the doctor tell them so their doctor can order some tests to help diagnose this now it may progress to unstable angina this is where the chest pain is not relieved with rest it's more intense they may take some nitroglycerin doesn't work and this is a medical emergency needs to be treated immediately see what's going on also the patient may just feel tired feeling run down okay how is this diagnosed what do physicians normally order because as the nurse you need to know what's ordered how to educate your patients things like that so number one a lot of times this is usually routine for everyone getting a checkup is a blood test they will look at your lipoprotein file a protein profile and what this is going to look at is going to look at your ldl remember that's your bad fats your hdl that's your good fats your total cholesterol levels and your triglycerides and if these are high they will educate you about managing your diet cutting out some fatty foods and if that doesn't work putting you on some medications which we'll cover in the next video the statins help decrease that cholesterol level another thing is they'll probably order an ekg very simple to do hook them up to that and they will look um at your qrs pqrs rhythm and what they're looking for is problems with st segment or your t waves and this can tell them a lot it can show if a heart attack's in progress if you're having chest pain right now let's look let's see what's going on with your st segment and see if you've had a previous heart attack if there's been injury to that heart or if you're having some compromised blood flow going on another thing they may order along with this i put this under the ekg category is they may order a 24-hour or a 48-hour halter monitor and this is where the patient wears a heart monitor that will monitor their heart rhythm for that amount of time and the patient needs to usually keep a log whenever they're having chest pain so when the physician goes back to read the 24 hour or 48 hour holster monitor they can see if there was any changes in their ekg rhythm whenever they're having that maybe stable angina to see if there was some compromise blood flow so let's go over some normal little st segments and let me just give you an idea of what it looks like now whenever you are looking at a 12 lead ekg there's a lot of different areas you're going to look at to see if there's st depression or st elevation and here i just want to go over the basics i'll be making a video in the future that will go in depth in this but let's just look what a normal one looks like with and then what one looks like with depression and elevation okay a normal um pqrs complex you have the p wave your qrs complex nice st segment with your t wave normal looks great then you come over here and you notice your p wave your qrs complex and then you have this depression right here notice here straight no depression it's going underneath because whenever you're looking at your ekg you have an isoelectric line and what you're looking at is you're measuring how many millimeters this is actually dipping below that isoelectric line and usually two milliliter two millimeters is um something that's very suspicious as a nurse working in the stress lab i have seen this and it's very an interesting phenomenon we'll do a stress test a patient may be exercising on the treadmill and all of a sudden they get chest pain and we'll be watching that ekg and the st segment will start dipping and their chest pain will be getting more severe we'll get them off the treadmill medially give them some nitroglycerin and as that chest pain is being relieved that blood flow is going back because they're not getting blood flow it's causing ischemia so you're seeing that st depression but once we give them the nitroglycerin they rest this starts to return to baseline at the isoelectric line and that tells us hey we got a blockage going on we got some ischemia right now it's reversible we can fix it um but we've got to do something so they'll probably go for a heart cath or something like that to see what's going on but then on the other hand you can have st elevation have seen this as well and what happens as you can tell it completely looks very funny it can vary on how much elevation you have but here your st segment is completely elevated and what has happened is that there has been injury to the muscle of the heart and it's irreversible and we need to um right here with depression we can hopefully go in fix it find that blockage but here it's a little bit too late there's been some damage done so those are the differences between the depression and the elevation another thing that may be ordered is a stress test and this is where the patient will go to a stress lab they will either exercise on a treadmill or have it done chemically if they can't and what will happen is that their ekg will be monitored while that heart has stress on it because remember with stable angina it's aggravated with exercise or stress because you're increasing that workload on the heart so if there is a blockage that is significantly um compromising the blood flow to the heart you will see some ekg changes like s t segment depression now sometimes a nuclear stress test can be ordered with this this is where instead of just exercising on the treadmill looking for ekg changes the patient will do this as well or get the chemical but a tracer will be injected during that activity which will allow the patient to take pictures of the heart with a special machine to look to see how that blood flow is actually flowing to that heart muscle during activity is there some areas that isn't aren't getting good enough blood flow compared to other areas and a lot of times what happens in the hospital setting is that the patient will come in with stable angina they're not really sure what it is but some things look suspicious so they'll have this stress test and stress test does not show the imaging looks very suspicious there could possibly be a blockage then they will go for a heart cath which is another thing that is diagnosed so typically they want to do the most non-invasive route first and then progress but if they're having unstable angina that medical emergency they're going to go bypass the stress test and they're going to go straight for a heart cath a heart cath catheterization is where a catheter is inserted either into the femoral or radial artery they're starting to use the radial artery instead of femoral because complications are a little less risk return recovery times a little bit better or the patient whenever they go radial and a dye is injected into those coronary arteries and they inject the dye in there they take x-ray imaging and they're looking for those blockages to see where it where it's at and what they can do about it now whenever they have this procedure they're breathing on their own they're given moderate sedation now if the doctor finds anything cardiologists is who's doing this if they find anything they will do what's called pci percutaneous coronary intervention sometimes people call it angioplasty and they will do they can do a couple things one of the most popular things that they do is um a balloon angioplasty and this is where they inflate a balloon and that clogged artery they see the clogged from the imaging from the x-ray where they injected the dye and they take a balloon and they compress that plaque up against that artery wall and then they go in and place a stent to keep that artery open so now that artery that wasn't getting any blood flow all of a sudden is opened up and it's getting blood flow a lot of times after patients have this in order to keep that scent from getting clotted they will have to be on plavix and things like that and which i'll be going over in part two talking about the medication so be sure to check that out another thing they may do instead of that is a arthrectomy which is where they go in and they remove plaque from that artery now sometimes these arteries are blocked so bad that they can't put a stint in them and if that's so that a surgeon will have to be consulted and they will do a coronary artery bypass grafts sometimes i have seen where the patient went for a heart cath it was so bad whenever they got in there and looked at the heart cath that they immediately just took them to the or and the patient had open heart surgery and opened that up because it was worse than they thought so that is how coronary artery disease and how it works and what it is so be sure to go to my website registerednessaurian.com and take the free quiz and collect quiz that will test you on this material and be sure to check out part two which will include the nursing interventions and the medications for this disease management and thank you so much for watching and please consider subscribing to my youtube channel
Medical_Surgical_Nursing	Anaphylactic_Shock_Anaphylaxis_Treatment_Nursing_Interventions_Symptoms_NCLEX.txt	hey everyone it's sarah thread sterner sorry and calm in this video we're gonna continue our series on shock by talking about anaphylactic shock and after you watch this youtube video don't forget to take the free quiz that will test you on this condition so let's get started anaphylactic shock occurs when there's an introduction of an allergen in the body and this introduction leads the mast cells or basophils to release massive amounts of histamine and other substances system-wide now histamine plays a huge role in anaphylactic shock and it causes all these particular signs and symptoms on the body that leads to a decrease in tissue perfusion so we know from all of our other shock videos whenever we have something causing decreased tissue perfusion we have shock so that's why anaphylactic shock is we have this allergen that has triggered this response in the body massive amounts of histamine is being released and we're getting decreased tissue perfusion hints we're having shock now anaphylactic shock is a type of distributive shock which means that the small vessels in the body that deliver all that nutrients specifically oxygen to the cells that make up our tissues and organs are disruptive they're having an issue distributing blood flow and this is really coming back to the effects of all this histamine that's being released some of the things that the current is massive vasodilation so those vessels are widening and blood is not really flowing also you're gonna get increased capillary permeability and this is going to shift fluid out of that intravascular space into the interstitial space and we're gonna have an issue getting blood flow to those cells now how does an allergen actually enter in the body where this whole reaction is going to take place well there's various routes that an allergen can actually enter the body number one they can enter through an injection of some type that we give the patient or inhalation the per inhales their particular allergen that can cause anaphylaxis or they can take it orally where they ingest it with like food or even some medications or the skin it comes into contact with the skin now what are some known substances that actually cause anaphylaxis that can lead to anaphylactic shock well one thing of course is food this can be anything from shellfish peanuts eggs milk or medications like IV contrast eye vaccines insects antibiotics specifically like penicillin or insect venom like bees a lot of people are allergic to bee stings latex can cause it along with physical exercise some people their inner flexes is triggered by exercise and then of course there's cases where we just don't know what the cause of the anaphylaxis is and we refer to that as idiopathic now let's talk about what is occurring in the body Deering and a phylactery shock and to do that we have to talk about the two different types of reactions that a patient can have that can lead them to enter into anaphylactic shock the first type of reaction is called an anaphylactic reaction and this is due to the immune system the immune system sees the allergens so in response to that it creates the antibody IgE so it's IgE related the other type is called anaphylactic reaction and this really isn't related to the immune system the body and this type of reaction isn't creating the antibody IgE so it's not related to it so first let's dissect anaphylactic reaction so it's related to the immune system specifically this IgE that has been created in response to the allergen so in order for this anaphylactic reaction to occur that patient has to undergo sensitization and then once that patient is sensitized to this allergen this reaction can occur so it's known as a type 1 hypersensitivity reaction so let's look at how this reaction happens so we have this allergen that enters the body and whenever it comes into the body it's going to trigger the body to produce IgE antibodies so these I GE antibodies are going to go and attach to the surface of the mast cell or beza fill and they're gonna hang out there for a while so right here whenever this occurs the patient has been sensitized this was their first exposure to the allergen now let's say next week the person is exposed to the same allergen again so they have a subsequent exposure to this allergen now what's gonna happen is that we have these IgE antibodies on this mast cell or basal film well this allergen is going to go and bind with those IgE antibodies and this is gonna trigger this cell to release histamine and other mediators and we're going to get this reaction and here in a moment we're gonna talk in depth about the role of histamine and how it affects the body and anaphylactic shock but some of the things that histamine is going to do it's going to increase capillary permeability and this is going to cause major vasodilation now with anaphylactic reaction it's not related to I GE and so the person doesn't have to be sensitized for the reaction to occur what's going to happen is that you can have various substances that can lead to an anaphylactic reaction they can be like IV contrast I in said or chemotherapy agents they get in there they can attack the membrane of the mast cell or the basal feel cause it to break down and whenever that happens histamine is going to be released so you're going to have like the same type of reaction signs and symptom wise of how you would in the anaphylactic reaction where we have IgE being responsible but the thing with this anaphylactic ide related I think she doesn't have to be sensitized because we don't need the IgE to be present on that self because it's directly going to affect that cell in this in Aflac toyed so it can happen with the very first exposure now let's talk about the signs and the symptoms that are occurring during an Aflac tech shock now as the nurse you want to be able to recognize these little subtle signs and symptoms that you may see in your patient or they may tell you to let you know hey they may be going into anaphylaxis and Aflac tech shock and this will cause you to intervene so we will prevent them from actually entering into severe shock territory where they're going to have decreased tissue perfusion to their cells and organs which could lead to death so to talk about our signs and symptoms first we need to talk about histamine because histamine is what's really causing all of our problems and why you're seeing these signs and symptoms and when we talk about nursing interventions and treatment our interventions and treatments are geared to reversing the effects that this histamine has done to our body so one thing that histamine does that causes us major issues is vasodilation and when you have enough histamine you can vasodilator everything throughout this body and it's going to cause your vessels to widen and whenever vessels widen what does that do to blood pressure it drops it and this is going to decrease the amount of blood that's gonna flow to the cells that make up our tissues and organs it's going to deplete them of oxygen and they're gonna get stressed out and they're going to die because that blood is gonna be pulling and not going where it's supposed to go in addition histamine increases our heart rate so you can see tachycardia it also increases capillary permeability of your vessels so makes your vessels leaky so fluid that's in that interstate and in turn ask you ler space is going to move out and leak into the interstitial space so whenever you have this this will even further drop our blood pressure because we have like no blood volume in the inner vascular space will lead to that it's also going to cause more swelling because the fluid is going to leave the intravascular space and go into the tissue so you can have swelling this can cause issues with our airway we have the swelling up in this area you can also play a role in decreasing our cardiac output because if our fluids leaving our inter vascular space what's really draining back to the heart not a lot so that's gonna decrease cardiac outfits not gonna let have the heart the heart's not gonna have enough blood to pump through the body if we're losing fluid in addition histamine causes itching now another big thing that's dangerous that histamine causes is it causes bronchoconstriction so this is where you have narrowing of your Airways so your patient's not going to be able to breathe they will go into respiratory failure it also affects our GI system which will cause gastric secretions to increase and it increases the contraction of our smooth muscle in our GI system so we can start getting GI related signs and symptoms so whenever you're thinking about these signs and symptoms think about the system because histamine is going to affect the respiratory system cardiac system GI and skin so let's quickly go over these signs and symptoms respiratory we know we're having narrowing of our Airways so what your patient gonna look like they're gonna have difficulty breathing wheezing from where air is trying to flow through those narrow Airways you can hear that swelling in the upper Airways and they can have rapport they feel tightness and their throats hard to swallow they may even have issues speaking to you they'll be coughing also they can have watery eyes stuffy nose the lovely effects of histamine cardiac wise their blood pressure from that massive vasodilation is going to draw up they can have hypo hypotension and they can have increased heart rate from that tachycardia and because of their blood pressure going so low that hypotension they can lose consciousness as well GI system because of the increased secretions increase contraction of that GI smoothness they can have vomiting nausea diarrhea GI pain and the skin we have major vasodilation going on so and kissing me makes you itchy so your skin can be itchy red and swollen now let's wrap up this lecture and let's talk about nursing interventions and treatments for our patient with anaphylactic shock so first of all as a nurse what do you think is one of the most important things we can do to make sure our patient doesn't go into anaphylactic shock well it would be following preventative measures making sure we are always assessing our patients allergies and this is done best on admission asking them what do you allergic to have you ever had an anaphylactic reaction if so what happened during it making sure we're aware of that then we go and we document that put it where it's supposed to go so pharmacy doctors other nurses other people who are part of the healthcare team can know that this patient has these allergies and before you do anything give a patient new medication do any type of procedure that's going to be using something that's one of those known substances that can cause anaphylaxis we make sure that we're reviewing our patients allergies and always avoiding them now sometimes as we learn with anaphylactic reactions those patients don't have to be sensitized to the allergen it can happen with first exposure and with that we want to make sure that we're aware of those little subtle signs and symptoms that we were talking about with what can happen in anaphylactic shock now let's talk about nursing interventions and treatments a little bit deeper so we've established that you want to recognize those signs and symptoms because this can happen in a fact 'ok reaction can happen within seconds two minutes of exposure so to help us remember these nursing interventions and treatments let's remember the phrase act fast because it's a nurse we want to act fast if this occurs because we want to reverse the effects so a would be for allergen and airway if we know or suspect this particular thing is causing a patient's anaphylaxis we want to remove it or if they're started on a new IV antibiotic we want to stop that Medicaid until we can determine what's going on airway remember histamine can cause that bronchoconstriction so we want to make sure we're managing that airway and giving them high flow oxygen you're also going to beacon doing continuous monitoring of their vital signs then c4 call rapid response or initiate any the emergency system wherever you're at you want to get this patient treatment you need help when caring for this patient you can't do it all by yourself so you're gonna start CPR if that is needed until help arrives then t4 Trendelenburg position this position is going to help with what's going on remember we have massive vasodilation we have a drop in blood pressure and the Trendelenburg position is where you lay the patient supine with their legs elevated now you want to be wary of this position if you have a patient who's actively vomiting and if they're having really major airway issues because this could make it worse over there vomiting you may want to lay them on their side so they don't aspirate the emesis so what this position is going to do is it's going to increase the venous return to the heart so that blood return to the heart and increase our cardiac output and blood pressure then f4 first line drug is epinephrine remember epinephrine for anaphylactic shock this drug can be administered I am or sub-q the dose can be repeated if needed also if the patient's just having a really severe reaction with severe hypotension they're in the hospital setting where we can give them IV they may can have this the IV route and what this epinephrine is going to do is it's going to cause vasoconstriction which is what this patient needs so it's going to compress those vessels this is going to help increase blood pressure it's going to reduce that swelling that's occurring and it's also going to cause bronchodilation and we need this because remember those Airways were narrowing next is a for administer per MD order the following drugs now the drugs used for anaphylactic shock it really depends on what's going on with the patient how severe every this is but you want to be familiar with what can be given during anaphylactic shock and one thing of course is IV fluids because what happened with all this hissing well it caused our vessels leak so fluid left that intravascular space went to the interstitial tissue and we need fluid back in there so fluids can be ordered this will help replace that compartment and increase our blood pressure another thing is albuterol like a nebulizer a respiratory treatment and this will help dilate those Airways because we had bronchoconstriction so if that patient has persistent breathing issues albuterol can be given another thing is antihistamines and this is great because we have a histamine problem so these antihistamines are gonna reverse the effects of histamine and we're talking about like h1 or h2 blockers h1 would be diphenhydramine which is benadryl that can be given or an h2 blocker would be Redentor ranitidine which would be like zantac you can give that and reverse the effects another drug is like corticosteroids this would be given to prevent a recurrent attack later on it's not going to give you like immediate treatment so remember what was that first line drug epinephrine that's really the big one that we want to remember with that then s4 stay and monitor the patient if you have a patient who's went into anaphylactic shock they appear that they have recovered and you want to watch them very closely because they are at risk for what's called a biphasic anaphylaxis and this is where the in a factor reaction will occur again even if they're not exposed to that allergen so this can happen hours after the initial attack and the signs and symptoms that they may get during this attack may be less worse or the same so that's why we tell people who have been at home they've had anaphylactic reaction they've had to use their EpiPen that they need to get treatment immediately because they're at risk for developing another attack and lastly tea for teach as a nurse we play a vital role in helping our patients understand what anaphylaxis is what anaphylactic shock is and how to avoid it in the future so what are some things we can teach our patient to help them with this so one thing would be of course is the importance of avoiding this particular allergen and that they may need allergy tests to determine if they're allergic to anything else also the importance of wearing medical alert bracelets in case they pass out where someone could see hey this person is allergic to this so maybe having anaphylaxis we need to call help and to make everyone aware that will be providing care to them of their allergen especially with your pediatric patients if they have like a peanut allergy the parent needs to know that the teachers the school any caregivers need to know of this child's allergy in addition you want to educate the patient about always carrying an EpiPen no matter what activity you're doing always carry it with you have easy access to it in regards to epi pens you want to make sure that the patient's aware that they do expire that they need to replace them when they're expired and they need to know how to prepare and administer the injection patient doesn't need to learn how to inject the medication when an anaphylactic reaction is happening so epi pens come in trainer devices and you can use a trainer device to teach your patient and have them demonstrate how to use this so some highlights of how to administer this epinephrine can be injected through the clothes if needed with this EpiPen and when they inject they need to hold it in place for three seconds so that medication can drip into that muscle fully and then they remove it and after injection they'll want to massage the injection site for at least ten seconds what's this going to do it's going to increase the absorption then they want to call 911 and get care okay so that wraps up this lecture over anaphylactic shock thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Myocardial_Infarction_Heart_Attack_MI_Nursing_Management_Interventions_Medications_NCLEX_Part_2.txt	hey everyone it's Sarah with register nurse rn.com and in this video I'm going to be going over part two of myocardial infarction in this video I'm going to be covering the nursing interventions and the medications given in this condition now be sure to watch part one because that video builds upon this video where I cover the patho the anatomy how it's diagnosed reading an EKG and things like that and as always over here on the side or in the description below you can access the quiz the lecture notes and part one and the other videos in the inlex cardiac Series so let's get started first let's talk about nursing interventions what are you going to be doing for this patient as the nurse remember time is muscle we talked about in part one those cells in the heart when they quit receiving blood they die really fast and within 30 minutes it it's irreversible we can't fix them and once they're gone they gone they cannot be replaced so as a nurse we want to make sure we're assessing our patients and we're acting fast okay so we will assess our patients for chest pain a lot of times patients will tell you if they're having chest pain or if they're there for cardiac issues you need to always assess them for chest pain because some patients may not tell you and take steps to evaluate it hospitals have protocols what you do for whenever a patient has chest pain so typically what you're going to do is you're going to start assessing the cardiovascular system you're going to get a 12 lead EKG per Physician's order and your job as the nurse is to get that EKG and to look at it in the previous video that's why I really want you to watch it I talked about how to read these EKGs as a nurse what we need to know to do our job the different areas that reflects in the heart and what you're looking for because you're looking for ST segment elevation or depression you're looking at those t- waves are they hyperacute are they inverted and you're looking for pathological Q waves so watch that video to figure out how to look at those things another thing is you want to put them on continuous bedside monitoring because they are at risk for going into lifethreatening um dysrhythmias like vfib vtac things like that also dis rythmia like atrial arhythmia or AV blocks you want to monitor their blood pressure their heart rate again like for those dysrhythmias place them on oxygen nasal panula as ordered by The Physician it's usually 2 to four lers whatever the physician orders um have a working IV make sure that you have um at least one for sure and if you can get multiple IVs typically um you'll probably you may be starting them on drips and you'll need another IV to give them other IV push medications so make sure you have working IV site monitor the respiratory sounds because as we talked about in the previous video we talked about complication from an MI you want to make sure that they're not having crackles or also called rails which could represent that that we're having some heart failure problems we have some pump failure going on because that heart muscle has died so that blood is backing up into those lungs fluid overload so listen to that strict bed rest I can tell you that is a for sure thing do not let your patients get up who are having chest pain because getting up while having chest pain will increase that chest pain and make it worse a lot of patients want to get up move Pace the floor they're very anxious they're very scared they may need to use the bathroom um you need to get men a urinal or a bedside commode for women because moving around is going to put extra stress on that heart and we don't want to do that uh you're going to collect cardiac enzymes as ordered by The Physician again we talked about those usually that includes troponin levels for sure maybe some ckmb things like that and a big part of our job is that we're going to be administering medications that the doctor has ordered so as a nurse with medications this is what you want to be familiar with whenever we start going over this in the lecture the side effects of the medications how the patient should respond you need to evaluate is the patient responding propriately is this what we want patient education where you going to educate the patient on because a lot of times they'll be going home on these medications to manage this condition how they work on the body and the typical medic medications given for an MI so what medications are used to treat a patient experiencing a myocardial infarction to help you remember this remember this pneumonic to help you remember the categories of drugs acute angina means nasty artery blockages and cardiac complications the first drug category is anti-coagulants this will include anti-thrombotics and anti- platelets first let's talk about anti-thrombotics this will include loow ox and heprin these are one of the most popular ones used in the hospital setting what how did they work they prevent clot formation because remember when we talked in part one about the patho of how these little coronary arteries can become blocked remember um there was rupture of a plaque all those um clotting factors went there to form a thrombus and that actually caused more problems because it blocked the blood spot even more to this heart muscle so this will prevent any further my cardial infarctions from happening so Lenox this is usually given as a subq injection as the nurse because it um decreases formation of clots you got to watch the patient for bleeding you want to assess their gums make sure they don't have any bleeding on gums their stool is it dark and tarer they having a GI bleed um watch their urine is it turning light pink they may have be bleeding in the kidneys or is there a drop in blood pressure and an increase of heart rate you don't see the bleeding actively maybe it's inside the body somewhere but a low blood pressure hypotension and tacac cardi represents that they're bleeding out another drug use is called heprin a lot of times you will be starting to heprin drip or be given a subq injection depending on whatever the physician wants again you'll be monitoring them for bleeding as well but as the nurse it's very important that you are watching their platelet levels a lot of times times um cbcs will be ordered and platelets will be on there and you want to make sure that they're not dropping because the patient has been on heprin for several days you may notice a significant drop in platelets and I have seen this happen so this really really does happen and patients develop this and it's known as Hein induced thrombocytopenia also called hi hip and what will happen is that you will see those platelets drop less than 150,000 typically if this happens will be discontinued and the physician may switch them to argatroban or angiomax those are medications used for patients who have Hein induced thrombocytopenia now whenever a patient is on heprin what's your role you're going to monitor for bleeding of course and you'll be collecting or lab will be collecting FL body will be collecting a PTT this is called a partial thromboplastin time this is um the amount of seconds it's taking for the patient to um form a cla a normal PTT is 25 to 35 seconds however whenever we have them on heon we want to delay that a little bit remember because that's the whole purpose of this is prevent clot formation so depending on whatever facility lab is and a therapeutic heprin PTT is generally 60 to 80 Seconds long the next a part of our pneumonic is antiplatelets antiplatelets work by decreasing platelet aggregation and thrombus formation some popular ones are aspirin and Plavix aspirin how does that work it's usually prescribed in a low dose and it decreases the clot from forming so hence another Mi just in case another plaque ruptured um it would decrease those platelets from aggregating at that s of injury however with this you have to watch out for GI bleeding patients who've had a history of that are definitely at risk for developing again with Aspirin another thing is pavics a lot of patient times this is prescribed if the patient can't take aspirin they can't tolerate it however with this as the nurse remember this they can develop a complication known as thrombotic thrombocytopenia Pera uh we'll call it TTP and this is where clots form in vessels little vessels and decreases the blood flow to the tiny to vital organs so as the nurse you may see decreased platelets the patient may all of a sudden have neuro changes renal failure they may have a fever anemia or bruising so it's very important that you educate the patient that if you notice you start getting really confused you're having fever renal problems you can't pee things like that they need to report that because they could be entering into this another thing another part of education is if the patient is scheduled for a surgical procedure that they need to let their surgeon know that they take platics because it takes a while for the body to clear pavics up to 5 to seven days so it's not something that you can just stop the day before surgery they would have to stop it and be placed on something else okay another part of our pneumonic the M morphine this is prescribed a lot of times in the acute situations when your patients having chest pain a lot of times nitroglycerin you will find is not even relieving their pain Nitro is not working remember that was one of those signs and symptoms that we talked about in part one but the morphine helps this is usually given IV route however watch for hypotension lowering that blood pressure and respiratory depression next in for nitrates this includes nitroglycerin a lot of times this can be given as an ointment a sublingual tablet underneath the tongue Ivy like in a drip or transdermal with a patch and how this works is it baso dilates those coronary arteries and this causes increased blood flow to the hard so if you have some esea going on you give some Nitro you open up those coronary arteries hopefully some blood can get to those myocytes that are being deprived of nutrients however with this you got to monitor their blood pressure this can cause a massive drop in blood pressure um also assess their chest pain if they're on a drip you'll need to titrate the drip based on their chest pain and their Vital Signs watch their EKG and have continuous bedside monitoring while they're on a drip side effects of this medication includes a headache because you have vasod dilation all that blood is just pumping to that head so teach a patient that you'll probably get a headache also you may feel warm or flushing or dizzy next a for ACE inhibitors which stands for Angiotensin converting enzyme Inhibitors and these typically end in p r i l one uses linil and this works by blocking the conversion of angot tensin one to angot two which causes Vaso dilation drops the blood pressure and decreases the workload on the heart however a side effect from this medication is that the patient could develop a dry nagging cough where literally they cough every like five minutes it bothers them and they may not be able to tolerate this also these drugs can increase the potassium level so educate educate your patient about watching how much potassium they take in through their diet and how it does this is because this decre increases aldosterone in the body which causes the body to retain potassium and excrete sodium so that's why you get hyperemia next B for beta blockers some use like Coreg low pressor that's the brand name the generic names end in o l o and they work by decreasing the workload on the heart you will get a slower heart rate and a slower blood pressure lowerer blood pressure as a nurse you want to monitor their heart rate make sure it's staying Within 60 to 100 um what you need to educate your patients especially if they're diabetic these beta blockers can Mass the symptoms of hypoglycemia which includes the tacac cardia hence with beta blockers you're not going to get tacac cardia or the sweating so let your um diabetic patients know that because they need to monitor their blood sugar more closely also with patients with cop or asthma they may not be a candidate for beta blockers because they can cause um bronos spasms problems with that and not to take these beta blockers with grapefruit juice because grapefruit juice decreases the absorption of the beta blocker next a for arbs this stands for Angiotensin receptor blockers also they end in stin s a r t a n um for instance like Lo sartin these are typically used in place of ACE inhibitors if the patient can't tolerate the ACE inhibitors maybe due to that nag and cough they'll be placed on this and it works by blocking Angiotensin too so um you get Vaso dilation however side effects of this is an increased potassium level just like the ACE inhibitors however you don't get the dry nagging cough next for the C for cholesterol lowering medications a lot of times patients have high cholesterol levels that's why they developed a mardial infarction because they got AOS scerotic scerotic and the plaque ruptured so they may be started on a Statin to decrease the ADL level like Lipitor so this works by lowering LDL which is your bad cholesterol uh lowers your lower total cholesterol your triglycerides and helps to increase your HDL which is your good cholesterol um educate the patient that this is not to replace diet and exercise just because they're taking a um cholesterol medication and to notify the doctor if they develop muscle pain cuz stat can um cause muscle issues also as the nurse you'll be monitoring if the doctor orders a CPK level to um monitor if there is muscle damage because this will increase if there is muscle injury due to a Statin causing it also you'll be monitoring Li liver function because this drug works by acting in the liver to decrease cholesterol level level so we want to make sure our liver is functioning good the last uh C part of the pneumonic is calcium channel channel blockers sometimes this is ordered um maybe noras cazum one of the other calcium channel blockers and this works by stopping transport of calcium to the mardial muscle or and smooth muscle so whenever this happens you get Vaso dilation of those coronary arteries that set on the heart that feed it blood supply so as a nurse you want to monitor for H hypotension monitor the heart rate and also educate the patient because you get more blood flow for some reason this drug causes um hyperplasia of the gum so you get enlargement of the gum so they'll want to have good oral hygiene while taking a calcium channel blocker okay so that is part two of my cardial infarction be check be sure to check out part one and don't forget to take the quiz and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Renin_Angiotensin_Aldosterone_System_RAAS_Nursing_Mechanism_for_Blood_Pressure.txt	hey everyone it's a earth register nurse sorry and calm and today we're going to talk about the renin-angiotensin-aldosterone system also called the RAF's system and as always after you get done watching this youtube video you can access a free quiz that will test you on this system so let's get started what does this system do and what is its whole goal well the rath system what it does is it manages our blood pressure specifically when that blood pressure drops so what it's going to do is it's going to kick into gear and it's going to increase the blood pressure by getting a naturally occurring substance on board in the body called angiotensin 2 so that is the whole goal of this system is to get angiotensin ii activated and functioning to help cause major vasoconstriction in the body because when we constrict vessels we increase blood pressure plus angiotensin ii will help increase our blood volume as well which will also increase our pressure so let's go through this system step by step until we get to the end result angiotensin ii now as we study this really let the names of these substances help you out because it's called the renin-angiotensin-aldosterone system and this is really the sequence of how these substances are released so very first thing happens our blood pressure drops the body senses this and says oh no we've got to deal with this so the sympathetic nervous system is stimulated and remember this is our fighter flight system that helps save our life so these nerves stimulate the kidney specifically these cells called juxta glomerular cells also called JG cells and these cells are stimulated and they will release a substance called renin which is the first part of our system so renin enters into circulation now as it's flowing through circulation it's going to do something it's going to activate a substance in the liver called Angie Oh ten Synod jinn and once the substance is activated because of this Wrentham it is going to turn into angiotensin one now remember we need to get to angiotensin 2 so we have angiotensin so we're in the second part of our whole system name and since this angiotensin is in the system and the vessels it is going to really get this ace involved because we need ace ace is going to help us convert angiotensin 1 into angiotensin 2 so ace stands for angiotensin converting enzyme so it's going to convert it for us and this ace is found on the surface of the lung and kidneys in the endothelium so it's going to convert our angiotensin one to angiotensin 2 now we're here we have this awesome active vasoconstrictor agent in our body that's going to help us increase our blood pressure but how does it do that we need to talk about aldosterone right okay so angiotensin 2 it's gonna act on our smooth muscle vessels it's going to constrict our vessels when we constrict vessels that's going to increase systemic vascular resistance and increase our blood pressure to help you visualize it or understand it think about a water hose when we take that water hose and we narrow it what happens to the pressure of the water coming out it's really gonna increase now another way we can increase the water the pressure coming out of that water hose is if we increase the volume of the amount of water coming out of the house so we go to that faucet turn it up that's going to increase the pressure even more so that's what this angiotensin ii is also going to do so it's not only going to constrict our vessels but it's going to help increase blood volume now how does it do this well it stimulates some other things number one our kidneys are going to be stimulated kidneys are going to start conserving sodium and water at those tubular sites within the nephron and it's influenced by also another substance which is produced by the adrenal cortex called aldosterone which is the last part of the name of our system now Dahlstrom what it is they're gonna do it's going to also cause the kidneys to keep sodium in water and it can also lower our potassium level because the kidneys will start to excrete it another gland that's going to be stimulated because of this angiotensin ii is the pituitary gland and it's going to release a substance called ADH antidiuretic hormone also called vasopressin and what this substance does is it causes our kidneys to keep water so we're keeping water even more water we're gonna keep more water and sodium over here and the kidneys are gonna do that so what it's gonna do is it's gonna increase the volume of blood which is going to increase our blood pressure even more so the end result of this wrath system whenever it is working correctly is we are going to increase our blood pressure now in the previous lecture we talked about ACE inhibitors in these medications what do they do they help lower the blood pressure and right here what ACE inhibitors do they prevent this ace the angiotensin converting enzyme from working and so you don't get the conversion of angiotensin 1 to angiotensin 2 so we have lower blood pressure now let's illustrate this and do a quick recap of this wrath system so it will stick in your mind so we have that drop in blood pressure sympathetic nervous system is stimulated which will send nerve impulses to those JG cells in the kidneys which will cause them to release renin into the circulation when written as president of circulation it's going to activate a substance in the liver called angiotensinogen and this will turn into angiotensin 1 now we want angiotensin 1 to turn into that active vaso constrictor so to do that you have to have a switch is angiotensin converting enzyme I remember this was found on the endothelium in the lung and the kidneys so ACE will turn angiotensin 1 in angiotensin ii and angiotensin ii it's gonna have some effects on the body one thing it's going to do is it's going to cause vasoconstriction so constrict those vessels it's gonna cause the kidneys to keep sodium and water which is going to help increase blood volume also you're gonna have aldosterone being produced by that adrenal cortex and that's found on top of the kidneys it's going to help the kidneys also keep sodium and water but remember potassium will be excreted and then we also have the pituitary gland who is going to produce antidiuretic hormone ADH and that's going to cause the body to keep water all together they want to increase blood volume we're constricting vessels and this angiotensin ii is going to help us increase blood pressure okay so that wraps up this review over the renin-angiotensin-aldosterone system thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Cystic_Fibrosis_Nursing_Cystic_Fibrosis_Symptoms_Causes_Treatment_NCLEX_Review.txt	this is cigarettes Turner's Orion dot-com in this video I'm going to be going over cystic fibrosis in this video is part of an Inc Lex review series over pediatric nursing and as always at the end of this youtube video you can access the free quiz that will test you on this condition so let's get started cystic fibrosis is a genetic disorder that causes the extra cream glands in the body not to work correctly and because these glands are not working like they should this leads to major complications in the body and it affects several systems one of those systems it affects is the respiratory system and it affects both the lower and upper respiratory system and what happens is that thick sticky mucus starts blocking the Airways and that's one of the big things that I want you to remember about CF thick sticky mucus because this is where a lot of our issues are arising because of this mucus so what it does is it'll block oxygenation puts the patient more at risk for infections which in the long run these chronic infections over and over damaged the lungs and they have major issues and it can affect the sinuses as well another system affected is the reproductive system a lot of patients with CF will have infertility issues have difficulty conceiving or not conceiving at all in addition it can affect the skin and integra mentary system what's in there we have our sweat glands which is an extra pin gland and what happens is that these glands produce way too much salt so our skin is affected along with our pancreas and our pancreas what's one of the big things it does it produces those pancreatic enzymes that we need to go into our small intestine to help us digest fats and proteins and important things like that so we can have nutrition well guess what that mucus is blocking that duct that allows those pancreatic enzymes to flow down into that duodenum so the person doesn't get that so they have issues and plus their pancreas starts to become damaged over time which can lead to diabetes and our bile duct that help drain or bile starts to be affected with this thick mucus the bile can become thick and gall stones can develop as well so as you're already seen a lot of these systems are being affected it can affect the liver furthermore the intestines can be affected as well patients can have bowel obstructions and one thing you're gonna see in your infants one of the first signs and symptoms that some babies will present with is a meconium ileus where that meconium actually gets stuck in the intestines because of this thick sticky mucus and they're not able to pass it and that's one of the things that tips the physician off hey this child may have CF okay so before we dive into our lecture let's talk about some quick facts about cystic fibrosis okay CF is most common in Caucasians and males however it can occur in any race both male and females but this is who it's most prevalent in and some statistics which are by the NIH the National Institute of Health the life expectancy in the 1960s was age 10 now today it is 37 which is great compared to what it was in 1960 so that's the median life expectancy now it's usually detected in the first year of life so in our pediatric patients and what happens a lot of times they'll present with GI issues the infant like I've talked about the meconium ileus and respiratory issues in severity of CF is not the same in all patients and cystic fibrosis is an autosomal recessive genetic disorder and I would remember that so what this means is that in order for a child to develop cystic fibrosis they have to receive one mutated CF gene from each parent so the mother will give them one mutated CF gene and the father will give them one mutated CF gene and that will leave the child with two mutated CF genes and they will develop cystic fibrosis and have the signs and symptoms and the complications associated with it now the parents if you notice they have one normal and one mutated gene so the parents are carriers they don't have the signs and the symptoms of cystic fibrosis like their child will now let's talk about how CF is diagnosed okay how side nose is through a sweat test and I would remember this test now this test is a painless test and what it does is it measures the amount of salt in the sweat because like I was talking about earlier these sweat glands are producing way too much salt so they will use pilocarpine and an electrical current to help the skin sweat and they usually do this on the arm and have a gauze over the area that's going to be sweating and it will collect the sweat then they'll send it to a lab and they will measure it and here are how results are interpreted okay 39 millimoles per liter or less that's considered negative patient doesn't have cystic fibrosis if it reads 4259 millimoles per liter this means that the test results really aren't conclusive they either need to repeat the test or need further testing and a positive result is 60 million moles per liter or more so patient has this this means they do have cystic fibrosis and have tested positive for it so now let's talk about the pathophysiology of cystic fibrosis because this is going to help us understand those nursing interventions and while we're seeing these certain complications in these patients with CF okay so we already know that cystic fibrosis there's something wrong with those extra cream glands now what are exocrine glands what do they do well they produce and transfer secretions via a duct now that is different than endocrine glands don't get the two confused endocrine glands secrete their substances like hormones directly into that bloodstream the extra cream glands have to go through like a duct or something like that in order to get where it needs to go now what are those secretions and I want you to remember the secretions because this is the whole problem in cystic fibrosis these glands will secrete mucus tears sweat and enzymes ethically pancreatic enzymes and what's happening really in a nutshell is these substances aren't really looking or presenting them the way that they should the sweat it's producing way too much salt in that sweat the mucus it should be thin and slippery and said it's thick and sticky which leads to blocking passageways and providing a great environment for bacteria to live Ian so really pancreatic enzymes and mucus really go hand-in-hand together because the mucus is being blocking that pancreatic duct from delivering those pancreatic enzymes now why aren't these extra cream glands doing what they should well they have a mutated gene that makes them up so this prevents those immigrant glands from doing their job properly of producing the mucus to select the tears and what gene is that the gene is the CFTR gene in this stands for cystic fibrosis transmembrane regulator which is why we call it CFTR and this name is fitting because it really tells us what this gene does ok cystic fibrosis it's related to that transmembrane trans means a cross through so it regulates something going across or through this part of the extra crandall and so CFTR what it normally does when it's not mutated is is that it's a protein that controls the channels of sodium and chloride so in other words it's controlling the sodium and water in and out of that extra cream gland cell now what's happened in CF it's mutated not working so what's happening to her mucus what should it be like normally thin and slippery here it's not because this regulation of the sodium water ain't happening so what's happening is that it's thick and sticky and this is where we're seeing a lot of her problems so let's talk about where we're seeing our problems respiratory system the lungs okay thick sticky mucus is going to block Airways and when you have these Airways walked in here what's happening to this lung tissue those a viola sax they're not working good and what's going to happen is that the patient's going to experience obstructive pulmonary disease such as emphysema and this is going to lead up hyper inflation of the lungs so they're enlarged where they shouldn't be and this can cause air trapping in those alveoli sacs which can lead to blebs rupturing and when one ruptures this can lead to a pneumothorax where half are part of that lung just completely collapses and then we're in big trouble and the patient needs chest tube some type of treatment fast in addition all that strain on the lungs can lead to pulmonary hypertension you can see that a lot of your patients who are older with cystic fibrosis and that pulmonary hypertension is going to put a lot of work load on the heart which in the end can lead to heart failure and you can see Nell clubbing and these patients do to where they struggle with proper oxygenation and bloody sputum you're not going to really see bloody sputum and your infants and your children but in your teens and your young adults who have CF the bloody sputum can be just where they're experiencing severe lung damage or they have an infection present which leads me to infections one huge thing you need to remember as the nurse is that your patient with CF is majorly at risk for infection because that mucus just isn't really good mucus and it's a great place for bacteria to thrive and survive and cause your patient a lot of problems so if you've ever taken care of a patient with cystic fibrosis they have been probably on a lot of antibiotics throughout their life and some common bacteria they can get is like Pseudomonas or Staphylococcus aureus things like that and the trouble is because they have to take antibiotics a lot there is issues with antibiotics becoming resistant to the bacteria and the person having allergies to the particular antibiotics and so the position is limited and what they can prescribe the patient to take to fight these infections and a lot of patients with cystic fibrosis the lung issues and the infections is causes a high mortality rate in these patients now these patients because of the lung issues that they have there are excellent candidates for lung transplants and a lot of patients to get lung transplants and they are a lot better after they have that now that was really talking about her lower part now it also can affect the upper part of the respiratory system the sinuses a lot of patients end up having to have sinus surgery to help with their sinuses they can also develop nasal polyps which can cause stuffiness or snoring it also affects the GI system and it affects several structures within the GI system first we're going to talk about the pancreas now what does our pancreas do again it one of the things it does because it does many things is it produces pancreatic enzymes that are in a sense squirt it into our duodenum which mixes in our small intestines and helps us absorb important substances now what are those pancreatic enzymes I like to remember the word pal because it's a pal to us to aid in digestion and it includes like protease amylase and lipase those are the three that we're not getting in CF they're being blocked by thick mucus in that pancreatic duct that would normally drain those down into the duodenum so these three pancreatic enzymes helps us with digesting vitamins fats and proteins now if they're staying in the pancreas and not coming out where they're supposed to that's going to cause some problems in that pancreas can cause damage and flame it and lead to fibrosis of the pancreas which can alter the body's ability to control blood sugars so the patient can develop cystic fibrosis related diabetes where they will have hyperglycemia they can also have drops in their blood sugar and they'll have to be treated for diabetes because of damage to that pancreas so what you can see in your patients okay well they're not digesting fats they're gonna have weight loss because they're not getting the fat that they need they're also going to have malabsorption which is going to lead to not absorbing those vitamins especially those fat soluble vitamins which are I like to remember at deca vitamin D ek and a they're gonna have to take those as a supplement we're going to be giving them those and you'll learn about that in our nursing interventions also they're going to have issues with low protein because they don't have those enzymes to help with those proteins so they can struggle with that and have some swelling in addition they can have delayed puberty and a lot of these patients are going to have a feeding tube and it's going to help them get that extra nutrition that they need to help them during these times because especially during times of infection when they're sick they don't feel like eating their body demands a lot of calories and protein and that's a really the type of diet that these patients want to be on so a lot of times these patients are going to be prescribed pancreatic enzymes and you want to remember that especially whenever we go over that here in a second in Turner Singh interventions now if your patients on pancreatic enzymes you should they should not have the following whenever they're low on pancreatic enzymes or don't have any at all their stools are going to have a unique look to them they'll be greasy because all that fat is coming out into the stools also have a foul odor abdominal pain and bloating so always be assessing your patients for that because if they are on pancreatic enzymes and they're still having that the physician may want to redress that to make sure they're getting a proper dosage of pancreatic enzymes another structure affected is the liver and the liver plays a role with our bile ducts and what can happen is that the hakeem you kiss can block that bile duct which can cause the bile to become thick and can lead to gall stones in the gallbladder so watch out for that intestines as well are going to be affected we talked about our infants they can develop a meconium ileus and we all know from maternity nor meconium that that first stool that an infant will pass after they are born we're always looking for that we want that to come out well child with CF that meconium gets stuck in the Ilia so they have a meconium ileus also patients can develop di OS which is distal intestinal obstruction syndrome where stool and thick mucus get together and get stuck in the intestine and cause a blockage so a lot of these patients are going to be on line miralax some type of substance to help prevent constipation and keep things moving through there next is the reproductive system and as I said earlier patients with CF have issues conceiving children and why is that well goes back to the thick sticky mucus for women the reason is is because cervical mucus normally plays a huge role in getting pregnant because the cervical mucus will help the sperm travel up to where the eggs act well and a woman who has CF that mucus is thick and sticky not very sperm friendly so the issues with conceiving are a little bit more difficult for males the vas deferens duct which helps deliver that sperm sometimes it's not even developed correctly or it's blocked with mucus which allows that sperm not to get out and fertilize an egg our other system is an intimate tree system and we talked about those sweat glands they were producing too much of block salt so they have very very salty sweat and tears now that can lead to some problems they can have electrolyte imbalances and they can experience dehydration so deary episodes where they're having a lot of sweat or excessively sweaty exercising doing something strenuous they may have to take extra supplements of salt to help with that and that is why that sweat house that we talked about earlier is great at diagnosing cystic fibrosis because it measures the amount of salt and these sweat glands are producing just way too much of it now let's switch gears and let's talk about nursing interventions and treatments for patients with CF okay as a nurse our focus we're focusing on mucus we want to really focus on that mucus in the rest taury system and help them clear that out to prevent any respiratory problems in addition we're focusing on infection how to prevent it how to take their antibiotics monitoring them perfection let them know that you're at risk for it nutrition are they getting enough calories enough protein how do their stools look do they need more pancreatic enzymes how are they doing what are their weights and Gi blockages making sure that they know the importance of taking their miralax and the signs and symptoms of a bowel obstruction things to look for with that so first let's talk about the mucous okay because that is our big thing with the airway being blocked and how we can do that and help the patient clear their airway with this thick sticky mucus is through number one chest physiotherapy which is chest PT which will include postural drainage along with percussion vibration HUS coffee to help expel that thick mucus also using pet devices those positive expert ory pressure devices which we'll talk about here in a moment and using nebulizers routinely and as prescribed and this can include anything from like bronchodilators mucolytics anti-inflammatories even saline sprays and nasal sprays --is to help with the sinuses and things like that and if you've ever taken care of a patient with cystic fibrosis or have a family member who has it this is a huge part of treatment especially this chest physiotherapy the chest PT so let's talk about it what is it okay this is where the Airways are going to be drained of that thick mucus that sticky mucus that's in there and it's going to be coughed up and what they do is they do postural drainage and this is where you get in certain positions different positions to help drain the lobes of the lungs and while they're in these positions they will have percussion where you take your hands cupped hands and you go over those areas of the lung field some patients use the vest that caused vibration to help do that all depends on the patient if you do percussion you want to watch out for those bony prominences like the breastbone the ribs going over the stomach going over where the areas of the kidneys the spine things like that you don't want to cause injury so make sure you watch that so they will have percussion of vibration the drainage the postural drainage and then in between sessions however the physician wants them to do or whatever the patient does they will stop and do Huff coughing which is a special technique where they Huff and then they coughs oh they'll go and then cough and this will help expel that mucus that they're helping drain from the percussion and the postural drainage and they'll spit that out now this is done a lot through the day this takes up a big chunk of the day for a person with cystic fibrosis they do it anywhere from two to four times a day or even more depending on if they're battling some type of respiratory infection whatever is going on with them sessions can last anywhere from 20 minutes to an hour now tests remember this when is it best to perform chest physiotherapy if you're asked this on a test usually it's best you want to do it when their stomachs empty because if we're going on that chest and we're percussing and they have a full stomach what's gonna happen they can possibly regurgitate their food aspirate it have reflux so we don't want to do that so about one to two hours after a meal so in between the meals is when you want to do it not before because the reasoning for that is if you're doing this percussion and they're coughing up their mucus you do your session from where they've coughed up that mucus which can have a bad taste a smell it can decrease their appetite they won't want to eat their food after they've just been coughing up all this mucus so it's good to do it in between those meals another thing that helps with mucus is the pep devices and again that was the pause of expert ory pressure devices and how do these work they work with helping clear the Airways by assisting moving mucus from out of the lungs so what the patient does it's like a handheld device and they breathe in and out on this device and it creates a vibration and some resistance especially whenever they breathe out and this helps up mucus migrate upward and after they do that a few times they huff cough and Huff cough will help them expel that mucus and they will do that to help remove it now some device names are like the flutter valve or a cappella so just to be familiar with those another thing is aerobic exercise what this does is it helps strengthen the lungs and it helps clear secretions but you want to educate the patient to make sure that if they are experiencing a lot of excessive sweating they may be at risk for salt needing salt supplementation's along with watching their calorie intake because naturally a patient with CF needs high calories already so if they're doing strenuous exercise they may need to increase their caloric intake even more and of course they're at risk for infection so during those times when it's flu season or they're just feeling unwell they're having some respiratory issues going on when they're getting when they go out in public or around others they'll want to wear a mask so they won't get those germs also strict hand-washing of course vaccines making sure they're up to date with their flu their pneumococcal and all those other respiratory illnesses that they can get and we have a vaccine for and of course avoiding sick people now let's talk about nutrition interventions because we know that they're at risk for nutrition problems and why is that because those pancreatic enzymes can't get into the small intestine to help them break down their food so they're gonna need some help okay they want to follow a high caloric high protein high fat diet and they're going to want to be taking supplements fat soluble supplements specifically and again what were those fat soluble vitamins dek and a so remember those also they're going to be taking pancreatic enzymes some common ones or pink really pays or pancreatin and these are going to help replace those pancreatic and that should normally have left the pancreas and went to the do team to help the to digest the food now normally they'll swallow these in a capsule but if you have a 2 year old patient they can't swallow these pills so you'll have to open up the pill and sprinkle it in food you'll want to educate the patient's parents and just for yourself you don't want to crush it or the person doesn't want to chew it and you want to mix it in an acidic food like apple sauce no that's something that's alkaline or milk base because once these enzymes hit that alkaline or Milton based product it will inactivate the enzyme so don't give it with like ice cream or pudding or yogurt anything like that because it can mess up the enzyme now test when as a nurse are you gonna give these pancreatic enzymes or you're gonna educate the patient when to take their pancreatic enzymes they will want to take them before all meals and snacks because it will aid in digestion so before next is the GI blockage prevention what interventions are we doing for that ok we want to tell our patient to bring drink plenty of water this guy is going to help keep those mucus secretions as thin as they can be hopefully preventing a blockage also most patients are prescribed by the physician some type of stool softener to take daily popular one is polyethylene glycol which is a long word for the word miralax and they take that and educate them about the importance and why they are having to take and some signs and symptoms of a possible blockage would be not having a bowel movement can't pass stool they can't pass gas and they're having abdominal pain and again that cystic fibrosis diabetes related diabetes they may have diabetes so you want to monitor their blood sugars educate them about signs and symptoms of hypoglycemia to watch out for that and they may need treatment for their diabetes with insulin okay so that wraps up this in klux review over cystic fibrosis thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	PotassiumSparing_Diuretics_Pharmacology_Nursing_Mechanism_of_Action_Review.txt	hey everyone it's sarah thread sterner sorry and.com and today we're going to talk about potassium sparing diuretics and as always whenever you get done watching this youtube video you can access the free quiz that will test you on this medication so let's get started as we've been going over these medications in this pharmacology series we have been remembering the word nurse because this allows us to remember those important concepts we need to know for exams about these medications so first we're going to start with the name the name of the drug tells us how the medication works which lays the framework for understanding everything else so we're dealing with potassium sparing diuretics well that name right off the bat tells us we're dealing with a diuretic so we're going to be someway altering how this nephron is dealing with sodium and if we mess up how it's dealing with sodium we can alter the way the body's going to reabsorb water but this sigh retic is potassium sparing so it actually spares potassium compared to those other diuretics we talked about in this series like loop diuretics and thiazide they wasted potassium so this one's actually going to spare it so let's talk about how it does that well potassium sparing diuretics work to inhibit the sodium and potassium exchange that's occurring within these cells that make up the distal parts of the nephron and we're specifically talking about the late parts of the distal tubule and the collecting duct and what it's going to do these medications is it's going to affect the sodium channels so to help us understand how these medications are affecting the sodium channels let's talk about our nephron so if we're dealing with any type of diuretic it's a really really high probability that these diuretics are going to somehow affect some structure within this nephron like with loop diuretics they affected loop of Henle with the thiazide it affected the early part of the distal convoluted tubule so our nephron just to recap there's millions of these little structures within your kidneys and they're like the functional unit of the kidney because they help our kidney and produce urine so it starts up in here in the glomerulus it's going to filter your blood as blood is receive and it's going to in a sense drip down what it filters down into Bowman's capsule and it's gonna start going through the parts of the nephron and each part of this nephron you can see them in different colors we have the proximal convoluted tubule the live of Henle the distal convoluted tubule and then the collecting duct each part is really assigned its own role for tweaking that filtrate so what's going to happen to the filtrate hence what will eventually become urine is that it's either going to take ions and water and put it back into the blood that's what we call reabsorption or the blood is going to secrete things it doesn't really need into the filtrate so it can be excreted that's like secretion or and then eventually it's just going to leave the body and be excreted as urine so in a sense you're nephrons like maintaining homeostasis of your fluid electrolytes water and waste in the blood so how the tascam sparing diuretics work is they alter those sodium channels that make up that late part of the nephron specifically that late distal tubule and the collecting duct and what they're gonna do is they're gonna alter how sodium is actually going to be reabsorbed out of that filtrate to go back into the blood and remember if we're keeping more sodium in this filtrate within that nephron which is eventually going to become urine we're gonna keep more water with it and that will provide that diuretic effect so to help us understand that a little bit better and to be able to visualize it let's look at that process of what's happening with how like those ions actually cross over from the filtrate to go into the blood because that's the process that these drugs are manipulating so here we have an illustration and this middle area represented in pink represents like the cells that make up the distal tubule and the collecting duct and within these cells you have to have these channels in these pumps to facilitate the movement of these ions so they can cross back and forth over here represented in red this red area this is our inner stitch um slash blood and it has you know ions and other substances hanging out in it and some of those sentences want to get over here to the filtrate and over here in the orange that is represented with our lumen the inside of that nephron /the filtrate and again it also has ions in it don't want to get over there to the blood so to do that has to use those channels and pumps one thing we want to concentrate on is this sodium channel so the sodium channel just like its name says allow sodium to leave the filtrate and go into the cell but once it's there it needs to get into the blood stream so in order to do that a sodium potassium pump will help it do that so what that this does is it takes the sodium pumps it over there into the blood but it has to exchange something for that sodium it just put in there it has to take potassium and hydrogen ions and move it in the opposite direction and it will go this way and this is occurring to allow that to happen so we have sodium channels and potassium sodium pumps however whenever we throw on a potassium sparing diuretic it's going to stop this channel that sodium channel from doing that so you're not gonna have sodium leaving this filtrate going in over here so more staying in the filtrate means more water is gonna stay in the filtrate we get that diuretic effect however it's going to alter how this sodium potassium pump works it doesn't have very much or at all any sodium to pump over into the blood so because it's not going to do that it's not going to have the exchange of the potassium leaving the blood along with those hydrogen ions and going into the filtrate so you're going to keep more potassium in the blood hence its potassium sparing so one thing I want you to remember with potassium sparing diuretics is that there when the directs that keep potassium through that process but patients can have hyperkalemia where their blood level of potassium is increase so remember that now there are two different types of potassium sparing diuretics they will all work together to achieve these same results but they will do it in different ways with what they influence so the first time I want to talk about are called epithelial sodium channel inhibitors these drugs directly inhibit this sodium channel so by doing that it's going to cause more sodium to stay in the filtrate which will draw more water and we'll have that diuretic effect but it'll spare the potassium because we didn't have that exchange with sodium and potassium via that pump so there's that risk of hyperkalemia and some drugs that fall into this category of potassium sparing diuretics are triamterene and a miller ID and the second group of potassium sparing diuretics are called aldosterone antagonists sometimes called aldosterone receptor blockers and just as their name says is that they antagonize aldosterone so they're gonna work against the effects that aldosterone would try to create in your body now what does aldosterone do normally aldosterone causes your body to want to keep and reabsorb the sodium and the water so it'll tell that nephron hey I need you to reabsorb sodium and water in exchange for wasting potassium and hydrogen ions and one way why your body would want to do that is to help with blood pressure management the blood pressure Falls to low aldosterone can help increase blood volume to help increase blood pressure but how these drugs work is they tell aldosterone no you're not going to do this because our dosterone influences the number of these sodium channels and these sodium potassium pumps so if we're limiting their number we're going to be limiting how this whole process is taking place so they have this same effect like these direct epithelial sodium channel inhibitors did with their diuretic effects they're just doing it under the influence of aldosterone and these drugs include spironolactone and Appler anon now let's talk about what these medications are used for what do they treat well because potassium sparing diuretics alter how we reabsorb sodium in water they can be really beneficial in treating high blood pressure hypertension they can also help patients who have excessive fluid volume where they're having edema and swelling related to like heart failure liver impairment or maybe Neph rhotic syndrome they can also treat hypokalemia where you have a low potassium level in the blood due to a side effect that's related to maybe the patients on a loop diuretic or thiazide so they may pick them on a potassium sparing diuretic to help prevent that and they can be used to treat hyperaldosteronism specifically the medications that antagonize aldosterone and medication that's most commonly prescribed for this is spironolactone and with hyperaldosteronism the adrenal glands are producing too much i'll dosterone and if we do that what's going to happen we're going to be keeping lots of sodium and water in our blood but we're gonna be wasting lots of potassium so the patient can have high blood pressure and hypokalemia so we throw on this aldosterone antagonist this is going to help make it where we're not keeping so much sodium and water so we can lower the blood pressure and we won't be wasting so much potassium so we can keep our potassium levels stable now one thing I want to point out about potassium sparing diuretics is that they tend to be the weakest in there diuretic affects compared to the other drugs that are diuretics like loop diuretics and thigh azides because they don't have such a profound effect on how we're dealing with decreasing sodium reabsorption like with loop diuretics those are very powerful because they're dealing with a part of the nephron that really plays a huge role in reabsorbing loss of sodium this isn't really the case with potassium sparing diuretics which is why a lot of times potassium sparing diuretics will be combined with either like a loop diuretic or a thiazide now let's wrap up this lecture and let's talk about the nurse's role the side effects and education pieces for the patient who may be taking a potassium sparing diuretic so we have learned that these medications are going to increase urination because they're altering how we're reabsorbing sodium which hence affects how we're going to deal with water so because they're going to be urinating out more fluid they're at risk for dehydration so as a nurse we have to watch out for that how can we tell our patient is dehydrated well we can look at their vital signs house their blood pressure if their systolic is less than 90 that tells us that we've depleted their fluid volume a little bit too much or how's their heart rate is it increased where the body is trying to compensate for that low blood pressure anything greater than 100 their attack of Kartik how's your patient acting are they really thirsty or they fatigued they have mental status changes this could indicate that they are dehydrated because of those signs and symptoms and you want to teach the patient how to identify that that's happening to them at home and to report that to their physician also we want to monitor their intake in their output we want to make sure that they're not putting out so much fluid compared to how much they're taking in because we don't want to dehydrate them plus we want to look at their renal function that'd be you in and creatinine that tells us how well our kidneys are really working to filter our blood and if we dehydrate them too much we can cause some renal issues and potassium sparing diuretics are not for patients who have renal failure another they were watching out for our electrolyte imbalances and what was the big electrolyte imbalance I told you to watch out for is hyperkalemia because these medications spare potassium so a normal potassium level that you definitely want to put in your memory is three point five two five millionths per leader so anything greater than five we're getting in hyper Kaleem 'ya territory so what are some signs and symptoms that your patient's potassium level may be high without really even looking at the lab result well you want to make sure you're looking at their EKG how do their tea waves look if they're tall and peaked that could be an indication that they're in hyperkalemia remember that that's a big test question that they'd like to ask about fluid in electrolytes also how's your patient reacting are they reporting muscle cramps muscle weakness are they having difficulty breathing or do they have paresthesia where their skin feels like it's tingling and burning they're nauseous or vomiting also teach the patient to recognize these signs and symptoms as well of course they can't recognize the tall peaked t-waves because I don't have an EKG monitor at home but teach them these other things also you want to teach your patient to avoid foods high in potassium because we're already keeping potassium we don't want them to just go and eat lots of food rich in potassium so to help you remember foods that are high in potassium remember the word potassium and this includes foods like potatoes and pork oranges tomatoes avocados strawberries spinach fish mushrooms and musk melons like cantaloupe in addition you want to tell your patient to avoid those salt substitutes because those actually contain potassium and many patients who are taking potassium sparing diuretics may be taking it for a heart condition like heart failure or high blood pressure and they've been educated watch your salt watch your salt so they may use a salt substitute not knowing that it's really high in potassium so educate them about that as well now some medication interactions that you definitely want to watch out for again like I said patients who are taking potassium sparing diuretics may have heart failure so they may need to be taking an ACE inhibitor an ARB and those medications can increase potassium as well we talked in depth for why that was if you want to check out those videos so you want to be watching that looking at the potassium level looking for those signs and symptoms hey the potassium level may be high also NSAIDs can cause that as well they're taking something for pain that can increase potassium levels and lastly another thing is about drug wise is em because we're altering how the nephron is working and reabsorbing and excreting and everything we can alter how the body can actually clear lithium where it could actually build up in the system so the patient's lithium levels would need to be monitored closely because they're at risk for lithium toxicity in a normal lithium drug level that you want to remember is 0.5 to 1.2 millimoles per liter so anything greater than that there is a risk of lithium toxicity and some miscellaneous side effects that you want to remember as a nurse so you can teach your patient is that some of these medications can upset the stomach so they may want to take this medication with food or right after they have a meal to help decrease those signs and symptoms and these medications can produce an anti-androgen effect and we're mainly talking about those aldosterone antagonists specifically spironolactone because this medication affects the androgen and progesterone receptors so some patients may experience gynecomastia minstrel problems and sexual dysfunction okay so that wraps up this review over potassium sparing diuretics
Medical_Surgical_Nursing	Heart_Sounds_S1_S2_S3_S4_and_Murmurs_Nursing_Assessment.txt	hey everyone it's Sarah with register nurse rn.com and in this video I'm going to be going over heart sounds what I want to be doing is I'm going to be covering the basics of the things you need to know about listening to those heart sounds S1 S2 those extra heart sounds like s3s4 heart murmur and in the next video I'm actually going to be performing an assessment on a person and showing you by using the stethoscope how to find those anatomical positions when listening to the aortic pulmonic tricuspid and mitral Valves and walk you through how to do that now after this video be sure to go to my website registernurse rn.com and take the free quiz that will test you on this theory of listening to heart sounds because a lot of times in your health assessment classes for instance you may be asked certain questions about when do you hear S1 where do you hear it best and things like that so that can help you prepare for your exams and a card should be popping up so you can access that quiz so let's get started first let's talk about the goal what is the purpose of listening to heart sounds well the reason we listen to Heart sounds is to assess the closure of heart valves that are located in the heart where blood flows through because it tells us a lot about what's going on with the patient's heart and we're listening to four valves they're categorized into two sets and the first set are your avioventricular valves which are short for AV valves and that includes your tricuspid and mitral valves your mitral valve is also called your bicuspid valve so commit that to memory and whenever these valves close your tricuspid and your mitral that is signifying the first sound you hear the love sound which is S1 then we're looking at our semilunar valves SL valves and these are your aortic and pulmonic valves and when they close that is the S2 sound and that is the dub so it goes hand in hand whenever you're listening to the heart you hear lub dub love is S1 dub is S2 now whenever the heart is relaxing and Contracting relaxing phase is diastole the relaxing part I like to remember that because a lot of people get those too confused dye um whenever a person dies they're relaxing so that's how I remember that and the opposite of that is Sicily contraction so when the heart is Contracting and resting these valves will be opening and closing During certain times and let me walk you through this it's very important you understand how the blood flows through the heart I have another video on heart blood flow if you're Rusty on that a card should be popping up and you can access that but let me walk you through it and tell you how the valves are open and closing during diastole and systole okay first let's cover some basic anatomy of the heart and then we'll talk about the heart blood flow okay you have your Superior and inferior vena cava you have your Atrium your right atrium your tricuspid valve your right ventral cool then you have your pulmonic valve pulmonary artery then you have the pulmonary vein then you have the left atrium bicuspid valve left ventricle aortic valve and then that aorta so what happens is that you whenever blood is flown through this side is flowing through that side so what's happening on this side is happening on that side keep that in mind so what happens is that these blue arrows signify unoxidated blood and what's happening is that blood has been used by the system it needs to come back through the heart to go through the lungs to get oxygenated so it can go back and do its job so it flows in through the superior and inferior vena cava then it goes down to through your right atrium down through your tricuspid valve and into your ventricle now right now we have diastole going on dastly again what was that that was relaxation so it's nice and relaxed over here and blood is just flowing down through the tricuspid valve and how I can do that is in the Atrium the pressure is a lot higher than in The ventricle but as The ventricle becomes full it has a lot of pressure and whenever it becomes full it has a lot of pressure it closes that avioventricular Valves and whenever those close you will hear S1 and when you hear S1 that is the beginning of systole the contraction phase so systole happens which is contraction your ventricle contracts that causes a lot of pressure on your semilunar valves and they open up and allow blood to rush through up through the pulmonic artery right here and then they close because pressure Falls once that blood goes through the pressure will fall and then you will hear S2 which is signifying the closure of those semilunar valves and then it will flow through the pulmonary artery it will become oxygenated with blood through the lungs and then it will enter back through the pulmonary vein down through the left side of the heart and it'll go through the left atrium again we have we've entered back into diastole and it's relaxed because blood is nicely flowing down through the bicuspid valve right here and the pressure is building in The ventricle and whenever it builds it will cause your bicuspid valve to shut so those Avio ventricular valves will shut you will hear S1 again and then um that will be the marking of systole The ventricle will contract which will cause that increased pressure will cause those semilunar valves to open up which right here is your aortic valve and the blood will flow up through the aorta go through the body and give the body all that rich nutrients it needs and then it just starts all over and sometimes whenever you're listening to the heart listening to that S1 and S2 those closing of those valves you will sometimes hear extra heart sounds which will go in depth here in a second and you could hear a sound like S3 S4 heart murmurs and splits and I'm going to go over in great detail on how to position the patient properly how to use the proper part of your stethoscope whenever you're listening for those sounds because it takes a little bit of technique and in the next video I'll be covering that in depth as well okay so let's go over the stethoscope Basics because in order to hear these heart sounds you have to know how to use is your stethoscope okay the diaphragm of your stethoscope that is the big part of it this is um found on your chest piece and it hears high pitched sounds it is great listening throughout the chest for S1 S2 and your aortic and pulmonic murmurs where you have regurgitation so that is great for that then you can use the Bell to switch it over depending on what type of stethoscope you have this is a smaller part and this is best for low pitched sounds remember low is small remember the smallest side of the stethoscope is the bell and that likes to pick up those low pitched noises and this is perfect for assessing for S3 S4 and your mitral stenosis murmurs which we'll go over here in a second and also as you're listening with your stethoscope it's best to inch the chest piece across the chest instead of just picking up and just moving it just into it so you can continue hearing that Rhythm because the main goal is trying to distinguish S1 from S2 so inch it over don't listen over close because that interferes with sound and especially if you are new to listening to heart sounds you need to make sure that you're listening straight on the chest because you need to learn what normal sounds sound like and make sure you're decreasing your background noise because that can interfere and get a stethoscope that fits your ears and practice practice this skill takes a lot of practice okay patient positioning the key to hearing a lot of these sounds depends on patient positioning because your heart is behind you're sternum and your ribs you need to make sure you're moving the patient to get the best acoustic sound so here are some tips okay whenever you're listening you normally start out you can have the patient lay down sitting up and you are going to be listening with the diaphragm of your stethoscope for S1 and S2 and we'll go over the anatomical positions here in a second and then to listen for that S3 the S4 because after you get familiar with S1 and S2 you'll turn them over on their left side and why do you do that majority of the heart is on the left side of the body so when you lay the patient back turn them on the left side those want to shift that hard over there and you're going to listen at the Apex the Apex is the bottom it's the opposite of the heart it seems like the bass would be here in the Apex up there but it's the opposite the Apex is at the bottom and the base is at the top so you're going to listen at the apex of the heart whenever you're listening for S3 S4 and those mitral murmurs then you'll want to set the patient up lean them forward and have them exhale and what this does as if you're looking at the diagram of the chest this moves the heart forward because you're one to pay attention to the aortic and the pulmonic valves and you're listening for that regurgitation that murmur now it's really important whenever you're starting out that you understand where your landmarks are where you will place your chest piece to listen to those Valves and what each vowel what sound it reflects so this is the meat and potatoes of the lecture okay to help you remember the order of how to listen to these valves I like to remember the mnemonic all patients take medicine a for aortic P for pulmonic t for tricuspid and M4 mitral and to do that what I like to do is I like to find the clavicle then I like to go find the angle of Lewis and right below that angle because attaching to that is your second rib and what we're going to do is we'll start on the right side with our chest piece of our stethoscope and we're going to listen to the aortic valve and it is found in the second intercostal space and no it is the only Landmark area found on the right side of the chest it's right next to the sternal border and again what does the aortic valve reflect the sound of whenever it closes S2 and is found at pretty much the base of the heart then you're going to go right across so you're just going to take your stethoscope and then you're going to go right across to the other second intercostal space which is on the left side of the heart and and you're going to listen to the pulmonic valve and again these two are semilunar valves and this reflects the sound of S2 the closure of S2 and this will be your pulmonic valve then you'll find the third rib go down to the third intercostal space and this is Herb's point this is the halfway point between the base and apex of the heart then you'll Interstate the scope down to the fourth intercostal space and listen to the tricuspid valve and this reflects S1 when it closes and it is an Avio ventricular valve the AV valve then after listening to that you'll enter chest piece down to the mid covicular area which here's your clavicle you're going to go Midway through that and you're going to go to the fifth intercostal space and you're going to be listening at the mitral valve part this is also the point of maximal impulse and this is the apex of the heart so you will listen there okay whenever you start out listening for those heart sounds simply what you're going to do is you're going to either have the patient laying down you're going to have them sit or sitting up and you're going to listen with the diaphragm of your stethoscope at these landmarks starting with the aortic and working your way through the pulmonic herbs Point tricuspid and mitral and as you were listening you were listening to the Rhythm is it nice and regular is it irregular and the right then you are trying to listen for and distinguish between S1 and S2 whenever you're first starting out this can be complicated but there are some tricks you can do to help you find out Is This Love or is this dub okay first what you want to do is you will use you can use this trick S1 is louder at the apex of the heart so in the mitral area it's going to be like love dub lub dub love will be louder than dub which is S1 now S2 2 is louder at the base so it'll be more like love dub lub dub so listening at those different areas can help you distinguish also another thing you can do is if your patient is on a bedside EKG monitor this helps whenever you are looking at your QRS complex the r-way will correlate with S1 so as you're listening with your stethoscope watch that bedside monitor every time you see that peak of the r wave and you hear that noise that's S1 so that helps you distinguish that or you can have the patient while you're listening you can feel on the carotid arteries pulsation whenever you feel a pulsation you hear the sound that is S1 because they go hand in hand so those are some tricks on how you can distinguish those because it's important you distinguish those so you can hear those other extra heart sounds if they have them like S3 S4 and things like that um also note a patient can have splitting of S1 and S2 so that's another thing you're listening for and what that is is as we were talking about through the blood flow of the harp the AV valves over ventricular valves which are your tricuspid and bicuspid they are closing usually normally they are closing at this opening and closing at the same time but sometimes if they have a split one will close before the other and that's just what you're hearing and that can also happen with s to remember your s semilunar valves represent S2 and your aortic or your pulmonic valves are not closing at the same time so you're hearing them close a little bit differently now S1 a typical cause of S1 just to let you know could be a right bundle branch block that's where the right bundle is being blocked through the electrical conduction system of the heart I have a video on the electrical conduction system if you're not familiar with that and that is why the patient may have an S1 now let's talk about those extra heart sounds that you may or may not hear s3s4 and murmurs okay S3 what you need to know is when it's heard what are the causes this is typically heard after S2 and let me explain the pathophysiology behind this okay what's it going to sound like it's going to sound like represents S one the closure of S1 your AV valves um dub represents S2 the closure of those semilunar Valves and then you hear ta now remember when your semilunar valves close what does that represent it's the end of it's the end of Sicily contraction and now it's what's going to happen is the heart's going to relax and allow it to fill up again so what's happened your semilunar valves shut because they've already done their job by shooting the blood out and then the hearts and dastly where you have the atrium flowing the blood down through the ventricles and what you're hearing is that vibration noise of the ventricles feeling up so that's why you're hearing it after S2 and a cause of that could be by could be fluid volume overload or heart failure and this is typically again best heard if you put the patient on the left side and use the bell of the stethoscope because it's a low pitched noise okay let's look at S4 now S4 is heard before S1 so it's going to sound like you're going to hear that extra sound before the love duck which is the opposite of how S3 was you heard it after the loved up and this is usually caused due to that Atria kick that during that precisely part and where the atrium is trying to push blood down into those resistant ventricles so the ventricles are resistant they don't want to do their job so the A3 just has to get one more kick and what you're hearing is that murmurs water murmurs heart murmurs are where you hear with your chest piece whenever you're listening throughout the heart you will hear either like a blowing or a swishing noise and this is due to the turbulence of blood flow either through the blood Chambers or through the valves maybe there's a wall defect or the valve like the mitral valve any of the valves are too narrow which are like mitral stenosis or they're having regurgitation issues where the valve isn't shutting all the way and blood is back flowing and you're hearing that and it can be at different levels how loud they are they are braided as the following a grade one it's hard to hear but you can hear it you barely hear it a grade 2 is faint but you hear it grade three is easy to hear grade four and onward the patient will have a thrill and this grade four is usually loud with a thrill um a grade five is very loud with a thrill and you can lift just the corner of your chest piece of your stethoscope off and you can still hear it and a grade six is the loudest of them all and they'll have a thrill and you could lift the whole chest piece off of the chest and you can still hear the murmur okay so that is a little bit about heart sounds the basics of what you need to know for nursing school now thank you so much for watching be sure to go take that quiz to test your knowledge on this and be sure to check out my next video where I will be performing the assessment skill on how to auscultate heart sounds and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	How_to_Memorize_the_PQRST_EKG_Rhythm_Strip_Wave_for_Anatomy_Pathophysiology.txt	hey everyone this is Sarah with register nurse rn.com and today we're going to go over some EKG material in this video we're going to cover the basic EKG strip the pqrst um EKG tracing that you'll see I'm going to explain what each part of it where it's located and how what each part of it represents before you even start analyzing strip rhythms such as AI vac any of that you need to know the basics so this is the foundation of it and our later videos we'll be going over different types of rhythms and um what to look for as a nurse but first let's just go over the basics so we can lay the foundation so you'll understand it plus you'll need to know this for a lot of your nursing classes your patho class and this will just help give you a firm grasp on it and I've tried to take the material and make it as easy as possible and point out the highlights that you may be tested on in nursing school so after we go over this video go to our website register nurse rn.com and test your knowledge on how well you grasp this material that we learned today a lot of those questions you may see on your tests in school so it'll just help you so let's get started here we have um a regular EKG tracing you have your PW your QRS um complex and your t-wave and I'm going to go over all that and tell you what each of it represents in the previous video I made we went over the electrical conduction of the heart because that's all your waveform is it's electrical condu ction that your little electrodes are picking up that the heart is making and it makes this cool thing for us to look so we can analyze and treat the patient better so if you don't know how the electrical system flows through the heart I really recommend that you check out that video and um understand that because we go over where it's located in the heart and we break it down and make it easier for you to remember and also there's a quiz on that if you want to watch that as well so first let's let's get started with the pway on almost every EKG strip unless the patient's in a dis rhythmia you're going to have a p wve your p wve is atrial contraction it originates in the SAA node which is the pacemaker of the heart which Beats at 60 to 100 beats per minute um in some dymas you every time you even look at a wave you want to look at your p waves that is where you start because some p waves can be messed up they can have a long PR interval and it tells you a lot about how your patient's doing so there's your P wve again it represents atrial contraction it's those atriums in the heart Contracting which is also the fancy term called depolarization they're Contracting then you have your QRS complex this is what's called your ventricle contraction which they call it ventricle depolarization this is when your ventricles are Contracting they're pumping that blood so the ventricles are just so big that they produce this huge complex and then after that you have a t-wave the t-wave is your ventricles repolarizing they are resting again the ventricles are so big whenever they contract they make the huge QRS complex that whenever they rest you can even see them repolarization repolarizing because they're so big so you're going to see your t-wave now sometimes you can see a uwave it's not very common um in the clinical setting I've only seen it like once or twice it's it's not very common to see on a patient but they think that the uwave is produced by the resting of the peni fibers they're not really sure but that's what the literature says and your peni fibers remember you have your AV node the bundle of His and your bundle of His branches off to the right and left bundles and then you have those peni fibers so whenever they're saying that the peni fibers have already depolarize and they're resting they're saying the uwave is being caused by that and sometimes you'll see that in patients who have severe hypoc IIA which is a low potassium level so you can see that um so that is how what your common pqrs complex looks like now let's go over the intervals that you'll see in the clinical setting okay let's talk about now how the EKG tracing is split up into different intervals and segments and um complexes because on exams a lot of time you are given a blank wave and you are expected to to label where the p wve is where the PR interval is and things like that so on that quiz that I was talking about on the beginning of the video we have blank diagrams and you'll be required to fill this stuff in so it'll just help prepare you before you take a test so let's go over these different types of complexes and segments okay the very first thing we're going to go over is called the PR interval the PR interval starts at the um P wve which is where you have atrial contraction remember the P wve represents atrial contraction and it ends right before you have ventricle contractions so that is where your PR interval is and notice that little delay that remember we were talking about in the last video The Av node is the gatekeeper it's responsible for the delay so that's where you're seeing that delay right before you see the contraction of the ventricles because whenever you have you want that delay because if you don't your ventricles your Atrium will not completely deliver blood to your ventricles and you'll have back flow of blood so you want that little delay that you're seeing right there now the QRS complex remember that is the contraction of the ventricles your ventricles are so big that they're causing this huge impulse on this electricity conduction and you see the QRS interval so complex um then you will have What's called the ST segment this starts at the end of ventricular contraction and begins right before the t-wave which is showing you your ventricles repolarizing which resting so you will see the ST segment the ST segment is really important when diagnosing cardiac M um a lot of times working in the stress lab we will really pay attention to the s for any St elevation it tells you a lot about what's going on with the patient so that's what they're talking about whenever you hear St elevation things like that they're looking at your ST segment so that is about everything that you would need to know about your pqrs waves that you will see in the clinical setting again this is just a baseline to help you to start understanding dysrhythmias which we'll be going over in our other videos um be sure to go and take that quiz on register nurs rn.com to test your knowledge on how well you grasp this we have other quizzes that'll prepare you for inlex Doses and calculations abgs personality quizzes everything so be sure to go there and thank you so much for watching and if you like this video please give it a thumbs up and I hope you have a great day
Medical_Surgical_Nursing	Nephrotic_Syndrome_vs_Glomerulonephritis_Nephritic_vs_Nephrotic_Syndrome_Nursing_NCLEX.txt	hey everyone it's Sarah threader nurse ran.com and in this video we're going to be doing an inlex review comparing a cute Glo nefritis versus nephrotic syndrome and this video is part of an inlex review series over the renal system so be sure to check out those videos and as always at the end of this YouTube video you can access the quiz that will test you on these conditions so let's get started first let's start out talking about a cute glomo nef Rus okay what is happening in this condition well what's happening is that there's inflammation of the glomerulus and what is the glomus it is part of your nefron and each kidney contains millions of nephrons and it is very bottle in helping filter your blood it receives all this fresh blood from the heart it goes through the glomerulus and then the substances leak down into Bowman's capsule and normally what leaks down are ions water and waste and your body will take and pick and choose what it wants to go back into circulation and what it doesn't and it'll exit the body as urine now normally the glomus is not permeable to blood cells and proteins so keep that in mind so in this Condition it's became permeable to red blood cells and protein and the amount of protein that is lost is mild compared to nephrotic syndrome so with nephrotic syndrome what's happening well we have changes to the glomus so the glomus is not working how it's supposed to and it causes a massive amount of proteins to be lost so to help you remember when you're trying to compare the two I remember nephrotic has an o in it and that reminds me that there's only one substance that is lost in this condition and it's proteins I remember the O and proteins so red blood cells are not lost in here only proteins and it's a lot of them compared to over here it's a mild amount so now let's look at the main cause with aaral nephritis what causes it main cause is a post streptococcal infection so the patient gets strapped maybe didn't get treated or wasn't treated appropriately and it shows up about 14 days after that infection it can be of the skin or of the throat and it tends to affect the Pediatric population ages 2 to 10 so if you're in pediatric nursing right now probably studying this condition and what is happening it's really interesting is that the body has actually created these antigen antibody complexes to help fight that strp bacteria and what happens is that these antibody antigen complexes collect in the glomeruli and it congests it and it inflames it which allows these red blood cells and proteins to leak through so in a sense it's not really the strap bacteria in the glomus causing it it's the body's ability from where it's created those antigen antibody complexes doing it now with nephrotic syndrome what's happened is that there's changes to the glomerula and they're not 100% sure why there's changes to the glomeruli it's idiopathic it's unknown but one of the most common diseases that can cause nephrotic Sy syndrome is called minimal change disease and this is where they will biopsy the glome look at those and they look under look at them under an electron microscope which is one of the strongest microscopes and they see that there's these changes there that are allowing all these proteins to leak into the urine and it tends to affect again pediatric population ages 2 to 5 years old now other things can cause this as well secondary causes and this is where diseases are affecting the function of the kidney and this can be from lupus diabetes heart failure Etc now with acute glome nephritis remember we only lost losing red blood cells and a mild amount of protein now from nephrotic syndrome we're losing those massive amounts of proteins and we're losing various types the main type of protein that we're losing is called albumin and because we are losing so much in our urine it's going to deplete our blood from alumin and you're going to see here in a second with our signs and symptoms why since we're losing so much albumin it causes these unique signs and symptoms from that now other things that can be lost are immunoglobulins which help fight infection so your patient is going to be at risk for infection and they can also lose proteins that help decrease clot formation so if you're losing proteins in your urine that are decreasing clot formation the patient is at risk for developing these random clots okay now let's look at the signs and symptoms of these conditions and how they differ between each other first let's look at aute Garo nephritis now remember what's happening in this condition is that these antigen antibody complexes have congregated in this glomerula it's inflaming it and making it permeable to red blood cells and proteins now your glome marilus filters the blood and if you have some complexes in there inflaming it congesting it what is going to happen to the ability of that glome to filter the blood it is going to decrease so you're going to get a decrease GFR glomular filtration rate now that's going to lead to some things what's that going to lead to it's going to lead to hypertension more blood volume the body is not the kidneys are not removing that excessive water from the body it's going to stay there then you're going to get where you're going to lose proteins and here in a second you're going to see how protein specifically albumin plays a role in regulating oncotic pressure so you're going to be getting more fluid in the body another thing is you're going to get increased waste in the blood specifically bu and creatinin because the kidneys those glome marula aren't able to remove the waist from the blood and put it in the urine so it can be voided out and another thing is your urine is going to look abnormal because you're losing those red blood cells so it'll ttin the urine to maybe look like a cola colored or teac colored urine so to help you remember these signs and symptoms let's remember the pneumonic had strap because that is one of the reasons of this condition okay H for hypertension and again that is because of that decrease GFR the extra blood volume in there kidneys aren't working appropriately however in nephrotic syndrome hypertension is rare this is a lot more common with this condition so remember that these little red asteris that you're seeing these are really the big glaring different signs and symptoms that you're going to see in this condition compared to nephrotic syndrome another thing a for ASO which is an anti- strepen titer it will be positive and this is just a test used to test for strep and if they test positive for strep then and they have this condition most likely because of strap D for decrease GFR and again whenever you have a decrease ability of that glomerulus to filter that blood what's going to happen you're not going to be producing as much urine as you should because there's it's can't filter so you'll have low urinary output with this condition now if that happens as a nurse you really want to monitor the potassium level because the body is not able to excrete pottassium normally and it can build up causing hyperemia as for swelling in the face and the eyes this can be mild the dematin to be a little bit more mild than compared to nephrotic syndrome and it can be worse in the morning especially in the face t for te- colored urine again that Cola colored urine and that's because of that hematuria R for recent strep infection e for elevated bu and creatinin and again that's tied back to that decreased GFR because the kidneys aren't able to filter the blood normally so the waste products build up and then of course last part p for protein UA and keep in mind that the protein UA is going to be mild compared to nephrotic syndrome now let's look at nephrotic syndrome sign and symptoms okay with this again we're losing massive amounts of proteins and we're losing mainly albumin but we can be losing those other proteins that help us fight infection and decrease claw formation so protein Uria they will have massive protein Uria because they're going to be losing three gram or more of protein per day and that is a lot of protein now because of that the urine is going to have this Unique Look to it it can be foamy and frothy urine and the urine can have this like dark color like a dark yellow to it now because we've lost so much protein in the urine what's going to happen to our protein level specifically albumin in the blood it's going to decrease so you're going to get hypo alumia and whenever you get low albumin levels in the blood the liver says hey I've got to make some more albumin we're low so the liver tries to make more album and thinking it helps but whenever it does that it increases our lipid levels as well like triglycerides and cholesterol so the patient will have hyper lipidemia which looks sort of funny on your pediatric patients who should not be having hyper lipidemia now also that low albumin level level is going to lead to edema a lot more edema which is going to lead to noticeable weight gain in this condition then compared to acute glom Maro nephritis because remember it's mild protein we're losing and it can be in the face around the eyes it will progress to the extremities the legs ankles hands and the abdomen causing atis now why is a low albumin level causing so much fluid to go into the interstitial tissue which will present as a Dema well albumin plays a very important role in regulating oncotic pressure so let's talk about that okay so here's like a capillary and your capillaries have finestra which are little pores that allow substances to flow in and out from the capillary to the interstitial tissue well here in the brown those are albumin and albumin and water they're like a magnet together albumin regulates how much water really is going to flow out of the capillary into the interstitial tissue now if the albumin levels start dropping and going away you don't have anything water doesn't have anywhere to go so instead of staying there because that's what albumin does is it keeps it with him is it will cause the water to go out into the interstitial tissue because there is no album in there to regulate it then you will get the swelling in the interstitial tissue and that's why you will see that okay now let's look at the main nursing concerns based on each condition cuz depending on what the patient has we're going to focus on certain areas okay so for acute glone nephritis remember the patient can have hypertension so we want to monitor their blood pressure and the physician May prescribe anti-hypertensive drugs to bring that blood pressure down or diuretics as well depending on if their renal status is sufficient enough since diuretics act on the nephrons of the kidneys another thing is we want to monitor that fluid status closely specifically their eyes and O's especially that output are they putting out the normal amount that a child should put out which is 1 milliliter per kilogram per hour depending on their weight or at least 30 cc's an hour if it's an adult because remember they have a decreased GFR which as it decreases they enter into renal failure and you'll want to notify the doctor if that urinary output is not sufficient enough then you want to monitor that potassium level because the body is not excreting the potassium and it can lead to hyperemia also assessing their swelling is it decreasing or is it getting worse because with this condition we're really worried about the renal function next limiting sodium and following a fluid restriction diet again just because of all the swelling they have going on we'll want to watch that and if they have low low urinary output you'll want to limit their consumption of foods high in pottassium and with this condition relapse is not as common as with nephrotic syndrome but you'll want to teach the patient how to monitor for future strip infections and how you can go to your Physician's office and get a simple culture and they can test to see if you have strep of either your skin or your throat now let's look at our nursing concerns for nephrotic syndrome okay with this we're also going to monitor our fluid status and our swelling one thing you want to keep in mind is that the physician May order diuretics along with IV albumin which is going to help decrease that swelling how's that going to help well we know our blood level is low in albumin so putting albumin back into the blood will help start regulating oncotic pressure so put albumin back in the blood hopefully water will come back into that capillary from the interstitial tissue and the diuretic can work on the kidneys to help remove that excessive water in the system another thing is we want to monitor these patients for infection because they're at risk compared to if they had AGN acute glome nephritis especially around those areas that are swollen when you have a emitus areas they're at risk for breakdown because these patients are going to have a lot more swelling than compared to over here so watch that also one of the treatments is corticosteroids or an immune suppressor and this will help decrease the amount of protein that is being lost in the urine and help prevent relapse because relapse can happen with this condition also you'll want to assess them for blood clots because remember they're losing various proteins those imunoglobulin which help with infection and the proteins that help decrease clot formation so you want to assess their skin their extremities make sure they're not red swollen or painful which could represent a deep vein thrombosis or a pulmonary embolism so you'll want to look at that respiratory status another thing is Diet you'll be limiting per Physicians order consumption of sodium fluid restriction and if they're experiencing that hyper lipidemia you'll want to limit their fat consumption as well so a lowfat diet then you'll want educate the patient or the parents about the risk of relapse because this can happen with this condition and how to monitor for it so performing daily weights every day making sure you're not gaining weight getting overthe counter kits to test your urine for protein and things like that okay so that wraps up this lecture on acute glome nephus versus nephrotic syndrome thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Acute_Kidney_Injury_Acute_Renal_Failure_Nursing_NCLEX_Review_Management_Stages_Pathophysiology.txt	hey everyone it's Sarah register nurse rn.com and in this video I'm going to be doing an inlex review over acute kidney injury also known as acute renal failure and this video is part of an inlex review series over the renal system and don't forget to check out at the end of this YouTube video the quiz that will test you on acute kidney injury so let's get started so what is this condition it is where there is a sudden decrease in renal function so it comes on quickly and the kidneys aren't able to filter the blood like it should and because of this you get buildup of waste in the blood like bu and creatinin which are waste products from muscle breakdown and protein breakdown you also we'll see fluid build up in the patient because again those kidneys cannot remove that excessive fluid from the blood and electrolyte in balances now acute kidney injury can be reversible if it's caught early and the cause is treated appropriately so what exactly can cause acute kidney injury well we have three different causes based on the location where it's located in the body the first type of cause that we're going to talk about are the pre-renal causes and for inlex and your nursing lecture exams be familiar with the causes that can cause this and where it tends to be located before the kidney inside the kidney or after after the kidney because that's where a lot of test questions like to come so prerenal prerenal just like the name says it's before the kidney so any problem that's really arising from the renal AR artery upward upward to the heart so your heart and your kidneys work hand inand together what your heart does is it takes the blood and it oxygenates it through the lungs and it goes back to the heart and then it pumps it out through the body and that fresh blood will go down through the heart through the descending aorta and then go into the kidneys through the renal artery and Branch off into all these arterials and go and feed to the nephrons of the kidneys and remember each kidney has millions of nephrons and those nephrons are responsible for filtering the blood and reabsorbing nutrients and then creating urine filtrate which is voided out through the bladder through the urethra so it all works together like this beautiful process however if you get a profusion issue this can decrease the function of the kidneys so you have decreased profusion which is going to decrease the function of the kidney now what happens is that there's a decreased amount of blood going to the kidney to be filtered and the kidney is being deprived of nutrients so it's not able to work like it should and eventually this can actually lead to intrarenal injury where those nephrons inside the kidney become damaged and they quit filtering like they should so what exactly can lead to a prerenal injury causing that decrease profusion okay a f one thing is a cardiac issue and what can happen is if there's damage to the heart muscle it's not able to contract properly these ventricles become weak they cannot pump that blood down through that descending aorta so you get decrease cardiac output which is going to decrease the profusion to the kidney what kind of conditions can cause this well one thing is a mardial infarction the patient has a heart attack and some of that part of that ventricle has died maybe a large part of it because of aeia to the muscle it was irreversible and so that heart muscle is just weak and it cannot pump get decreased cardiac output another thing is bleeding if you get Massive Internal or external bleeding there will be decreased blood volume going to that kidney not profusing it dehydration with excessive diarrhea vomiting the patient becomes hypovolemic and another thing are Burns which again is depleting the system of fluids then there are interrenal causes and this is where there is damage to the nephrons so the problem is within the kidney itself so if you took the kidney and you sliced it in half you could find where the mil where these millions of nephrons are located and if you drew out a nephron and stretched it out it would look something similar like this you would have the following structures and the nephron can really be divided into two areas based on what they do you have the renal Cor pusle which is your filtering structure and that includes your glomus and Bowman's capsule then you have the renal tual which includes your proximal convoluted tubal Loop of Henley distal convoluted tubal then your collecting tubal and collecting ducts and this is really where uh the body where the renal system is going to remove excessive water or put more water back into the bloodstream and really tweak those electrolytes based on what you need so it's really maintaining homeostasis in the body then whatever you don't need you're going to void it out and each nefron sets within the kidney but the top part of the nefron sets in the renal cortex and the bottom part of the nefron specifically the loop of Henley and part of the collecting tubule SL duct sets in the renal medulla and that's why whenever you look at the kidney structure you see those striations on the renal pyramid it's because of the bottom part of the Nephron giv giv it that appearance so if you have a problem with your nefron what's going to happen you're going to have a decreased ability to filter the blood which is going to lead to excessive waste building up into the system it can't remove it you're going to have excessive water building up and it's not going to be able to maintain electrolyte levels where they need to be so what can cause intrarenal injury well one thing is never talk drugs drugs that are really hard on the kidneys and this includes drugs like ineds antibiotics specifically the aminoglycoside family chemotherapy drugs or contrast dye like the dyes that patients receive for certain testing another thing is infection and we talked about this in our glomo nephritis video which is one of the causes if it's not treated appropriately and they have a really severe case they can enter into this condition and injury to the kidney and lastly there are postrenal causes and this is where you can have blockage in the urinary system after the kidneys that can even extend all the way to the urethra and what this will cause is it will prevent the urine from draining out of the system so you'll get build up of pressure in the kidneys from where all that urine is just staying in there and back flowing to the kidneys and you have all this waste that isn't leaving the kidneys so this can decrease the kidney function so for instance say that you have a renal calculi that can be a cause it's obstructing urine flow and remember it can be anywhere from the uror to the bladder to the urethra so another cause could be an enlarged prostate prostate in men it can squeeze that urethra close so they have problem emptying the bladder and it can cause backf flow of urine and then things that cause a brain injury a neuro damage where like a stroke where the bladder does not empty like it should so they get the retention of w of urine it it can back flow and cause acute kidney injury so before we look at the stages of acute kidney injury let's cover the basics about the kidney and look at the labs that are ordered by The Physician to determine if this is renal failure because whenever we're going through the stages our nursing interventions and the signs and symptoms it's going to make sense why you are seeing an increased bu in creatinin or a decrease GFR and it'll help you understand that material a little bit better okay so Basics about the kidney okay it's important to know how much a an adult should be voiding normally they should be voiding one to two liters per day because depending on the stage like if they're in the aloric stage of acute kidney injury they will be voiding usually less than 400 MERS of urine so you'll want to be watching out for that because they should be voiding at least one to two now they're voiding more than two like three to four maybe five or six liters of fluid they could be in the diuresis stage now what does urine consist of substances really our body doesn't need so you're going to be finding water in there ions that will rain from sodium to Chloride to calcium phosphate bicarb everything like that because remember our nefron pick and chose what we needed to maintain that homeostasis in our body along with waste products because we do not want that to build up in our body like Ura Ura is measured in The Bu level the blood Ura nitrogen level and this is a waste product from protein breakdown in the liver and then we have creatin which is a waste product from muscle breakdown and we want to maintain a fine balance of this and a normal creatin level is 0.6 to 1.20 millgram per deciliter so let's talk a little bit about creatinin because now we're getting into our Labs so creatinin is measured a lot whenever renal failure is suspected because they will take your creatin level your creatin clearance and your glomular filtration rate along with the bu to really determine how well those kidneys are filtering and removing waste from the body so creatinin creatinin is solely filtered from the blood via that glomerulus so blood's going through the Glarus creatinin is dripping down in there now normally other substances that go through there like water and sodium potassium will go through the renal tubal and it's going to parts of that of the sodium and water are going to be reabsorbed back into the system and what we don't need will void it out well with creatinin it's not going to be reabsorbed or secreted in the nefron it is solely just filtered out which is why creatinin is a great measurement to help us determine the ability of how the kidney is filtering so we can measure how much creatinin is in the blood and if we have too much creatinin in the blood we know that we have decreased functioning of our kidney which is why we can also look at what is called the creatinin clearance level and this is the amount of blood the kidneys make per minute that should be free of creatinin and it the varies differ based on gender so for females the normal range is 85 to 125 Mill per minute that is the amount of blood that that woman should be producing through the kidneys that should not contain creatinin and for males it'll be 95 to 140 milliliters per minute now you can use the creatin and clearance values along with the patient age gender weight race to determine what is known as the glomular filtration rate the GFR and what is the GFR the GF R is the rate of blood flow through the kidneys so it tells us how well the glomus is filtering the blood because that's that main structure in that nefron that is doing that job so a normal GFR should be 90 milliliters per minute or higher and again it takes all these other things like the age of the gender the weight and the race into consideration when calculating this estimation so let's take a little quiz if our GFR is decreased our glomus is not filtering that proper amount of blood what's going to happen in our body what are we going to see in our patient okay what is their urinary output going to do when you have a decreased GFR is are they going to be putting out a lot of urine or is it going to decrease their urinary output is going to decrease they're going to become they may experience aoria less than 400 milliliters per day of urine and that urine is going to become concentrated because that glomus is not filtering the amount of blood it should it's decrease what is going to happen to the water in the body it is going to increase because the glomus is not removing the right amount of water so it's going to stay in the blood what's going to happen when we have too much blood water in the blood we're going to get some hypertension edema swelling now what will happen to the waste in the blood specifically The Bu and creatinin levels they're going to really increase as well so your patients going to start experiencing azotemia which is the buildup of waste in the blood and they can enter into metabolic acidosis acidotic conditions because they are not excreting those hydrogen ions like they should and you have decreased bicarbs so we're going to get that and then another thing what do you think is going to happen to your electrolyte they're going to be all over the board specifically you're going to see high potassium levels like hyperemia phosphate levels can be high and their calcium levels can be low among those other types of electrolytes so anytime if you get to have clinicals on a renal floor or you're working on a renal floor always look at those labs before the patient is scheduled for dialysis because dialysis is one of those treatments for this condition and you will notice that before they go for out dialysis the patient blood pressure is going to be super high they're going to have swelling you're going to go look at their Labs they'll have an increased bu and creatinin their potassium level will be Sky High and uh they will have in their folley if they have a folley usually they do their urine will be really really dark and they'll just be like a very small amount in the Foley bag and then after they go to dialysis their blood pressure usually is better and whenever you draw Labs morning Labs those levels will be down because it's removed it's replaced the job of what your nefron should have done in the first place that dialysis machine okay so now let's look at bu what was bu that was measuring that Ura level it's blood Ura nitrogen level a normal level for this should be six 6 to 20 milligrams per deer and again Ura is the breakdown of protein in the liver so liver breaks down the protein secretes it into the blood because it knows whenever it does this that the kidneys are going to take it and filter it out however if the kidneys aren't working properly it's not going to be able to remove that Ura so you'll have high levels of BU greater than 20 in this condition and also something that can increase be levels are conditions like that cause dehydration now let's go over the stages of acute kidney injury and as I do that make sure you pay attention to the name of each stage how they occur and the signs and symptoms that present in each stage along with the nursing intervention that goes along with that sign and symptom because that is where test questions like to come from whenever you were studying this condition okay so the first stage is called the initiation stage and just as the name tells you this is when it starts so it starts Whenever there is something causing that kidney to become injured either pre-renal postrenal or intrarenal cause and it ends when the signs and symptoms start to appear which can occur a few hours to several days and this is really when you want to find out the cause and treat that cause to prevent long-term damage to those nephrons because if it's not corrected soon enough they can enter into chronic renal failure which is what we will be talking about in the next video okay now after after the initiation phase patients can go into What's called the aeric phase now it's important to note that some patients will actually skip this stage and enter into the next stage the diuresis stage so you may have a patient who has renal failure the beginning stages of it but they have massive amount of urinary output and they're not putting out Le a low amount of urine that you would expect so they may have skipped this stage and went to the next stage okay so the augc is where you will notice that your patient's urinary output is going to be less than 400 m per day and why why is the urinary output so decreased well remember it's because the garus has decreased in its function to filter the blood so when you look at the labs they're going to have a decrease GFR okay so let's look at the signs and the symptoms because they have a decreased GFR they're going to have a an increased bu and creatinin that waist level azotemia so your patient is probably going to have some neurostatus changes they're going to be confused really sluggish and tired and sleeping all the time and they can also itch from where that waste has built up and it causes itching on the skin nursing interventions for that you want to watch their protein consumption so limit that because remember the breakdown of protein in the liver increases Ura levels so you want to limit that and their safety because they're going to be confused may not know where they're at they can get up and fall things like that another thing is hyperemia and this is because there's an decrease excretion of pottassium in those kidneys and what can happen whenever you have a high potassium level you have to watch out for cardiac issues they can have a significant cardiac event so you got to watch the EKG and look for tall and peaked tea waves wide QRS complexes and prolong PR intervals that can represent hyperemia so your nursing interventions would include restricting potassium rich foods we don't want to give them any more potassium they have enough monitor their EKG they need to be on a bedside monitor to watch that assessing Labs The Physician May order a medication called K exelate either orally or rect and this will help bring down that potassium level so be familiar with that another thing is they will have increased fluid in the body because the glomerulus is not removing that excessive water so you can see swelling throughout in their face around the eyes and their legs so edema uh they because of that they are at risk for pulmonary issues from where all that extra flu is going to go into the lungs cause breathing issues they can have cardiac issues from that hypertension from The increased blood volume so nursing interventions would include limiting their fluid intake uh monitoring their intake and output very strictly we want to know exactly what they're taking in and exactly what they're putting out daily weights get them up every morning use the same scale and weigh them because weighing a patient is a great indicator of how much water they are retaining and then as a nurse you want to look at the weights okay today's weight they were 200 yesterday they were one one 90 so they've gained 10 pounds that's very significant monitor their blood pressure because they're going to have hypertension assessing those lung sounds for crackles which would represent pulmonary edema monitoring their oxygen saturation looking at that swelling going on is it decreasing or is it getting worse okay next they can go through what's called metabolic acidosis and this is because you have decreased excretion of those hydrogen ions so you're getting very acidic blood and their P blood pH could be less than 7.35 and they may present with confusion with that along because they have an increased V and creatin level too and they may be doing a type of breathing called cosmal breathing and this is a deep rapid breathing and it's your body's way of trying to compensate to increase that blood pH because it's very acidic so carbon dioxide is an acid so your body is causing them to breathe deeply and rapidly to blow off that carbon dioxide out of the system hoping to increase the blood pH so you may see that so what you want to do nursing intervention wise is monitor their safety because of confusion and their respiratory status as well and patients can also present with mild hyponatremia so a low salt level it'll be very mild or it could be normal it could be the reason for this is because the blood is diluted from the extra fluid that's in the blood so that level can run low also they'll have they may have an increased phosphate level and a decreased calcium level because remember phosphate and calcium are opposites if one's High the other ones L ones or vice versa so you want to restrict their phosphate foods and monitor that and another thing they can have is that really concentrated urine so if they produce any urine really at all it'll be really dark and concentrated and it'll have a high urine specific gravity and that will be any value greater than 1.020 now how long does this stage tend to last tends to last a week to two weeks and you want this stage to be as short as possible because the longer the stage is the longer and more of an increased chance there's going to be damage to those nephrons and again they can enter into end stage renal disease chronic renal failure and the treatment for this stage is dialysis our next stage is called the diuresis stage and this is where our nephrons are on their way to recovery but they're not 100% yet but they're getting there so now they have the ability to actually filter the blood so they can start bringing down our waist levels that bu and creatinin getting that out however they can't concentrate the urine yet so we're not really going to get some electrolyte balance and our water levels are still going to be crazy now the GFR is improving but it's still abnormal so that's why you're seeing the decrease in The Bu and creatinin but it will those levels will still be abnormal but your patient will start to become more aler and oriented compared to how they were in the previous stage the aloric now your patient is going to be voiding a massive amount of urine about 3 to 6 lers per day and why is this this is due to what's called osmotic diuresis okay so remember the kidneys can filter the blood now now it has a lot of waste to filter out so what's going to be in that filtrate a lot of Ura so that newly created filate is jamack full of Ura this is going to cause osmotic diarrhea it's going to pull a lot of water out they're going to be voiding 3 to six lers per day now because of that think use nursing knowledge because we have V we're avoiding so much fluid out what's going to happen to our fluid status in our body in the previous stage we are fluid overloaded now we're fluid depleted so we're going to become hypovolemic we're at risk for dehydration hypotension what's going to happen to our electrolytes well before we are struggling with hyperemia now we're voiding so much out we're going to be wasting potassium so we're going to have hypokalemia and how's our urine going to be it's going to be really diluted so they'll have less than 1.020 urine specific gravity the urine's going to be really diluted so nursing intervention wise what we want to do is we want to maintain strict eyes and oath because they're going to be losing a lot of fluid those daily weights signs and symptoms of dehydration and the physician May ordering supplements to replace those electrolytes that are low because they're being voided out and they may be on IV fluids which seems like a paradox for someone who's a renal failure but if they're in this stage they need it so they don't go into dehydration now this stage can last anywhere from a week to three weeks okay so after they go through this stage they hit the last stage called recovery and this start s when the GFR returns to normal now let's ask ourselves what is going to happen with our urinary output since our GFR has returned to normal we're going to be normal so one to two lers is what they should be putting out per day what's going to happen to our bu and creatinin it's going to become normal it's going to stabilize and our electrolytes are going to be normal where where they need to be so every everything will be maintained and that's how we know that we are in the recovery stage now this stage can take a year more depending on the amount of damage that was done how long they spent in the aorc stage and the patient age so it's different for every patient now some patients unfortunately never make it to the recovery stage because there's just too much damage and instead they develop what's called chronic kidney disease infe adrenal failure which we will be talking about in the next lecture so this wraps up this lecture on acute kidney injury thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	COPD_Chronic_Obstructive_Pulmonary_Disease_Chronic_Bronchitis_EmphysemaNCLEX_Part_1.txt	hey everyone it's sarah thread sterner sorry and calm and in this video I want to be doing an in CLECs review over COPD also called chronic obstructive pulmonary disease and this video will be part one of a two-part series what I'm going to be covering is the path of COPD the signs and symptoms the different types and how it is diagnosed and in part two I'm going to be covering the medications and the nursing interventions so be sure to check out that part and as always over here on the side or down in the description below you can access the quiz and the notes that go along with this video so let's get started first let's start out talking about what is the definition of COPD what is this it is a pulmonary disease that causes chronic obstruction of airflow from the lungs so before we get into the pathophysiology and dive into this lecture let's talk about the key points that you need to remember so whenever we're talking about the path or the signs and symptoms you'll have a little basic understanding of what we're talking about okay okay so key point one with this disease there is limited airflow and why is this because the bronchioles which you can see right here and this right here is a viola sac there is inflammation which has become chronic and has led to this wrong he'll become in deformed and narrow then you have excessive mucus production so it's limiting the amount of oxygen that can get in to the bronchial to go to alveolar sac for gas exchange and it's limiting the amount of carbon dioxide that's coming from the alveolar sac to be exhaled so you're going to be getting some problems another key point is that there is the patient does not have the ability to fully exhale and this is due to the loss of elasticity in these alveolar sacs and here you can see there mutated looking in a sense their floppy your IV OS X should be nice and circular and uniformed and here it's completely lost elasticity and what you have Yolo sex do is they inflate and deflate platon deflate and if they don't have their form they fully can't do that and if they can't do that you're not going to have proper gas exchange so it's going to throw your blood Casas off and air pockets are going to develop over time so we'll talk about that especially in your emphysema patients this happens okay so COPD is irreversible there's not a cure cases vary from patient to patient some patients will have a mild case while some will have severe I've had some patients they cannot talk a complete sentence without stopping taking breaths or hyperventilating during the sentence because they have COPD so bad and then some patients I've had you wouldn't really know that they had COPD unless you sing their test results or they told her so it varies and COPD is managed with lifestyle changes and medications which will really go over in part two with the nursing interventions patient education and the medication regimen now the causes of this the most common cause of COPD tends to be environmental from harmful irritants that the person has breathed into their lungs for example smoking is a huge cause of this because they're smoking their cigarette that all those chemicals are constantly entering into the lungs exhaling and that wreaks havoc on the pulmonary system over time however this can happen in people who do not smoke for instance say they live in an area where there's really bad air pollution or their job and they're around irritants 24/7 or they're a welder maybe don't wear the protective mask they need to and they can develop this and COPD tends to happen gradually people will start to notice signs and symptoms in middle age they may start to notice that over time they became more short of breath with normal activity they can normally tolerate they notice that they have this chronic sometimes productive call constantly especially like that smokers Hoff in the morning and they're getting real current lung infections like pneumonia things like that then they go to the doctor the doctor runs on them and they have this condition now let's talk about the types of COPD COPD that term is used as a catch-all term for diseases that limit airflow so what we're going to concentrate in this lecture is the one type called chronic bronchitis and emphysema so let's talk about chronic bronchitis first okay sometimes you may hear these patients refer to as blue bloaters why are they referred to as blue bloaters because with emphysema those patients are referred to as pink puffers so with the blue bloaters with chronic bronchitis these patients tend to have cyanosis due to the hypoxemia that they're having the low oxygen which you will see blue around their lips mucous membranes skin things like that and they tend to have edema swelling in the belly the legs because depending on how severe this is it leads to right side of heart failure so let's look at the path though of what's happening with chronic bronchitis okay here on this diagram you have what a normal healthy lung looks like and then over here you have a lung that's been affected with COPD specifically we have some wrong chronic bronchitis and emphysema going on so first let's talk live the healthy lung and talk about how normally gas exchange goes through this and then we'll compare it with a lung that's experiencing chronic bronchitis so you breathe in some oxygen it goes down through your trachea which your trachea splits at the chorion up into your bronchus your rotten left bronchus and rotten lip bronchus your primary bronchus enter into the lungs at the hilum and then the bronchus even breaks and branches off into further smaller Airways like your secondary bronchi your tertiary bronchi and then eventually your bronchioles and then you're a vor sacs and yeah and you're a vor sacs are opening and closing inflating and deflating for gas exchange and what helps you to do this breathing is whenever you breathe in your diaphragm which is normally dumb sheep is going to contract and it's going to go down and this is going to create a negative pressure in your lungs to allow you to suck in that air which is going to go through gas exchange then all that pressure has built up your diagram is going to relax back into its dome-shaped position that's going from all that increased pressure in the lungs that's going to cause you to exhale and force that air out so they're constantly inflating and deflating and you keep a nice shape a small hyper-inflated now let's look at the COPD lung with chronic bronchitis so let's say that this person is a smoker and constantly smoking and over time the smoke is going through all these Airways and just really messing it up and as what's happened is that over time these little areas you see right here your bronchioles have become inflamed and they start to produce all this mucus so um whenever the person is trying to breathe in that oxygen can't get to these a viola sacs because all these narrow little airways and all this mucus in the way so oxygen doesn't get in then they're trying to exhale that air that they just breathe in well they can't exhale it fully because again of the narrowing and all that mucus so they're going to be retaining the carbon dioxide now when that patient takes another deep breath in they're going to be adding more air volume to whatever they already breathe in previously so this is going to lead to overtime hyperinflation of the lungs lungs going to like enlarged now when the lung and large is you have your diaphragm below your lung it's going to cause your diaphragm to flatten and whenever it flattens you and have issues with being able to breathe because your diaphragm does 80% of your breathing and then the patient's going to start using their accessory muscles to breathe which will really see with our emphysema patients who are called the pink puffers and that's for that reason now let's talk a little bit more about that gas exchange because said there's not enough oxygen getting in and we're retaining that carbon dioxide so that person's going to be experiencing what's called respiratory acidosis but because there's not a lot of that oxygen getting in because just so you go through gas exchange with you real fast here's a blown-up version of an a vo lie and what happens is that you have capillaries on these alveolar sacs and this capillary is delivering carbon dioxide through this capillary wall to be exhaled because that is a waste product of metabolism and once they get rid of it then these little red blood cells want to get re oxygenated because right now they're exhausted they've done their job through the heart and they need more oxygen so oxygen that you've breathed in will go through that wall and attach to those red blood cells and then go back to the heart and become through the body and do its job but here this is not happening so what's going to happen you're going to have low amounts of oxygen the patient is going to become cyanotic we're going to display that cyanosis then your body's like wow we've really got to compensate for that because if you've learned through all of our lectures every time something bad happens in the body the body tries to do something with some other system to help compensate it and try to save your life so what happens is that the body will start increasing the production of these red blood cells because it's like well if we get some more red blood cells in the system we can get the body oxygenate because we're not getting a lot of oxygen but this causes a problem it causes the blood to become too thick then the body sees well that's not really helping so let's throw some other things in so what will happen is that there will be an increased pressure in the arteries specifically your pulmonary artery because remember your pulmonary artery brings an oxygenated blood to the lungs to become oxygenated then that pulmonary vein sit back to the left side of the heart to be pumped through the body and do its job so your pulmonary arteries coming from the right side of the heart so what happens it starts shifting blood which is going to increase the pressure in that artery and you're going to get what's called pulmonary hypertension and whenever you get pulmonary hypertension and that artery what is happening is that that blood is going to start back flowing in that pulmonary artery into that right side of the heart and we really went in depth in this in a heart failure videos and that blood starts backing up you start getting a lot of problems it will affect your liver because you'll get congestion in those hepatic veins and fluid will start building up in the abdomen eventually into the legs and it can even lead to left-sided heart failure as well so that is where the patient is getting the bloating and that's where the blue bloating comes from now let's look at emphysema these patients are sometimes called pink puffers why is that patients with emphysema tend not to have the cyanosis as with the blue bloaters why you get the name pink and the puffers comes from what's going on due to compensation and because the body has low oh two levels from what's going on with these alveolar sacs the body will hyperventilate increase that respiratory rate so in a sense they will be puffing in order to breathe they're really breathing rapidly to get more oxygen in to increase the oxygen level so you'll have no sign of cyanosis and the pink complexion now let's look at what's going on up close okay so what's happened is that say for instance this patient is a smoker and they're inhaling that constant irritant to their lungs what happens is that an inflammation process starts going on because of all that smoke affecting the sac and the body actually releases a substance that causes those of Yolo sex to lose their elasticity so they're not going to be inflating and deflating properly and they become deformed and they don't work and whenever that happens it's not good because you're not going to have proper gas exchange happening where those ovular sacs are inflating and deflating which is allowing that carbon dioxide to pass through that capillary wall so you'll be keeping carbon dioxide and it's not going to allow that oxygen to attach to those red blood cells to go through the body so you're going to have low oxygen now also another thing that happens because you're those sacs are not fully deflating because they don't work good air is going to get trapped in those sacks which is going to lead to hyperinflation of the lungs and whenever the lungs enlarge remember what's below your lungs is your diaphragm and the diaphragm is going to go from that beautiful dome shape to flatten and how you the way you breathe what makes it effortlessly is your diaphragm it plays a huge role in it so to compensate because the lungs have to in a sense squeeze that air out the body is going to start using accessory muscles on your chest to help the person get that air out and they're also going to hyperventilate to get that air out and to hopefully get some more oxygen in so this will lead because they're using their accessory muscles so much to that barrel chest look that patients with a massima may have which is that increase anterior posterior diameter that you may see on inspection and the hyperventilation again is the compensation to help get that oxygen level where it needs to be so that's why you're not going to see we're not going to be blue while they'll have that pink complexion compared to patients who have chronic bronchitis now let's talk about the signs and symptoms of COPD to help you remember the typical signs and symptoms of COPD let's remember the mnemonic lung damage because that is what is going on with COPD they have lung damage to the lungs that is limiting the airflow from the lung so el they are going to have lack of energy and this is because they have a limited supply of oxygen flooding through the body in order for your organs and everything to work properly it needs oxygen so anything for them for them to do is very hard and requires a lot of effort you for unable to tolerate activity they will get a lot of short really short of breath and if they have it really severe even getting them from a chair to the back to the bed or walking to the bathroom it's a big deal and it makes them very short of breath in for nutrition it will be poor especially with your patients within fuzzy manaos link back to the path oh why would they have poor nutrition well they are spending a lot of energy breathing and they're burning more calories than normal a person with healthy lungs would burn just with their breathing so they're going to have weight loss also eating if they have it really released severe and just chewing their food and swallowing their food exhausts them so they may not be up to eating so you really have to manage that which we'll talk about nursing interventions with your patients with emphysema g4 gases abnormal those arterial gases your po2 pco2 will be greater than 45 usually that's carbon dioxide and your po2 which measures your oxygen less than 90 because remember they have low oxygen and high carbon dioxide and usually we'll have respiratory acidosis because of those lab results D for dry or productive call and the productive cough all these possible be constant and chronic patients will call it wrong card tend to have the productive cough because remember they have the increased mucus production from where those bronchioles have become flamed and they narrowed so that's why they have that a four accessory muscle usage for breathing again that was with your patients with emphysema and that was because that diaphragm has flattened those lungs are hyper-inflated so now they their diaphragms aren't there to help them exhale that air so they've got to compensate by using those accessory muscles and the other a for abnormal lung sounds it can vary they can be diminished where you don't hear much of anything especially in those lower bases coarse crackles especially in your chronic bronchitis because of that you because that's what you're going to be hearing or wheezing and I have a whole video if you're not familiar with what these lung sounds sound like a card should be popping up and you can access the video it has audio clips where you can actually hear these lung sounds in for modification of skin color from pink to cyanosis and this again was with her chronic bronchitis patients they have a tendency because of their low oxygen will have the blue around lips or mucous membranes or the skin and a four anterior-posterior diameter increase and that's that barrel chest look and that's mainly with the patients who are suffering from emphysema because the usage of those accessory muscles built up the chest and the hyperinflation of the lungs G and four gets in the tripod position to breathe a lot of times in order to help these patients breathe whenever they're having difficulty breathing they will get in the tripod position and this is where they're standing they're leaning forward and while supporting their hands on their knees or on an object and just being bent over like that helps them breathe better so you may see that sometimes and ii4 extreme disney a-- and that just goes along with everything that's going on they just get really short of breath a lot of times now let's look at the complications of COPD and how it is diagnosed and a few complications a patient could experience with COPD is heart disease like heart failure again and we talked about that with the path especially the chronic bronchitis patients it can lead to pulmonary hypertension which will cause increased pressure on that right side of that ventricle and I mean get right-sided heart failure another thing is pneumothorax where the lung just collapses spontaneously and this tends to be spontaneous and patients who have a history of COPD and it's because of the formation of those air sacs in those alveoli and especially your patients with emphysema and I have had patients who have been admitted with this so this does happen I have seen it lung infections pneumonia for instance and they have an increased risk of developing lung cancer okay so how is this diagnosed from a nursing standpoint just be familiar with what may be ordered so if you're taking care of a patient with this you know what to look for for their test results and physicians will order what's called a spirometry which is a test where patients breathe into a tube which measures the following it's going to measure how much volume the lungs can hold during inhalation and it's going to measure how much and how fast air volume is being exhaled because remember that's the whole problem with this disease process they have an issue with retaining too much so they don't exhale too much compared to how much they took in so it will measure that and what it's measuring the two things mainly is it's measuring the the fvc which is the forced vital capacity and if they get a low reading on this this represents restrictive breathing and this is the largest amount of air exhaled after breathing in deeply in one second another thing it looks at is it measures the force expert ory volume which is how much air a person can exhale within one second and a low reading will end okay how severe the disease process actually is so that is about COPD part one now be sure to check out part two and don't forget to take the in CLECs review quiz that goes along with this lecture and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Congestive_Heart_Failure_CHF_Treatment_Management_Nursing_Interventions_Medications_Part_2.txt	hey everyone it's s with register nurse rn.com and in this video I'm going to be going over part two of heart failure this video is part of a Cardiovascular inlex Review series that I'm going to be covering and in the previous video I covered part one of heart failure and I talked about the patho of heart failure the signs and symptoms the different types and things like that so if you haven't watched that video be sure to check that out because that video builds upon this video and a card should be popping up so you can access that so what I'm going to do in this video is I'm going to be covering the nursing interventions and the medications given specifically in heart failure because that is really what the inlex exam and your nursing lecture exams like to hit on because as the nurse you need to know what your role is you need to know how to educate the patient and those common side side effects of those medications you'll be giving in heart failure and then after you watch this lecture be sure to go to my website register nurse rn.com and take the free inlex quiz that will test you on heart failure and a card should be popping up so you can access that so let's get started first let's recap and talk about what is heart failure heart failure is where the heart is to weak to pump efficiently so it can't properly give your body the cardiac output it needs to maintain the metabolic needs so you get some major issues going on and remember from the other video your left side of your heart or your right side of the heart can be affected or you can have both so remember with left-sided heart failure you're going to get the pulmonary symptoms and with right sided heart failure you're going to get those peripheral symptoms and the most common type of heart failure is left-sided and it can cause right-sided heart failure so keep those things in mind whenever we're talking about medications and things like that so what are the nursing interventions let's cover that first what is is your role as a nurse in a nutshell what you're going to be doing is you're going to be assessing that patient educating that patient and administering medications so first let's talk about the assessing part what are you going to be doing okay as a nurse you were going to be assessing assessing their symptoms how are their symptoms are they presenting worse than before like if they're in right-sided heart failure how is that peripheral swelling is it going down because chances are they're going to be on medications are they responding appropriately to that or they getting worse um left side remember you get those pulmonary issues is the patient breathing better is there less crackles how are they doing with that next you're going to be assessing the patient's responsiveness to those medications medications such as digoxin you got to watch that heart rate because it can slow the heart rate down beta blockers things like that so you want to have them on continuous monitoring or be checking their Vital Signs often watching their blood pressure because they're going to be on ACE inhibitors arbs or vasodilators and that really messes with the blood pressure and plus you're shifting fluids out of the body they're in fluid overload and you're getting rid of fluids because they're so they're at risk for orthostatic hypotension and you're going to be monitoring their volume status because we're trying to diase them we're trying to remove that fluid so they're going to be on diuretics Chances Are The Physician will order fly catheter because a lot of times these patients come in they're in fluid overload they're going to be started on Ivy maybe Loop Diuretics like lasic it's very strong diuretic especially going the intravenous route so they may need a foli to help drain all that urine that's going to be coming out because getting up and going to the bathroom will wear them out because they're already the respiratory system is already compromised and just going back and forth to the bathroom puts a lot of strain on them and you're going to be monitoring assessing those daily weights every morning you're going to get them up on a scale or use the bed scale and you want to monitor that weight because it's very important how much weight they're losing or possibly gaining then you're going to monitor and look at those labs specifically you really want to watch potassium levels because a lot of the medications given in heart failure can cause hypo calmia or hyperemia for instance Lasix Lasix is a diuretic that wasts potassium so you really got got to monitor that lasx level um especially if they're on dexin because if you have low potassium that can increase the chances of dexin toxicity hyperemia medications that can cause that that are sometimes prescribed in heart failure are like those potassium sparing diuretics that actually do the opposite of Loop Diuretics they keep potassium like alao and ACE inhibitors and arbs they can increase potassium so if you have a patient on an Ace inhibitor and aldactone are at Major risk for hyperemia so you have to tell the patient to watch their potassium intake also you're going to be assessing and making sure they are following their cardiac diet and their fluid restriction diet a lot of patients have issues with this because um especially the fluid restriction diet normally they can only have about 2 liters of fluid a day so you have to constantly monitor what they're having for breakfast for lunch and dinner and in between make sure they're not cheating on that diet because we're getting r of that extra fluid and we don't want to just be putting it back in then we're going to assess the edema in the legs that goes back to the patient's responsiveness uh helping keep those legs elevated whenever they're in bed will help promote returning that extra fluid back into the vascular system hopefully being excreted through the kidneys and keeping them in high fowers position to help with respiratory that position setting upright helps the lungs expand and helps decrease dispan next safety this is a big issue with your heart failure patients because number one chances are they're going to be on some Vaso dilators or some other blood pressure medicine and um the body whenever they shift positions maybe lying in the bed they get up they can get really dizzy and they're at risk for falling so you want to make sure you monitor them for that and the extra swelling and the legs and the feet make it really hard to walk and put the feet on the ground and it can lead to them falling okay now educating this is a big piece so remember this stuff write it down because as the nurse we want to educate our patients with heart failure and regardless if you're not working on a cardiac unit maybe you're going to work on Ortho your chances are you're going to get patients with heart failure because this affects a lot of patients so our goal with educating is that we want to prevent readmission this disease process causes a lot of readmissions to the hospital and we want to prevent C um heart failure exacerbation so what you want to teach your patients is the following follow a low sodium diet guidelines are no more than two grams per day sometimes three so no more than two to three grams of sodium per day in your diet watch uh the hidden salts like in canned foods your sandwich meat your frozen meals things like that that you wouldn't normally think have a lot of sodium in but do it in soft drinks next fluid restriction the doctor wants them on fluid restriction they need to make sure they monitor how much they drink a day because some of these medications can make you thirsty so um no more than two lers a day of fluid vaccinations make sure that they are they need to be aware that they need to get an annual flu vaccine and that they're up to date on their pneumonia vaccine because illnesses can EXA exacerbate heart failure because it stresses the heart out when a patient gets sick next aerobic exercises that's like your cardiovascular exercise they need to do light moderate exercise to keep that muscle nice and strong and do that as tolerated once their sympt symptoms start dissipating next daily weights it is so important that they weigh themselves every day because it is an early sign of CHS um heart failure exacerbation if they're gaining weight so the guideline is if they're weighing theirselves make sure they're writing them down um they need to notify their doctor if they're gaining any more than 2 to three pounds per day or 5 pounds per week that is signaling hey you're starting to retain fluid something's going on let's go to the doctor um maybe they can prescribe some more diuretics so I don't have to go to the hospital and readmit it so daily weight's very important next compliance with medications a lot of times especially working as a nurse I have just seen where patients have quit taking their medicines maybe they couldn't could afford their medicine so they quit taking them and this sent them into heart failure exacerbation so um very important they take those medicines next smoking sensation quits smoking very bad with the heart causes Vaso constriction hard on the heart and limiting alcohol consumption next um teach your patient those early signs and symptoms we just talked about the weight gain also if they notice that all of a sudden they can't tolerate normal activities that they were doing like just getting up and going into the kitchen they notice that they're starting to get a little short of breath or at night whenever they're trying to sleep that they have to put a couple pillows behind them to sleep better which is called orthopedia those are some warning signs that hey I may be going into heart failure exacerbation now let's look at the medications for heart failure when you're studying these medications for the enclex or for your nursing lecture exams make sure you know the drug categories that are given in heart failure and what drugs are included in that category and how they work on the body the pharmacodynamics and their side effects and patient education very important key points you want to remember okay to help you remember the drug categories that are given in heart failure remember this pneumonic always administer drugs before a ventricle dies in heart failure our issue is with the ventricles they are either not pumping they're not Contracting properly or they're too stiff so they're not filling properly so we want to make this heart work easier especially these ventricles so that pneumonic should help you remember those drugs that are included so the first a ACE inhibitors ACE inhibitors stands for Angiotensin converting enzyme and this is usually the first line of treatment in patients with heart failure and and it's sometimes prescribed with a beta blocker which we'll go over a little bit later these drugs tend to end in p iil and one example of a ace inhibitor is linil and how this drug works is that it blocks the conversion of an Angiotensin one to anot tensin 2 so you don't have the conversion of anot tenson one going to anot tensin 2 and what does what how does that work well we know when ever Angiotensin 2 works it causes Vaso constriction but it's not allowed to do that so in turn you're going to get vasodilation which is going to decrease the heart the blood pressure and you're going to get kidney excretion of sodium think back whenever Ang Angiotensin is being blocked what's going to happen is it's going to cause your aldosterone levels to decrease what does aldosterone do aldosterone whenever ever it's being decreased it will cause your kidneys to keep potassium but excrete sodium which is what we want in heart failure we're trying to get rid of all that extra sodium and fluid in the body and this strug is helping us get rid of that extra sodium however because it's doing that it's going to keep this H potassium but get rid of the sodium we have to watch out for side effects of hyperemia H potassium levels and for some reason with this drug these patients can develop a nagging dry cough and I have seen this as a nurse it's for real and it really does happen they will literally cough every 3 to four minutes just this just over and over and over and it drives them crazy and it drives the people around them crazy so some people can't tolerate this drug next drug arbs they if the patient cannot tolerate an Ace inhibitor they'll be place on an ARB and how do arbs work ARB stands for angiotensin two receptor blockers so they're a little bit similar so let's look okay these like I said are used in place of ACE inhibitors they end in stin s a r t a n type of drug of this is low sartin and they work by blocking anot tensin 2 receptors so instead of blocking the conversion of angiotensin one anot tension 2 like the ACE inhibitors did this works by just blocking The receptors so again you're going to get some Vaso dilation and it's it's going to have the same effects on the body as your ACE inhibitors because you're going to have that decreased aldosterone and the patient's going to keep potassium but excrete sodium however a side effect with this is hyperemia just like with ACE inhibitors but they will not get that dry hacking cough okay our other draw diuretics D these um either patient will be prescribed on Loop Diuretics or potassium sparing diuretics and these diuretics are used in a combination with these ACE inhibitors or an ARB they're used together and um what your diuretics do is it helps your body get rid of that water and that sodium retention because in heart failure what we're doing is retaining all this water we got edema everywhere retaining sodium so it helps us to excrete that decrease that edema and it helps the heart pump easier because it doesn't have all that fluid volume in its Chambers trying to pump so it's getting rid of that however a side effect of this is that this patient will urinate a lot so as a nurse you want to be monitoring that urine output very very closely and you want to monitor their bu and creatin and making sure we're not diuresing them too much and putting too much strain on those kidneys okay an example of a Lube diuretic is Lasix remember with Lasix or Loop Diuretics they waste pottassium so before you get potassium I mean before you give Lasix check those potassium levels to make sure that they're good because you go in and give some lasic and their pottassium levels already too you're going to bottom that out even more so a lot of times Physicians will prescribe potassium supplements along with lasx and potassium sparing drugs drug alao um what these do they do the opposite of Loop Diuretics they keep um potassium so you have to watch out for um educate the patient not to consume foods that are high in potassium and to especially watch if your patient is on an ace or an R because remember they keep potassium and if they're taking alaon you have a double risk of increasing that potassium level next beta blockers how do beta blockers work they work by blocking the nor epinephrine effects on the heart muscles so norepinephrine will naturally increase your heart rate so we're going to block that from happening so beta blockers are going to slow down the heart rate they have a negative inotropic effect which increases my cardial contraction hence a fancy word for slowing the heart rate which will in turn decrease your heart's workload because it is overworked in heart failure these drugs end in LOL typical ones used in heart failure are mopol carvol and bisol now typically the way that these beta blockers work they slow down your heart so they weaken the heart heart's contraction so in some forms of heart failure especially acute heart failure that deals with systolic dysfunction you don't initially want to use these beta blockers because let's think back to the other lecture what is systolic ventricular dysfunction systolic that is the squeezing phase of the heart so there is an issue with this ventricle being able to squeeze that blood out so if we throw if this patient is an acute systolic dysfunction and we throw a beta blocker on them it's going to weaken that heart contraction even more and we don't want to do that because we have a contraction problem so it will sometimes the beta blockers will be used in stable systolic dysfunction and a lot of times these beta blockers are prescribed with ACE inhibitors or those arbs in combination now a lot of times beta blockers are used in disa diastolic dysfunction heart failure and what was ventricular diastolic dysfunction that was where remember di is the filling phase of the heart the resting phase and there's an issue with the ventricle maybe it's too stiff and it doesn't fill properly with all that blood it needs to fill with but what a beta blocker can do is slow down that heart rate let that ventricle rest a little bit longer and fill more with blood so it can squeeze it out because it's squeezing mechanisms gray it's just the feeling so sometimes it will be used to treat um ventricular diastolic dys function now side effects of your beta blockers remember this um braa cardia so before you give a beta blocker check the heart rate make sure they're not too braed cardic um it can mask hypoglycemic signs and symptoms in diabetics a lot of times a diabetic knows when their sugar is low because they may get Tac cardic hence you're not going to get Tac cardic with brocard with beta blockers because it slows the heart rate down or they can get sweaty things like that and that mask those symptom so you need to teach your diabetics that and beta blockers can cause respiratory issues so it's t they're typically not prescribed especially the ones that aren't selective for patients with COPD or asthma because it could cause Bronco constriction and um whenever the patients take these tell them not to take them with any type of juices especially grapefruit juice because it can interfere with your body's absorption of the beta blockers okay next let's look at a for anti-coagulant these are not used in every patient with heart failures so um typically it's going to be used in heart failure patients who a lot of times heart failure and atrial fibrillation go hand in hand uh and you know with aib those Atrium are just quivering blood is pulling in there when blood pulls that's not good because a clock can form can shoot through the heart and we can have an embolism so um if a patient's in aib with heart failure they may be starting on an anti-coagulant or they have a history of blood clots or they have an ejection fraction less than 35% we talk about we talked about in the other video what ejection fraction was and um this is where your heart is not squeezing all that blood out properly so contraction isn't good and if it's not squeezing all that blood out that's normally going in there with systolic dysfunction you're going to have more blood pull in there so there's a increased chance of developing a clot and shooting it through the heart okay next the for vasod dilators um a lot of times these are prescribed if a patient can't tolerate an Ace inhibitor or an arm because it works by causing dilation and um One Drug which is an arterial dilator is hydrazine and it's a lot of times sometimes prescribed with a nitrite called isroil and that is a Venus dilator hydrazine is is a specific drug that acts specifically on your um arteries and isoil is what acts on your veins so what happens is that you get dilation going on of those arteries and veins what how does this work how does it benefit the heart it decreases blood and fluid going back to the heart because the heart is already overloaded in heart failure with all this blood and all this fluid so we got all this nication going on and it will decrease the amount of fluid that's going back and the workload that your heart has to undergo however side effects with this are hypotension because anytime you have dilation going on the patient is at risk for hypotension so you want to measure that blood pressure make sure it's good before you get it and they are at risk for orthostatic hypotension so say your patients on these medications they're laying in bed they need to get up to go to the bathroom you want to get them up slowly and gradually because they can get dizzy they can pass out and fall so you want to watch safety issues with that next D for de how does dexin work on the body I would remember this for sure okay it has a positive inotropic mechanism which means that it has that the heart has an increased ability to pump stronger however it has a negative chronotropic mechanism that allows it to beat slower so it's a win-win it beats slower but it pumps more efficiently so this allows the heart to rest and P pump more blood which is great if you have left ventricular systolic dysfunction which is what this drug is sometimes used in however it's not used as first line treatment for heart failure um it's going to be used alongside with your ACE inhibitors or your diuretics because dexin can be a nasty drug it has toxicity issues and if a patient um has a low pottassium level goes into hypokalemia potassium level less than 3.5 they can go into into dexin toxicity so with this drug you want to monitor the drug levels um I would remember this a normal dexin level is .5 to two nanograms per milliliter this is where you want that patient to hang out anything higher than two is bad deox and toxicity and signs and symptoms of dit toxicity classic I have seen this this does happen um they'll have nauseum vomiting and they'll report some Vision change es uh they may all of a sudden start seeing some yellowish green Halos um they can be bra aaric as well and what would happen you notify the physician immediately don't give another dose of dexin and um The Physician will probably order the antidote for dexin which is digine very easy to remember it tells you what it is digine d i g i b i n d matches dejin that is the antidote for that um whenever you are giving dexin as a you all always want to check the apical pulse and make sure it's greater than 60 beats per minute before giving the dose okay so that is a review the part two review of heart failure be sure to go to my website register nurse rn.com and take that free quiz and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	ACE_Inhibitors_Pharmacology_Nursing_Angiotensin_Converting_Enzyme_Inhibitors.txt	hey everyone it's sarah thread sterner sorry and calm and today we're going to go over ace inhibitors and after you done went to this YouTube video don't forget to access the free quiz that will test you on this medication so let's get started what are ace inhibitors well to help us learn this medication we're going to use the mnemonic nurse which is going to tell us the name of the drug and that tells us how this drug works on the body what it's used for what is it treat our responsibilities as the nurse side effects we can expect from this medication and education pieces we need to provide for our patient so first let's talk about the name the letters a stands for angiotensin converting enzyme so what these drugs do is they inhibit this enzyme from really doing its job so ACE plays a huge role in our wrath system the renin-angiotensin-aldosterone system and what this system does is the whole goal of it is to manage our blood pressure especially when our blood pressure is low so when the blood pressure is low this system kicks in what it wants to do is it wants to get angiotensin ii in the body working because angiotensin ii as we learn from our short series is a major vaso constrictor of our vessels so that's going to increase our blood pressure plus it triggers the release of aldosterone which is going to help put more sodium and water into our circulation which is going to help increase our blood volume and this patient can get their blood pressure back up so that is what a steps but if we want to throw an ACE inhibitor it's going to cause the opposite effect it's going to lower the blood pressure now one thing you want to remember to help make things easier on you while you're studying is to remember that ACE inhibitors in with pril P R I L so when you're looking at your patients medication list trying to figure out which one's an ACE inhibitor or you're taking an exam look for prio and some examples of an ACE inhibitor is like captopril lisinopril ramipril or bins Aprill so what ace inhibitors do is they inhibit this wrath system and again that stands for renin-angiotensin-aldosterone system and if you can understand how this system works it's a breeze learning ACE inhibitors because ACE inhibitors do the opposite and what this system is really supposed to do so let's quickly talk about this system so a patient's blood pressure drops it's really low and the kidneys sense this and they're like hey we got to do something about this low blood pressure we're not gonna get enough blood supply and we're gonna die so what they do is they release renin into the circulation and when Renton is present in the circulation this causes angiotensinogen which is a protein created and produced in the liver to create angiotensin 1 now remember the goal of this whole system is to get angiotensin 2 on board because it's a major vaso constrictor so in order to do that we have to have a spread the angiotensin converting enzyme so whenever that is present it's going to convert this angiotensin 1 into angiotensin 2 when we have angiotensin 2 present in the body we're gonna get major vasoconstriction of vessels increasing systemic vascular resistance increasing blood pressure and it's gonna trigger the release of aldosterone which is going to help increase our blood volume now if we throw an ACE inhibitor on what's it gonna do it's going to prevent this ace from doing its job so we're not going to get the conversion of angiotensin 1 into angiotensin 2 so we're going to lower our blood pressure now let's talk a little bit more about this angiotensin converting enzyme ace in angiotensin 2 to help drive home some points so you can really understand your role as a nurse and those education pieces there will be really no reason to memorize it because it just makes sense okay so angiotensin converting enzyme when we're not inhibiting it what it does as we've already established is that it converts angiotensin 1 into angiotensin 2 we get major vasoconstriction we increase blood pressure systemic vascular resistance now another thing that it does when we're not inhibiting it is that it activates a substance called bradykinin by breaking it down now let's talk about Brady cotton Brady honey is a substance that's an inflammatory substance that really helps dilate the vessels when we dilate vessels we decrease like systemic vascular resistance hence the blood pressure so whenever you have the right system kicking in the renin-angiotensin-aldosterone system kicking in it doesn't need dilation so it's very important that it inactivates this substance because we don't need dilation if our blood pressure is low but if we're throwing on an ACE inhibitor we can benefit from this Brady Cotton's actions of dilation so it will inhibit these ACE inhibitors will inhibit this inactivation of this Brady cotton so we'll increase the amount of a Brady cotton present which is going to dilate vessels and help us decrease our blood pressure even more which is great but one thing I really wants you to remember because of this Brady con and it's an inflammatory substance some patients can have a side effect of having a persistent dry cough and literally it drops some patients just crazy because they're just hacking and coughing all the time and sometimes patients have to be switched to another medication because it's so bad and I've had patients who have had this so this does happen with ACE inhibitors so remember Brady Conan can lead to that persistent annoying dry cough now let's talk a little bit more about this angiotensin 2 well we've already established it's a major vaso constrictor so when we constrict our vessels was I do it increases systemic vascular resistance and our blood pressure now another thing angiotensin 2 does when it's in the is this going to trigger the release of this aldosterone and aldosterone influences the kidneys to keep sodium and water and the whole reason for that is it's gonna really help increase our blood volume which will help increase our pressure even more now while it's keeping the sodium in the water the kidneys are going to be excreting potassium so if we throw an ACE inhibitor on we're going to prevent remember angiotensin 1 turning into angiotensin 2 so that right here is not going to happen so our ace comes it X's it out so what's the effects going to be whenever we give our patient an ACE inhibitor well we don't have the conversion of angiotensin one to angiotensin 2 so our blood pressure and systemic vascular resistance will drop what is going to happen with this sodium and water well instead of keeping it like how we did over here we're going to excrete the sodium in water which is going to provide like a diuretic effect for our patient now this is good for patients for instance who are in fluid overload due to heart failure so here in a moment we're going to get in what this drug is really useful in potassium over here we were excreting it well with ACE inhibitors because how it's working on the kidneys you can actually keep too much potassium so with many patients you have to watch their potassium levels because they're at risk for hyperkalemia so remember that ACE inhibitors hyperkalemia so nursing considerations will have to be looking at those potassium levels and educating our patients on what foods to watch out for so that we don't increase those levels now let's talk about what ACE inhibitors are used for well we've established that ACE inhibitors help lower the blood pressure because we're preventing that angiotensin 1 to angiotensin 2 so it's great for people who have hypertension it will lower their blood pressure another thing it's used to treat is heart failure specifically systolic dysfunction and this is where that left ventricle can't really empty or pump blood forward out of it through the aorta into the body so instead that blood can back up go into the and lead to heart failure fluid overload so our ace inhibitors what they can do is they can help decrease after load and remember after load and we're talking about the left ventricle is where is the pressure that the ventricle must overcome in order to get that semilunar valve open so blood can leave it so if we decrease that resistance that pressure that that ventricle must overcome hence the systemic vascular resistance it'll make it a lot easier for that ventricle to pump blood forward in addition ace inhibitors are gonna help decrease our preload and preload is the amount of that ventricle has stretched at the end of its filling phase with blood so at the end of diastole another thing that ACE inhibitors will help treat is a patient who has suffered a myocardial infarction an MI so when their post mi and what ACE inhibitors will do because it alters a lot of this after load and preload it will help limit the effects of damage that can happen to the heart once a patient has had a myocardial infarction now let's talk about the responsibilities of the nurse okay whenever a patient is on an ACE inhibitor what are you gonna do well of course you're going to monitor their blood pressure and their pulse routinely you want to look at that see where they're running with our blood pressure because with ACE inhibitors there's a risk of hypotension where that systolic is less than 90 and that increases even more of your patients on diuretics where they're urinating a lot they're losing other fluid volume and that can decrease pressure or if they're on other blood pressure medicines because a lot of cardiac patients are going to be on a variety of medication so you definitely want to watch their blood pressure in addition you want to monitor some things like their potassium level make sure that they're not experiencing hyperkalemia and we talked about the reason for that a normal potassium is three point five to five so you want them within that rain and if they if you get an EKG or they're on bedside monitoring you can look at their EKG and one sign in symptom of hyperkalemia with their EKG is that they have tall peaked t-waves also you want to be looking at their renal function so their bu in and creatinine because remember this drug can alter how our kidneys work we're messing with the sodium and the water and the potassium so making sure that they're within range and normal be you in is about 5 to 20 normal creatinine is 0.6 to 1.2 and of course looking at how they're urinating what is their urinary output we want it in an adult at least 30 CC's per hour another thing to remember with ACE inhibitors is that you want to watch out for a condition called angioedema this is where they're a swelling of the dermis and the sub-q tissue so we have really deep swelling it's not superficial swelling like you to care yeah this is deep down in there and that can be life-threatening so how your patient will present with this is that they can get swelling on their face their mouth or extremities and it can affect the airway where they're gonna have difficulty breathing so you want to educate your patient about that what are the signs and symptoms of it it's rare but it can happen to any patient it's most common they have found in African American patients and if it happens it's dangerous and they need medical treatment immediately and lastly with our responsibilities you want to look at how your patient is really tolerating this medication because I mentioned that persistent dry cough it will literally drive some people crazy because they're constantly just hacking and coughing but because this medication is prescribed with people who also have heart failure as a nurse you want to look and make sure is this the persistent dry cough associated with this medication or is this heart failure exacerbation where they're going into fluid overload so you'd want to determine the two and how you would look at that is you would listen the lung sounds what is our lung sunlight are they wet where they you can hear crackles are they having difficulty breathing on exertion just getting up from the chair to the bed they're really winded they can't breathe and they're having swelling and they're shrim ADIZ where the retaining fluid so make sure you look at that and assess that and just don't write it off that it's that dry hacking cough that you get with ace inhibitors because it could be that they are in heart failure exacerbation they'll talk about the side-effects of ACE inhibitors well this medication can cause that persistent dry hacking cough and that was related to that Brady Kannan and this is usually harmless so if your patient has that let them know that another thing is that it can cause dizziness because we're changing dealing with the blood pressure so tell the patient to change positions slowly when they get up because they can become dizzy and they might fall it can also cause hypotension because it can lower the blood pressure too much it can increase potassium levels at hyperkalemia and it can cause angioedema that dangerous swelling of the deep tissues and if they experience that they need medical treatment fast now let's wrap up this lecture and let's talk about the education pieces for the patient so since your patient is taking an ACE inhibitor which alters blood pressure it's really important you educate your patient to check their blood pressure and pulse regularly and to record it and to bring those recordings to their follow-up visits so the physician can see if this medication is doing what it's supposed to do also you want to educate your patient to avoid salt substitutes with potassium and consuming foods that are rich in potassium like potatoes bananas pork oranges tomatoes spinach avocados because we could increase the potassium level even more because remember ace inhibitors how they work on the kidneys they will call us the kidneys to keep potassium now this education piece is really important if the patient is also taking other types of medications that keep potassium like those potassium sparing diuretics like spironolactone so the patients at double risks for high potassium level so really drive that point home to them another thing is if they do have that dry cough and can't tolerate it some patients can tolerate it and it's just fine but a lot of patients when they do get it they can't tolerate it they need to speak with their physician about it instead of just stopping taking medication because some patients like it was driving me crazy I just quit taking it you don't want to quit taking an ACE inhibitor because it can lead to a condition called rebound hypertension and this is where the blood pressure is rebounding it's just like super high and it's really hard to treat and bring it down also teacher patient the signs and symptoms associated with angioedema can really occur at any any time so let them know what may happen and what they should do and miss dose because we don't want our patient to just abruptly quit taking this we want them to take it whenever they need to how it's scheduled and even if they feel unwell they need to take the medication because of the rebound hypertension so they miss a dose and and they remember that same day that they're supposed to take it they can go ahead and take the dose but let's say they didn't remember until the next day well they would skip that dose that they miss but take that scheduled dose that is due that day they would never want to double doses because that could lead to severe hypotension okay so that wraps up this lecture over ACE inhibitors thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Lung_Auscultation_Landmarks_Sounds_Placement_Nursing_Assessing_Lungs_Part_1.txt	hey everyone it's Sarah register nurse rn.com and in this video I'm going to be going over lung oscilation specifically the sites of where you osculate and I'm going to be going over normal breath sounds versus abnormal breath sounds and as always you can access the quiz and the notes over here or in the description below now in the next video I'm going to be performing an assessment on a patient and show you how to listen with your stethoscope to these sides so let's get started first let's talk about our objectives of this lecture what I want you to learn is lung Anatomy because it's really important you know what you're listening to the specific oscilation sites I'm going to give you some landmarks to make your job easier so you'll know what intercostal space correlates with which lobe of the lung um we're going to go over some audio clips of normal breath sounds and where you should hear them at CU that's a big thing of you should know where you should hear bronchial versus bicular and we're going to go over abnormal breath sounds and I'm going to let you listen to them and you can compare the two so first let's go over lung Anatomy whenever you're osculating you're going to be listening to the anterior part of the chest and the posterior part of the chest now one thing you want to remember whenever you're listening to anterior mostly what you're going to be hearing a lot of because it's predominantly in the anterior part are the upper low loes however on the posterior part what is predominately made up on this is the lower loes so first let's take a look of the anatomy of the anterior part of the chest in this illustration you have your right lung and your left lung and how I set up this illustration is that I wanted you to be able to see what is over the lungs because whenever you're listening with your stethoscope you need to know where your clavicle is and certain intercoastal spaces because they correlate to which lobe of the lung you're listening to for instance if you're listening down in the six intercostal space mid axillary you're assessing the lower loes of the right and left lung which we'll go over in depth whenever I cover these osculation sides so first let's cover the right lung your right lung is made up of three loes very important so you have your right upper lobe then you have your right middle lobe and right here here you have the horizontal Fisher and then you have the oblique Fisher and this just separates the middle loow from your upper and your lower and then down here you have your right lower then over here you have your left lung you have your left upper lobe and then your left lower lobe and if you notice in the drawing mainly whenever you're listening to your lungs you're mainly going to be assessing because you can see more of it of your upper load then we have our trachea which is up here and it goes down and it branches off into your broncus your bronchi and then your broni go even further and Branch off into bronchials with your avolar Sachs and this is where gas exchange occurs and then of course you have your breast bone and all your ribs right here now let's look at the posterior view of the lung here is the posterior view of a patient's back if you were to look inside look at the lungs you'll have the clavicle on the front then it comes around and it forms into your scapula and you have your left lung and your right lung they're on they're flip then compared to the anterior View and here as you can see you have mostly lower lobe that you're assessing and it's separated by your fissures here so you have your right upper lobe and you have your right lower lobe notice you can't really assess the middle lobe like as you can with anterior View and then over over here you have your left upper lobe and your left lower lobe and you have your spine in the middle and um it's really important you find C7 to T10 whenever you're assessing which we'll go over in the oscilation sites because this will help you know where to place your stethoscope in between the spine and the scapula on those intercostal spaces right in between the ribs before you start listening to a patient's lungs let's talk about some tips to make your job easier so you can get the best sound possible and be able to assess those lungs correctly okay first tip listen directly on the patient's chest with the diaphragm of your stethoscope that is the big part of the stethoscope which you'll see a little bit later and the reason you want to listen directly on the skin and not over cloes is because a lot of times your diaphragm can rub up against the patient's clothes and that can make like a rustling sound sound like one of those adventitious lung sounds and it'll muffle and decrease the sound quality of what you're trying to hear also whenever you are listening on women you want to have the woman raise up her breast so you can get underneath those sights so you can hear those lung sounds because the tissue will muffle the noise and you won't be able to hear that so remember that whenever you're listening on a female patient also whenever you're listening to the chest you're going to listen to the both the front and the back side and whenever you're listening you're going to note a full cycle of in inspiration and expiration and what you're listening for is you're listening to the pitch is it high is it a medium or low pitch what's the sound quality and its duration is is inspiration longer than expiration or vice versa or are they equal which are characteristics of normal breath sounds and and um on that sound that you're hearing is there any extra adventitious sounds that shouldn't be there maybe on inspiration or expiration so you really want to not that and whenever you listen you are going to start from the top and work your way down and you're going to compare sides so be something like this you're going to start up here at the apex of the lung listen here and then you're going to go over and listen on the other side to compare it then you're just going to drop down a little bit listen here and then you're going to go over here and compare sides drop down again and just keep repeating until you've reached the bottom another thing what you want to do to help get the best sound quality is have the patient sitting up so you can get to the front and the back of that chest posteriorly because this is an area that may give you trouble because as we went through the anatomy you have your spine here and you have the scapula here so if you have the patient sort of move their arms forward maybe in their lap to separate those shoulder blades you can get in those little intercal spaces better so you can put your diaphragm and listen to those sounds also whenever you're having the patient breathe you want them to breathe in and out through their mouth slowly so you can hear those lungs inflate and deflate however um a lot of patients who may have breathing difficulties you'll have to take your time with them because they can hyperventilate easily and and make sure your patient doesn't get dizzy and just take your time while you're having them breathe now let's go over the oscilation side okay first we're going to assess the anterior part of the chest first and what I like to do is I find the clavicle and um we're going to start at the apex of the lungs the top of the lungs and we're going to get our diaphragm which is the big part of your stethoscope and you are going to place it right slightly above that clavicle where the Apex is you're going to listen there for a full inspiration and expiration and then you're going to go over and compare on the other side and this is listening to the apex of the lungs then you're going to find your second intercal space this is one of those landmarks we were talking about because this is going to assess our upper loes of our right and left lung and this is found mid cularly so the middle of where the clavicle is in the second intercostal space so you will listen here compare your side and then just go a little bit lower maybe into the third intercal space and just keep listening to those upper loes then we're going to go down to our fourth intercal space this is another big Landmark for specifically the right middle lobe so we're going to go down to our fourth intercal space we're still in the left lobe in the upper lobe and now we're going to go over here and compare sides now we're in the right middle lobe and this again is mid perly and we're listening in here and then we'll just inch a little bit down maybe in the fifth and still assess our right middle lobe and then we'll go over and compare sides still being in the upper lobe on the left side now we will inch down to the sixth intercostal space but mid axillary so where their armpit is go Midway and we're down in the lower lobe of the lungs and we'll have them in inhale and exhale and then we'll go over and compare it on the other side which we're in the right lower lobe here and assessing this and then we'll just inch a little bit down maybe to the seventh space down the lung and just listen in those lower loes a little bit more and compare sides and then we're done now let's look at our sides on posterior just like with anterior in the posterior we're going to start from top to bottom and compare sides and work our way down and we're going to start right above the scapula right where the Apex is and we're going to listen here and then we're going to go over to the other side and compare and remember to get the best sound quality so you can hear so you're not listening over the shoulder blades because that will muffle your sound and you won't be able to hear have your patient put their arms in their lap or just separate those shoulder blades from each other so you can get in between that spine and shoulder blade area then what we're going to do we want to assess first your upper loes so from C7 to T3 your cervical and thoracic spine that is where your upper loes are and as you can see here's your Fishers right here and you have the upper loes there so what you want to do is just go in between where the shoulder blades and the spine are and just work your way down so we're going to listen to our upper Li so we'll go here and then we'll compare over here and then we'll go down a little bit towards where T3 is listen here still being in the upper lob then we'll go over and compare sides now from T3 to T10 that will allow us to assess our lower loes so we'll start around T3 and work our way down again just staying in between where the scapula and the spine is and we will just compare sides and inch our way down and you want to move around almost mid aill where you were moving before on anterior so you can just get a good feel for what's happening in those lower loes first let's start out talking about normal breath sounds okay there's three different types a tip for whenever you're trying to learn these normal breath sounds is to get a stethoscope listen to yourself or listen to others and get a rhythm down for how long inspiration expiration is and where these are located because that's the key with these three different sounds because they're heard in different areas throughout the lung field so let's go over them the first one is bronchial this is heard anteriorly only you're not going to hear this posteriorly anteriorly why because they are mainly hurt over the tracheal area with the stethoscope so up here in this area they are high pitched and loud and you will notice when you listen to them that the inspiration will be slightly shorter than the expiration and this is what bronchial breath sounds sound like next is bronchovesicular these are heard both anteriorly and posteriorly and they posteriorly you will hear these at the first and second intercal space so about in this area right in here with your stethoscope is where you're going to hear them anteriorly now posteriorly you're going to hear them in between the scapula so about right here where T3 T4 and the small little areas where you will hear those and they will have a medium pitch to them and inspiration and expiration will be equal and here's what Broncho visic sounds like and the third breath sound is called vesicular this is heard again an both anteriorly and posteriorly and it is heard throughout the peripheral lung Fields so you're going to be hearing these all throughout in this area over here anteriorly and posteriorly and it will have a low pitch that will be sort of soft and inspiration will be greater than expiration and here is what vesicular sounds like now let's talk about those abnormal breath sounds that you could hear that may be thrown in with those normal breath sounds okay they are separated into continuous and discontinuous now first let's go over continuous what does continuous mean this is a extra sound that you're hearing that is lasting SE more than 2 seconds with a full respiration okay the first type is called a high pitch polyphonic whe let the name help you okay so what is it it is mainly heard in expiration so when the patient's breathing out but it can be in Inspiration as well and it is a high pitch musical instrument sound with many different sounds to it that's why it's polyphonic and this is what a high-pitch polyphonic whe sounds [Music] like another type of Wee you can have is called a low pitch monophonic wheeze and this is again heard mainly in expiration but you can hear it any time A lot of times you'll hear it whenever the patient's breathing out it is a low pitch whistle so instead of being high pitch like the high pitch wh it's going to be low and it's going to be made up of one sound quality that's all you're going to be hearing and it can sound like a whistle or a whine and this is what a low pitch monophonic wi sounds [Music] like and the third type of continuous adventitious breath sound is called stri spider and this is heard on inspiration because what's happening is that the airway is being obstructed by inflammation or some foreign object something like that and once you hear this you will never forget it's very unique sounding it is a high pitch whistling or gasp with a very harsh quality to it and um patients like pediatric patients if they get the cro or cute epiglottis or you have a patient who has an airway struction you will hear this sound and this is what Strider sounds like now let's go over the second type of breath sounds abnormal breast sounds called discontinuous This is an extra sound that you're hearing that is La lasting less than2 seconds okay first type um is coarse crackles crackles for nor Al has been known as rails so if you hear that that's what it means crackles rails they're interchanged just like ronai and Weis so course crackles they are mainly heard in Inspiration when the patient's breathing in and can extend into expiration and what it will sound like is a low pitch wet SL bubbling sound and this is what coar crackle sounds like the second type of discontinuous abnormal sound is called Fine crackles this is heard on inspiration and it is a high pitch crackling sound compared to the coarse crackle this is like low pitch like a bubbling noise this fine crackles is high pitch it sounds completely different than coarse crackles and it has like a crackling a fire sound to it and the key with this is that it does not clear when you have the patient cough so you listen you hear that you ask patient to cough and it's still there that would be fine crackles and this is what it sounds like and the last sound is called a plur friction rub this is heard both on inspiration and expiration and it is a low pitch harsh grading sound and what's causing this is that your plora on your lungs those two layers are rubbing against them each other and they normally have this little thin layer of Cirus fluid around the lung but it doesn't right now due to all that inflammation going on so you can actually hear that when that patient's breathing in and breathing out so that's why you're hearing it on inspiration and expiration now it can sound similar to a parac cardial friction rub how do you tell the difference um if you are wanting to know is this the lungs or is this the heart just listen have the patient hold their breath and if you can still hear that harsh grading sound it's the heart because they're holding their breath their lungs aren't moving so you've rolled out the lungs and this is what it sounds like okay that is lung occultation and normal breast sounds versus abnormal breast sounds don't forget to take the free quiz on the website and check out the other videos in this series to help you with lung oscilation and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Hypovolemic_Shock_Nursing_Treatment_Management_Interventions_NCLEX.txt	hey everyone its ears registered nurse Orion Colin today we're going to continue our series on shock by talking about hypovolemic shock and as always after you watch this YouTube video you can access the free quiz that will test you on this condition so let's get started hypovolemic shock occurs when there is low fluid volume in the blood hence where the named hypovolemic comes from hypo means low vol means volume and emic means blood so we have low blood volume and we're specifically talking about the blood volume in the intravascular space and this space contains the volume of blood in a person's circulatory system so if we deplete that volume of blood in a person's circulatory system what does that leave that heart to pump throughout the body not very much so what will happen the amount of blood that this heart pumps per minute is going to decrease and we're talking about cardiac output so if we decrease cardiac output the amount of blood that is going to the cells tissues and organs is going to dramatically decrease too so those cells are going to be deprived of oxygen and when we do that cells start to die and then we start seeing signs and symptoms of shock now a person needs to lose about 15% or more of their volume for signs and symptoms of shock to occur now in the average human adult they have about 5 liters of blood so a person loses 1 liter of that 5 liters they've lost 20% of their volume so whenever they lose that much they're gonna start showing signs and symptoms of shock now let's talk about the causes of hypovolemic shock so why can lead to a loss of fluid in the intravascular system well any conditions that really cause fluid to leave the body externally like there's some type of major injury so that person is just outwardly bleeding or there is some type of inside shift of fluid leaving that intravascular space so let's talk about the two types of hype Lehman shock first type is called relative hypovolemic shock and this is where you have an inside fluid shift from that intravascular system and this tends to be a little bit more concealed than the absolute type which we're going to talk about next you're not gonna see just bright red blood leaving the body like how you could and absolute and you know that that patients losing fluid there's gonna be a little bit more concealed so this is where fluids or blood is collecting or leaking inside the body and this can occur with internal bleeding or where you have third spacing a fluid like with severe burns and this occurs due to increased capillary permeability and we talked in depth about this in our Burns video in addition long bone fractures they're very vascular can cause a lot of fluid loss in addition damage to organs like in acute pancreatitis you can see this when a patient develops colon or Turner sign and colon sign is where you have severe bruising around the belly button and Turner sign is where you have severe bruising on the flanks and that can indicate that the patient is having internal hemorrhage and that occurs with acute pancreatitis and another thing is like massive vasodilation that occurs in sepsis the next type is absolute hypovolemic shock and this is where you have an outside fluid shift from the intravascular system and this is more noticeable compared to the relative type and this is where fluid is leaving the body externally you can see it and this can occur with massive bleeding that's been experienced due to blood loss with surgery or some type of injury excessive fluid loss and this can be through the oral route with vomiting or the GU route urination or GI diarrhea or sweating with your skin and many times whenever that occurs it's being caused by some type of disease process the patient's really sick so they're just throwing up a lot or some type of endocrine disorder now let's talk about the pathophysiology of bloomix off and tie in the signs and symptoms associated with this condition okay let's say we have a patient who's in hypovolemic shock and it's due to like either a relative or an absolute cause vote regardless what's happened is that their intravascular system their circulatory system has been depleted of fluid volume so what's going to happen is that you're going to get a decrease amount of flu evolve as returning to this heart to be pumped so we have a low venous return to the heart that intravascular system has been depleted of it so there's really nothing to drain back now whenever that happens it's going to affect cardiac preload now what is preload this is the amount that these ventricles stretch at the end of diastole at the end of that filling face of the heart so it's the end diastolic volume well we don't have a lot of fluid volume draining back to that heart those ventricles really aren't going to stretch they don't have to stretch because the fluid volunteer now cardiac preload is a determining factor in stroke volume and stroke volume is the amount of blood that this ventricle pumps each with each beat which should be anywhere between 50 to 100 MLS well when our stroke volume falls it decreases cardiac output because remember cardiac output is heart rate times stroke volume and cardiac output is the amount that this heart pumps per minute and it should be anywhere between eight to four liters but if we have a decrease in stroke volume that's going to decrease our cardiac output now when we get a decreased cardiac output this is going to decrease the mail of blood that's flowing to our organs and our tissues specifically to those cells so we're going to get decreased tissue perfusion and what's that magical substance in the blood that cells love oxygen so when you decrease the amount of oxygen that is flowing to these cells they're going to start struggling they attempt to try to save themselves at first by switching the way they metabolise from aerobic to anaerobic but the problem with that is that you're going to get the built-up the build-up of lactic acid which is going to throw off at our pH of our blood entering into acidotic conditions and then the body's going to try to compensate and it's going to activate the sympathetic nervous system and the NGO Tinson the renin system it's going to be shunting blood all in an attempt to help save the body save those organs now the signs and symptoms of hypovolemic shock are affected by the percentage of fluid volume loss that patient has experienced so hypovolemic shock can be divided into four classes or four stages and to help you remember those stages / classes remember the criteria numbers for each percentage loss so the numbers you want to remember are 15 that's class 1 15 to 30 that's class 2 30 to 40 that's class 3 and then the last class last stage is 40% ok so class 1 this is where the patient has lost less than 15% of their fluid volume and that's about 7 to 750 ml's in an adult now during this class / stage the body can deal with this it can come and say enough to maintain cardiac output now because of that your patients really going to be asymptomatic with a fluid volume loss of less than this because remember beginning the lecture I said that patients who have 15% or more are gonna start showing those signs and symptoms of hypovolemic shock because the body really can't compensate for that and it has to turn on its sympathetic nervous system and all of that so in this class last stage how do you expect our heart rate to be it's going to be less than 100 they're not gonna have tachycardia so it's going to be within normal limits maybe a little bit on the high end maybe 80s or 90s blood pressure it's going to be within normal limits our body is maintaining our cardiac output respirations within normal limits we're not having any issues with decreased oxygen just yet because our body can deal with this blood loss Mental Status they're probably going to be normal they may have lit they may be a little anxious but nothing major their skin is going to be warm to the touch their capillary refill is going to be less than two seconds whenever we check that and their urinary output is going to be greater than 30 CC's an hour so kidneys are doing great that's where we want them next we have class two and this is where we've lost 15 to 30 percent of fluid volume so anywhere between 750 to 1,500 ml's in an adult so with this because we've lost more fluid volume than compared to here our cardiac output is decrease the body cannot maintain its own cardiac output with this amount of fluid volume loss so it has to activate that sympathetic nervous system the body's receptors in the body since hey we can't do this so those baroreceptors activate it and that's in turn going to activate our renin-angiotensin system you're gonna get shunting of blood away from non vital organs so in a nutshell what you're gonna have is vasoconstriction from those catecholamines from angiotensin ii and this is going to constrict vessels and this is going to increase venous return to the heart we're just going to increase our cardiac preload stroke volume cardiac output and increase our blood pressure so we're going to be maintaining tissue perfusion making ourselves happy giving them oxygen also we're going to be increasing blood volume through some hormones under the influence of angiotensin ii so we're gonna have a th-the antidiuretic hormone on board that's going to cause us to retain water and aldosterone which is going to help us conserve sodium and water and all that and hope of increasing blood volume volume in the blood which is going to end crease the venous return to the heart preload stroke volume and cardiac output so our signs and symptoms are going to really be around what's going on because our body here is compensating with its built in system so how do we expect our heart rate to be it's going to be increased because of the fact of the catecholamines on the heart so we're gonna have some tachycardia going on it'll be mild it's going to be less than 120 so less than 120 our blood pressure is going to be decreased from where that patient normally is but they're not gonna be hypotensive just yet because the system is working to maintain our cardiac output but it'll be slightly decreased our respiratory array is going to be increased a little bit just mildly from everything that's going on we've dropped in our oxygen so the body's increasing respiratory to take in some more oxygen to help increase that level urinary output well what's going on with her ADH and aldosterone it's causing us to keep water so our urinary output is going to decrease so instead of being the normal where we want it 30 emails per hours it's probably going to be between 20 to 30 so it's going to decrease skin now we're diverting blood away from non vital organs the skin is one of them so instead of our skin be warm and flushed it's gonna be cool and clammy from where blood is being diverted capillary refill the same concept there instead of being less than two seconds it's going to be increased so greater than two seconds peripheral pulses because we're shifting blood away from those extremities they're going to start becoming diminished and how we fill them and Mental Status instead of just having being normal or maybe just a little bit anxious they're gonna start to have some mild anxiety going on next is class three and this is where the patient has lost 30 to 40 percent of their fluid volume and this is anywhere between 1,500 to 2000 MLS of fluid now because it is this much the body can no longer compensate so compensatory mechanisms are going to fell they're not going to be able to do it and our cardiac output is just really it is fel because they've lost so much blood in that circulatory system that the heart doesn't really have much to pump out maintain perfusion so you're gonna see those cells that make up those organs and tissues you're gonna see malfunctioning of our body system so we're ending up having failure so our heart rate is going to be significantly high it's going to be greater than 120 we're gonna have tachycardic tachycardia their blood pressure they're gonna have severe hypotension because we don't have the body being able to maintain blood pressure so we're gonna have some hypotension going on respiratory rate is going to be majorly increased their hitting respiratory failure territory so they need mechanical ventilation intubation possibly to help assist them urinary output is going to be low Oh Gloria so it's definitely gonna be less than 30 CC's an hour we're getting in the renal failure territory we're being creatinine is going to be increased you're gonna start seeing buildup of Weiss in the blood liver is going to be failing to help rid us of those toxins in addition perfusion to the brain because our blood pressures are so low mean arterial pressure is going to drop and so brain isn't going to be able to be perfused so you're gonna start seeing some major mental status changes here you're gonna see confusion agitation until it progresses to the next stage where they'll be actually lossless and a coma their skin is going to be cool clammy but even taking a step further and be modeled and their pulses are going to be absolutely poorer their peripheral pulses and the last stage we have is class four and this is where the patient has lost 40% or more of their fluid volume so greater than 2000 MLS and this is where death is near we need to get this patient some very very fast treatment dynamic treatment if possible to help prevent that and what you're gonna see with this is just all these vital signs that we're talking about they're gonna be significantly abnormal so you're gonna have major tachycardia greater than like 140 severe hypotension and major respiratory failure they're gonna be and Eurex they're not gonna be producing any you're and there's like hardly and you flew it to even produce fluid for urine off of mental status like I said they're gonna be lifeless and in a coma so in a nutshell whenever you're looking for signs and symptoms like for your exams for high potent hypovolemic shock you need to be looking at that heart rate how's it gonna be it's gonna be high it's when we tachycardic how's your blood pressure are gonna be hypotensive rest story right it's going to be increased and their urinary output is going to be decreased their skin perfusion it's gonna be cool clammy capillary refills going to be down Mental Status is going to be confused so be keeping all that in mind and whenever a patient whenever they have like hemodynamic monitoring whenever they start getting in these classes of hypovolemic shock they're gonna have that hemodynamic monitoring so whenever we're looking at central venous pressures how do you think that that number is going to be it's gonna be low this is where you measure the pressure over here in this right reom you don't have any fluid hardly even in the heart so the pressure there is going to be low and if you looked at a pulmonary capillary wedge pressure over here that which looks at the filling pressure in the left atrium it's going to be low as well because we're depleted of our fluid volume so remember those two numbers and it's different whenever we talked about cardiogenic shock remember I talked about the CVP being high that central venous pressure and that pulmonary capillary wedge pressure being high because cardiogenic shock we don't have a loss of fluid volume or hearts just wheat and that fluid volume the pressure of is actually increasing we have fluid volume over loop so those numbers would be high in cardiogenic shock now let's talk about nursing interventions for hypovolemic shock okay what are some treatment goals first because that really dictates where we're going with our nursing interventions one thing of course is replacing flu into this intravascular system we can increase the venous return to the heart we can increase preload stroke volume and increase cardiac output and we get better tissue perfusion so fluids ordered by the physician are really going to help this patient and as a nurse we will be giving those fluids and monitoring them and it can vary it depends on what class or stage of hypovolemic shock that patient is in and you can use various fluids like crystalloids colloids blood blood products and we'll be talking about all those here in a moment and of course correcting the underlying cause of the reason why that patient is losing so much fluid from the intravascular system so if they're having a massive bleed somewhere they need to have surgery repair that to stop of the bleeding so nursing wise we're looking at a lot of things we're looking at circulation perfusion oxygenation and we're going to put our nursing interventions and goals for that patient around that so oxygenation wise we want to make sure that they're getting oxygen because o 2 is a problem here because those cells are being deprived so we want to make sure that they're not entering into respiratory failure so they may need intubation mechanical ventilation place on oxygen circulation wise are they actively bleeding they are you want to hold firm direct pressure call rapid response get someone there to help you fast because you need a team to help you with this patient addition something taneous lee you're gonna be doing all this you're gonna be looking at signs and symptoms of adequate perfusion is this patient going into hypovolemic shock so you're gonna pull from those signs and symptoms that they are and very simple you can look at their skin cool and clammy that would be back look at their Mental Status how are they acting what's their blood pressure their heart right number blood pressure will be low they can be tachycardic will be heart rate will be high urinary output what are they putting out and looking at all those things in addition you want to make sure that you have IV access we need access to that intravascular system so we can give them fluids and drugs whatever we need to get that cardiac output up replace that fluid so you need at least two IVs sites and they need to be a large cannula there in those large veins those antecubital veins a C's at least 18 gauge are higher you're gonna be giving rapid fluids fast and other medication so we want to make sure that they're nice and working in addition they may need a Foley catheter so you can monitor that urinary output precisely collect that instead of depending on the patient to use the bathroom which they're probably going to be so sick they can't do that and we want to be able to collect that and so many patients who have severe hypovolemic shock they're not responding to the fluids I'm gonna have central lines hemodynamic monitoring which will help us monitor the cardiac output and how well we're replacing those fluids and we can look at some numbers so whenever you have a patient in hypovolemic shock severe hypovolemic shock how again is that central venous pressure going to be it's going to be low how's that pulmonary capillary wedge pressure gonna mean it's gonna be low but we're giving them fluids so one thing whenever you give fluids you have to make sure you're not giving them too much we're we're gonna actually flip them into cardiac it overload so if we were giving them too much fluid how would those numbers start presenting central venous pressure can start becoming elevated the pulmonary capillary wedge pressure can be started becoming elevated as well because putting too much fluid in the heart it's too much so it's increasing the pressure over here or right atrium so CVP pressure and the filling pressure on the left atrium for pulmonary capillary wedge pressure so you want to look at those things now position wise what's a good position for these patients we want to position that's going to increase nice cardiac output venous return to the heart so one position is modified Trendelenburg this is where the patient is supine with their feet / legs elevated at that 45 degrees doing that it's going to increase venous return and help us increase cardiac output a bit lab wise we have to monitor what's going on with the patient so physicians will be ordering this and we'll want to be either collecting that and looking at those labs coming out hemoglobin hematocrit looking does this patient need blood products depends on protocols but usually less than eight to seven for hemoglobin they'll need some blood transfusions ABG's arterial blood gases remember these patients can go into acidotic conditions we want to be looking at that looking at lactate levels because our cells are switching from aerobic to anaerobic we're gonna get the buildup of lactic acid livers may not be working building up more toxins or kidneys like an electrolyte CBC's looking at bu in creatinine telling us our renal function now let's talk about our fluid types use for the treatment of hypovolemic shock okay first thing we're going to talk about our crystalloids and colloid solutions these are two types of volume expanders use for hypovolemic shock and again this varies depending on the patient status volume loss of what will be used so first let's talk about crystalloids okay crystalloids what is a crystalloid well normal saline or lactated ringers and how they work is that they add more fluid to the intravascular system and this is going to increase preload because it will increase how much fluids coming back to the heart and stroke volume in the cardiac output so what's this you have to watch for fluid volume overload like I was talking about earlier and you can look for many things just simply listening to their lungs you hear fluid in the lungs with crackles they having difficulty breathing are they having elevated CVP pressures or pulmonary wedge capillary pressures or just looking for edema in legs or do they have jugular venous distention things like that can point to that they're retaining too much of the fluid and one thing about crystalloid solutions I want you to remember is that these solutions are able to diffuse through the capillary wall so less fluid remains in the intravascular system compared to colloid solutions now normal saline or lactated ringers are most commonly used number one they're really cheap easy to access and how they're given is by remembering the three to one rule and what this rule says is for every ml of approximate blood loss three ml's of a crystalloid solution is given so let's say a patient has lost 750 ml of blood how much of a crystalloid solution would they get well according to that rule it would be 2250 MLS because we're going to be giving 3 ml of a crystalloid solution for every ml blood loss another fluid type is colloids and an example of this is like albumin or head of starch and what colloids are they consists of large molecules examples like proteins that can't diffuse through a capillary wall so in the long term more fluid stays in that intravascular system for a longer period of time compared to those crystalloids however colloids are more expensive to use and patients can have anaphylactic reactions so again just with crystalloid solutions as well you would want to monitor for fluid overload now as a nurse it's really important to remember if you are giving large amounts of fluids like these crystalloids colloids it's very important that you warm them before giving them because this will prevent hypothermia and we don't want a patient to go into hypothermia because hypothermia alters the way clotting enzymes work so we want to keep the patient warm keep the fluids warm and but we don't want the patient's sweating so remember that whenever you're giving large amounts of fluids the last floor time gonna talk about of course is blood and blood products this can include packed red blood cells platelets or fresh frozen plasma now packed red blood cells are going to help replace the fluid that has been lost and it's gonna do another thing that really our crystalloids and colloids couldn't do it's going to provide the patient with hemoglobin and hemoglobin will carry oxygen to those deprived cells so that is one benefit of that now it may be used when the patient is not responding to crystalloid fluid challenge has experienced severe bleeding or severe hypovolemic shock and some other type of blood products shoes are like platelets and these would be used for patients who are having uncontrolled bleeding due to thrombocytopenia so they need some platelets to help with that also a fresh frozen plasma this is for when patients need clotting factors now anytime you're giving any type of blood blood products you always want to monitor for transfusion reactions with these products and I have a whole video on the nurses role with blood transfusions if you want to check that out as well okay so that wraps up this video over hypovolemic shock thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Pharmacology_NCLEX_Review_Question_Bronchodilators_and_Corticosteroids_Asthma_Nursing.txt	hey everyone its Aires registered nurse re and calm and in this video I'm going to be going over an ink Lex practice question specifically over bronchodilators in corticosteroids use for respiratory disease so let's take a look at our NCLEX question the physician prescribes a patient to take in health fluticasone which is flovent h fa and inhaled albuterol which is ventolin hf a for the treatment of asthma as the nurse how will you administer these medications a first administer the fluticasone and then give the albuterol five minutes later be first administer the albuterol and then give the fluticasone one minute later si first administer the fluticasone and then give the albuterol immediately or D first administer the albuterol and then give the fluticasone five minutes later so this question wants to know how we are going to administer this fluticasone and this albuterol because there is a certain way in the order of how we should give them based on how they work so let's take a look at how they work okay fluticasone which is also called a flow vent do you remember what drug this is what category it falls into it falls into our corticosteroids and this patient has asthma so what this corticosteroids going to do is it's going to decrease inflammation because remember it really suppresses our immune system which is going to take away that inflammation because that's what it means is I'm suing its inflaming the body so it's great at preventing symptoms in that person with asthma now one thing I just want to throw in at the side because it's a nurse you are going to be administering these corticosteroid inhalers and I have a whole video where I went over how to give metered dose inhaler administration for meds but whenever you give these corticosteroids you want to make sure that these patients gargle and rinse their mouth with water and spit that water out after using because these medications can cause thrush and irritate those mucous membranes so remember that okay our next drug is albuterol which is ventolin which is type of albuterol now what is that we're all remember it is a bronchodilator and specifically it's a short-acting one so it works for a short period of time and what does this drug do just as its name says it's going to open the bronchi and bronchioles of the lungs so you're going to get more airflow through those lungs and this is what a person with asthma really needs because they have bronchoconstriction going on so they need this bronchodilator after they inhale it it pops those lungs open and they can breathe and get air now how are we gonna be giving these who needs to go first whenever you're giving the inhaler you have two inhalers once a bronchodilator once a corticosteroid well based on how it works what do you think the answer is you want to give that bronchodilator first because it's gonna open up those Airways so this is what we're gonna give first then we're going to give the corticosteroid because once the lungs are nice and open that corticosteroid whenever they inhale it can get in those small Airways and decrease that inflammation because if we didn't give that bronchodilator first those Airways wouldn't really be opened up and that corticosteroids taking it in there and do its job so we'll give that second okay but how long do we really need to wait in between those we need to give that albuterol time to work to do its job so we're going to wait five minutes in between those two doses okay now let me just throw something out there just for more information say you were giving how beautiful and they needed two puffs and you weren't gonna be given corticosteroids and this is the same if you're just going to be giving corticosteroids so they need to bus of albuterol you would give one puff and then you would wait one minute because it's the same drug and then you would give the other one okay so just remember that to keep that straight because sometimes students get that confused so our answer is going to be D first administer albuterol and then give fluticasone five minutes later okay so that sup this NCLEX review question be sure to check on the other questions in this series thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Nephrotic_Syndrome_Nursing_NCLEX_Lecture_on_Pathophysiology_Treatment_in_Children_Pediatric.txt	hey everyone it's SE Earth register nurse rn.com and in this video I'm going to be going over nephrotic syndrome and this video is part of an inlex review series over the renal system and as always at the end of this YouTube video you can access the free quiz that will test you on this condition so let's get started first let's start out talking about what is nephrotic syndrome this is a set of symptoms due to damage to the filtering structure of the kidney and this leads to a massive amount of proteins being leaked into the urine so let's take a step back and let's look at the nephron let's see what's going on in this condition okay so your nefron in your kidney that is the functional unit of the kidney in a nutshell what it does is it produces urine and it has several structures to it and the problem here in this condition is with the glomerulus now your glomus is the filtering structure of the kidney so it takes your blood it receives the blood from the apir arterial and this is fresh blood that's came from the heart and it's going to take and it's going to filter ions and water and waste and things like that into Bowman's capsule then it's going to travel down through the renal tubules where it's going to be secreted excreted and what you don't need it's going to be turned into urine and you're going to pee it out well normally this glomerulus is not permeable to proteins they're too large to get through there along with red blood cells but for this condition we're just concentrating on proteins and what happens is that they leak through here they go down through Bowman's capsule and to the renal tubules and you're just voiding out all this protein that needs to stay in your blood because protein does its job in the bloodstream and here in a second you're going to see what type of proteins we're losing and why it's going to cause problems in these patients who have severe nephrotic syndrome so how much exactly can these patients lose in their urine of protein per day they can lose three G or more so as you can see they're going to have a massive amount of protein Uria now let's look at the proteins that can be lost in the urine because this is where you're going to start seeing those signs and symptoms and for your nursing exams you really want to remember these signs and symptoms because they like to compare this condition nephrotic syndrome with acute glomo nephus which is one of those other conditions that we talked about in the previous lecture okay so the main type of protein that is being lost in this condition is albumin and what does albumin do it does a lot of things but one of the important things it does is it regulates oncotic pressure so if you losing all this albumin out of the blood because it's being filtered into the urine what's going to happen to the blood levels of albumin in the body they are going to drop and whenever they drop you're not going to be regulating oncotic pressure very well so the patient is going to to have a sign and symptom when you look at their Labs they're going to have hypo Aluma alumin emia and what happens when um albumin levels drop the patient will start to get swelling major swelling also called edema in the body you may first start to see it in the face and around the eyes and as the this syndrome gets worse and worse they will begin to get it in their legs their feet their arms and then their belly aides now why is this happening okay let's think about albumin here we have just a simple drawing of like the capillary and alumin hangs out in your blood and alumin regulates water so in a sense think of albumin and water together as a magnet it keeps it with it to prevent it from really flowing too much of it flowing in this interstitial TI tissue right here because in your capillaries you have these finestra which are pores that allow water to flow in and out and other substances into this interstitial tissue so the albumin controls that well if we start deleting getting rid of these albumin proteins they start going away what's going to happen water has no albumen to cling to so it's just going to start going out into the interstitial tissue and you're going to be getting major major swelling now the low albumin level also causes problems with our cholesterol and triglyceride levels okay here we have the liver in response to those low albumin levels the liver says hey we need to make more albumin because we know if this body doesn't have enough alumin we're going to have major issues so it tries to make more albumin but in the process of doing this it leads the liver to also make more cholesterol and triglycerides so in severe cases whenever you check lab work you will notice that this patient will have hyper lipidemia and this condition nephronic syndrome we're really talking about it with our pediatric patients for the encl exam and when you have a two to 5year old because this is what um ages this can occur in and you see high cholesterol levels is going to throw up a red flag because young children should not have high cholesterol levels now albumin was the main thing that's really going to be messed up in this condition other proteins that the patient can lose in the urine are proteins that help fight infection called immunoglobulins and this is going to increase the patient risk for infection because they've lost those proteins that help with the immune system plus some treatments for this condition are like corticosteroids and we learned in our endocrine series that corticosteroids suppress the immune system so it's like a double whammy for these patients so you want to be thinking risk for infection what is my role as the nurse so be thinking of that and in here in a second we'll be talking about nursing interventions next these patients are going to lose proteins that play a role in preventing clot formation so if we're losing proteins that are preventing um random blood clots from forming in our body what's a patient at risk for increased blood clots so as a nurse you want to watch for signs and symptoms of a possible pulmonary embolism uh for a deep vein thrombosis things like that now let's talk about the causes of nephrotic syndrome because remember nephrotic syndrome is not a disease it's a set of symptoms associated with that disease and we have primary causes and secondary causes first let's look at primary okay primary causes are associated with a problem with the kidney itself so something's wrong with those glami uh the most common type of disease that can cause this is called minimal change disease and this most commonly affects our pediatric P patients from ages 2 to 5 and the reason for this disease is not truly understood they know when they go in and they look at those glami that they can only see changes to the glami when they use a really strong microscope called the electron microscope not with a regular one they have to use a electron so they see that hey there's something wrong with this glami that's allowing all these proteins to leak into the urine another type of cause is called focal segmental glos sclerosis and this is where there is scarring to the glami which again allows all those proteins leak into the urine and then the third type is membrano proliferative glomerulo nephritis and this is where you have thickening of the glami due to an antibody collection in those glami then we have secondary causes and secondary causes are where a disease is causing damage to the kidney those glomi and some diseases include lupus diabetes metis hepatitis heart heart failure HIV or medications like ineds and one thing you want to remember about this condition is that the patient can go into remission but they can also relapse so whenever you are educating the patient or the child's parents you want to teach them those signs and symptoms of nephrotic syndrome and these signs and symptoms will include protein Uria which again is going to be massive cuz remember these patients are losing about three grams or more of protein per day in the urine which will cause the urine to look different it can be dark and it will be foamy or frothy looking another thing they'll have remember hypo alumin emia where they're going to have low albumin in the blood which is going to lead to edema it can start out small like you can see it in the face around the eyes typically early in the morning it'll be worse and this will progress where it will go to the extremities in the legs and in the hands the ankles and in the abdomen where they can have acies and again the face and the eyes which will lead them to feel really tired fatigued because they're carrying all this extra fluid and it will cause them to lose their appeti they won't feel like eating anorexia because they have all this extra fluid especially if they get atis and that will be pushing on that stomach causing them not to feel hungry and they will be gaining weight so a lot of times the patients parents will say they're not even eating they feel horrible but I notic that they're gaining all this weight so I don't know where the weight's coming from because it's they're not eating and what it is is because they're retaining all this water from the low albumin in the blood which is caused remember the water to go into that interstial tissue because it's not regulating on IC pressure anymore and again because of the low albumin level in the blood this is going to lead to hyper lipidemia so you're going to see those high lipid levels now let's look at our nursing interventions what are we going to do for this patient who has nephrotic syndrome okay we know that they are going to possibly have fluid overload a demmon swelling they are at risk for infection they have possible hyperlipidemia and they risk for blood clot so we want to taper our nursing and interventions make sure we're monitoring them for complications from those potential things so first thing we really want to do is we want to monitor that fluid status closely and we're going to do that by performing daily weights getting them up every morning weighing them on a standing scale and looking at that weight comparing it to yesterday are they gaining weight or they losing weight we want to monitor their intake and output I's and O's very closely because chances are they're probably going to be on a fluid restriction so we want to know exactly how much they are consuming and the doctor May order diuretics to help them it'll stimulate those nephrons in the kidney and allow them to void out that extra fluid and they may order IV albumin to help replace that albumin level that's already low and if that is happening you definitely want to watch that output so for your pediatric patients you want to make sure they're putting out at least 1 milliliter per hour per kilogram based on their weight and for adults at least 30 cc's per hour cuz diuretics can be really hard on the kidneys and we want to make sure we're not sending them into renal failure then you want to assess the swelling that's going on is it decreasing or is it getting worse and you want to watch that swelling in the abdomen the AES by measuring the abdominal girth now because they have swelling in those extremities they are at risk for skin breakdown over those areas they very vulnerable for that and remember these patients are at risk for infection so we don't want to have the skin breakdown cuz that's going to allow easy access for bacteria to get in there and harbor that sight and that patient can't fight that infection how they normally could so we want to frequently turn them we want to make sure that they're wearing loose clothing like gowns make sure they're not tight and use any sensitive tapes because if you use really sticky hard tape that on a swollen area and you go to remove it if you don't do it with care you can rip off that top layer of skin now that will lead us to our next nursing intervention we want to prevent infection because again just to recap they're losing possibly those proteins that help fight infection in the urine and they may be on some type of treatment to help with this condition to help suppress the immune system which sometimes are corticosteroids or immune suppressors and if they're on corticosteroids we want to monitor that blood sugar because remember we learned in our endocrine series that corticosteroids can cause hyperglycemia so how to prevent infection meticulous handwashing we'll perform that we want to also educate the patient themselves and the family members monitor their temperature especially are they running a fever and look at that heart rate and blood pressure because we're monitoring for sept sepsis if they have Tac cardia increased heart rate low BL blood pressure not doing good respiratory status compromis may be in septic shock and we want to limit the number or performing invasive procedures during this time because again we don't want to introduce bacteria into places where the patient because they're not able to fight this infection next we want to monitor them for blood clots and again that's because we're losing those proteins that help decrease prevent the body from making a blood clot so so we want to make sure we're watching the respiratory status uh are they have an increased respiratory rate are they having difficulty breathing where they weren't before are their oxygen sat is their oxygen saturation decrease where it was high how's their heart rate are they complaining of chest pain that can be um signs and symptoms of a pulmonary embolism and I have definitely seen that so that can happen if um a PE develops another thing is a deep vein thrombosis uh DVT you want to check those extremities while you're looking at those for swelling and see if you see any red warm swollen areas that are painful Um this can happen in the legs or in the arm and this could be a sign and symptom of a deep vein thrombosis which you would want to let the doctor know so they could confirm that another thing is you want to implement the diet for whatever the physician orders and educate the patient about it and their family typically they're on a low sodium diet because of all the swelling we have going on more sodium you get in the body more water likes to just stay there because sodium and water love each other along with the fluid restriction and another type of diet that may be implemented on top of this is a lowfat diet because they can have hyperlipidemia because of those low albumin levels causing the liver to make more cholesterol and triglycerides so you want to inform them about that now about the relapse again like I said patients can go into remission but they can also relapse so you want to educate the patient especially the parents if this is a pediatric patient on those signs and symptoms of what of what may be happening when they're going into relapse so they can get overthe counter kits to monitor for protein in the Ura because that's what's happening with this condition and also they'll be wanting to look at the urine how does it look is it frothy that's a sign that there's protein in the urine weight gain are they noticing that there child or they're gaining all this weight all of a sudden so they'll want to be weighing the child every day get that part of their morning routine and looking for any swelling and also the risk of infection especially if this patient is taking those corticosteroids or those immune suppressors they need to avoid people who are sick wash their hands and things like that so this wraps up this lecture on nephrotic syndrome thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	COPD_Chronic_Obstructive_Pulmonary_Disease_Nursing_Interventions_Management_Treatment_NCLEX_Part_2.txt	hey everyone it's sarah thread sterner sori and calm and in this video I'm going to be going over part two of copd where I'm going to be covering the nursing interventions and the medications be sure to check out part one because that video lays the foundation for this video because I discussed the pathophysiology the types of signs and symptoms the complications and how it is diagnosed and as always over here on the side or in the description below you can access the quiz and the notes that go along with this video so let's get started first let's start out talking about the nursing interventions what are you going to do for this patient as the nurse okay number one the most obvious is that you are going to monitor their respiratory system which will include listening to those lung sounds what's going on in there and if they need suction they may need nasotracheal suction you'll assess their need for that based on their effort of breathing and their oxygen saturation also you're going to be monitoring that sputum production your patients with chronic bronchitis as we learned in part one tend to have really unproductive coughs so if ordered you may need to collect a sputum culture because these patients are at risk for developing pneumonia another thing is that you want to monitor that oxygen saturation and keep it between 88 to 93 percent why this number because a lot of people are like 95 to hundreds where we want to keep it well the reason is is because how COPD patients are stimulated to breathe they are stimulated to breathe due to low oxygen levels and as we learn in the previous video this is what these patients have because of obstructive airflow so they're stimulated to breathe by low oxygen levels rather than high carbon dioxide levels which is how a person with healthy lungs is stimulated to breathe whenever their carbon dioxide levels are high it stimulates them to breathe to blow that off but not in this case so we don't want to give them too much oxygen through a nasal cannula because this will not give their body an incentive to breathe so they could stop breathing causing them to hypo ventilate which in turn is going to increase that carbon dioxide even more and become toxic okay so another thing is that we want to administer oxygen as prescribed by the physician usually one to two liters you don't want to usually go any higher than that monitor their effort of breathing because these patients are at risk with any activity depending on the severity of their COPD four episodes of shortness of breath so you want to teach them about purse lip breathing and dot - chromatic breathing and what are these I would know these four tests how to do it how to teach a patient about them okay let's talk about pursed lip breathing first and this is a great thing to use whenever your patient is having those disick episodes it usually works even better than putting the oxygen on them because what it does is it increases the oxygen level it encourages them to breathe out longer so remember the issue with this these patients are retaining a lot of air volume due to what's going to be going on with their viola sacks and the bronchioles so what they will do is they will breathe in and then blow out through pursed lips like they're trying to blow out a birthday candle so it'll be something like this and this encourages them to breathe out longer to force that air out help slow down that breathing and increase that oxygen level now let's talk about diaphragmatic breathing this breathing uses the abdominal muscles rather than those accessory muscles for breathing because what has happened is these lungs have become hyper inflated it's pushed the diaphragm rather than having a dome shape and your diaphragm plays a huge role in your ability to breathe effortlessly so what happens whenever you breathe the diaphragm will help when it can try it when it relaxes back up to force that air out so you're getting all that volume out but here it's flat and it's not doing their job so your body starts using those accessory muscles to help get that air out of the lungs so um what will what will happen whenever you teach them this is that it will help strengthen that diaphragm it will slow down the breathing rate and make it easier and decrease the energy used to breathe because using those accessory muscles to breathe burns a lot of calories and that's why your patients especially ones who have emphysema will have weight loss and you need to encourage them to eat a lot of frequent small meals so how you do that you have the patient lay down you can put a pillow underneath their knees and they will put one hand over their chest and one hand on their abdomen and what they will do is that with their abdominal muscles they will inhale in move those muscles not moving the chest muscles with abdominal muscles to force that area then they will pursed lip breathe out using the abdominal muscles instead of those accessory muscles and that helps strengthen the diaphragm and discourage the use of those accessory muscles another thing is that you'll be administering breathing treatments as the nurse a lot of times in hospitals respiratory therapy will participate in this as well they give a lot of nebulizer treatments especially those short-acting um médico dilators like albuterol atrovent things like that but as a nurse you will be giving scheduled or as needed inhaler so your role which we're going to go over later in the lecture is to know those category of drugs like long-acting versus short-acting if they're having an acute episode shortness of breath you want to give a short-acting bronchodilators because it acts fast and those corticosteroid tailors and things like that now let's talk about the education pieces that you want to provide to your patient who is struggling with COPD okay the first thing is about nutrition needs especially patients who have the form called emphysema which is your pink puffers because they hyperventilate they breathe rapidly they use those accessory muscles as a call as a compensation mechanism to keep that oxygen where it needs to be so they use a lot of energy doing this so they need to be educated to eat high calorie and protein meals and they need to be small but frequent because they don't want to eat three large meals a day why the anatomy of how your body set up you have your stomach somewhere in this region they already have hyper-inflated lungs and abnormal flattened diaphragm so if they go in eat a lot of food that something's going to push up on those lungs up on that dock room it's going to cause them difficulty breathing so it's best for them to eat small but frequent meals that are high and rich in protein also they want to stay hydrated drinking about two to three liters per day unless it's not contraindicated like the patients with renal failure or heart failure who are on fluid restrictions and the reason they want to stay hydrated is to keep those mucous secretions thin they don't want them to be thick because it's going to block the airway and cause a lot more problems they want to avoid sick people and irritants out in the weather so they need to watch forecasting see if it's going to be a high alert day for air pollution they need to avoid those days because this can trigger COPD exacerbation and a lot of patients who have severe COPD if they go outside whenever it's really really hot or humid it smothers them because of the humidity and extreme cold temperatures affect them as well so let them know about that and if your patients smokes educate them on the importance of salt smoking because this can help improve the function of the ones and to avoid people who smoke that secondhand smoke is just as bad been smoking themselves also have their vaccinations up today because if they get influenza or anything like that that's when an attack the lungs this can cause COPD exacerbation and it's really hard for these patients to recover from this and and so they'll need to get the flu shot annually and the pneumonia vaccine every five years because they are at risk for developing certain forms of pneumonia and this shot can help prevent that or mild the symptoms okay so let's look at the medication regimen for patients with COPD as the nurse what you need to be familiar with are those group those drug categories that's going to be given in COPD the major side effects that you need to watch out for that may be thrown on in clicks and patient education pieces for the most important drugs so to help you remember the typical drugs given in COPD remember this new morning chronic pulmonary medications save lungs here we have lung issues these medications along with lifestyle changes and help the patient have a better quality of life with their breathing so first the C corticosteroids what do corticosteroids do they decrease inflammation and mucus production in the Airways because especially with chronic bronchitis those bronchioles are inflamed they're producing lots of mucus corticosteroids going to help decrease that and help that immune system slow down its attacking these are given and give them orally IV inhaled many times and then held ones will be given with a bronchodilator mitt and sometimes there's combination drugs some drugs you want to be familiar with is prednisone solu-medrol palma core or symbicort simba core is a combination one it is a steroid and it's a long-acting dilator so side effects of corticosteroids we covered this a lot in the endocrine series so if you really want to dive into this and you can check out the endocrine series I have a card should be popping up so you can access that but side effects is easy bruising patient a lot of times you'll see them the bruises on their arms and their legs their skin will even be really fragile and tear easily so be easy with that and they're at risk for hyperglycemia I have seen this has happened especially your diabetic patients you'll or even if they're not diabetic they can increase their sugars really really high so you want to monitor their Sugar's they're at risk for infection because corticosteroids suppresses the immune system so they need to watch out for that and avoid those sick people and if they use these over time they're at risk for osteoporosis okay piece they really need to take away with bronchodilators and COPD I mean corticosteroids and COPD is um if a patient is prescribed and inhaler that's a bronchodilator and then inhaler that's a corticosteroid how which one you're going to use first it's very important first they want to use the bronchodilator inhaler because what this does is they take it in and opens up those Airways it dilates those Airways then five minutes later they're going to use their corticosteroid inhaler because those Airways are nice and opened up and that corticosteroid can get in those Airways that would have normally been closed off because they didn't use a bronchodilator and it can do its SHA so remember that another thing you want to remember after a patient uses their corticosteroid inhaler they need to rinse their mouth another drug use the p4 phosphodiesterase force inhibitors one is called with Yuma last and this is used for people with chronic bronchitis and it helps decrease COPD exacerbation now it's not a bronchodilator okay what you want to remember about this drug are the side effects of it you want to assess your patients mental status whenever they're on this because it can increase and the thoughts of suicide ideation so how I remember this because there's a lot of drugs you have to remember eyes a nursing school I look at the name and the last part of refu my last is last and last it could be their last day so you want to assess them for thoughts of suicide and rapport that's with the doctor because this is not a good thing and also they can have weight loss with this so monitor their weight and teach the patient you know if you start having these thoughts please report them and monitor your weight okay next methylxanthines a drug and this category is known as the awful and this is many times given orally and it's a type of bronchodilator so it works by relaxing the smooth muscle opening up those Airways and it is used for long-term for patients who have severe COPD now remember this about the off limb it has a narrow therapeutic range a lot of times test questions like to throw out patients on theophylline you have a dose schedule to give here's your lab work on theophylline it has a narrow therapeutic range and you want it between 10 to 20 micrograms per milliliters so anything above that's bad and anything less than that they're not receiving enough medication now the off link an increase digoxin toxicity so if you're on digoxin you'll want to make sure that there's auxin levels being monitored and it can decrease the effects of lithium and dilantin okay next s for short acting bronchodilators these relax the smooth muscle of the bronchial tubes and their short acting so they're great in emergency situations where you're having some severe shortness of breath going on those Airways are constricting up is going to go in there open those up so the patient can breathe and when they need quick relief so as the nurse know which ones are short and which ones are long some typical short ones beta-2 agonists albuterol that's what that is an anticholinergic such as atrovent next the last one l4 long-acting bronchodilators these works the same as short but the effects of the medication lasts longer so the patient is going to use them over a period of time they'll probably be scheduled maybe once or twice a day and just be familiar with which ones are long you have beta-2 agonist like saw metro and then you have anticholinergic like spy Revis pairi but that's a real popular one and what you want to remember with this is of course you use the bronchodilators before you use if they're on corticosteroids that are inhaled so you would use this first open up the airway then use your inhaler of the corticosteroids and some side effects the beta-2 agonists they can cause increased heart rate and you're an area where chick retention and the anticholinergics can cause dry mouth and blurred visions so be on the lookout for that educate your patient about that so that is about the nursing interventions and the medications used in COPD don't forget to watch part 1 and take the NCLEX review quiz that goes over these lectures and if you like this video please give it a thumbs up and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Chest_Tubes_Nursing_Care_Management_Assessment_NCLEX_Review_Drainage_System.txt	hey everyone it's Sarah with register nurse rn.com and in this video I'm going to be going over an inlex review about chest tubes what I'm going to do in this video is I'm going to cover the things you need to know exactly for the inlex exam I'm going to cover the anatomy the different types of Drainage Systems the purposes and the nursing interventions whenever you're maintaining these systems and after you watch this lecture be sure to go to my website register nurse aan.com and take the free quiz that will test you on your knowledge about how to take care of chest tubes and a card should be popping up so you can access that so let's get started first let's start out talking about the purpose of a chest tube what is it and what does it do okay it is a tube that is inserted into the plal space of the lungs to remove air or fluid to help re expand the lung so let's look at what it does okay we have our lung here that is that little red area on the drawing then around the lung we have a little protective layer called the visceral plora and then we have this small little space and then around that space that attaches to our thoracic cavity is called the paral plura and what happens is that whenever you breathe in and out these two layers Glide gently over each other because in the pluris space there's a small amount of Cirrus fluid that allows them to Glide nice and gently to prevent them from rubbing together but while they're gliding they're creating a negative pressure which allows your lungs to work properly and to inflate and deflate now whenever something gets into this space like air or fluid the lungs are like oh no this is not right it's messing up our pressure because we have a negative pressure and it causes the lung to collapse so the physician will go in there and insert a chest tube to help drain out that air and that fluid that's causing this lung issues now there's another type of chest tube which is um called a media styal chest tube and this is a tube that that is inserted into the medianum space and it's typically placed under the sternum to to drain fluid from around the heart after cardiac surgery because a lot of times after card cardiac surgery there can be extra blood or fluid and this can get around the heart and compress it and send the patient into cardiac tampeno so those are placed as well now let's take it a little bit deeper and look at some other reasons why a chest tube might be placed okay the first one we hit on this is a pneuma thorax and this is just where air enters into this small little space and causes the lungs to collapse this can happen because of like trauma or spontaneously happen I've had patients who've been admitted they the doctor wasn't sure why they had a numa thorax it just happened spontaneously another thing is called a plora effusion and there's different types of PL fusions depending on what type of fluid is in that PL space and what it is it's just fluid in the plor space so here's your nice little space and some fluid gets in there messes up that pressure are setting and the lung collapses and they have some major breathing issues okay different types of plor fusions you have hemothorax which is where blood enters into the plor space hemo means blood and this can be due to trauma a a disease like tuberculosis or a blood clotting issue they're um not clotting so blood is leaking in there another thing is called epema where they can get an infection in the plor space and last type of PL Fusion is a silo thorax which is where lymphatic fluid can get into the plora space and of course another reason for a chest tube is the cardiac surgery now let's look at the different types of chest tube Drainage Systems um whenever you get a job as a nurse be sure to familiarize yourself with the different types of chest tube Drainage Systems your facility offers and make sure you get a good in service on that because different places have different chest tube Drainage Systems okay here are your basic ones I'm going to be going over um for inlex purposes the wet suction and the dry suction and let me go over the basic setup of how a typical chest strain is set up and then we'll talk about the differences between the two okay so you have your little suction device the tube will go will be coming from the patient and this tube right here is from the patient and it's draining down into the drainage chamber these are your drainage chamber where whatever is coming out of that lung is Flowing down into there then in the middle you have your water seill chamber and there's blue water in this and as the patient breathes in and breathes out this water will TI will osculate up and down and sometimes there's a little ball in there that will move as well and then you have a little mo an air leak monitor area and in this area you were looking for bubbling because if you see continuous bubbling which we'll go over in depth whenever I'm covering the nursing interventions and there could be an air Le and then over here at the very end you have your suction control chamber now notice on the wet suction and the dry suction it looks a little bit differently and that is the biggest difference with these two systems is the suction how the suction works so let's cover it okay wet let's talk about the wet section okay the wet section is regulated by the height of the water in the suction control chamber when it's connected to wall suction so whenever you're setting up a wet suction chest Tu drainage you will be filling this with the water that it comes with and um depending on what the physician orders you'll fill it up to whatever they order um typically it's -20 cm of water and this right here once you connect this tube to the wall section will regulate the suction control of the chest tube and you will hear bubbling and see gentle bubbling in this as it's working so that is normal now with dry suction the water there is no water column and the suction is controlled and uses a suction monitor Bellow that balances the wall suction and um you can adjust the wall suction pressure by using a little rotary suction dial on the side of the system so this area right here this is where your suction monitor Bellow is and it looks like a little orange accordion area and whenever you turn on the wall section to this tube this little orange accordion will start to expand out and you have this little triangle there that tells you once it gets to that triangle it's regulating suction it's good and then here you have your suction control regulator and you have a little dial on the side where you can set the prescribed suction of whatever the physician orders and here it's set on -20 like how it would be over there in the water suction now with the dry suction systems you can get a high you have higher suction pressure options there's no bubbling of water because you don't have a water column like how you do on wet suction and there's no water evaporation with the wet suction because you have this water you have to fill it over time this can evaporate so you'll have to monitor that make sure it's at a good level here you don't have that so you won't have water evaporation now let's look at our nursing interventions of things that you have to do for this patient who has a chest tube the biggest thing you want to do whenever taking care of a patient with a chest tube is you want to monitor the patient's respiratory status very closely you want to monitor the drain system itself and you want to know what to do when things go wrong like if the chest tube becomes dislodged accidentally or the system breaks and how to assist the physician with removing the chest tube and I'm going to be covering all those things so first let's talk about the drainage system and the tubing okay the drainage system itself needs to keep needs to be kept below the patient's chest and the tubing especially the tubing coming from the patient it tends to be long and bulky and patients roll over on it gets caught up in a side rail so you want to make sure that those connections are secured and that they're draining down into the system and that there's nothing no stagnant fluid collecting in those and clots and that your connections are sealed next while you are taking care of this patient with the chest tube you're going to be be watching The Collection chamber the water seal chamber and the suction control chamber and this is going to tell you a lot about what's going on with the patient but first let's talk about the drainage collection chamber the drainage collection chamber is whenever you're monitoring this you want to note the color of the drainage how much they're putting out typically less than 100 cc's per hour and you want to record it very very well regularly because Physicians are going to ask you how much is that chest tube putting out next the water seal chamber this is your water seal chamber on the dry suction and on the wet wet section what does the water seal chamber do it performs an underwater seal to allow air to be remove from the plor space while preventing outside air from entering into the lungs because remember we want to create a negative pressure in there because that's what the lungs like so that water still helps us do that now one thing you want to know this is normal the water will fluctuate in this water seal chamber it will osculate up and down so that's normal you want that and whenever the patient breathes in it the water height will increase and when they expire have expiration decrease the water will decrease however it's the opposite if the patient is on positive pressure mechanical ventilation whenever the vent breathes in for them the water will decrease when the vent breathes out for them the water will increase so just commit that to memory now inlex question what if the water in the water seal chamber you notice it's not fluctuating at all what could be the issue well the lung may have re-expanded corrected our problem or there's a kink somewhere so you want to check that out next the air leak monitor area this is part of the water SE chamber and it's at the bottom and what we're looking for in that is bubbling inlex loves ask questions about bubbling so what's the big thing normally there should be no bubbling in there because it's monitoring for heirs however if you have excessive bubbling noted in that area that could mean an air leak however if the patient has a numo thorax and there could be intermittent bubbling in this now let's think back to to a pneumothorax what is a pneumothorax remember we talked about at the beginning of the lecture it's where air enters in to the plora space so as that air as that patient is recovering air will escape and leak from the lungs into the water seal chamber so you could see a little bit intermittent intermittent bubbling so that could be normal for them but the excessive continuous bubbling is not that can indicate an air leak okay next part of it is the suction control chamber remember on the wet section we have the water column and on the dry section we have the suction Bellow um little regulator that works with that biggest thing you need to know is that um with wet suction you're going to hear a continuous bubbling noise and you're going to see gentle bubbling in this that is normal because it's connected to wall section and that's telling us it's working with and the water can evaporate over time so you want to make sure that you're adding water if it does evaporate evaporate to keep it at the prescribed amount of suction with the dry suction there's no water column and it's regulated by that suction monitor Bellow that little orange accordion thing other thing you want to do is you want to monitor your patient's lung sounds how fast they're breathing if they're having any complaints of difficulty breathing like dmia um watch the insertion side look at it make sure it's free from infection and also check for any subq crepus or subq osine also called that this is where carbon dioxide escapes into the tissues and whenever you feel it'll be puffy and you feel it you'll never forget it if you ever feel it it feels like a crackling sensation underneath the skin and also you're going to be having the patient cough and deep breathe that helps move fluid and keeps their lungs nice and functioning and you're going to be repositioning them okay what to do if the chest tube becomes dis loded if this happens cover the site with a sterile dressing and tape it on three sides doing this will allow air to escape and prevent a tension Numa thorax and notify the physician immediately okay what happens if the system breaks you walk into the room it's fell over cracked you need to get a new one while you're waiting on your new one to arrive order a new one um you'll take the tubing and insert it one inch into sterile water to make that water seal and get a new system okay what about milking or stripping the tubing this used to be done a long time ago however it's not really recommended anymore um due to increasing pressure so always follow your hospital protocols with this another thing clamping another issue always follow your hospital protocols what do they say to do with that um because there's an increased risk of increasing the patient's chances of developing tension numo thorax and never do it without a physician's order okay so removal of a chest tube typically the Physicians will do this in some facilities nurses have been checked off through competencies to do this but typically for inlex purposes you will be assisting The Physician usually done at the bedside and what you will do is you will gather the supplies uh typically varies on physician preference so always make sure you know what your Physicians like uh sterile gloves dressing supplies um this could be a clusive petroleum base tefla whatever a mask gloves a suture removal kit and rubber tipped hemostats okay one thing you're going to be doing prior prior to removal you're going to teach the patient how to do what's called the Val Salva maneuver and this is where you will have the patient take a deep breath exhale and bear down and they will do this during removal the reasoning for this is to prevent air from entering that plural space during removal so that helps decrease that from happening then if ordered uh you'll premedicate the patient for pain because this can be painful uh position the patient in semi fowers position and afterwards you're going to monitor the respiratory status listen to those lung sounds watch for equal chest rise and fall make sure it's not unequal any drainage is the patient breathing okay are they complaining it's hard to breathe and typically after a removal is done the physician will order a chest x-ray to assess lung expansion so that is an inlex review about chest tubes now go to my website register nurse rn.com and take the free quiz to test your knowledge and be sure to check out my other inlex review videos and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Nephron_Structure_and_Function_Physiology_Filtration_Reabsorption_Secretion_NCLEX_Review.txt	hey everyone it's sarah thread sterner sorry and calm and in this video I'm going to be going over nephron physiology this video is part of an inkless review series over the renal system so be sure to check out those other videos and at the end of this video you can access the quiz so let's get started so in the previous video we went over kidney and nephron anatomy now we're going to take it a step further and we're gonna dissect this nephron and we're gonna pay close attention to what is being filtered what is being reabsorbed from that filtrate and what is being secreted into that filtrate which can leave the body as urine and just to recap a little bit we know that the whole role of our kidneys is to filter our blood our kidneys receive that fresh oxygenated blood from the heart via the renal artery then it branches off into like arterioles which go to those nephrons and remember each kidney has like millions of nephrons and these nephrons part of it sets in the cortex of the kidney and another little part of the nephron sets in the medulla of the kidney and filtered through there and then the whole thing that's what the nephron does is it filters reabsorbs secretes and then excretes urine and urine will flow out of the renal pyramid through the renal papilla down through your minor and major k lex then down through the renal pelvis out through a year the ureters store it in the bladder and then and it will be voided out through the urethra now let's take a closer look at the nephron okay whenever I look at the nephron I like to divide it up into two sections based on its function okay the first section is the renal corpuscle which includes your glom areas and Bowman's capsule and they work together to filter the blood so that's what the renal corpuscles do then the second section are your renal tubules and what they do is they play a role in reabsorption taking the substances out of that filtrate and putting it back in the blood and secretion where the peritubular capillaries are secreting substances into the filtrate to be excreted through the urine so let's talk about the filtering parts of the nephron okay first part of the nephron is the Gloam areas and the glomerulus is just this mesh of circular capillaries and it's receiving its blood flow through the afferent arteriole and remember this came from the renal artery drain down from the heart that is really nice and oxygenating it's gonna go to the nephron to be filtered out so it hits the glomerulus and due to that mesh of circular capillaries this secrete this causes a very high pressure which will cause ultra filtration and what will happen is that filtrate will start to leak from the glow Marius and collect in this capsule I like to think of it as if you have a strainer and you put maybe like pus in your strainer and the waters dripping out of the pasta in a sense it's the same thing if you need a visual aid to help you so it's dripping down so what exactly is coming out of the blood and collecting in this filtrate the following water some glucose amino acids ions which are like calcium potassium magnesium phosphate chloride things like that urea and creatinine and I want to say one thing about creatinine creon and as you're gonna see whenever we go more in depth with the tubules it's not really going to be reabsorbed or secreted it's exclusively filtered from your bloodstream by the glomerulus let's it lets us know based on the rate of its excretion from the blood stream how well the kidneys are working so that is why we pay such close attention to creatinine because it tells us how well our kidneys are filtering the blood now some substances that are not normally so filtered by Demaryius are blood cells and proteins then after the blood is done circulating through the gua Marius and has got filtered it leaves the gall Marius through what's called the efferent arterial every it means a way and every arterial goes and it turns into another important structure called the peritubular capillaries and these capillaries have a very important role they the capillaries go and they in a sense surround and go around your nephron because they're gonna help play a role with reabsorption and secretion and let me show you this right here we have these orange arrows and this in their diagram is representing the filtrate that is flowing through the nephron that's left Bowman's capsule the black arrows represents substances from the filtrate that is leaving the tubules and going back into the bloodstream and it enters into the peritubular capillaries through there and then you have secretion which is wet represented by these blue arrows and this represents substances leaving the peritubular capillaries and going into the filtrate to be excreted so that's what the peritubular capillaries do they play a role in allowing the reabsorption process and the secretion process with the nephron and up here we refer to them as peritubular capillaries and down here on the loop of Henle and they are referred to as the Bastow rectum now the filtrate is going to leave the capsule and it's gonna travel through these renal tubules and depending on where the filtrate is and the certain part of the tubule depends on what's going to be reabsorbed and what's going to be secreted because different areas reabsorb different amounts and secrete different amounts so on this nephron pay attention to what parts lay in the renal cortex and which parts are in the renal medulla this black dotted line will help you differentiate these parts are up in the renal cortex and these parts which are the loop of Henle and part of the collecting duct are in the renal medulla okay so filtrates coming through here through what's called the first part of the renal tubular the proximal convoluted tubule and here this is where most of our reabsorption is going to occur so what is going to be reabsorbed the biggest thing that's going to be reabsorbed is glucose and amino acid nearly hundred percent because these substances are very vital for our survival we need them another thing that's really going to be absorbed is bicarb and we learned in our acid base and balance videos that we need some bicarb and if we don't reabsorb enough bicarb put it back in our bloodstream we can enter into acidotic conditions so that's five we really want some bicarb and then we're going to take in a lot of water and sodium and chloride salt about 60 to 70 percent from there because we need that as well as survived and then other ions like potassium magnesium calcium phosphate things like that and about 50 percent of urea we're going to reabsorb now also in this proximal convoluted tubule we're going to experience some secretion from the blood stream into the filtrate to get rid of it what will be secreted is like uric acid and other things like antibiotics or other drugs like diuretics things like that then the filtrate is going to flow down through what is called the loop of Henle and as you notice the loop of Henle is the only part of the nephron that is completely in the renal medulla and let's talk about the renal medulla for a second because it's interesting inside the renal medulla it has interstitial fluid and that interstitial fluid is super super salty it's considered hypertonic so what happens that filtrates flowing down through air in through the descending limb of the loop of Henle and it comes into contact with this highly salty environment and we know that what's in the filtrate is water and all of our islands and things like that well the unique thing about the descending limb of the loop of Henle is that it is only permeable to water so it only allows water to flow through it it does not allow ions like your sodium your chloride your potassium to go through will not let it go so once that filtrate which house water hits this all this water is going to come out of that descending limb because we learn through osmosis that water loves salt so here comes that water sees that salt and it rushes out and allows us to reabsorb all that water which is why our loop of Henle main job is to really concentrate our urine and take the water that we need to maintain homeostasis and that renal medulla interstitial fluid of the hyper tonic fluid allows it to do this so water has left the descending limb then your filtrate gets down here and when it reaches this area it's really concentrated because most of the water is left all that we have is our sodium and her chloride asking our ions now it's going to go up through the ascending limb in this thick part of the sending limb descending limb is very unique because it only allows ions to leave it's only permeable to ions it is not permeable to water so water will not leave this any lamp only ions so once it gets there it act actively these ions specifically sodium and chloride chloride and a little bit of tasking leave it and enter in this interstitial fluid which allows that renal medulla to keep that hyper osmolarity environment so this can keep continuing another thing I wanted to point out is that sometimes the loop of Henle secretes urea and whenever it does that it plays like a process in your recycling which will help keep the osmolarity in the medulla increase because we want that osmolarity because it will help us save water so it helps with water reabsorption and it helps maintain concentrated urine as it flows through the tubules then the filtrate will go through the distal convoluted tubule and this is where there's going to be some tweaking of that filtrate even more a little bit more reabsorption of this and secretion of that so some things that are reabsorbed we have some sodium and water which will be under the influence of the hormone aldosterone and remember aldosterone conserves sodium which will cause water retention then some reabsorption of calcium under the influence of the parathyroid hormone and a little bit of bicarb a lot of our bicarb was reabsorbed in the proximal convoluted tubule but here it takes just a little bit more again just to maintain that pH in our blood some things secreted by the distal convoluted tubules are potassium and hydrogen ions then the filtrate is going to go down through the last part of the nephron called the collecting tubule and this is where there's going to be the final touches on that filtrate what needs to be reabsorbed gets reabsorbed back into the bloodstream and what doesn't exit the body as urine so I'm the collecting to me what generally is reabsorbed is sodium water which is under the influence of the hormone and antidiuretic hormone which helps regulate the amounts of water in our body and some urea so that happens then it leads the collecting duct which connects straight to the renal papilla and remember the renal papilla was the endpoint of where the renal pyramid is and then it goes down into the minor calyx the major calyx down through the renal pelvis out through the ureter stored in the bladder and then out of the urethra to be voided out so after all this goes through the filtrate what acts is in the urine what makes up your urine the end product is the urea which is a waste product that you don't want high amounts in your body water excessive water that your body didn't need it says we have enough so let's get rid of this creatinine which is another waste product and a bunch of ions that your body has enough up that your body said I don't need this let's get rid of this we have enough of sodium chloride potassium magnesium phosphate and calcium okay so that is the nephron physiology thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Blood_Flow_Through_the_Heart_Heart_Blood_Flow_Circulation_Supply.txt	everyone this is Sarah with register nurs rn.com and today we're going to be going over the blood flow of the heart in many nursing classes such as anatomy and physiology pathophysiology um medical surgical nursing all these nursing classes you have to take you're expected to know how the blood flows through the heart and many times on an exam you'll be given a blank sheet of the heart and you'll have to fill in each blank or um you'll be given questions and it'll test your knowledge on how you truly understand how the blood flows through the heart so here I've tried to make it as easy as possible to learn the blood flow of the heart I've researched many pneumonics people use um different techniques that they use but what I've learned and from personal experience you just have to understand what the heart looks like and how the blood actually flows through it that's the best way because there's so many steps of where the blood flows through a pneumonic really doesn't help because it's so long and it just doesn't make sense I haven't found a pneumonic yet that makes sense so what I'm going to do I broke it down into I've split the heart in half we have the right side and the left side and um there's 12 parts to each side there's 12 Parts total and the right side has six parts and the left part has six parts so I think that this has made it a lot easier in how to understand the blood flow of the heart now when you get done watching this video go to our website registered nurse rn.com and there's a quiz you can take to test your knowledge on how well you grasp the blood flow of the heart also there's inlex quizzes dosage calculation quizzes ABG quizzes a lot of quizzes to help you along in nursing school so let's get started first what I want to do is I'm just going to go over the anatomy of the heart because you have to understand how the heart is laid out in order to understand how the blood flow is so let's go and take a look at the heart we have split the heart into two sides you have the right side and the left side what we're going to do is just go over the anatomy of a heart here we have the superior vnea and the inferior venne this strains blood into your right atrium you have your tricuspid valve right here which lets blood into The ventricle this is your right ventricle then blood shoots up through the pulmonary artery because it has to get through the lungs and in order to get to pulmonary artery you have the pulmonary valve this is the pulmonary artery right here which is sending unoxygenated blood to the lungs so it can get some oxygen then it enters back in through the pulmonary veins right here are your pulmonary veins once it hits the pulmonary veins it's going to go into your left atrium shot through the um bicuspid valve which is also known as the mital valve or the atro ventricular valve that really confused me because I would hear people talking about a mitro valve a tri cusped valve and I was like which one's which how many valves are there so so um the bicuspid has three different names it's bicuspid either mital or um atrio ventricular so keep that in mind because you'll might hear Physicians or your teachers refer to it as different names so that is your bicuspid valve um below the drusin valve is your left ventricle uh the blood will shoot up because it wants to get through the to the aorta the aorta will send it up through the body and this is your aortic valve and it shoots up through the aorta right here and goes up through the body so that's the anatomy of the heart okay next we're going to go over um I'm going to show you how I've split up the right side and left side and go over that and then we'll go through the blood flow of the heart again okay now since we went through the quick anatomy of the heart let's break it down and see how the blood actually flows through the heart and gets to the body like I said in order to memorize the blood flow of the heart you really just got to understand and formulate it in your head how it works it's the heart is such an awesome muscle and how it delivers um blood through the body is really cool so what we're going to do is I'm going to try to break it down try to give you some things to remember and whenever you take your test a lot of people what they like to do is draw a little heart with lungs and then just label each part of heart so that can help you so first let's get started okay as we said in our anatomy demonstration we have the the blood will enter into the body through the superior an inferior vena this is blood that your body has already used there's no oxygen in it it has very low low amount of oxygen in it and it's coming to your heart so it can be filtered through the lungs to get some more oxygen to get back through the body so everything's draining into your Superior and inferior vnea and notice it is blue that means it's unoxygenated we have the right side and the left side hence why this is in blue and then this is in red everything that goes in will be unoxygenated then it will go into the right atrium okay that's your Atrium then once the blood's in the atrium it's going to be shot into the right ventricle in order to get through the right ventricle it has to go through the tricuspid valve there's two important valves you want to remember in blood flow you have the tricuspid or the bicuspid an easy way to remember that because we're starting on the right side of the heart you um your tricuspid valve is first and then your bicuspid so remember this always try it before you buy it whenever we buy stuff we always want to try it out before we buy it so your tricuspid valve is first and it's on the right side so shoots through the trius valve which opens and closes shoots it down into the right ventricle our Mi the mission of the blood is to get to the lungs on the right side so we're going to go through the pulmonary part of the heart remember lung and Pulmonary pulmonary means lung so in order for this right side blood to get through to the lungs it's got to go through the pulmonary part of the heart so it goes through the pulmonary valve which opens and closes and allows blood to go up through the pulmonary artery so you have the pulmonary valve shoots up through the pulmonary artery then it goes and was filtered through the lungs after the blood attaches and gets some oxygen it's going to shoot back through the heart because this part its goal on the left side is to get to the body the right side side wanted to get some oxygen in the lungs that was the right side's goal the left side's goal is to get to the body because it has oxygen in it and it wants to feed the brain and feed her extremities and her organs so it enters in through the pulmonary vein okay once it hits the pulmonary vein it's going to go into the left atrium a lot of people get confused on um the atriums and the ventricles they want to say that the ventricles are on top and atriums are on bottom try to remember in the alphabet a a is before V so A's are always going to be on top of the v's because it's before V so atriums are always on top of ventricles enters in into your Atrium and then it has to get down to the ventricles in order for the blood to get down it has to cross through a valve okay and this is your bicuspid valve remember try before you buy we're on the left side of the heart so it goes through your bicuspid valve and also just as a side note bicuspid valve is known as mital valve it's also called the atro ventricular valve so just remember that cuz some people like to use those interchanging once it hits your bicuspid valve it's going to go down into the left ventricle remember the goal of the blood on the left side is to get to the body so in order after The ventricle contracts it's going to shoot up through the aortic valve because it has to go up through the aorta remember that the aorta is a nice big artery that's going to shoot blood up through the body so in order to do that it has to go through the aortic valve then up through the aorta which goes to your brain and goes through your body so that is I think an easy way to remember blood flow of the heart remember it h the blood has to go through 12 different areas you have the right side always start with the right side and then it ends up into the left side there's six parts on the right side and six parts on the left side which give you a total of 12 also always remember that your atriums are always above your ventricles you can remember that by a is before V and another part that people get confused on are your tricuspid and bicuspid valves remember you always start on the right side when you're trying to go through blood flow and you're going to try before you buy so your tricuspid valve is on the right side and on the left side is your bicuspid valve so that is some information on how the blood flows through the heart um remember go take the quiz on our website register nurse.com go there and on the homepage click the slider that says quizzes and you can take that quiz and see how well you grasp the blood flow thank you so much for watching be sure to check out our other uh video tutorials and if you like this video please give it a thumbs up and have a great day
Medical_Surgical_Nursing	Pericarditis_Nursing_Management_Treatment_of_Pericardial_Effusion_Friction_Rub_Pericardium.txt	hey everyone it's Sarah register nurse rn.com and in this video I'm going to be doing an inlex review over pericarditis this video is part of an inlex review series over the cardiovascular system so if you're studying that system be sure to check out the videos included in this series so what I'm going to do in this video is I'm going to cover what paric carditis is the causes the different types the complications the nursing interventions and the pharmacological aspect of caring for a patient with this condition and then after you watch this lecture you can go to my website register nurse rn.com and take the free quiz that will test your knowledge on pericarditis and a card should be popping up so you can access that so let's get started first let's start out talking about what is pericarditis it is the inflammation of the pericardium layer of the heart so what is the pericardium and where is it okay first let's take the word par cardium Perry means surrounds and cardium means heart so it is a double layer sack that is filled with Cirrus fluid paracardial fluid that surrounds the heart and it plays a vital role with your heart number one it anchors the heart to the mediastinum it also protects your heart from infections say you get a lung infection that protective layer protects that infection from being transferred from your lungs to your heart heart it keeps the heart from overexpanded when that patient is experiencing fluid volume overload and it lubricates the heart while it beats so you don't have those two layers rubbing up against each other but that is what happens in pericarditis which we'll go over here in a second whenever we talk about signs and symptoms so let's look at the pericardium layer in depth okay this whole part surrounding the outside of the heart is called the pericardium and the pericardium is made up of two layers so let's go over those layers the outside part which is the green that is outlining the heart is called your fibrous pericardium then your next layer which is um Illustrated here with the red the blue and the brown is called the Cirrus pericardium but it is made up of two layers and then it has fluid in the middle of it so the red part is called the paralal pericardium then you have the Cirrus fluid which is known as paracardial fluid and then after the Cirrus fluid you have the visceral pericardium which is also called the epicardium so what causes this condition pericarditis number one one cause that can cause this is an illness patient gets a virus or bacteria attacks the parac cardium on the heart and you get inflammation of it or trauma to the heart heart like with a heart attack patients who've had an MI are susceptible for pericarditis or after heart surgery or a physical trauma to the heart with um an outside injury or autoimmune the body attacks itself like in conditions like lupus or it's completely unknown it happens they are not sure why it happened so they consider it idiopathic now let's talk about the different types of parac carditis okay you have a cute and chronic what is acute acute is where a patient develops parac carditis for less than six weeks this is your most common type now a lot of cases of parac carditis tend to be mild and they don't require treatment and they go away by the by itself however there is chronic and this happens over time and and lasts more than six months so the patient is struggling with this chronically now because of this constant inflammation on the pericardium this can lead to what's called constrictive pericarditis and what happens with this just as its name says it res it is constrictive to how the heart can pump because what happens is that paric cardium becomes thick and it develops into like scarlike tissue so it prevents those ventricles from properly filling up and pumping out blood and um it can lead to Patient having signs and symptoms of heart failure and typical treatment for this is a pericardia ectomy which is where they go in surgically and remove the pericardium now let's look at the complications because that leads me into the complications of pericarditis okay another complication other than constrictive parac carditis is pericardial affusion this is where in that paracardial space where that ser fluid there's too much fluid that enters into that space and this can develop due to inflammation over time and um so you get all this flu in that paracardial sap this in turn can become very dangerous if not treated appropriately or they catch this fast and the patient can enter into cardiac tampen which I'll talk about a little bit later whenever I'm talking about nursing interventions and a treatment for this paracardial infusion because they want to go in and remove that extra fluid that's in the paracardial pite is called a paracardial centesis and this is where they go in with a sterile sterile needle and they remove excessive fluid from the paracardial sac now a patient can develop um also another complication is they can have both they can have the affusion and the constrictive together where it would be an affusion constrictive paric carditis now let's look at the signs and symptoms and the nursing interventions and the pharmacological treatments first signs and symptoms what what are the typical signs and symptoms that you're going to see in a patient with pericarditis okay to help you remember this remember the word friction because the problem with pericarditis is that inflammation is causing those layers to rub up against each other so that is why the patient is having a lot of pain especially chest pain so remember the word friction to help you remember all those other signs and symptoms okay first F friction rub whenever you're listening with your stethoscope you will hear over the heart what is called a pericardial friction rub and what this sounds like it sounds like a grading harsh sound of two things sliding up against each other sort of like sandpaper also the patient will have a fever so that's the other F next R for radiating substernal pain that can radiate to the left shoulder the neck the back it's very similar to the pain that a patient may have whenever they're having a mardial infarction so the patient will probably think I'm having a heart attack next I for increased pain in the suime position whenever the patient lays flat they're going to notice that their chest hurts a lot more than whenever they're setting up or leaning forward so that's another tell taale sign hey this is probably not my cardial infarction since positioning is making the test pain worse next C for chest pain like I said big Hallmark thing with this is the chest pain and that paracardial friction rub and like I said the patient's going to feel like they're having a heart attack next t for trouble breathing when lying down again that goes back to the Supine position they're going to be feeling more pain and they notice that it's hard to breathe too whenever they're laying on their back and then I for in whenever they're H like in having inspiration or they're coughing they notice that the pain is increasing as well because whenever you're coughing or breathing in those lungs are expanding pushing more on that heart causing those layers to rub even more and that inflammation really hurts o for overall just feeling sick and weak they feel yucky but and they're also having these other signs and symptoms as well and then in for noticeable ST segment elevation so on an EKG you will see those St segments elevated now right here I have these little asteris that are orange for the friction rub the increase pain the substernal pain the chest pain and breathing whenever they breathe in it causes them more pain those are typically your most common signs and symptoms your Hallmark signs of paric carditis now let's look at the nursing interventions what are we going to do for this patient to make them more comfortable okay first what we want to do as a nurse we is we want to assess their pain this can be very painful so we want to make sure we're utilizing what the physician has ordered to give them for pain which we'll go over those medications here in a second next we want to teach the patient about sitting in the high Fowler's position or leaning forward because that helps relieve pain and to avoid lying down in that Supine position because they'll have more pain with that next we want to monitor for cardiac tampen remember this is where there is excessive fluid the paracardial infusion in the paracardial sac and it's compressing the heart so some signs and symptoms for that number one pulsus paradoxus what is this this is whenever the patient breathes in the inspiratory phase there is a 10 mm of Merc Mercury drop in the systolic blood pressure next they may have jbd which is jugular Venus distension but they don't have but they have clear lungs normally in heart failure you have jvd and you're going to hear um crackles throughout the lungs are going to have swelling because of that increased pressure of fluid in the body but here they don't have that they'll have the increased juggler distension with clear lungs so that is a warning sign that hey this patient is probably in this condition and whenever you listen to those heart sounds they're going to be muffled you're not going to be able to hear them very well and the reason for this is because there's a buildup of fluid in the heart so it's muffling out those heart sounds you could normally hear because that layer surrounding the heart is keeping those sounds in there patient will also be tartic and hypotensive okay let's look at the medications what is typically given in pericarditis um as prescribed by the physici they may order aspirin or an inid what is an inid it's a little acronym for non-steroidal anti-inflammatory drug remember we have inflammation problems in pericarditis itis that's inflammation so we're going to give them something to combat that anti-inflammatory typically a popular one is ibuprofen however with ibuprofen you have to watch for GI upset and bleeding with this drug so as a nurse you want to make sure you're administering this to the patient with a full glass of water another drug that may be used is puline this helps decrease inflammation it's also used in patients who are suffering from gout and with ccine there is an increased risk of getting toxic with this drug and you need to educate the patient that they do not take cine with grapefruit juice because it increases the risk of them becoming toxic with this drug your body absorbs too much of the drug than it normally should and you can take this drug with or without food and some early signs of toxicity are nauseum vomiting and abdominal pain so if your patient starts having that all of a sudden after they've been taking culine you need to educate them about that they may be toxic another thing that may be used whenever the patient's not really responding to these other medications are corticosteroids and um this just helps decrease the inflammation and one drug you sometimes is called prednizone so that is about pericarditis now go to my website register nurse rn.com and take the fre inlex quiz that will test you on this condition and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Myocardial_Infarction_Heart_Attack_Ischemia_Pathophysiology_ECG_Nursing_Signs_Symptoms_Part_1.txt	hey everyone it's sarah thredson our RN comm and in this video i want to be going over myocardial infarction this video is part 1 of a part 2 series and what I want to be covering is the path of complications or signs and symptoms and how its diagnosed and in part 2 I'm going to be covering the nursing interventions and the medications used to treat in mine and as always over here on the side or in the description below you can access the quiz the notes and the other videos that are in the cardiovascular NCLEX review so let's get started first let's start out talking about what is the definition of a myocardial infarction also refer to some time as an MI or a heart attack it is where there has been limited blood supply to the myocardial tissue that causes it to die or become necrotic or necrosis and some causes of this what causes it the most common cause is blockage in a coronary artery due to coronary artery disease and we talked about this in depth in the in CLECs review about CA D and if you want to watch that a card should be popping up so you can access that another cause is a coronary spasm and this can be from drug use like cocaine or the patient has uncontrolled hypertension and what happens with this is that the coronary artery spasms it constricts so these little arteries on the heart and what happens is when you have that constriction you have no blood supply going to that heart muscle so that muscle is deprived of all that rich oxygenated blood and it starts to die another cause is damage to the artery due to a coronary artery dissection and what this is is that you have your artery it's made up of different layers and there is a tear in the inner layer of the artery the Tunica intima and what happens is you have this tear and Blood starts leak and it links into the tunica media and this causes think of it like a little bulge and limits the size of the lumen of the artery so whenever you have that you have stricted blood flow restricted blood flow go into that heart muscle and this can happen in young women who are young and active its most common type and it happens spontaneously now let's look at the anatomy and the pathophysiology of how this happens I'm going to walk you through a little bit later of what happens minute hour days and see what happens and how this heart tissue was nine okay so first let's go over the anatomy of the coronary arteries in this drawing here you will see the right coronary artery and the left coronary artery and these two coronary arteries branch off from the aorta which has just received rich oxygenated blood from the lungs and the job of these coronary arteries is to supply the heart muscle with fresh blood so we can work appropriately and notice it sets right on top of the tissue now in this drawing I wanted you to see where each coronary artery sets in relation to the atriums and the septum and the ventricles because if you get blockages in these specific arteries it's going to cause problems to either the left atrium the ventricle or the septum and you're going to have damage there because you're going to get a necrotic tissue so whenever you're learning this it's really important you remember wet which artery supplies what so let's go over that real fast okay your right coronary artery comes right off through here and notice where this whole runt coronary artery is setting it branches off into these little branches which we'll talk about here in a second but it supplies your right atrium and the right ventricle here is your right atrium and here is your right ventricle next you will have the right marginal artery and this supplies your right ventricle and your septum and you see it right here it's branching off here's your right ventricle and your septum then we have our left coronary artery and over on the other side of the heart because this right here is our anterior view the left cornor coronary artery comes out and that's why you see an outline these two right here the posterior descending because these are on the other side of the heart but I wanted you to be able to see them in this view and the left coronary artery as we said supplies the left side of the heart but it branches off into little areas and it branches off we have the left circumflex artery circum means a round so this artery actually comes around the heart in this area and notice where it says it supplies the left atrium and the left ventricle then you have the el-ad the left anterior descending artery comes down through here and this supplies a lot of areas of the heart it supplies the right ventricle the left ventricle notice how it's branching out over here and your septum now let's remember some things about the led the LED is the most common sight of blockages in patients and blockages in your left coronary artery especially the led can cause the worse damage from amma cardial important because of the damage to the anterior wall of the heart which we'll be going over the different anterior lateral parts of the heart a little bit later when we talk about EKGs and why why does it do this well and heart failure we learned that our left ventricle is the biggest area for pumping action to get our pumping to pump our blood so if it gets affected you have an anterior wall mi your L ad causes a lot of damage here you will get ventricular felt left ventricular failure over here so that whenever this happens you get a lot of damage in the heart whenever you have a blockage especially in your Li D and if it happens before where a branch happens quickly let's review how a coronary artery can actually become blocked now remember coronary artery disease is the number one cause of why you have a blocked artery also you can have coronary spasm or dissection of the artery but let's look at how it builds up over time with coronary artery disease so here you have a healthy coronary artery you have blood flowing through it and you have a little bit of LDL which is your bad cholesterol now over time this happens the what happens is that maybe the patient has as factors such as they're a smoker which is caused damage to this artery or they have high cholesterol or they're they have uncontrolled hypertension what happens is that this artery becomes damaged when it becomes damaged your LDL likes to stick into this artery wall and over time it grows as you can see here whenever it grows it limits blood supply now some of these plaques that's turned into a plaque can rupture vulnerable plaques and whenever it ruptures as you see here it spills its contents into the blood but the body sees that hey we have damage to our artery wall we've got to fix it so if think nobody thinks it's helping but in reality it's going to call us a major problem so it sends all those platelets there to go and to fix that artery wall so they come and they aggregate which is represented in this blue area right here and what happens I thought I was fixing the artery wall but it actually completely stopped blood flow to that heart muscle those heart cells and those cells die quickly and when this happens my cardial infarction happens and you start getting the following complications when the muscle is a hundred percent block there's no nutrients going to those cells those cells will die and it is irreversible after approximately 30 minutes so as the saying goes time is muscle we've got to get in there fast as healthcare providers try to save as many of these heart cells we can to prevent as much damage as possible and when these cells die they cannot be replaced they are gone forever now early signs we'll talk about this whenever there's a blockage those heart cells cells start to die there are no physical changes to the heart yet until about six to eight hours however when those myocytes die they start to release some things that lets us know whenever we go in and draw blood that hey there's an injury to the heart I'll talk a lot about this whenever we're going over nassim part but I'm just going to hit on the highlights okay so whenever these micelles myocytes die my Oh glob Yulin is released one hour post-injury and it's an early marker however it's not too specific though we like to look at troponin levels this is one of the gold sanders that we look at in the healthcare field there Drammen sets usually every six hours times three depends on how the physician orders them and it is released two to four hours post-injury another thing is ck-mb and it is released four to six hours after injury now you also start to see EKG changes early on which we'll talk a little bit later about like ST segment elevation or depression t-wave inversion or it's hyper acute now later on about 24 hours to 36 hours later inflammation starts to set in and neutrophils come onto the scene at the side of injury where that damaged tissue is a neutrophils start to come however even though they're coming there to do their job it can cause complication the patient is definitely at risk for pericarditis talk about this in in clicks review this is where all of a sudden your patient might start complaining of pain whenever they're coughing or lying down on their back it's relieved when they're leaning forward and on auscultation of the heart sounds you may hear a harsh grating sandpaper noise called a pericardial friction rub and this is one of the signs and symptoms of pericarditis also the patient is a huge risk risk for going into cardiogenic shock you've got some pump failure going on and also lot of times in patients who've had a myocardial infarction you are going to see arrhythmias like atrial and ventricular arrhythmias and AV blocks then ten days afterwards at that site of injury the tissue will start to experience granulation due to the microphages coming on the scene and what are they these they are white blood cells that come to clean up the dead cells however whenever they come on the scene just like neutrophils they're going to cause and they increase the chances of complication the complication they increase is because whenever they're coming in to clean up that side they cause the tissue to become weak and unstable so there's a risk of cardiac rupture then within two months there is scarring the last phase of healing you will have scarring which will affect the size of the heart and the function do the increase collagen and other side other complications that a patient may have after an MI or heart failure depression or ventricular aneurysm so what are the typical signs and symptoms of a myocardial infarction that you need to be watching out as the nurse okay to help us remember let's remember the mnemonic crushing Y crushing because a lot of times whenever patients are having an mi they will say it's like crushing chest pain that's one of the big things that pop out I used to remember crushing okay so si for chest pain this chest pain will be described as intense and heavy very severe are four radiating chest pain this chest pain will normally be heavy and intense but it will radiate to the left arm the jaw or the back that's a telltale sign if they tell you it's radiating you the chest pain is unrelieved by nitroglycerin or arresting s sweating it will be a cold sweat H for hard to breathe have shortness of breath just because of the intensity of the pain literally taking their breath away I for they may have an increased heart rate or blood pressure which is going to make the chest pain even more intense or an irregular heart rate in for nausea and vomiting and G they are going to be absolutely anxious and scared and as a nurse with patients who have actually experienced this in front of me I can tell you that I have seen this and that this is really real and it really happens now some things you need to take into consideration women women for some reason in a little bit differently with chest pain or their signs and symptoms of myocardial infarction so if you are educating patients the signs and symptoms take this into consideration because some women may not have that typical heaviness on their chest but they feel short of breath to have pain in the lower part of their chest and they feel really extremely fatigued and they'll just play it off like I think I have an illness like a flu I've had women patients who actually thought they came in they were having a myocardial infarction and it turns out that they thought that they had had the flu so they had put off coming in because I just thought they were sick so educate women that this could be a sign also patients who are diabetic and a silent mi this is where they don't have any pain at all they just don't feel good comes in their EKG shows that they've had one and the reason is due to diabetic neuropathy where those nerves have been damaged that feel pain in the heart so they had a heart attack but they didn't feel it because those nerves I would pick up that pain normally or damaged now let's look at the diagnostic tools used to diagnose a myocardial infarction that may be ordered by the physician as the nurse your role will be collecting these for instance the cardiac markers or educating a patient about them or just knowing what to expect whenever a patient does have an MI so let's review these okay cardiac markers as we talked about in the path up are those myocytes release these markers that helps us to determine hey there's been injury from a possible myocardial infarction so the first thing let's talk about our troponin this is the most regarded as of right now in the hospital setting in detecting a ma cardial and marching along with an EKG this is a protein released from the heart muscle when injured from an mi they are typically drawn in a series a lot of physicians order them every six hours times three-fifths it can vary depending on your physician's preference so your job as a nurse it's very important you know when the first repentant level was drawn and make sure that those necks and levels get drawn and you're going to be watching those lab results come into your computer system and monitor them if they're elevating if they are elevating you need to notify the doctor immediately so they can order whatever needs to be done to further evaluate this next is myoglobin this is released from the myocytes again and it is an early marker used for early detection but one thing with this is that it's not very specific to the heart so you need further tests to evaluate it and it's released one hour after injury it's one of our all the markers it's one that's released the earliest next CK this is another test that may be ordered and it's a protein which is released whenever there is muscle damage however it's not just specific to the cardiac it could it could represent skeletal muscle as well so the physician will need to order to further evaluate it to see if it is heart specific the CK M B and this elevates four to six hours after injury but again most regarded our troponin levels but you will probably see these ordered as well as cardiac enzymes okay other tools that may be ordered by the physician that you just need to know be familiar with as the nurse is an echocardiogram what is this this is an ultrasound of the heart to see if there's any damage to the heart muscle another thing a heart calf this is where they go in either in the femoral artery or the radial depending on the position and they inject a dye into the coronary arteries and this died after they injected they take an x-ray and they look in these arteries to see if there's any blockages if there are blockages where are they located is there any damage that's been done to the heart and can they possibly put a stent in there and open up the artery to start replenishing that heart muscle with some more blood another thing that may be ordered is a stress test with myocardial perfusion imaging also called mpi this assesses the heart's response to exercise they can do it with a chemical or on a treadmill and they take imaging they do that and it evaluates the heart muscle how that blood flow is getting to the heart muscle with imaging another tool ordered is an EKG anytime a patient is having chest pain comes into the yard they're going to get an EKG so you need to be really familiar with this as the nurse and a water pause fiddles are set up where there's a physician protocol if the patient anytime they're having chest pain you obtain an EKG either you will obtain a your EKG tech if you have one or a nursing assistant that has been trained in this so what you will be doing after you obtain it is that you're going to look at the EKG and you are going to assess for any changes if you see any changes you need to notify the physician immediately and what's really important is that you compare your EKG that you just got to previous EKGs as the patient has had in their chart and on telemetry strips and you want to know what areas in the EKG reflect certain areas of the heart and how to read it so let me go over that with you real fast here is a drawing of a basic 12 lead EKG at each of these little areas represent different views of the heart and as a nurse what you're going to be doing is you're going to be looking in these specific areas for any EKG changes what you're specifically looking for is any ST segment elevation or depression and you're going to be looking at your T waves are they hyper Q are they inverted and you're going to be looking for any pathological Q waves as well so real fast let's go over what each part of this EKG represents which view of the heart of looking at and what coronary arteries are probably being affected if you've seen changes in that area okay the lateral view is represented in the purple this is seen in lead one AVL v5 and v6 and the lateral view of your heart right here on this diagram is about right here now if you notice from where we covered in the beginning what's in this lateral view what area of the heart is being but what corny arteries are feeding the lateral lateral part of the heart your circumflex and your led your left anterior descending so if you're seeing EKG changes v v e6 AVL and leave one probably may have a blockage in your circumflex and your left hand harrier descending now inferior this is represented in to lead to lead three and a VF this is represented in the green the inferior part of your heart is about in this area right here and if you're seeing EKG changes in these areas right here in the green you may have a blockage somewhere throughout your right coronary artery now septal this is represented in v1 and v2 and it's where your interventricular septum is located and notice what is feeding this area of the heart your septal area mainly your el-ad your left anterior descending so if you're seeing changes there probably have a blockage there anterior view of your heart is represented with v3 and v4 and this is about right here in this area and that again is supplied by your el-ad your left anterior descending and it's represented in those two areas right there and just again to recap remember whenever I was talking about if you have damage and your el-ad you're going to have a lot of damage on this and here on this well your anterior side and in your heart and notice where a lot of your led is feeding your heart muscle at now let's look at the specific EKG changes that you were looking for as the nurse first let's go over what a basic pqrst complex should look like okay first you have this red line this is your isoelectric line certain things should fall above and certain things should fall a little bit below and that's a big thing you're looking for whenever you're looking for these elevations and depression so here you this little bump you have a P way then you have just a little smidge of a dip which is your Q and you have at all our way then a small little dip yes then you have your ST segment this extends from s to T so that right here this is the big part we are looking for whenever we're looking for changes so not notice it's nice and flat it's on the isoelectric line and then you have a little bump of the T wave it's nice and rounded not too tall it's not flipped so that's perfect we like that now ST segment elevation we don't like notice here you have your P wave you have your Q then you have your R then all of a sudden remember your ass over here it's dipped and then it goes straight and then you have your bump it's not this is elevated your isoelectric line would be right here and it's way above the isoelectric line so this is ST elevation and you see this patient having chest pain all that good stuff it's representing injury to the cardiac muscle another thing you need to be looking for as well an ST segment depression they may have either or ST segment depression this is where there's your peak QR and then ST notice just it's supposed to be on isoelectric line nice and straight it went way below the isoelectric line and then you have your T wave so this is ST segment depression and this represents ischemia next another thing you may see that you also need to be looking for is those hyper acute T waves this is different remember in the hyperkalemia videos we talked about tall T waves for hyperkalemia well this is a little bit different these waves are going to be tall they're not going to be pointed like how in hyperkalemia they're gonna be nice and round and tall so if you see this and the patients complaining of chest pain you got some ischemia going on not good because that's your T wave in there so pqrs and then nice hypercute t way or you need be looking for some inverted T waves notice our T wave is absolutely flipped underneath the isoelectric line so if you see that patient having chest pain ischemia not good then you may have a pathological Q wave you really got to pay attention to this Q wave it's just a little area and you got to you're you need to take a lot of practice and looking at this but this could represent a current or prior an old infarction and I want to show you a normal one here where the arrow is pointing that is a normal cue way but just barely dips below the isoelectric line now you can have different variations of this pathological cue a notice right here you don't have a dip at all it's the key wave it's literally opps and it's not even there so that could be one or your cue wave can go way below that isoelectric line even and then just be really long and then you have your R and then your ST segment so those if you see those that can represent a current or an old infarct ssin okay so that was part 1 of myocardial infarction now be sure to check out part 2 to learn about the nursing interventions and medications used to treat this condition and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Coarctation_of_the_Aorta_Nursing_Pediatrics_Congenital_Heart_Disease_Defects.txt	this is sands red sterner sorry and.com and in this video I want to be going over coarctation of the aorta in this video is part of an in clicks review series over pediatric nursing and as always after you watch this YouTube video you can access the free quiz that will test you on this condition so let's get started what is this condition it is a congenital heart defect where there is narrowing present in a section of the aorta and your aorta should never have any narrow areas it should be nice and open because it allows blood to flow throughout the body because what's the role of our aorta well number one it's the largest artery in the body and it comes off of the left side of the heart specifically in the left ventricle and the left side of the hearts goal is to take blood it just received from the lungs that's become nice and oxygenated and pump it all throughout the body and your aorta is that big structure that plays that role it delivers that fresh oxygenated blood to the body and it does this by branching off into all these various arteries which is why we have problems with an aorta that is narrow so depending on where the aorta is actually narrow the areas before the narrowing are going to be affected they're gonna have experience a higher pressure and the areas after the narrowing are gonna experience a decreased pressure and I want you to remember that because that's going to help you for your exams and knowing and being able to point out those telltale signs and symptoms of this condition so real fast let's go over the various sections of the aorta and what areas of the body it actually feeds okay the first area we're going to talk about is the ascending aorta and just like the name says ascending up it's the part that you order that's going up and the sending aorta what it does is it comes off and it branches off and becomes like the coronary artery and we know the coronary arteries set on top of the heart muscle and it delivers fresh oxygenated blood to the heart muscle and if blood supply decrease or block what happens that heart muscle will die so that's role in ascending aorta then we have the aortic arch and just like the word arch says is this part of the aorta that forms a little art and it goes up and it branches off to feed the head hence your brain your neck and your upper extremities then we have the descending aorta and this is where the part that I order after they or decart starts to go down and it feeds the chest structures and the ribs then we have the abdominal aorta and this has found a little bit below the diaphragm and it goes down and it supplies your abdominal and pelvic cavity organs and your lower extremities now let's talk about some quick facts about coarctation of the aorta okay we just learned that this condition is occurring because there is narrowing within this a Horta and due to this narrowing we're gonna have blood pressure changes proximal and distal e from that actual narrowing in and the body which here no moment when I go over the path oh you're gonna see why okay but where does this narrowing tend to occur in this actual a Horta it tends to happen after the left subclavian artery which is this artery right here so it's going to occur a little bit after it and before the ductus arteriosus now let's talk about the ductus arteriosus what is that structure well this structure I have it illustrated here it's present in a fetus who is still in the womb and what it does is it acts as a bypass because in the womb the baby's lungs are not working yet once it starts breathing on its own the ones will start working and that's after birth but because of that the right side of the heart it's not advantageous for it to shunt to take blood and get it to the lungs because the lungs aren't working so in the heart there's some bypasses and the ductus arteriosus is one of those bypasses and it allows blood that comes in on that right side of the heart and that fetus to go and travel over - they order so it creates this connection between the pulmonary artery and the aorta so blood that comes in the right side is gonna go over there to the aorta but after birth the baby's going to start using its lungs and that right side of the heart needs to start working so what happens is that this structure shrinks off and it goes away and this will allow blood to start going to the lungs and doing its thing so that's what that structure is now keep that in mind someone talked about that a little bit more with the causes ok so there's different types of coarctation of the aorta one type is called pre ductal infantile type and this is where the narrowing is occurring between the left subclavian artery and the ductus arteriosus which is that structure again that should shrivel up after birth so our narrowing is occurring there then you have the post ductal type this is the adult type and it's hints most common in adults and this is where you have narrowing after that ductus arteriosus now according to the CDC gov 1600 babies born in the US every year will have this condition now how is it diagnosed many times it can be diagnosed during the fetal ultrasound whenever mom is having her prenatal visits they would alter some of the baby they can look at that heart and sometimes they can see where that narrowing is occurring or it can be diagnosed with an echocardiogram if babies born starts having those telltale signs and symptoms of this condition they can easily do an ultrasound of the heart and look at the aorta and see if there is narrowing now what is this caused by well they think it's caused by what's happening is that this tissue that is making up that ductus arteriosus has extended into the aorta so whenever that structure naturally goes too close after birth because that tissue has also extended and embedded itself in the aorta when he goes to close it's gonna take some of that a order with it and cause it to become narrowed now let's talk about the pathophysiology of the condition okay in our previous videos when we were talking about other congenital heart defects a lot of those problems were due to pumping problems like blood was being shunted from left to right right to left there were holes and the symptoms that were leading to that or the great vessels were like slipped coming out of places they shouldn't have but in this condition it's a little bit different because the pumping mechanism of the heart is really fine we don't have any holes within these atrium ventricles vessels aren't switched or anything like that really the main problem is coming from this narrow a Horta that's causing pressure changes so that's a big thing I want you to take away from the path oh so let's talk about that okay as I pointed out before when you have narrowing now this narrowing can depend like it varies in severity among patients some patients have extreme narrowing why some it's just a little bit and they have to monitor it and it can be in different locations so we're talking about the most common and the severe cases so as I pointed out before whenever you have the narrowing before the narrowing so proximal before the narrowing the arteries the sections of the aorta those arteries that they're supplying are going to experience a really high blood pressure okay now the areas that are after the narrowing the sections of the order that are feeding the other parts of the body the distal after the narrowing is going to experience low blood pressure so here you have this like in a sense pinched off area that's really small all the blood that's normally going to be shot from this left ventricle up through this a Horta it can't get into this little area so it can't allow blood to flow down which is going to decrease blood pressure to all those important organs and extremities but it's gonna leave like a concentration of pressure that's gonna build up here in this proximal area it's gonna be shot to those areas now this is going to affect structures now let's talk about what structures that's going to affect and the signs and symptoms and if you can get back there's no memory aid like pneumonic we need to memorize that cuz it all makes sense okay so the areas that are going to be affected with high blood pressure we are going to be your left ventricle one of those structures now why is that okay you have this area that's narrowed in the aorta all this pressure is building this way well there's that Levin trickle it's having to pump against all that pressure that just has built up in there so over time this left ventricle is going to enlarge it's going to be exhausted and it's going to quit working eventually which is going to lead to back slowing a blood and we call that heart failure so you'll have back flowing of blood decreased cardiac output your leg ventricle just can't pump the way it used to because of that extra pressure that has built up so they'll be to prevent that a lot of times or started on medications to help with that now also other structures that are going to be affected from this way up remember those arteries that we were talking about like the arteries from the aortic arch for instance they feed the head the neck the upper extremities well they're gonna have all this high pressure going to them and that's not good so what kind of signs and symptoms can that lead to well we have all this high blood pressure going to our brain that's going to cause headaches infants can't tell you I have a headache so they're just gonna be irritable and act like they're in pain all the time from the increased blood flow it can cause nosebleeds from where all that pressure is pounding up against those capillaries in the nose so random nose bleeds fat little babies children shouldn't be having also it can cause stroke it's the same concept like with adults we want to get their hypertension managed and if we don't it can all that extra pressure hitting those arteries constantly can cause a stroke and decrease brain function over time other things I want you to remember big things that exams love to ask about those pulses okay you have high blood pressure going to the arteries that feed your upper extremities how do you expect those pulses to feel they're gonna be very strong in those upper extremities called bounding and when you take blood pressures in those upper extremities it's going to be I like hypertension compared to our lower extremities and that goes for the pulses and the lower extremities as well and it can be about a twenty millimeter of mercury difference compared to the upper and lower now let's switch and let's talk about the low blood pressure again this are the areas after that narrowing so distal to the narrowing and it's going to affect our lower body so you have all this pressure concentrated up here before the narrowing and then after the narrowing is just diminished greatly so you just have a little bit of blood flow trickling in low blood pressure so lower body how is that really going to present well whenever you go to fill those pulses because you don't have high pressure you're gonna have absent or severely diminished femoral pulses so that's why after birth you always want to check that newborns pulses in that femoral area how does that feel also those extremities can feel cool to the touch and the lower extremities and the blood pressure of course is going to be lower in those lower extremities compared to that upper so that's a big take away on one chest remember are the differences between the pulses that you're gonna feel and the blood pressure that you're going to feel compared to the upper and lower extremities in addition let's talk about heart murmurs almost all these congenital heart defects cause some type of heart murmur you're gonna have like a systolic heart murmur where is that going to be hurt it's mainly going to be hard where your aorta is and generally where you can hear it best will be on the back in the intra scapular area on the left is where that can be noted also a little bit later on patients can develop what's called rib notching now what in the world is that well it's whenever they take a chest x-ray it's just like the name says whenever they look at the ribs and the chest x-ray instead of being nice and smooth they'll literally look like they're like notched out and what this is is it's from where the body has created what's called collateral circulation and your body is really smart its senses hey we have some narrowing here and we need more blood flow after that narrowing because you know those tissues and organs aren't going to make it so they create extra vessels to go around that area which is going to go into the ribs to deliver that blood flow so that's why you see the notching of the ribs now let's talk about nursing interventions and treatments for this condition okay we know that we have a narrowed section of the aorta and that can cause a lot of problems you can cause heart failure it can cause changes in the pulses throughout the body and as a nurse what are we going to be looking at what's our role well number one we're going to be monitoring for heart failure and over time this can cause this again it really depends on the severity of this condition some newborns once they're born and those bypasses start closing they can suddenly develop this from where they order so stenosis it's causing so much pressure on that left ventricle so nursing diagnosis round we can be thinking at risk for decreased cardiac output because over time when that Lev intrical fails our cardiac output amount of blood or heart is able to pump is not going to be very good also we can be thinking about respiratory issues oxygenation impaired gas exchange because as the left ventricle fills blood will back up and go into the lungs you could hear crackles they can have difficulty breathing which can lead to poor feeding and their growth can be affected as well and risk for fluid volume overload as the heart continues to fell so as a nurse we really want to focus on checking blood pressures in those upper and lower extremities checking and filling those pulses and again where are we gonna have high bounding strong pulses upper lower extremities upper extremities where we're going to have a higher blood pressure in the upper extremities compared to the lower extremities and remember you can even have just completely absent or severely diminished femoral pulses and that goes back to the narrowing and how it's affecting the areas before the narrowing and after the narrowing because like no blood is going through after the narrowing okay in mild cases of narrowing when some children and may go undetected until childhood and darted the nurse doctor may notice hey you have really strong pulses up here but those femoral pulses and those lower extremity pulses not very strong and they take their blood pressure there's a huge difference they have hypertension up here but not down there also they have that heart murmur on that back at the left area next to the shoulder blades where you can hear the aorta and that can tip them off to that get an echocardiogram look at how bad the narrowing is and proceed from there so there are some cases where it's very mild and it has to be watched now in severe cases let's say babies born has a completely severe case of this typically what happens is that they may be started on a prostaglandin infusion and we talked a lot about this in our other congenital heart defect video so you may remember this but what does this do it helps keep open that bypass specifically that ductus arteriosus now why would we want to do that in this condition well it does a couple things number one it's going to help decrease that workload on that left ventricle because now we have a connection between the pulmonary artery and the aorta I can alleviate some pressure on that left ventricle help hence prevent heart failure in addition it's going to help increase blood flow to those lower extremities which very badly need that extra blood flow so that can help with that then in the meantime they're going to be prepped for surgery they may be started on some medications to help preserve that heart function already like digoxin what does that medication do again it helps slow down the heart rate but it makes the contractions stronger so the heart pumps more efficiently but at a slower rate also they can we start on diuretics a lot of times they will be on mechanical ventilation prior to surgery and what kind of surgery do they do there's various techniques that surgeons may use but typically the most common is they go in they cut out that narrowing and then reconnect the two pieces of the aorta where they were where it was removed and another thing that we do as a nurse which is really important is educating patience and educating while the parent of the patients usually about number one long-term follow up with a cardiologist many of these patients have this repaired but there's some things they have to watch out for that they have to be monitored for number one after surgery this aorta has to be closely monitored because restenosis can occur where it actually narrows again a lot of times whenever this happens they can go in and do a balloon angioplasty where and this is then during like a heart cath going through a great vessel put a balloon in that part of the aorta and open it back up so they have to monitor that them for that and in addition some patients blood pressure doesn't ever go down and they have long term hypertension so usually afterwards the pressure will their blood pressure because you know they're having high pressure in the upper extremities will start to decrease but some patients will have long term hypertension and they'll need medications to manage that so all that follow up and just continuing monitoring of the patient as a nurse you'll want to tell the patient about that okay so that wraps up this review over coordination of the aorta thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Peripheral_Arterial_Disease_vs_Peripheral_Venous_Disease_PAD_and_PVD_Nursing_Symptoms.txt	hey everyone its air threats Turner sorry and calm and in this video we're going to compare peripheral arterial disease to peripheral venous disease and as always whenever you get done watching this youtube video you can access the free quiz that will test you on these conditions so let's get started when you're studying these two diseases for exams you want to make sure that you know the big differences between how your patient is going to present with either arterial disease or venous disease so to help you remember those differences you want to remember these six things to assess and ask the patient to help you determine if it's arterial or venous and to help us do that we're going to remember the word vessel venous for various positions that alleviate the pain and you want to ask the patient about what type of position helps them alleviate the pain that they're having because this is really going to help you differentiate between arterial and venous with arterial the patient is going to prefer dangling their legs down in the dependent position and the reason for this is because with arterial you're having issues with blood actually going to the extremity so it's causing ischemia so whenever they dangle their legs that helps that blood flow get there however when they elevate the legs that makes the pain a lot worse and again because that is impeding the blood flow with venous disease patients are going to be alleviated with their pain by elevating the legs because what this is going to do this is going to help decrease the swelling because with venous we have a problem with blood returning back to the heart so when they elevate the legs that will help assist with that so dangling the legs or sitting or standing for long periods will actually make the pain in their legs worse along with the swelling is for explanation of the pain have your patient explained to you the characteristics that they're experiencing with the pain with arterial the pain is going to be sharp and it tends to be worse at night and they have something called rest pain this is where whenever they're sleeping their legs will be horizontal in the bed and this is going to affect the blood flow so they'll actually wake up from their sleep with leg pain and they'll throw their leg off the bed and let it dangle and this will actually alleviate the pain they will also have a hallmark sign and symptom called intermittent claudication and this is where when they do any type of activity like running walking they get this severe cramping tingling pain in their legs thighs or buttocks and it'll actually be relieved once they quit doing that activity now why is this happening well arterial we're having an issue with blood going forward to that extremity so whenever they're actually doing that activity that's using up the oxygen and it's depriving that muscle of that blood flow so it starts to hurt but when they rest it the blood starts to go back to the muscle so the pain goes away however with venous disease patients are going to describe the pain as being heavy dull throbbing and aching and the pain will be worse when they're standing or sitting with the legs dangled for long periods of time and that's because the blood flow is not traveling back to the heart and being in that type of position does not allow that to happen so when they elevate the legs that eases the pain and the swelling then as foreskin of the lower extremity as a nurse you want to look at the color of the extremities compare them and feel the temperature is it cold is it warm for arterial disease they have an issue with profusion so that extremities I'm gonna be perfused it's going to be cool to the touch and because that skin is not getting the nutrients it needs the skin is going to appear thin dry and scaly it's probably going to be hairless and half thick toenails now one thing you want to remember for exams is what will happen to the color of that lower extremity if you dangle it or elevate it so remember dr. F for dangling the legs or putting them in the dependent position they will be ruber which means they will become red and warm from the inflammation of those arteries it's getting blood flow that when you elevate those legs that's going to impede blood flow so the legs will be compel with Venus disease there's not an issue with perfusion that blood can get just fine to those lower extremities the problem is it can't leave those lower extremities and drain back to the heart so the extremities will be warm to the touch they will actually because you have so much pulling of the blood you don't have the clearance of that cellular waste the skin is going to be thick and tough it's also going to be swollen from edema and it can have a brownish color to it as you can see here in this picture the next s is for strength of the pulse in the lower extremity for arterial because circulation is compromised to that extremity it's going to be very poor and in severe cases it can be absent whenever you're checking pulses in a patient with PA d you can palpate but you want to use a Doppler device as well so you can actually hear it and grade it accordingly with venous disease we don't have a problem with blood getting there to the extremity so the pulse will be present and it's typically normal efore edema is it present with arterial no it's not common they will not have swelling with venous it's very common and the swelling tends to be worse at the end of the day and that's because we don't have that blood being able to return back to the heart and lastly l4 lesion specifically ulcers and ask the nurse you want to know about where these are going to be located and how they look because they're different so for our Terrier ulcers they're going to be located on the ends of the toes the dorsum of the feet which is the top of the feet or the lateral malleolus which is the lateral ankle region that's where you're going to find these ulcers their appearance is that they're gonna have little drainage remember blood flow is compromised to these ulcers so they're not gonna drain a lot and they're not going to have tissue granulation meaning new whoo healing so they're gonna be Pell and very lot pink or they can even be necrotic and black another thing is that they're unique and how they look because they're deep and they look like literally someone has punched out the skin and that's a term that is used law a punched out appearance with noticeable margins and edges and they'll have this deep round area and here in this picture here you can see an example of an arterial ulcer it is found on the lateral malleolus notice it has that punched out look it's nice and round it's deep it's Pell on the inside and that skin is even scaly and dry around it however with venous ulcers also called venous stasis ulcers they tend to be located on the medial parts of the lower legs and the medial malleolus area so that medial part of the ankle the ulcers tend to appear swollen the skin will be tied around them there'll be a Dima and there will be drainage along with granulation present because remember we don't have a blood flow issue blood flows getting there just fine we have a problem with it returning back so the base of the wound will be pink to a deep red and the edges will be irregular they're not gonna be nice and round and the depth of the wound tends to be shallow and here you can see an example of a venous stasis ulcer it's found on that medial part of the lower leg and the medial malleolus area and notice the skin is very tight around it swollen in the base of the wound is that deep red and it's very irregular in shallow okay so that wraps up this review over arterial versus venous disease
Medical_Surgical_Nursing	Chronic_Renal_Failure_Kidney_Disease_Nursing_End_Stage_Renal_Disease_Pathophysiology_NCLEX.txt	hey everyone is Sarah Chris Turner sorry and calm and in this video I'm going to be going over chronic kidney disease also known as chronic renal failure and this video is part of an inkless review series over the renal system and as always don't forget to take a free quiz that you can access at the end of this video so let's get started first let's start out talking about what is chronic kidney disease it is where you have a significant decrease in renal function and this happens over a long period of time and it is irreversible now that is the complete opposite of whenever we talked about in the previous lecture are about acute kidney injury remember that was a sudden decrease in renal function and it tends to be reversible if they can figure out the cause and treat it appropriately now let's look at our kidney and we're going to look specifically at the nephron because whenever we're talking about a decrease in renal function we're really talking about this glomerulus and how it is filtering specifically the glomerular filtration rate or GFR so we'll be using that term a lot GFR because if you can understand the GFR everything else tends to make sense okay so the kidney the functional unit of your kidney that actually produces urine are the nephron and in each can you have millions of these nephrons and the whole goal is to filter our blood that are received from the heart and the glomerulus is the structure that does that so it filters all these substances such as water ions which are like your electrolyzed 5-card things like that urea and creatinine which are waste products and remember urea is a waste product from protein right down in the liver and creatinine is a waste product from the breakdown of muscles so it filters back now the glomerulus does not filter proteins and blood cells you should not find that in your filtrate unless your glomerulus is messed up in here your long barrel is mess up so we can probably expect to find an address down into Bowman's capsule and then it's going to go down through the renal tubules in the renal tubules our innocence what they're going to do is they're just going to tweak that filtrate because the filtrate was created by the glomerulus and it's going to take what the body needs to maintain homeostasis so it's going to reabsorb the amounts of water you need it's going to reabsorb a little bit of urea and it's going to reabsorb our electrolytes that we need however it is not going to reabsorb creatinine so let's talk about creatinine for a second so creatinine is that waste product and it's fully filtered by that Vomero is from the blood stream and it's not going to be reabsorb in that renal tubules so that's why we care so much about creatinine when we measure it in the urine in the blood because it gives us a good indicator of how well that glomerulus is filtering that blood so whenever we measure a lamellar filtration rate we take a lot of things into calculation such as their creatinine clearance level the patient's gender their age their race and their weight and that helps us determine that now what is AGA GFR specifically it is the rate that the glomerulus filters waste ions and water in the blood so it tells us how well the kidneys are performing physically that nephron in helping our body maintain that beautiful homeostasis environment now we want a normal GFR in our patients and a normal GFR is greater than 90 milliliters per minute so ninety milliliters per minute or higher is a normal GFR so in chronic kidney disease what happens is that that GFR progressively decreases and there's various stages of CKD and for exams I would be familiar with the GFR for each stage especially stage four and five because that's when you have severe loss of renal function because sometimes pests like to ask questions about that so let's go over this okay Stage one is where you have kidney damage with normal renal functions so their GFR is going to be normal greater than 90 milliliters per minute but there's going to be proteinuria protein in the urine that has presented for three months or more then they can progress in stage two which is kidney damage with mild loss of renal function with a GFR between sixty to eighty nine milliliters per minute and they'll have proteinuria that's been present for three months or more then stage three is mild to severe loss of renal functions with the GFR between thirty to fifty nine milliliters per minute and then we go into the really severe stages stage four is severe loss of renal function where the GS are between fifteen to twenty nine milliliters per minute and then the very last stage which is the worst stage of all at Stage five and this is in stage renal disease and this is where the GFR is less than 15 milliliters per minute and this is where the patient's going to getting dialysis regularly and will be a candidate for a kidney transplant and these stages are sourced from the National Institute of Diabetes and digestive and kidney disease health statistics therefore as that GFR is decreasing the patient is going to have issues they're going to have issues with ways with electrolyte imbalances and fluid overload and as you've seen in those stages as they go from one to five that GFR is progressively decreasing so the patient who's in the early stages of chronic kidney disease they're going to probably be asymptomatic because that def R is normal compared to that patient in stage four or five where the GFR is really low so this is really what we're going to be concentrating on are those patients who are in the last stages of chronic kidney disease especially when we're talking about our nursing interventions and things like that okay so when we have a decrease yes or our glomerulus is not filtering the way it should so think of it this way every should be filtered is a stain in the blood and it's just building up because it's not going through here to be dripped down into Bowman's capsule and go through the tubules and the tubular will pick and choose what it wants so what is going to happen to our waste levels in our body specifically the view in which we measure it which is urea and creatinine it's going to increase in our body so those waste levels are going to be high and this is going to lead to problems such as Asia tinea uranium you're going to see neurological changes and itching things like that which we'll talk in more in depth and our nursing interventions then what's going to happen to our fluid status issues again the glomerulus is not removing the water it should so what's going to happen to that water it's going to stay in the blood so we're going to get fluid overload so we're going to be hypo or hyper bulimic we're going to be hi furball leeming now what's going to happen with that think about when there's too much water in the blood we have a lot of pressure in there our blood pressure is going to be high hypertension this can cause a lot of pressure on the heart which can cause it to become weak which can lead to fluid backing up into the lungs so pulmonary edema cardiac issues things like that how do you expect their urinary output to be if this squall Maryalice is not filtering the way it should will the urinary output be high or will it be low it will be low it'll be decreased okay so let's go over some terms if their urinary output was less than 400 milliliters per day what's that term it's terms of Luria okay if the urinary output was less than 100 milliliters per day what would that be that would be in urea so you'll be seeing some really low urinary output mutation okay let's go over to fluid and electrolyte okay so glomerulus is not removing the ion that should so we're going to do is those ions electrolytes are going to stay in the blood so which electrolytes are going to be high number one are potassium and we really care about the passing because it can cause cardiac issues so we're going to have hyperkalemia how their phosphate level is going to be they're also going to be high as well along with our magnesium levels now what about calcium levels well remember in our flu in an electrolyte series if you haven't checked it out I recommend you do because it'll help you when you're studying this material phosphate and calcium have a relationship and they are always opposite of each other so whenever you have high phosphate levels you're going to have low calcium levels now why is that okay calcium binds the phosphate so if we have all this phosphate in our blood it's going to take the calcium and bind it to itself which is going to remove the calcium from our blood so we'll have hypocalcemia now let's take it a step further what's going to happen with that well whenever your parathyroid gland senses high phosphate levels it causes the parathyroid gland to release PTH parathyroid hormone what does parathyroid hormone hormone do well we learn from our endocrine series it stimulates the bone to release calcium from within itself to go into the blood to increase the blood serum of calcium well what does that do to our bones it makes them weak and brittle so keep that in mind for whenever we're talking about nursing intervention so we're going to have hyperkalemia where you have hyper falsity Nia we're gonna have hypocalcemia and we're going to have hyper magnesium eeeh okay now let's look at this our protein and blood okay our glomerulus remember should not filter proteins and blood cells well here in chronic kidney disease the whole structure is being affected not only is our net we're going to be a fret affected but here in a second you're going to see that this whole kidney the cells with ended up to create form owns and activate vitamin D are going to be effective so what's getting through protein so the patient will probably have some protein in the urine and they're probably going to have blood in the urine as well so think what's going to happen when we're losing all this protein in our urine well we know that albumin one of those proteins regulates oncotic pressure whenever you have decrease oncotic pressure it allows fluid within that capillary to leak into that interstitial tissue so we're going to get even more swelling and edema then with the hematuria we're losing red blood cells in our urine we're going to get anemia because we're losing blood into the urine okay so now let's talk about our kidneys producing hormones because in a lot of patients have you ever work on a dialysis for flora renal floor you're going to notice these patients have very simular electrolyte imbalances and it will have these issues because of what's going on so the kidneys produce a hormone called EPO which is short for a reef Roco Etten and what does BPO do it helps create red blood cells in the bone marrow well in CKD EPO is not being produced like a show that's going to be decreased so we're not producing red blood cells where we at risk for we're at risk for anemia so patient can have that another hormone the kidneys produce is called renin cells within the kidney produce fat and what does Brandon do it plays a role in increasing our blood pressure it maintains our blood pressure for it so what's happening with the glomerulus how much water is it filtering it's not really filtering a lot of water so those cells sense that and they say oh the kidneys are filtering a lot of water that means our blood pressure must be low so we need to release some renin to increase that blood pressure which is not a good thing because remember we're already in a hyperbola McStay we already have hypertension going on so we're going to release more rhiannon which is going to increase our blood pressure even more and here in a second when we talk about the causes of this condition hypertension is one of them so we're causing even more damage to our kidneys okay and another thing that the kidneys do is kidneys activate vitamin D and what does vitamin D do it plays a crucial role in helping our body reabsorb calcium from the food we take in but with CKD you're not really activating that vitamin D so guess what you're not really going to be reabsorbing that calcium taken from food because we need that vitamin D to help us do that so they're going to be they're going to experience even more hyper hypocalcemia which remember with the high phosphate levels they're going to even have even lower calcium levels so that's going to be a double whammy with our calcium now let's look at the causes of chronic kidney disease okay one cause is diabetes mellitus and how does this cause this condition well when the patient has uncontrolled hyperglycemia so they have a lot of glucose in that blood their blood sugars are running very very high this causes glucose to stick to the artery wall and remember sugar is sticky so it sticks to the artery wall and that causes damage to the arteries that supply the kidneys so they can develop chronic kidney disease because your kidneys are being deprived of the nutrients it needs to function another thing that can cause it is high blood pressure so the patient has uncontrolled hypertension and we learned from our hypertension video that hypertension is one of those things that happen that causes really no signs and symptoms until it's too late it's like the silent killer so a lot of times the patient is unaware that they even have high blood pressure so there is a constant high pressure hitting those artery walls to the kidneys and the Khitan it becomes damaged which whenever the artery that's feeding the kidney becomes damaged that's less blood just going to go through the kidneys and go through that nephron and cause kidney damage so these two diseases these two issues are the most common causes for developing chronic kidney disease other causes can include acute kidney injury acute renal failure is what we talked about in the previous video maybe they don't progress to the recovery stage of that disease and they progress to chronic kidney disease instead polycystic kidney disease they can develop this and this is a genetic condition where this develops in the kidneys causing issues with renal functions infection or nephrotoxic drugs those drugs that are very very toxic to the kidneys like incest I mean I like a size chemotherapy drugs or contrast dye for testing procedures okay so what is the treatment for chronic kidney disease okay remember we have various stages so in those early stages where that GFR is normal why is usually ordered is to for the patient to control their blood pressure and to control the blood glucose level to prevent any further damage to that kitty so they can hopefully preserve that current GFR not how to decrease anymore also they may prescribe the physician may prescribe blood pressure medicine to keep that blood pressure low and to help protect the kidneys because there's two groups of medications that they have found that actually provide a protective mechanism to the kidneys and they include ACE inhibitors which are those angiotensin converting enzyme inhibitors and those are your drugs that engine krill like lisinopril or the arms the angiotensin receptor blockers and these are the drugs that end in Fartman Sarpa in likes losartan and in addition to that they'll be monitoring their GFR regularly making sure it's not getting progressively worse and having the patient monitor their blood pressure and making sure it's same within a normal range now when they progress or in those advanced stages like stages 3 4 & 5 especially that last stage stage 5 where that's where the GFR is abnormal the patient may need dialysis on a regular schedule a lot of patients are like they have the alysus on Monday Wednesday Friday or Tuesday Thursday and what is ballast again this is really what it is is it's a machine that's going to take the blood and filter it like how the nephron of the kidneys should have so it's going to remove the excess of water the waste and regulate those electrolyte levels and if it's really really bad like in the in stage renal disease they if they're attended it they can be a candidate for a kidney transplant now let's look at our nursing interventions okay what are we going to be doing for this patient as a nurse well let's ask ourselves what is going on with this patient with those late stages of chronic kidney disease well they're going to have a buildup of waste in the blood they're going to have anemia electrolyte imbalances low urinary output and fluid overload so we want to tailor our nursing interventions based on what is going on with the patient so first let's talk about the build-up of wastes in the blood patients going to have what's called uremia and whatever they have this they will have some specific signs and symptoms because remember our goal merula still try some right and decrease so it's not filtering all that waste out it should so that waste is trying to go somewhere when we make an have is itching and this is due to deposits of your reer crystals on the skin and it's being secreted through the sweat glands and has a unique look to it it will actually look like this white frost on the skin and this is known as your emic frost another thing the patient had because of those all because of those levels really high in the blood they can have confusion and you need to be assessing their neuro status and they're at risk for injury Falls so you want to be thinking of safety issues and diet what kind of diet would we want them to follow we want them to follow a low protein diet because remember urea is the breakdown of protein in the liver so we want them to have some protein to prevent muscle lasing but we don't want them to have high milk because it's just going to be broken down into more URI more ways that our kidneys cannot get rid of and our blood is going to become really acidic from all this waste in there so the blood pH can be less than 7.35 and there they can enter into two conditions known as metabolic acidosis and whenever that happens you may see what's called cosmo breathing and these are deep rapid breaths and it's the respiratory system of trying to blow off carbon dioxide because carbon dioxide is an acid and it's trying to increase the blood pH so make sure you're watching the respiratory status counting those respirations as Labour does it rapid what's going on now another thing is anemia what's anemia again it's low red blood cells and what red blood cells do because they're really important in our body they help transport oxygen to our tissues to your body so it can function properly now why are we seeing anemia again just a recap because we have low production of EPO remember EPO a reef rope Owenton helps stimulate our bone marrows produce red blood cells if we're not getting that another thing is we can be losing blood through our urine so that can decrease it it even more along with being deficient in other minerals such as iron folic acid and vitamin b12 because those substances play a role in helping us produce hemoglobin which helps transport red blood cells throughout the system now your patient when you look at this they will be Pelle they will be very tired they can be short of breath just getting up from the bed to the bedside chair they get really winded and they can be confused so what are some treatments for this as a physician may order supplements of iron to help replenish those levels to help produce more red blood cells if they're low in that also a repro couette and shots EPO shots and these are given sub-q and this will help stimulate that bone marrow to produce red blood cells where your kidneys are able to stimulate them to do that anymore or a blood transfusion to replace them with some more fresh red blood cells okay another thing we have going on with lower urinary output and fluid overload so anytime we're dealing with fluid issues what are we always going to do in any type of patient we're going to monitor their intake and output very very closely we're also an performed daily weights because Wayne patient patients and looking at their weight is a good indicator of fluid retention so we'll be using the same scale every day in the morning and we'll be looking at those weights what's their weight today compared to their weight yesterday are they gaining any are they losing any we're going to assess the swelling status in their extremities and their legs and their arms and their belly and in their face is it going down or is it getting worse lungs film we're going to be listening to that because when you hear crackles that can indicate pulmonary edema so throwing fluid overload the heart maybe becoming weak and so it's allowing fluid to stay into the lungs or flow over into the lungs we're going to monitor the blood pressure because we want to get their blood pressure at a normal range because remember high blood pressure is really hard on those kidneys and assessing the respiratory status again that goes back to the fluid overload another thing that may be ordered by the physician is a fluid restriction because we want to watch their urinary outfit really closely and make sure that we're not just giving them or allowing them to have so much fluids compared to what their kidneys can actually put out so we based on what the physician orders with that and a low sodium diet because sodium loves water so the more sodium they have in their system because they're not really excreting the sodium as they should that draws more water into the vascular system which can increase the blood pressure even more along with other diet restrictions which we're going to talk about whenever we go over our fluid and electrolyte problems and again one of those electrolyte imbalances the patient can have is called hyperkalemia where you have a high potassium level and the potassium level can be higher than 5.1 million per liter and what is a normal - level three point five five point 1 million quid lent for leader that's where we want them now the reason the tapping is so important is because it plays a role in muscle contraction and what's happened is that there has been a decreased ability on the nephrons part to filter and excrete that potassium so the patient is at risk for a cardiac event so we really want to monitor their EKG have them on a bedside monitor and we're looking at that EKG specifically for any tall peak t-waves like this one right here also the QRS complex can widen as you can see right here and your PR interval can get long so you're looking at that but most tests they like to ask about this t way remember it's going to be tall and Pete okay on the nurses part you'll want to be restricting those foods that are rich in potassium and that includes foods like potatoes avocados strawberries bananas spinach and oranges and in my fluid electrolyte videos if you're wanting to know foods that are really rich in the certain substances goes to that series or on the website because I have new monix on how to remember those foods so check that out and the physician may order kayexalate which will you can give it orally or rectally and it will take that potassium and excrete it out of the body another thing that electrolyte known they can have is remember that hyper phosphate Amy aware they have a high phosphate level and that's greater than four point five milligrams per deciliter and normal false level is two point seven to four point five milligrams per deciliter and what is that going to do to our calcium level and phosphate high because remember phosphate likes to bind with calcium it's going to decrease our calcium levels so we're going to get hypocalcemia and that is a level less than eight point six milligrams per deciliter and you usually want your calcium levels between eight point six to ten milligram per decilitre and again this is because that nephron is damaged so that phosphate has increased from the blood and it's finding with calcium and bring that level down and what's another reason why we're having low calcium levels because of that decrease ability of activating vitamin D by the kidneys because we're not going to be absorbing as much calcium as we should so what happens this patient is definitely at risk for some bone issues because again just to recap that high phosphate level stimulates the parathyroid gland to produce PTH parathyroid hormone and parathyroid hormone stimulates the bones to release calcium into the blood to increase the serum calcium level well doing that it hurts bone health so that risk for injury and so you want to prevent that so what do physicians order to help bring those phosphate levels down because we want those normal so it doesn't deplete our calcium levels anymore phosphate binders and this will help decrease phosphate and some drugs are calcium carbonate or calcium acetate also known as false low and what these drugs do is they bind with the phosphate in the foods and it excretes the phosphate in the stool so ask yourself when is the best time to give a patient or calcium carbonate or false low right with meals like five minutes of for meals or immediately after because we want them to take it with food because it's working on the food that they're taking the house phosphate in it so we can excrete out of the stool so you want to give it with that and they want to follow a low low phosphate diet so this will be to restrict flu foods like poultry fish dairy products nuts especially your cam photos that have phosphate in them and oatmeal next patient is at risk for - I'm using yeah and this is a high magnesium level and the level can be greater than two point six milligrams per deciliter and we like our bat mag levels in between one point six to two point six milligrams per deciliter and when you have a high magnesium level it's usually because you have a low calcium level because those go hand-in-hand as we've learned in our fluid and electrolyte series and with this the patient's tendon reflexes will be diminished or completely absent depending on how high that magnesium level is and they can be lethargic so what you want to remember with this is you want to not give them any magnesium based antacid or laxatives because you're just giving them more magnesium and you want to make sure you're restricting those foods high in magnesium also the physician may order IV calcium to help decrease this level because as we replenish the calcium level our mag level will come back down to normal okay so that wraps up this video on chronic kidney disease thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	MeteredDose_Inhaler_MDI_with_Spacer_Demonstration_Nursing.txt	hey everyone this is cereth registered nurse sorry n.com and in this video I'm gonna demonstrate for you how to use a metered dose inhaler with a spacer okay so what is a metered dose inhaler it is an inhaler that will deliver a set amount of a medication into the lungs so it's used by people who have respiratory diseases like asthma COPD and those medications generally given are like bronchodilators like albuterol or corticosteroids like fluticasone like which is flovent and these medications will help either dilate the lungs which is a bronchodilator or corticosteroid which will help suppress immune system decrease that inflammation in the lungs now when using a metered dose inhaler it is best to use a spacer and why is that well whenever you're using those open or closed mouth techniques like I demonstrated in the previous video those take a lot of dexterity you have to be able to press the inhaler button down and inhale at the same time and if don't do it correctly a lot of the medication will end up in the mouth and instead of the lungs but using the spacer helps decrease that because it gives the patient in a sense time to hit the button and inhale and it helps permit a lot of that medications especially that corticosteroid from collecting in the mouth which can in the end cause thrush so always try to get one of these for your patients so let me show you how to actually use it so the first thing we want to do course is perform hand hygiene perform the patient's five rides make sure you have the right patient the right drug the right time the right route and the right dose because you'll be giving these in pups so check all that information out and another thing you want to remember is while you're doing your check off is that you want to make sure you know exactly which inhaler to give win for instance say you're giving a bronchodilator and a corticosteroid so the patient has two inhalers which one would you want to get first you want to give the bronchodilator first because it's going to dilate out that those lungs and then five minutes later you would want to you're corticosteroid so it can go in there and do its job and decrease inflammation also say that you were just going to be giving one inhaler but it required two puffs well you would give the one dose that they need the one puff and then one minute later you can administer the second puff so if you're giving the same drug you would wait a minute but if you're going to do bronchodilator and then a corticosteroid you would want to wait five minutes in addition after giving the corticosteroid inhaler you would want the patient to immediately gargle and rinse with water and spit that water out to remove any possible corticosteroids that have collected in the mouth because if they stay in the mouth they can irritate those mucous membranes and cause thrush so first of all you want to do is you want to prime the inhaler and you'll do that if this is the first time you're using the inhaler or if it's been dropped or the patient hasn't used it in a week or more if it's been recently cleaned and while you're in the process of doing that just check the inhaler make sure it's not expired you can do that by popping it off the canister and looking at the date and this expires in 2020 so we're good also just quickly check to make sure there's enough doses in this inhaler and of course if it's new there is enough doses but this has been used before you just want to make sure that you have enough puffs in here and a lot of times then hailer has a counter on it that you can look at it or the box will tell you how many doses are in each inhaler so check that out in this particular one there's two hundred sprays so you'll want to count out how many times the patient's going to be using it and how many days that's going to transpire over for instance if the patient was going to be using this inhaler four times a day twice in the morning twice at night that's four puffs and it has 200 puffs how many days is that gonna last us 50 days so you want to keep track of that so to prime it what we're gonna do is we're going to take the cap off and just check inside the inhaler make sure there's nothing hanging out in there sometimes patients like to keep these in their purse and some and other things can get in there and you don't want them to inhale it so make sure it's clean and we're going to give it a good shake so hold it in between your thumb and your fingers and shake it for about eight to ten seconds get it mixed up really well and then we're gonna give it four sprays so it's nice and primed so after priming inhaler you're ready to connect and hailer to the spacer so make sure that the cap of the inhaler is off and then take the cap of the spacer off because this is the mouthpiece where the patient's going to put their mouth at and actually inhale and then this part right here is where you're going to connect the mouthpiece of inhaler into the spacer so just connect it like so and it stays on then have your patient set up hold the inhaler with the thumb and with the fingers and then just give it a good shake for eight to ten seconds then have a patient breathe in through the mouth and then out through the mouth until they can no longer breathe out they will seal their mouth around this chamber with in between their teeth or tongue flat and then they will press the inhaler down and then inhale so it's different from those other techniques that we use where they had to simultaneously press it down and inhale so they press it down then inhale inhale until they can no longer inhale anymore and then they'll hold it for about 10 to 12 seconds and then breathe out slowly and again they would want to rinse their mouth if they use corticosteroids and if they have to repeat the dose they will do that in one minute so now let me show you what that would look like and after that of course you will have the patient rinse their mouth gargle and spit water if it was a corticosteroid and you will recap your inhaler and your spacer then perform hand hygiene and document okay so that wraps up this video on how to use a metered dose inhaler with a spacer thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Acute_Glomerulonephritis_Nursing_Poststreptococcal_Nephritic_Syndrome_NCLEX_Review.txt	hey everyone and Sierra's stoner sorry and calm and in this video I'm going to be doing an in quick review over acute glomerulonephritis and this video is part of an in quick review series over the renal system so be sure to check out those other videos and as always at the end of this video you can access the quiz that will test you on this condition so let's get started so what is accu glomerular nephritis this is where there is inflammation of the filtering structure of the nephron and remember your kidney contains millions of people nephrons and they are the functional unit of your kidneys and help you produce urine now what specific part of the nephron filters the blood that is the glomerulus so that is why we call this called mary lo ness Fratus and what happens is that it's implying and it's not working like it should so it starts to become permeable to proteins and red blood cells and normally in the glomerulus only filters like water ions and waste not proteins and red blood cells now for in CLECs purposes the type of a cube while Mary alone nephritis we're going to concentrate on is called the post streptococcal kine and you'll see why here in a second why it's called that but let me review this for a second okay the term glomerulonephritis is an umbrella term for various diseases of the kidneys where there is damage to that wall Mary Lou now you can have acute forms which is what we're discussing in this lecture or you can have chronic and there are different glomerular syndromes you have Neff Hritik syndrome which is the type of syndrome that this post streptococcal is and you can have Ness fraud it now in the next video we're going to be going over an S products syndrome because that's another topic NCLEX likes to cover now quick review on what's the difference between Neff riddick and nephrotic well if that critic you're going to see a loss of red blood cells and mile amounts of protein in the urine however on the flip side with Ness Roddick you're not going to see any red blood cells in the urine hematuria and there is going to be massive amounts of loss of protein in the urine so just keep that in mind for the next lecture now with this condition it tends to develop about 14 days after a strep infection and this could be a strep infection of either the skin or like the throat and it tends to mainly affect our pediatric patients usually between the ages from two to ten years old so how does this condition happen well what happens is that a person gets strep and they don't seek treatment for it maybe the parents of the child near the kid with sick but they didn't know that the child really need to go in and get some antibiotics so what happens is that the immune system responds to this bacteria by creating and antigen-antibody complex and these complexes start to collect in the glomeruli because remember your nephron receives all your blood from those afferent arterioles and these complexes will be in there and as that blood is going at high pressure in this glomerulus they're going to get stuck in there and it's going to cause inflammation so in a sense this strat bacteria is not inflaming the Squam area it is the immune system causing and producing those antigens that are getting stuck in there so remember that it's really an immune system due to those complexes not the strep bacteria getting in there causing inflammation so that is why you are going to see these signs and symptoms about two weeks after the parents or the person reports having a possible strep infection now let's take an up-close look at the glomerulus and see what's happening in this condition okay so normally your glomerulus is receiving all that fresh blood and it's filtering it out and what's happening is that as it filters it out it rips down into what's called the Bowman's capsule then Bowman's capsule that filtrate will flow down through the proximal convoluted tubule to the loop of Henle to the distal convoluted tubules and the collecting tubules flush duct and then it eventually X to the kidney annual voided out is urine well what's happening here as you can see within the glomerulus we have black areas and this is where complexes have got stuck and we have the massive inflammation going on so what is happening is causing areas to open up and allow those proteins and red blood cells to drip down into Bowman's capsule because normally these sensors can't go because they're way too large but here the inflammation has allowed that so the red blood cells go down and they start to change the color of our filtrate and you will see a sign in symptom called hematuria and these patients where the urine is going to look like tea colored or Cola colored urine and this will be one of those really prominent signs and symptoms for why a patient or the patient's parents are going to seek treatment because the urine looks totally abnormal then some proteins are going to be lost and remember this is a mile amount of protein that will be lost in the urine and nephrotic syndrome is for the massive amounts of protein and what is going to happen when you're losing all this protein in the urine your blood levels are going to suffer so you're going to have low protein in the blood now why is that important what is the significance of that well because of that low protein in the blood the patient's going to start to have some edema and in this condition it will be mild edema and you're mainly going to see it in a patient's face or around the eyes and it'll be most prominent in the morning time which tends to be common in kidney disorders so why are we going to have the most prominent edema in the eyes or in the face we'll think about your eyes your eyelids are very delicate and the tissue is folded it's pocketed and that is just a great place for extra fluid to collect and for a person to be able to notice it on another person because the tissue is just so thin so that's why you're going to see it there now let's talk about why this is happening because we have low proteins so one of the world is protein do and what's its relationship with edema and water okay let's recap here we have a capillary and we have our artery and branches all mature capillary we have our vein it's all just interconnected and behind it in this brown area that is your tissue cells and over here we have just like a little individual capillary and within the capillary your blood is running and the capillary has ministrations in it which is a fancy way of saying it has pores and in these pores fluid and other substances leak out and go into that tissue now control about several different things first thing that controls it what's called hydrostatic pressure which is controlled by your blood pressure and this controls the amount of fluid leaking out of the capillary into the tissue then we have another substance which is what I really want to hone in on called albumin our protein and it regulates what's called oncotic pressure and how human plays a super important role in keeping that water inside the capillary so ask yourself whenever we start to lose albumin our protein because we're losing it all a lot of it in our urine what happens there's nothing to keep that water inside the capillaries less amounts of it so what's going to happen fluid is going to start moving out of those ministrations those pores into the tissues so you're going to get swelling and when you get swelling in these patients depending on the severity of this condition it leads to what's called fluid overload now let's sing with our nursing knowledge whenever a patient has fluid overload what are they at risk for well fluid overload affects the heart there's way too much fluid in the heart it's going to increase the blood pressure and want to wear that hard out it will be able to function for a while but that muscle of the heart will become weak so they can end up in heart failure and the hypertension also they can have renal issues because the kidneys aren't able to filter as much as you're going to see here in a second so we go to renal failure and they can also have respiratory distress issues because whenever the fluid when the heart becomes a weak and the fluid starts to back up into the lungs they get congestion in there and they can't breathe so let's talk a little bit about that renal issues that these patients are going to have they are going to have decreased glomerular filtration rates and G a decrease GFR so what is this condition let the word help you it is how that glomerulus is going to filter the fluid so it's the flow rate of filter fluid through the kidneys it's going to go down I'm going to be able to filter as much blood now why is this well remember we have inflammation going on in that glomerulus now what happened on that immune system at cellular level when we have inflammation all those other cells and our music some come there and congregate and what this does is it can just the glomerulus so it's going to decrease the amount of blood that's going to be filtered it can't get through there to filter it so we can get that filtrate so we have decreased filtration so ask yourself what is going to happen to the way that's built up in our blood that needs to get to that kidney to be filtered like the urea in the creatinine whenever we go to draw their blood they're going to have increased amounts of vun and creatinine now how their urine outfit going to be Palmeiras is not filtering so it's not really producing that filtrate also called urine so we're going to have low urinary output also called eyelid urea so they're going to have low amounts of urine so that's why whenever we talk about nursing interventions in a second-- you've got to watch that urinary output now whenever they have low narak low urinary output you need to watch how much to top the American Sumi because they're going into renal failure if you've ever looked at lab work on a patient who is awaiting dialysis because they have renal failure you will know that their potassium you will see it's wholly super high and their bu in and creatinine will be high so they will get high potassium level so we want to watch their foods are consuming in potassium because less amounts of that blood is being filtered and we're not being able to maintain that homeostasis for electrolytes now the next thing which is talked about a little bit earlier is the hypertension this is one of the big things we're going to really be monitoring this patient for and they are getting this high blood pressure now why are they getting high blood pressure well it's highs back to all this up here to fluid overload the retaining sodium they have extra fluid volume well the kidneys isn't able to filter that blood remove that water and all those solutes and substances so we're getting hypertension we're retaining that and our decreased GFR is causing our hypertension well if this is not treated and if this patient has it for a long period of time it can lead to a condition called hypertensive encephalopathy and this is where you have massive amount of blood pressure just being pumped to that brain tissue which can alter their neuro status and lead to seizures and why and our nursing interventions we're going to be monitoring that blood pressure very closely now let's wrap up all those things we just talked about into those signs and symptoms that a patient may have with acute glomerulonephritis due to a post-tropical infection okay and to help you remember that remember the pneumonic had strep because they have strep and this is why they're presenting with these signs and symptoms okay so H for hypertension a for ASO which is an anti stressor licence titer it will be positive this is a test used to diagnose stress d for decrease GFR remember GFR was the glomerular filtration rate will be down hence they'll have low urinary output as swelling in the face and the eyes this is going to be mild and it tends to be most common in the morning key for T colored urine or that Cola colored urine again that's due to that hematuria those red blood cells we can insight urine or for a recent strep infection they may report to you well I may be I have shred a couple weeks ago I don't know that I think I might have e4 elevated B you in and creatinine and p4 proteinuria and that will be mild now let's look at the nursing interventions what are you going to do for this patient who has this condition okay think back to what we just learned what is going on with this patient because this determines what we're going to be doing for the patient well we learn that in the most severe cases of this condition because for in Plexus concentrate on the worst case scenario they have fluid overload they have hypertension and they have some renal impairment so we want to do a nursing interventions based on that first thing we want to do is we want to monitor that fluid status very closely physicians may prescribe diuretics which is going to cause the patient to urinate a lot which will help remove that excessive fluid in the body but these may not be used as a patient has a renal impairment another thing we're going to do we're going to perform daily weights this is the earliest sign of fluid retention so it's very important such a simple thing to do we will get them up preferably on a standing scale the same time every day and wave in if you have to use the bedside scale you can but standing tails are the best and we will also perform strict calculation of their intake and outfit so those eyes and O's now with our pediatric patient because this condition tense affects of pediatric children we want to make sure that their urinary output is at least this is usually rule from one milliliter a per kilogramme every hour so for every kilogram they way they should be putting out X amount of milliliters of urine per hour so the patient weighs 30 pounds how much here and should they be fit now well you'll want to convert 30 pounds to kilograms and for every 2.2 kilogram is 1 pound so 30 divided by 2 point 2 is 13 point 6 so they weighs 13 point 6 kilograms so they should be putting out 13 point 6 milliliters per hour now how about if they weren't putting that out there they were putting on like 10 they have low urinary output as a nurse you want to monitor them for hyperkalemia and we talked earlier about why that is and we'll want to restrict foods that are rich in potassium next we'll want to assess their urine color is it getting normal looking compared to that tea or cold colored house there be you in there creatinine which indicates their going into renal failure next we'll want to monitor them their edema is it got is it decreasing in their face and in their eyes are they getting better how do those lungs sound are they having fluid overload as they're crackles in there which can indicate pulmonary edema and also we really really want to monitor those bottle signs especially that blood pressure because remember depending on how severe they have this they can have hypertension which if it's not controlled and they have for a prolonged type a period they can enter into hypertensive encephalopathy and the physician may be ordering antihypertensive drugs to help combat that and nearing this acute phase when they do have this hypertension going on you want to initiate bed rest during that time diet includes usually they're on a fluid restriction because we have the swelling going on and a sodium restriction until they are recovered and then they can go back to their diet and some education you want to provide them is that strep infections can reoccur so if they ever suspect they have strep they need to go and get a culture and make sure it's not strep so they can get it treated separately if they do okay so this wraps up this lecture on a cube will marry alone esperadas thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Arterial_Blood_Gas_ABGs_Made_Easy_for_Nurses_Tic_Tac_Toe_Method.txt	hey everyone this is Sarah with register nurse rn.com and today we're going to solve arterial blood gas problems using the Tic Tac Toe method um in my previous video I showed you how to solve ABG problems using the TIC TCT toe method I talked about how to set it up what it looks like um normal lab values and water abnormal values so if you don't know how to use the Tic Tac Toe method I really recommend you check out that video previously it's called ABG Tic Tac Toe method um before you watch this video because you may be a little lost also when you're done watching this video test your knowledge on how well you know your abgs by going to our website register nurs rn.com and click the slider that says quizzes and you can go there and test your knowledge on how well you know your abgs so first what we're going to do is we're going to set up these problems and we're going to solve them I'm going to be working five problems I'm want to be covering metabolic disorders respiratory disorders and if they're compensated or uncompensated so um if you're ready let's start our first problem in nursing school normally what you're given are just basic little um lab values you're given the pH level you're given the metabolic level and the respiratory level right here I have written the normal level so if you want to go ahead and just write that down um your normal pH levels I'm going to go over this real fast is 7.35 to 7.45 anything less than 7.35 is an acid anything over 7.45 is a base which is alkalic your PCO pac2 represents respiratory levels and it's the opposite of pH anything over 45 is an acid anything under 35 is base alkalotic so instead of your first number being an acid your last number being a base it's flipped metabolic which is represented with the H3 22 to 26 is normal and is the same as pH anything less than 22 is an acid and anything over than 26 is alkalic so those are your normal values okay so for our problem we have a pH of 7.53 a respiratory P2 of 23 and an H3 of 18 so we set up our tic tac toe um grid we have written acid normal and base and that is our little Baseline and anytime we get straight up and down of three we know that we're done okay for our pH we ask oursel is this an acid or a base and we know because it's over 7.45 it is a base so it's alkalic so we are going to put pH under base and we're going to look at our P2 levels and it's 23 and remember it's the opposite so your normal was 35 to 45 it's 20 23 so we know that that is basic so we're going to put P2 under base and notice that they are lining up but we still need to look at our hco3 levels to tell us are we compensating or not and it's 18 and but the normal value is 22 to 26 and since it's 18 we know it's an acid it's acidotic so we're going to put this under acid okay and we have our Tic Tac Toe so let's interpret we're ready to interpret since this is under here and we got the Three cross we are seeing we got to ask ourselves is this a respiratory issue or a metabolic issue we know that this is a respiratory issue because it's the P A2 so it's respiratory next we have to ask yourself is this alkalotic or acidotic and we're under the base category so we know it's alkalic and we have to ask oursel is the patient compensating or not compensating and the other value of the metabolic will tell us this see the hc3 is abnormal the body is trying to regulate itself so it's thrown off the metabolic rate so we know that the body is trying to partially compensate so this would be respiratory alkalosis partially compensated now if your H3 was still normal the body isn't really trying to compensate so it would be uncompensated so it's respiratory alkalosis un partially compensated okay let's solve in our next problem we have a pH of 7.20 a P2 of 38 and an CO3 of 17 we've set set up our Tic Tac Toe with acid normal and base as our Baseline and our goal is to get as in Tic Tac Toe a line of three together so we're going to look at the pH at 7.20 we know that that's an acid so we're going to put under acid pH we're going to look at the P2 and it's 38 and um the normal P2 is 35 to 45 so it's normal so we're going to put this under the normal next we're going to look at the H3 and it is 17 the normal is 22 to 26 so we know that this value is acidotic so it's going to go under acid just like pH now we um like in t tic taac toe we have our cross so we're ready to interpret it um we know that um hc3 represents metabolic so we know that we have a metabolic problem and it's under acid so we have metabolic acidosis next we're going to see if it's uncompensated or partially compensated and our P2 the body is doing nothing about it so the respiratory system is still normal so it's uncompensated so your answer would be metabolic acidosis uncompensated if the P2 was under base the body would be trying to do something about it so it' be partially compensated but in this case it's uncomp compensated okay let's do our next problem okay for our next problem we have a pH of 7.48 a PA CO2 of 42 and H3 of 35 so we've set up our problem for the Tic Tac Toe you have acid normal and base and we're going to determine where each value goes in the Tic Tac Toe pH is 7.48 and anything over 7.45 is a base alkalic so pH is going to go under base our P2 is 42 we know that pac2 normal ranges are 35 to 45 so since it's 42 our pac2 is normal so that's going to go under the normal category hc3 is 35 our normal range for H CO3 is 22 to 26 six so we know that um our metabolic is um basic so we're going to put hc3 under basic and we have our Tic Tac Toe this will help us interpret we know that we have a metabolic problem it's under base so it's metabolic alkalosis next we have to ask ourselves is this compensated or uncompensated and remember if the body is trying to do something it would throw off the other value it's not our P2 is normal so we know that it's uncompensated so the answer to this problem is metabolic alkalosis uncompensated and again just to remind you if this P2 was an acid it would be trying to compensate the body's trying to do something to get that homeostasis back but in this case it's not so that's how you solve that problem let's do our next problem okay for our next problem we have the following lab values we have a pH at 7.21 a P2 of 50 and an H3 of 28 we've set up a problem using the Tic Tac Toe we have acid normal and base and now we want to plug in these values to get the tic tac toe and see what we have so first we're going to ask ourselves with the pH we have 7.21 is this an acid or a base and we know anything less than 7.35 for an pH is an acid so it's acidotic so under acid we're going to put pH for p CO2 we know that the normal range is 35 to 45 and we have a range of 50 so we know that this is going to be an acid so your P2 is acidotic so we're going to put that under acid and we already have our Tic Tac Toe but we still need to plug in the third value the H3 normal H3 is 22 to 26 it's 28 so we know that it is basic so we're going to put hc3 under base so now we are ready to determine what we have our problem is respiratory we have respiratory acidosis because that is where our tic tac toe is um so respiratory acidosis and we have to ask oursel next the last question are we compensating or are we uncompensated uncompensated so our H3 is thrown off it's an acid it's not in the normal range so our body is trying to comp compens so we would have respiratory acidosis partially compensated so that's the answer to that okay let's do our next question okay for this question we have the following lab values we have a pH of 7.50 a P2 level of 47 and an hc3 level of 27 we've set our problem up for the Tic Tac Toe grid we have acid normal and base and now we're going to plug in these values to see where we get a Tic Tac Toe so first let's start with ph it's 7.50 we know that a normal pH is 7.35 to 7.45 so we know that our pH is basic it's alkalic so we're going to put pH under base next we are going to look at our P2 levels it's 47 a normal P2 level is 35 to 45 so our P2 level is acidotic so acid we're going to put P2 lastly we are going to look at our H3 level and it is 27 a normal hc3 level is 22 to 26 so we know that that is basic it's um alkalotic so we're going to put hc3 under base and we have a Tic Tac Toe so do our line and we're going to interpret we know that this is a metabolic problem cuz hc3 represents metabolic and we know it's basic so we have metabolic alkalosis so we have to determine are we trying to compensate is our body compensating or not and the body is trying to compensate because the P2 level is abnormal it's acid so the body is trying to do some homeostasis and get the body corrected so we have our answer is metabolic alkalosis partially compensated remember if this P2 level was under normal it would be uncompensated cuz the body's not doing anything about it so that is how you solve these ABG problems um go to our website register nurse orn.com and click the banner that says quizzes it's actually a slider and it will take you to quizzes we have a lot of inlex quizzes ABG quizzes drug and dosage calculation quizzes and you can test your knowledge on how well you grasp this using the Tic Tac Toe method and thank you so much for watching I hope you found this helpful and please give it a thumbs up and I hope you have a great day
Medical_Surgical_Nursing	Blood_Flow_Through_the_Heart_Heart_Anatomy_and_Physiology_NCLEX.txt	this is say earth register nurse re and calm and in this video I'm going to be going over blood flow of the heart and after you watch this YouTube video you can access the free quiz that will test you on heart blood flow so let's get started to easily understand the blood flow of the heart what you want to do is you wanted to buy the heart into two sides we have the right side of the heart and the left side of the heart and each of these sides has its own mission now the mission of the right side of the heart is to take the UH Knox ajaita blood that it received and get it to the lungs so the right side is going to take the blood right to the lungs to get oxygenated now the left side of the heart is going to it's responsible for oxygenated blood so it's just received oxygenated blood that has left the lungs to go throughout the body and what's really awesome to make it even easier to memorize is that each side the right on the left side has six structures where that blood has to flow so let's go through the blood flow of the heart okay everything starts on the right side of the heart and blood is being drained to the heart from the superior vena cava in the inferior vena cava and it's exhausted and it needs to get replenished with oxygen so it drains in down through the right atrium the atrium are always on top of the ventricles so remember that then it flows down through a valve and there are valves that separate your atrium from your ventricles over here on the right side we have the tricuspid valve and on the left side we have the bicuspid valve the mitral valve now how can you keep the two separated I like to remember the same try before you buy so the tricuspid valve bicuspid valve so the blood goes down through here then it goes down through the right ventricle the right ventricle squeezes it up through the pulmonary artery but the blood has to go through another Wow and it's called the pulmonic valve so it goes from right ventricle pulmonic valve to the pulmonary artery which the right side again takes it right to the lungs so that an oxygenated blood goes through the lungs and on your alveoli sacs or capillaries and you have this gas exchange going on so oxygen that you're breathing in is crossing over its hatching to those red blood cells and the carbon dioxide that's built up in your blood from this exhausted blood that's just been used from your body it's gonna cross over and you're gonna exhale it so the blood is nice and oxygenated and it has left the lungs to go into the left side of the heart through the pulmonary vein then it's gonna go down through the left atrium goes through another valve again what was that back valve the bicuspid valve the mitral valve so right here then it goes down through the left ventricle and then it's going to be shot up through the aorta but in order to get up through the aorta has to go through another valve which is the aortic valve so it crosses through the aortic valve up through the aorta and then it's gonna replenish your organs and your tissues okay so that wraps up the blood flow of the heart thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Cardiogenic_Shock_Nursing_Management_Pathophysiology_Interventions_NCLEX_Review.txt	hey everyone it's sarah register nurse rn.com and in this video we're going to be continuing our series on shock today we're going to be talking about cardiogenic shock now after you watch this youtube video you can access the free quiz that will test you on this condition so let's get started first let's start out talking about what is cardiogenic shock it occurs when the heart cannot pump enough blood to meet the perfusion needs of the body so this condition is solely an issue with this heart itself hence why we call it cardiogenic shock now why does it occur well can occur for multiple reasons number one it can occur due to a feeling issue there's an issue with these chambers of the heart being able to fill properly and this is known as diastolic dysfunction or there can be an issue with contraction of the heart so the heart is having a problem actually getting that blood and moving it forward out of the heart and that is known as a systolic dysfunction or you can have some type of dysrhythmia presenting or some type of structural defect a little bit later we will go into some conditions that can cause diastolic or systolic dysfunction but just keep that in mind now one thing with cardiogenic shock i want you to remember is that it doesn't present due to a loss of blood volume for the heart to pump the heart has plenty of blood volume to pump it just really can't pump it out of the heart and maintain cardiac output so that leads to a decrease in cardiac output now i really want you to remember cardiac output because this is a big term we're going to talk about throughout this lecture now what is it well it's the amount of blood that the heart pumps per minute and it's determined by a couple factors the heart rate and the stroke volume and stroke volume can be determined by your preload afterload and contractility and whenever we're talking about treatment we can give medications that can help manipulate that stroke volume hence increasing our cardiac output so whenever we have a decrease in cardiac output we're going to have decreased perfusion because this heart can't get its blood volume out to go to supply the organs the tissues so there are those cells that make up the organs and tissues aren't being perfused so if they're not receiving fresh oxygenated blood what's going to happen they're going to receive a decreased amount of oxygen and that can lead to cell hypoxic injury and we talked in depth about that in our previous video about the stages of shock now to help us truly understand cardiogenic shock we have to go back to the basics and we have to talk about the role of the heart our heart is the pump of the body and there is no other organ in our body that can do what the heart does and what's interesting is that every organ in the body depends on the heart so if the heart can't pump correctly everything else suffers because the heart supplies your organs and your tissues cells with fresh oxygen and they need oxygen to work and if the cardiac output falls which is the amount of blood that that heart pumps per minute that means that those cells aren't receiving adequate amounts of oxygen so as we learn in the stages of shock once that cardiac output starts to fall the patient will enter into those stages and in the end if it's not corrected the cells that make up the organs completely shut down and die and death occurs so what your heart does is that it receives blood to its right side everything starts in the right side and the whole goal is to take blood recycle it put fresh oxygen in it and pump it back out to the body so we have oxygen we have blood that's depleted of oxygen comes in through the superior inferior vena cava down through the right atrium then through the tricuspid valve the right ventricle which shoots it up through the pulmonic valve and then into the pulmonary artery which goes into the lungs and in the lungs gas exchange occurs and you have the crossover of carbon dioxide that has built up in the blood person will exhale that out then the oxygen that that person has taken in will cross over and go into the blood and then it will go back to the left side of the heart through the pulmonary vein and the goal of the left side is to take that oxygenated blood and pump it throughout the body so it will go through pulmonary vein through the left atrium down through the bicuspid slash mitral valve then through the left ventricle and the left ventricle is the main pumping chamber of the heart it's extremely strong and it's a very important chamber because if it fails to work and contract we have major problems and you're gonna where we talk about the causes in an acute myocardial infarction if you get damage to this left ventricle it's muscle we can have cardiogenic shock so left ventricle pumps it up through the aortic valve then through the aorta and the aorta will supply the body it'll branch off into this complex network of arteries and will go to every single organ tissue and supply the body with fresh oxygenated blood now let's talk about this thing called cardiac output understanding cardiac output is really the backbone of understanding cardiogenic shock so let's go over it okay as i have pointed out cardiac output is what it's the amount of blood pumped by this heart per minute so how much blood should your heart be pumping per minute it should be pumping anywhere between four to eight liters per minute now how can we determine cardiac output well you can take the heart rate and multiply it by stroke volume now let's talk about stroke volume for a moment if we can increase stroke volume in the management of cardiogenic shock we can increase cardiac output we increase cardiac output which is the amount of blood this heart is pumping per minute we can increase profusion to those cells that make up the tissues and organs they receive more oxygen they're happy and they don't start to die so stroke volume is the amount of blood pumped by the left ventricle with each beat which should be anywhere between 50 to 100 ml now stroke volume is determined by three factors and these three factors can be manipulated with medications to increase stroke volume so let's talk about those three factors they include preload afterload and contractility so preload is the amount those ventricles stretch at the end of diastole diastole is where the heart is relaxing and it's filling with blood so at the end when it's done filling at the end of that part of asleep it's the amount that those ventricles have stretched once it's filled afterload is the pressure the ventricle must pump against squeeze against to get blood out of the heart and then contractility is how well those muscle cells that make up that heart that help it contract how well they're contracting so it's the strength of the heart with each contraction now let's talk about some examples okay if we give a patient a drug that increases contractility like a positive inotropic drug like butamine dopamine if we increase contractility we're talking about we're increasing how well those muscle cells are contracting what's it going to do to stroke volume it's going to increase stroke volume okay afterload let's say we decrease that resistance that that heart has to pump against it's going to make it easier for the heart to pump so if we decrease afterload we're going to increase our stroke volume we can do that with like vasodilators now with preload let's say we give them a vasopressor it's pressing down our vascular system it's causing vasoconstriction when you vasoconstrict you're compressing everything you're going to increase venous return to the body so you're increasing the amount of blood that's coming to this heart which is going to increase how much is feeling in that ventricle how much it's going to have to stretch you're increasing its preload you bet you're going to increase its stroke volume as well so we can increase preload increase contractility decrease our afterload we're going to increase our stroke volume which is going to increase our cardiac output now another term you may see whenever talking about cardiogenic shock is something called cardiac index and all this is is it's a more specific measurement of cardiac output based on the patient's body size so it's calculated by taking the cardiac output and dividing it by the patient's body surface area and for patients who are in cardiogenic shock their cardiac index will be less than 2.2 liters per minute per meter squared and you want a normal cardiac index to be anywhere between 2.5 to 4 liters per minute per meter squared now let's talk about the causes of cardiogenic shock okay what are some conditions that can occur in the body that will make this heart's cardiac output fall so low that it can no longer meet the perfusion needs of our cells tissues and organs so they receive decreased oxygen well one of the main causes of this condition is if a patient experiences an acute myocardial infarction which is also called a heart attack and what happens during a heart attack is that the coronary arteries that set on your heart muscle have become blocked they can become blocked with a fatty plaque a clot or something but whatever the cause it's decreased blood flow to that heart muscle and wherever it's decreasing blood flow to that heart muscle those cells that make up the heart are going to not work and after so long those cells can just die and it's irreversible so that can lead to your heart not pumping efficiently hence stroke volume is majorly going to be affected which is going to make cardiac output fall and this is one of those systolic dysfunctions so there's going to be an issue with this heart being able to move blood forward and out of the heart and one type of acute mi that can cause this is if the coronary artery that feeds the left ventricle becomes blocked because remember what did i say about the left ventricle it's the main pumping chamber of the heart so the coronary artery that sets on that left ventricle is blocked wow that left ventricle is really going to become affected it's not going to pump it's going to affect its preload after low contractility you're going to have a mess on your hands and then stroke volume is going to fall and so is cardiac output so patients who have those type of heart attacks are really at risk for cardiogenic shock other causes of this condition are like pericardial tamponade and this is a diastolic dysfunction where there's going to be issues with the chambers of the heart being able to feel properly because you have too much fluid surrounding the heart so they really can't feel cardiac output is going to fall in addition dysrhythmias as i pointed out earlier myocarditis endocarditis can cause this also structural issues like issues with the valves or the septums in the heart now let's talk about the signs and symptoms of cardiogenic shock so whenever you're trying to recall these signs and symptoms for exams think about what is going on with this patient we know that there's decreased cardiac output so we have decreased cardiac output there's a limited amount of blood that's going to all those organs and tissues that depend on that heart to pump them fresh oxygenated blood so a lot of your signs and symptoms are going to stem from that in addition remember at the beginning of the lecture i said that this isn't a blood volume issue the heart has plenty of blood volume to pump which because it's weak and it's not being able to maintain cardiac output that blood volume is going to start to back up in the heart go to the lungs and go to the right side so that's really where you're going to see your other signs and symptoms so let's look at it by systems our heart our hearts weak it's not pumping correctly either we have a feeling issue like diastolic dysfunction or we have a systolic issue where the blood can't be pumped forward it's having issues with contractions or some type of thing but whatever the cause eventually what's going to happen is you're going to have back flow of blood because remember our blood volume is fine it's going to go to the lungs so it goes from left side back into the lungs it's going to go backwards instead of going from right to left shoulder it's really going to go left to right and you're going to have pulmonary edema lungs do not do well with fluid in them so what's going to happen in gas exchange it's going to decrease so you're going to get low o2 levels in the blood patients going to have difficulty breathing they're going to have an increased respiratory rate they're going to have an increased heart rate and chest x-ray if they get one of those it'll show pulmonary edema in there with infiltrates on the chest x-ray and if they have hemodynamic monitoring we're going to talk more about this in our nursing interventions but i wanted to include this in the signs and symptoms they can have an elevated pulmonary capillary wedge pressure also called a pulmonary artery wedge pressure greater than 18 millimeters of mercury and what this is it's measured through a pulmonary artery catheter goes in through the right side up through this pulmonary artery and the catheter on the end of it is like a balloon that can be inflated and deflated and it's temporarily inflated and that pulmonary arterial branch and it can measure the pressure and if you have a lot of blood that's back flowing into the lungs you're increasing the feeling pressure really that left atrium and it can measure that pressure and it'll be greater than 18 millimeters of mercury so keep that number in mind in addition you have the backflow from the lungs it'll eventually go to the right side because here's a pulmonary artery or right side of the heart and then venous circulation and all become congested increasing pressures on that right side so you can have jvd which is jugular venous distension where those neck veins will be distended and you can have a high central venous pressure where again you can measure the pressure in that right atrium and it'll be elevated from where you have that back flow of blood and it's increasing the pressure now with cardiac output wise you can have weak peripheral pulses you feel those the heart just can't pump it so whenever you feel those pulses they'll be weak systolic blood pressure will be less than 90 90 millimeters of mercury patient can say they're experiencing chest pain and this is where those coronary arteries aren't receiving blood as much blood flow perfusion as they should so it can't perfuse that heart muscle those cells are becoming stressed causing the patient pain and again cardiac index which was a specific cardiac output based on the patient's body size will be less than 2.2 liters per minute per meter squared now another system that's going to be affected is the brain and whenever cardiac output decreases so does the perfusion to the brain so you're going to have a drop in cerebral perfusion pressure so the cells aren't going to be perfused you're going to start seeing mental status changes in the patient they can start becoming confused agitated in addition this confusion and agitation can stem from the buildup of toxins because the liver isn't really going to be working efficiently by filtering out toxic substances along with the renal system and you'll be having acidotic conditions from the buildup of lactic acid so the kidneys can be affected as well so you can have decreased perfusion to the kidneys of course when cardiac output falls and the kidneys try to in a sense save themselves by activating the renin angiotensin system and what this does in a nutshell is the end result is the release of angiotensin ii and that is a major vasoconstrictor and whenever the body senses angiotensin ii aldosterone is released along with adh anti-diuretic hormone and what aldosterone is going to do is it's going to cause the body to keep sodium and water and adh is going to cause the body to keep water because in the end what it wants to do is increase blood volume because if it can increase blood volume it can increase venous return to the heart because it can get more perfusion if it does that so whenever that's happening what you're going to see is a lower urinary output augluria where you're going to have a urinary output of less than 30 cc's per hour so as an rsp watching that urinary output and if it's falling you know your kidneys are not being perfused very well which in addition whenever your kidneys are really struggling not being perfused you get an increase of bun and creatinine so be looking at that because that tells us our renal function and you can start seeing signs and symptoms in the skin where tissue perfusion is just falling the skin where where it should be nice and warm won't be like that it'll be cold cool clammy pale and when you check capillary refill it will be delayed it can be greater than two seconds now let's talk about nursing interventions for cardiogenic shock what are we going to be doing as the nurse okay first we need to know the treatment goals what's the medical treatment goals for this patient well number one reprofusion if this cardiogenic shock is happening due to let's say a coronary artery being blocked that feeds this heart muscle which is causing this heart muscle to become weak decreases its cardiac output they can hopefully re-establish profusion by doing heart catheterization putting in a stent so blood flow can start going back to that heart muscle another thing is increasing cardiac output and we can do that by giving certain medications and that can increase the stroke volume by altering that preload after load contractility and ventilation a lot of these patients who have severe cardiogenic shock are going to go into pulmonary edema where all that fluid is backing up into the lungs and and they will need mechanical ventilation with this and some diuretics to help remove the extra blood volume from the lungs so the patient can breathe easier so as a nurse a lot of times these patients are going to be in the icu because they're very sick so you'll be maintaining the hemo dynamic monitoring the mechanical ventilation due to the respiratory failure this hemodynamic monitoring can tell us a lot about our patient how they're responding to the iv drips that they're on and how their cardiac output is with a central line placement to help measure those numbers for cardiac output and they can do that through a pulmonary artery catheter like a swan gans in addition you want to monitor for signs and symptoms of adequate tissue perfusion and you can look at certain body systems and tell hey are they being perfused enough based on our cardiac output so look at the blood pressure we want this to solid greater than 90. skin color how does it look is it pale cool clammy probably not being perfused very well how's the capillary refill is it delayed urinary output is it greater than 30 cc's an hour if not kidney functions probably not good look at the bun and creatinine that can show if the patient's entering renal failure mental status the mental status will start to deteriorate as perfusion to those brain cells is decreased so is your patient becoming more confused agitated restless lung sounds that really ties to respiratory failure are your lungs clear if you hear crackles you probably have some pulmonary edema in there and how is the rhythm furthermore you'll want to look at lab results and other diagnostic testing that will be ordered to help look at the heart's function and what's possibly causing this cardiogenic shock cardiac markers will be ordered and they will be elevated for example troponin level will be elevated and a bmp could be elevated now what is a troponin well troponin is a substance released when there is injury to the heart muscle cells and we know in cardiogenic shock that these cells are getting stressed out so this can increase troponin levels and especially can increase troponin levels if there's been significant damage to the heart muscle cells through like a myocardial infarction now what's a bnp well this is a substance released by the ventricles heart cells due to stretching from high blood volume in the ventricle and we know as that heart muscle is getting weaker and weaker blood volume starts to back up and that will increase the amount that those ventricles are having to pump other tests that can be ordered of course is like a chest x-ray where this would show fluid in the lungs pulmonary edema in addition a serum lactate can be ordered and this will be greater than four millimoles per liter and why are we having elevated lactic acid levels well remember when we talked about the stages of shock we talked about how the cells will switch from aerobic to anaerobic metabolism so they are using metabolism at first with oxygen the aerobic but oxygen isn't in supply so they're going to have to switch to anaerobic metabolism without oxygen and this leads to the accumulation of lactic acid as a result so then we'll start getting acidotic conditions where there will be a drop in the blood's ph less than 7.35 now let's talk about some hemodynamic monitoring numbers that you need to know when we're talking about cardiogenic shock okay the first one i've already hit on a little bit it's called the pulmonary capillary wedge pressure or the pulmonary artery wedge pressure and in cardiogenic shock this number is going to be high and normal is 4 to 12 millimeters of mercury but in cardiogenic shock it's going to be elevated greater than 18. and again that was with like a swan gans catheter pulmonary artery catheter it's inserted in that right side and it's going to go up into that pulmonary artery and it's going to be hence wedge the tip of that catheter and a balloon is temporarily going to be inflated in that pulmonary arterial branch it's going to measure the pressure and it's going to really tell us the pressure on that left side of that left atrium so if the pressure is high from where we're having the back flow of blood it's going to be elevated another thing we can look at is the central venous pressure the cvp it will be elevated as well and this is because we have back flow of blood causing venous congestion in this right side and it's measured over here in this area now let's talk about medications okay with medications for cardiogenic shock you can have various medications depending on what is causing it um how the patient is even responding to treatment you may use this medication on this patient while you wouldn't use it on this patient because the response is different these medications are going to be titrated their iv and things like that so keep that in mind so some medications that can be used are diuretics why would we need diuretics well remember with cardiogenic shock we don't have a blood volume issue this is one of the two shock types the other is neurogenic where we don't have decreased blood volume our blood volume is actually causing us some problems because our heart is not able to really pump it forward so we're getting congestion so diuretics can be used like furosemide which is the brand name lasix give that iv that'll help draw some fluid out it's loop diuretics they'll urinate that fluid and help remove all that pulmonary congestion in the lungs however when you give these diuretics especially lasix it can cause hypokalemia it wastes potassium so before you give any type of diuretics you always want to look at electrolyte levels and if they're getting this medication you want to make sure your potassium is within 3.5 to 5 milli equivalents per liter anything lower than that 3.5 you just want to give the physician a call so they can provide some supplementation before you throw on this diuretic so what the what's this going to do is it's going to remove that extra blood volume it's going to decrease that workload of the heart and you'd want to watch out for hypotension because if we're taking off blood volume through having them urinated out we can make them have a lower blood pressure and chances are we're already dealing with someone who is hypotensive so you'd want to monitor that closely and if they get too hypotensive they can throw on another medication to help increase that pressure so be watching out for that also looking at their fluid status what's the urinary output how's their kidney function because we don't want to cause them to go into renal failure by throwing these diuretics on another category of drugs used are called vasopressors and what these do is they cause constriction of the vessel so major vasoconstriction and as we talked about before you're going to have increased preload with that because it's really just going to clamp down on those vessels increase venous return and preload was the amount those ventricles stretched at the end of diastole and if you increase that in the end that's going to increase stroke volume so you'll have increased cardiac output increased blood pressure a drug that's a vasopressor uses called norepinephrine and we'll get the results of increased cardiac output with this to tissue perfusion our cells will be happy because they will get more oxygen now there are some vasopressors that have positive inotropic effects and inotropic whenever they have positive anatropic effects that means that they're increasing the contractility of the heart and that was another factor in stroke volume so we're going to increase the strength of the heart's contractions which is great because we're going to have better stroke volume higher cardiac output two drugs that can do that that are used in cardiogenic shock we have dobutamine so dobutamine increases contractility increases stroke volume but a side effect because the way that dobutamine acts on certain receptors it can actually cause vasodilation which can in our patient who already is hypotensive it can cause it to get worse and they'll probably have to be switched or started on norepinephrine or dopamine instead so you want to watch out with dobutamine worsening hypotension that's a big thing with that now dopamine is a positive anatropic effect as well it increases contractility which is going to increase our stroke volume however a side effect of dopamine is that it can cause a tachycardic can really increase that heart rate so you have to watch the heart rate with this medication in addition we have vasodilators that's another category and what these do is they decrease afterload which was one of those factors in stroke volume so whenever we decrease the afterload it's going to make easier for the ventricle to pump against that resistance so we have decreased resistance that that heart has to pump against and it also dilates our coronary arteries which is going to increase perfusion to the heart muscle so our heart's going to get more blood flow because those dilated coronary arteries but a side effect of this is hypotension so we really have to watch out for that blood pressure make sure it's stabilized because it can further make it worse and some vasodilators are like nitroglycerin or sodium nitroprusside and some other things that can be ordered in a patient with cardiogenic shock or like iv fluids like normal saline however they're typically not ordered if you have a patient in fluid overload with like pulmonary edema because if we throw more fluid in here in the heart they already have fluid in the lungs from where that heart's weak and not pumping correctly we're going to cause them some more issues so if they are ordered they're used with extreme caution and fluid challenges are more common in the other types of shock that we'll be going over rather than cardiogenic shock because remember blood volume is not really an issue with us it's our heart now let's quickly talk about intra aortic balloon pumps what are these they are a device used to help improve coronary artery blood flow and to increase cardiac output so this catheter is inserted through a vessel it goes up through this aorta sets in a section of the aorta and the catheter has a balloon at the end of it and what this balloon will do is it will inflate and deflate at certain times and this will actually increase blood flow to the heart muscle via those coronary arteries and increase cardiac output so during um sicily that balloon will actually deflate so here you have this balloon it's deflating and whenever the heart is in sicily contraction whenever you have that balloon that deflates it creates a suction like pressure so what that's going to do is it's going to suck more blood out of this weak side of the heart that's having trouble pushing blood forward it's going to suck it out help it go out through the body increasing cardiac output and pushing more blood into those coronary arteries because coming off the aorta is are the coronary arteries in addition whenever you have diastole where the heart's like resting and feeling the balloon is going to inflate so when you have to isolate this balloon inflates the aortic valve is closed during that time it's going to push blood flow into those coronary arteries and even further increase profusion to the heart muscle okay so that wraps up this review over cardiogenic shock thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Nitroglycerin_Medication_Nursing_Sublingual_Tablets_Oral_Spray_Pharmacology_Review_Adminstration.txt	this is Sara threats Turner sorry and calm and in this video I'm going to be going over sublingual nitroglycerin and the oral spray and I'm going to show you how to administer it now remember whenever you administer nitroglycerin you always want to follow your hospital protocols for this medication along with the manufacturer's instructions and always be sure you have the proper credentials when administering this medication and for this video we are using demo dose doses of nitroglycerin so it's a simulated dose and these do not really contain nitroglycerin so what does nitroglycerin use for it's used to relieve or treat chest pain and nitroglycerin is part of the nitrate family and because of this what it does is it causes vasodilation on those blood vessels so you have a patient they're having chest pain they're getting limited amount of blood to that heart muscle and what nitroglycerin will do open up those vessels and increase the blood supply to that heart tissue along with decreasing its workload so as a nurse what do you expect to see in your patient after you give them this drug well you can expect to see facial flushing from where they're getting increased blood flow through the body from that vasodilation they can also experience like a burning or tingling sensation underneath the tongue whenever you give this sublingual the tablets you will put underneath the tongue and the spray you will spray under the tongue as well also it can cause a very painful headache from all the extra blood flow they can experience dizziness and definitely hypotension it's going to lower the blood pressure so when your patient is having chest pain as the nurse of course you want to notify the physician and a lot of hospitals already have standing orders there for you to follow out they're usually called chest pain protocols and you will have this order set that you need to do for your patient which will include you know giving the nitroglycerin possibly morphine if the Nitro is not really helping along with oxygen administer via nasal canula of 20 obtaining a 12-lead EKG and drawing cardiac enzymes so before you administer a nitroglycerin to your patient of course you want to confirm that they are not allergic to it and that they haven't recently taken a phosphodiesterase inhibitor like sadena fill which is viagra or $2.00 fill which is cialis because this can lead to severe hypotension and possibly even death and of course you don't want to give this to a patient who has increased intracranial pressure then you'll want to perform hand hygiene perform the patient's 5 right and whenever handling nitroglycerin you want to wear gloves because if you get this on yourself you can give yourself some nitroglycerin and you can get some of the side effects that come along with this drug so first let's talk about sublingual nitroglycerin okay it comes in a dark vial and this vial is dark for a reason because nitroglycerin is very sensitive and it doesn't need to come into contact with white or heat or moisture and it's only good for three months when the bottle is opened and then you're gonna have the patient sat down before administering this to them because remember it can cause dizziness and hypotension and you want to obtain baseline vital signs especially blood pressure because you're gonna see a decrease in their blood pressure and you want to confirm that their systolic blood pressure is within parameters and most Hospital protocols require that that's a solid blood pressure that top number is greater than 90 and if it's not and your patients having chest pain you need to contact the physician for further orders and preferably you want them on a cardiac monitor so you can be monitoring that rhythm looking at the ST segment for normalities like St elevation or depression to administer you will place one tablet under the tongue so how the patient lifts the tongue up and it will dissolve under there the patient does not need to chew it or swallow it and not to rinse the mouth because they may feel like they need to do that whenever they have the tablet under the time because of the tingling sensation and it's going to absorb within that lining there and after giving the tablet you'll want to make sure that you're constantly monitoring their blood pressure especially that's systolic making sure it's greater then 90 and their chest pain how is it rated is it increasing is it decreasing is it going away and if their systolic blood pressure is still within parameters and they're still having chest pain you can do a second dose within five minutes again monitoring that blood pressure and their chest pain and the chest pain is still there you can give a third dose within five minutes now you do not want to get more than three doses and if the chest pain is still not relieved after the third dose you'll want to notify the physician now with the oral nitroglycerin spray what you want to do is of course remove the cap on the bottle and if this is a new bottle you'll want to prime it and a lot of times in the hospital setting and you're going to be using a new bottle of nitroglycerin and to prime it you're going to press the button to spray about five to eight times just to get that line in there nice and primed and whenever you do that tip keep it away from your face and other people's faces you don't want to inhale this so we're gonna probably about five to eight times all right okay and then it's ready to use and another tip with this spray is that you don't want to shake the bottle up and down remember nitroglycerin is very sensitive and it's in a dark bottle so keep it away from heat and light and keep it in the upright position at all times you don't want to store it upside-down and to give the world nitroglycerin spray you're gonna give one spray underneath the tongue and tell the patient to slightly hold their breath and not to breathe in the medication now after giving the oral spray you'll want to make sure that the patient doesn't rinse their mouth or eat or drink anything for at least ten minutes and you'll follow the same protocol as you followed with the sublingual tablet by monitoring that blood pressure constantly making sure it's within parameters and monitoring their chest pain and within five minutes you can give a second dose and within five minutes you can give a third dose and no more than three doses okay so that is how you give sublingual nitroglycerin and oral spray thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Epiglottitis_in_Children_Nursing_NCLEX_Lecture_Symptoms_Treatment_Causes_Interventions.txt	this is cereth registered nurse sorry and calm and in this video i'm going to be going over epiglottitis in this video is part of an ink lex review series over pediatric nursing and as always i pin to this youtube video you can access the free quiz that will test you on this condition so let's get started first let's start out talking about what is this condition it is where there's inflammation of the epiglottis and whenever this happens it can lead to an upper airway obstruction which is a medical emergency and our pediatric patients tend to struggle with this condition more than adults but adults can get epiglottis now to help us understand the path though and why our patients are presenting with these certain signs and symptoms we have to understand what is the epiglottis like what is its role and where is it located okay the epiglottis is a hinged piece of cartilage found at the back of the tongue and here in this picture you can see where the epiglottis is located and it's found on the inside of the thyroid cartilage now what does its role what does this structure do well it closes the entryway to the trachea during swallowing so when a patient is consuming like some type of liquid or some type of food they just shoot it'll go over the tongue and then it'll go down through the throat and our epiglottis which again is found at the back of the tongue will flap downward and it will block that liquid or that food from going down into the trachea into the lungs instead it'll go down through the esophagus and hit the stomach and be digested so we're epiglottis helps with / mini aspiration so whenever we're breathing what's up a glottis doing it's staying open and it's allowing air to flow in and out of the lung so it's a very neat structure however whenever it becomes inflamed it can be a dangerous structure so what do you think can happen if your epiglottis is so implying well we're gonna have airway issues because right here it sets nice width in the airway and it can block air from being able to flow downward because it'll be swollen another issue is swallowing they won't be able to swallow because there's inflammation and with talking so a lot of times that's why with these patients these pediatric patients they're going to complain a pain in their throat because it hurts when the epiglottis is swollen also they may have drooling from where they're not able to swallow down their slava very well and their voice may be muffled or have a soft sound to it because they can't talk properly because the epiglottis and the vocal cords all of that are close together in their anatomy now let's look at the causes of epiglottitis and I would remember this for testing purposes remember the most common bacteria and how it is prevented because as a nurse you want to educate the parents on how to prevent this condition okay so epiglottitis is spread by infectious droplets there's this bacterium these droplets this kid breathes it in goes down to epiglottis and flames it and causes some major problems so the most common type of bacteria to cause epiglottitis is called Hamas influenza type B it can also be caused by other bacteria such as streptococcus pneumoniae now let's talk about this hemolysis influenza type B good thing about it is that it is preventable in that there is a vaccine available for children to take to help prevent this condition which is why over the years we have seen a decrease in children developing epiglottitis based on the Hamas 'less influenza type B bacteria so as a nurse I would be familiar with this vaccine the vaccine that they can get is called the hip vaccine and the child needs about three to four doses of it depending on what brand they're receiving and they will receive it at two months four months six months and 12 to 15 months in between that range now as a side note in my next video I'm going to be going over the pediatric vaccination schedule and give you some mnemonics on how to remember all those vaccines so be sure to check out that video look at the signs and the symptoms that a child can present with with epiglottitis and to help us remember those unique signs and symptoms let's remember the mnemonic add air nurse because they need some air because they have a possible upper airway obstruction so a for abnormal position a lot of times these children will be in what's called the tripod position and this is where they will be setting up positioned forward with their chin in the air which helps open the airway with their mouth open and the tongue protruding just to get that air in and out and that helps them breathe and then d4 dysphagia this is difficulty swallowing we talked about that at the beginning of the lecture and this will lead to the drooling that you may see and then the other D difficulties speaking their voice may be muffled or soft and that's again the close relationship to the epiglottitis and the vocal cords the difficulty swallowing all the drool and everything like that all the information going on and then a for apprehension patient may be irritable have anxiety their oxygen levels can be low they will have agitation apprehensive just because they can't breathe and it's a scary situation and then I for increased temperature their temperature is going to be high it's not going to be a low-grade fever so remember that it's a high fever in this condition and then are for a rapid onset doesn't come on slowly but fast and the patient may even report the patient's family may even report to you you know he or she went to bed last night they were fine and woke up with a really high fever and a sore throat because remember sore throat is one of those things that these children can complain of and then in for nasal flaring and this is again where they're not getting good amounts of air in so their nostrils may flare while they breathe you for using accessory muscles to breathe that's tied again to the obstruction of the airway and they're having to use those extra muscles to get that air in and then our four retractions retractions on the chest and if you see this along with nasal flaring and all that patient needs immediate medical attention and this is where it literally looks like this skin is just stretched so tightly across the chest you can see all the ribs is just sunken in and they're just trying to literally get air in but it's not really happening and then s4 Strider and this is ins matauri Strider and this represents from where that airway is literally being blocked and they cannot get any air in along with the sore throat and here is an example of what Strider can sound like and then II enlarged epiglottis whenever an x-ray is ordered to help diagnose this condition it will be large on the x-ray and in some cases it can be even visible and another thing I want to point out is that compared to other respiratory pediatric conditions a coffee is usually not present with epiglottitis now let's talk about the nursing interventions okay where you gonna do for this patient first thing I wanted to include is something that will probably be on your pediatric exam whenever you're being tested over this condition and it is to never ever insert anything in the patient's mouth to assess it whenever this condition is suspected or died no so no tongue blades so just depress the tongue and look at the throat even though you'll be tempted because they say they have a sore throat but you don't want to do that no oral temperatures and said you need to do other routes like rectally tympanic lis and no throat cultures so if there is something on an exam and it says we're gonna do for this patient do not select these options because that is not the correct answer and why is that why do you not want to do this well it can cause spasms which will completely cut off the patient's airway and cause them major issues the other thing is you want to make sure you have the crash car intubation equipment everything you're going to need at bedside to maintain that airway and that trained staff who can quickly intubate are present because most likely when these kids have this it's severe and they will need to be intubated to maintain that airway other things is that you're never going to leave this patient alone because this airway can just shut off quickly and you need to be there to intervene fast and you're going to be assessing that oxygen status you're going to be maintaining that airway you're going to be looking at the respiratory effort and the rate with the pediatric population it varies in what a normal respiratory rate is I would remember all those variations but if anything is greater than 60 that's not normal for all of them so they have a respiratory rate of 60 or 62 or whatever that is not good another thing listen to those breath sounds checking for that Strider is that present oxygen saturation is it normal their color that tells a lot about them what's their lips look like are they turning cyanotic is their skin looking blue that's not good they're not getting enough oxygen their heart rate long times when patients are very hypoxic that heart rate will shoot up really high they'll become tachycardic do you see any chest retractions nasal flaring agitation all this together that means that our airway is closing off fast and we need to do something also we want to keep the child calm we don't want to do anything that's gonna cause them to cry or become agitated because that can hurt the airway even more so what are some things we can do we can keep the child with the parent or their guardian during treatments like they said on the parents lap allow them to be as close as possible to help keep the child calm don't restrain the child children do not like that scream out cry make it even worse keep the environment calm and allow the child to be in the most comfortable position which is usually going to be that tripod position so it can help them breathe and you want to avoid lying them flat in the supine position because that impedes air flow also you're gonna keep them nothing by mouth we don't want them to eat or drink at this time they will have meds like IV fluids antibiotics to treat bacterial infection that's causing this condition antipyretics to decrease the temperature and then corticosteroids to help decrease the swelling going on at the epiglottis and again how do we prevent most cases of epiglottis through the hip vaccine so be sure to educate the parent about that vaccination okay so that wraps up this lecture on epiglottitis thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Chest_Assessment_Nursing_Heart_Lung_Assessment_HeadtoToe_Exam.txt	this is cereth registered nurse orient home and in this video i'm going to demonstrate how to assess the chest and if you would like to watch a complete nursing head-to-toe assessment you can access this card up here in the corner or in the youtube description below now to do this skill what you'll need to do is you'll need to perform hand hygiene provide privacy to the patient and tell them what you will be doing and you'll need to grab your stethoscope so let's get started we're going to inspect the chest we're looking for any abnormalities like lesions or any wounds anything like that we're also inspecting the patient's effort of breathing is it really labored are they using those accessory muscles to breathe also we're looking at that anterior posterior diameter so turn to the side like that and you're looking for that barrel chest and can will be increased in patients with like COPD they will have what's called the barrel chest and now what we're going to do is we're going to listen to heart sounds and then we're going to listen to lung sounds so first let's auscultate heart sounds and we're going to do this in five locations and they're based on where the valves are located and I like to remember the mnemonic all patients effectively take medicine and the first letter of each word represents the valve except for effectively so a would be a or tick p and patients would be pulmonic effectively would be herbs point and this is just the halfway point between the base of the heart and the apex of the heart and there's no valve location there and then t is for tricuspid and then n is for medicine so again using the diaphragm we're going to listen at the right of the sternal border at the second intercostal space and that's going to be the aortic valve so to find that second intercostal space find the sternal notch go down to the angle of Luis and then just go a little bit to the right and you're in the second intercostal space and this will be the aortic and we're just listening lub-dub lub-dub s1 s2 and s2 the dub is going to be louder in this location then we're going to go a little bit over to where the pulmonic valve is found that's on the left of the sternal border at the second intercostal space so we were just right across Kandace listening to love dub lub dub and s2 dub is going to be louder in this location then we're going to go a little bit down to the third intercostal space and this is herb's point and again and here love dub that there's no specific valve here then we're going to go down to the fourth intercostal space and this is where the tricuspid valve is and love s1 is going to be the loudest at this location then we're going to go to the fifth intercostal space midclavicular line and we're going to listen to the mitral valve and again s1 is going to be loud us hear dub and there's something special about this site this is the point of maximal impulse this is where you're going to listen for the apical pulse so we're gonna set here and we're gonna counter it for one full minute and a normal apical pulse an adult should be 60 to 100 beats per minute and his apical pulse was 63 then we're going to switch over with the Bell of our stethoscope and we're just going to repeat in those locations and we're specifically listening for heart murmur so that's swishing blowing sound so that's what we're going to listen to with that and I did not hear any now let's listen to lung sounds now when you're listening to lung sounds you're listening for abnormal sounds and here are some samples of some abnormal sounds that you may hear crackles wheezes a friction rub or Strider first we're going to listen and tearily and what we're gonna do is we're gonna listen with the diaphragm over stethoscope and we're gonna start at the apex of the lungs and we're gonna always compare sides and just enter way downward and assess all the lobes of that right and left lung so first let's start up here okay and we don't want you take good deep breath in and out so here we go apex okay we're gonna come here sides then we're going to move down to the second intercostal space and this is going to help us assess the right upper lobe and the left upper lobe so another deep breath then we're going to go down to the fourth intercostal space and we're going to assess where our right middle lobe is and our left upper lobe because remember the right lung has three lobes and the left lung has two lobes so let's listen to our left upper lobe a little bit more then we're gonna go mid-axillary at the six six intercostal space and we're gonna listen to the right and left lower lobe so you just want to turn to the side right there okay other side okay now let's listen post eerily again using the diaphragm here the stethoscope you're going to start listening at the apex and work your way down and one thing to keep in mind when you're listening back here you have the scapula and you don't want to listen over those because you won't be able to hear the sound so you're gonna listen in between where the scapula and the spine are so down in these regions right here again we're just going to compare sides and you can do this part at the end if you wanted to whenever you turn your patient over to look at their back side but we're just going to go ahead and do it now so we're gonna start and the apex compared sides then we're going to find c7 which is that vertebral prominence it's the big ball right there you can't miss it and go down to about t3 and you'll be in between the shoulder blades and go a little bit in between the shoulder blades and the spine right in there and you're gonna assess the right and left upper lobes then from t3 to t10 we're just going to inch around and we're going to listen to the right and left lower lobes okay so that is how you assess the chest and don't forget to watch that video on a complete head-to-toe nursing assessment thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Lung_Sounds_Normal_Bronchial_Bronchovesicular_Vesicular_Breath_Respiratory_Sounds.txt	hey everyone this is Sarah register nurse rn.com and in this video I'm going to let you listen to Three normal lung sounds this will be part of a review series of the lungs I'll be doing a video on abnormal lung sounds as well as a lecture and skills demonstration video as part of this series so let's get started and okay thank you so much for watching remember you can go to our channel to find more videos on nursing skills inlex prep and more so please subscribe and share this video with others
Medical_Surgical_Nursing	Transposition_of_the_Great_Arteries_Vessels_Congenital_Heart_Defects_Nursing_NCLEX_Pediatrics.txt	hey everyone it's a earth register nurse Orion dot-com and in this video I'm going to be going over transposition of the great arteries in this video is part of an Inc Lex review series over pediatric nursing and as always after you watch this YouTube video you can access the free quiz that will test you on this condition so let's get started what is this condition which it's sometimes referred to as transposition of the great vessels or it may be called TGA or TGV well this is a congenital heart defect where the aorta and the pulmonary artery are switched hence third transpose which is where the name comes they have swap positions in the heart now a lot of times people get confused whenever they're studying these heart defects is what structures in this condition are switch well let the name of the congenital heart defect help you which is what I've been saying in all these videos we've been doing we're talking about the great arteries and what are really the two great arteries in the heart the helps with blood flow number one the aorta in a normal heart without TGA the aorta will take oxygenated blood that has came from the lungs and shoot it through the body it normally will arise from this left ventricle in this condition it doesn't actually comes off of the right ventricle the other artery is the pulmonary artery that's an easy one because it has the named artery with it and normally what that artery will do is it actually carries an oxygenated blood that has kind of came in from the right side of the heart so it's normally gonna come off of the right ventricle and shoot blood through the lungs which the lungs will oxygenate it and then it'll come back into the left side of the heart they here in this condition those two structures have switched positions now let's talk about some quick facts about this condition and the pathophysiology okay according to the CDC guv one in every three thousand three hundred and thirty babies born in the United States will have this condition now as we're talking about the aorta and the pulmonary artery are switched so what is this going to do it's going to some major problems this is a critical congenital heart defect babies will not survive if they don't have some type of medical intervention to help correct this so what's happening is that we have each side of the heart we have the right side and the left side the right side really deals with our pulmonary circulation because it's going to take blood that's uh knocks ajaita and push it to the lungs so it can become oxygenated but then it's going to flow back once it's oxygenated to the left side so the left side controls our systemic circulation in a normal healthy heart but in a heart that has this condition it's really not going to have any communication so they each have their own circulation without communication so the right side is just gonna do what it does and the left side is gonna do what it does and they're not gonna work together now to truly understand here in a moment we're gonna go over the blood flow in TGA but let's talk about the blood flow in a normal heart here's an illustration of a heart that does not have TGA and notice we have the pulmonary artery it's shown in blue it's coming off the right ventricle and then we have the aorta and it's coming off the left ventricle that's how it should be so everything starts in the right side blood is gonna drain in from the superior and inferior vena cava and it's going to go down to the right atrium and here our blood is exhausted its oxygen ated and it needs to get to the lungs then it's going to travel down to the tricuspid valve which is going to open and allow it to fill inside the right ventricle the right ventricle then is going to squeeze that blood up through the pulmonic valve you can't see it here but it's within that pulmonary artery it's gonna flow up through the pulmonic valve then through the pulmonary artery and into the lungs it's gonna get oxygenated in the lungs the blood and then it's gonna flow back through the pulmonary vein once it goes through the pulmonary vein it's gonna enter into the left atrium then down through the bicuspid also called the mitral valve it's gonna fill inside that left ventricle which is very strong left ventricle is going to squeeze it up through the aortic valve again you cannot see in this picture but it lies within the aorta then that blood is going to go through the aorta and be shot throughout the body and it's gonna be nice and oxygenated and it's gonna feed our tissues and our organs however this process is changed in a cart with TGA because we have our aorta and our pulmonary artery in the wrong location so blood is going to enter in that right side just like how it would in that healthy heart without TGA it's gonna be drained in through the superior and inferior vena cava it's gonna go down into the right atrium now what is specific about this blood it's exhausted it needs some oxygen so that's where it's hoping to go but in a heart with TGA that's not gonna happen so that blood will go from the right atrium down through the tricuspid valve which will open up and fill in the right ventricle then the right ventricle is going to squeeze that blood up through the pulmonic valve but it's gonna go up through the aorta and they order is gonna shoot it up through the body to the organs and the tissues now what does the organs and tissues think of this blood doesn't like it it's not good because it doesn't have oxygen in order for those structures to work they have to have oxygen so the right side as you're seen is doing our systemic circulation which it shouldn't be it should be doing pulmonary circulation okay so it's doing its own thing now over here on the left what it's doing is it's doing pulmonary circulation which the left side should normally be doing systemic circulation so the pulmonary artery is over here and it's pumping blood to the lungs it's going back through the pulmonary vein through the left atrium the bicuspid / mitral valve is opening going down into the left ventricle which is squeezing that nice fresh oxygenated blood up through the aorta valve and then back through the pulmonary artery to the lungs and it just keeps going and going and that nice oxygenated blood never enters into systemic circulation and we need oxygen to survive well how does a baby whenever they're still in the actually survived in utero with this heart condition but once they're born they start having signs and symptoms well it all has to deal with the changes that take place in the heart after birth it's really interesting what goes on once that baby starts breathing on its own and what structures in the heart will actually close and solve so let's quickly talk about those so in the womb the baby's blood is being supplied with oxygen through the placenta but when it's once it's born and starts breathing on its own there's no more placenta the lungs will start providing that oxygen however the heart has been created to allow itself to shift blood away from the lungs that aren't working and it does this through bypasses one bypass that's in a baby's heart who's in utero it's called the foramen ovale and this is a natural hole that is within the atrial septum and it allows blood that's coming into the right side to be shunted or bypass over to the left side because remember in a normal healthy heart the goal of the right side is to get it to the lungs while lungs aren't working so the blood will go through that frame and ovalle into the left side of me pumped through systemic circulation another structure that will help is called the ductus arteriosus and this is a little vessel that connects the aorta and the pulmonary artery so it'll allow blood to bypass that right side of the heart go to the left side and I want you to remember those two structures because after a baby is born starts breathing on its own there's pressure changes in the heart that will cause those especially the framin ovalle to seal off and the ductus arteriosus will in a sense shrivel up and be sealed off as well but in a child who has TGA we actually want those structures to stay open until surgery be performed on this child because these structures will actually allow mixing of blood so once the baby's born if those structures can stay open which we're going to talk about that and the nursing interventions the medical treatment a medication can be given to keep this ductus arteriosus open or a procedure can be done to actually enlarge the frame in ovalle and it will allow um arterial and venous blood to mix so the baby is getting some type of oxygenated blood before they have surgery where they can actually switch these vessels back now babies who do have transposition of the great arteries they usually do have some type of other congenital heart defect present in the heart as well which actually can be beneficial for that baby until surgery is performed to switch the aorta and the pulmonary arteries position so let me go over those three other defects they may have one type is called a VSD a ventricular septal defect and what this is is it's a hole in the ventricular septum so right here you have a nice hole now when you're looking at that you should be thinking hey that is actually beneficial for that baby it will allow a little bit of mixing of blood so that nice fresh oxygenated blood can flow over here a little bit of it to the right ventricle and then be shot up through the aorta to the body now some other defects that may be present which can be really beneficial the other type is an ASC which is an atrial septal defect and it's a hole in between the two atrium and what it does just like the VSD it will allow blood to mix and sometimes they can do a procedure to actually enlarge that ASD until surgery can be performed and another type of defect most commonly in this condition is a PDA which is a patent ductus arteriosus and that's where that natural structure that should normally close and seal off doesn't seal off and it stays open and like I said before we can give them medicine prostaglandin to actually keep that vessel open so we can have that blood flowing from that pulmonary artery into the aorta so we have that fresh oxygenated blood and it can go to the body now let's talk about signs and symptoms along with nursing interventions and treatments for this condition and what we're going to do is we're gonna take the main concepts you need to know for your exams we're gonna mesh it into one pneumonic because when you are studying for your pediatric exams these congenital heart defects you need to take away the main concepts about those defects like tetralogy of SLO you want to know about Tet spells that need a chest position squatting because that's probably going to be on the exam about that condition and for this condition you want to take away that telltale sign and symptom that that baby may be presenting with after birth that they probably have this condition along with interventions like that infusion to keep the ductus arteriosus open and the procedures to help correct this condition so to help us remember all that information let's remember the word swap because that is what's going on our aorta and our pulmonary artery have swapped positions and it's causing us a lot of problems so the first part of our mnemonic is s and it's going to deal with signs and symptoms and it's forced severe sino since that is that telltale sign that whenever the baby is born that they may have transposition of the great arteries because it's cyanosis that's not going to resolve and some babies can be severely blue and it can actually get worse and what will happen is that you can have various degrees of cyanosis is depending on if that baby has other heart defects present because remember we talked about they can have a VSD and a SC or a PDA and if those are present in the heart they are allowing some blood flow to mix and shoot that oxygenated blood through the body so they could be a little cyanotic then maybe a child who does not have any other defect so keep that Imani can vary and it will actually that cyanosis if they're not aware that this child has TGA a lot of times they know through the fetal ultrasound that was conducted there in prenatal visits but sometimes they don't but the child will be born the baby and it'll have severe cyanosis that will maybe it's a little bit mild it'll actually start getting worse and worse because the reason is is those structures that are naturally in the heart remember in utero that they needed to push the blood over to the left side of heart they're naturally starting to close off so that ductus arteriosus and that framin ovalle so the once you close those off you're gonna have really no communication at all between that right and left side and they're gonna have more cyanosis so keep that in mind okay how will cyanosis present why are we having cyanosis well first of all cyanosis is where it's a bluish tint color to the skin and it's because of low Oh two levels the body is not getting what it needs and it's not gonna survive that child is not gonna survive very long without medical treatment so you can see an increase heart rate increased respiratory rate that's just the body's way of trying to compensate the heart's trying to beat faster because like hey if I work harder I can push more oxygen but it's not aware that there's no connection between these two so it's never really going to do that and the respiratory rate is increasing so they can breathe in more oxygen to hopefully increase that gas exchange but again that can't occur because left side is doing its own thing and it's not going to get oxygen to the body in addition the baby can have poor feeding because of the low oxygen they're not going to want to feed eventually can lead into heart failure they'll have cool extremities decreased growth rate but a lot of times this is already detected before they start entering into the low growth rate things like that okay w-4 watch this is where the nurses rolled what you're going to be doing is you want to watch that heart rate watch that rhythm looking at the oxygen saturation levels you're going to be giving oxygen and preparing them for intervention because like I point out being this lecture this is a critical congenital heart defect and baby needs treatment fast which takes us to the last part of our mnemonic and it's a this is a medication it's called our process Adele in another form of that medication another word for it is prostaglandin e is that medication started as an infusion and it will keep a connection between the pulmonary artery and the aorta so it'll keep the ductus arteriosus open and allow blood that is nice and oxygenated to cross over into the aorta and go through the body so that can buy us some time until surgery can be performed so they're started on that now P this is for procedures to correct and this includes a balloon atrial septostomy and what this is is it is a heart cath a do with your heart house so they go through a vessel and they will actually take a catheter insert it within this atrial septum usually front into the framin ovalle and they will take a balloon blow up the balloon and pull it out and that will enlarge that framing ovalle because we won that why do we want that because we want that blood to be mixing to come over here from the left atrium over here into the right atrium and it'll be nice and oxygenated and go up through the aorta so again that will buy us some time it's temporary they can also insert that balloon into if an ASD was already present in within that atrial septum they can do that enlarge that now after that is performed they'll be on a prostitue have the balloon procedure to allow that mixing blood again a sinus time now another procedure they can do that is permanent I will actually treat this condition it's called an arterial switch procedure and what it's going to do is just like the name says is it's going to take the pulmonary artery put it back over here on the right side take the Horta and put it back over here on the left side along with the coronary arteries that come off each of those arteries and what that will do it'll help correct this condition now this is usually performed within the first few weeks of life once that baby's stable they just went through traumatic birth and all these other things so they let them recover just a little bit get the stress off of them and then perform that procedure okay so that wraps up this review of a transposition of the great arteries thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Angiotensin_II_Receptor_Blockers_ARBs_Nursing_NCLEX_Pharmacology_Cardiovascular.txt	hey everyone its erik register nurse RN comm and today we're gonna talk about angiotensin ii receptor blockers also called arms and as always after you get done watching this youtube video you can access the free quiz that will test you on this medication so let's get started as we've been studying these medications in this pharmacology series we have been remembering the mnemonic nurse this helps us remember those important concepts we need to know for exams so in again is for name specifically the family name of the drug because this really tells us how this medication works then you for use what's it used to treat are four responsibilities of the nurse with our role as four sod effects and then II for education for the patient those important teaching points we need to point out to the patient who will be taking this medication so first let's start out talking about the name we're dealing with angiotensin ii receptor blockers and these drugs are also referred to as arms now one thing to make your job easier is that you want to remember that these drugs is specifically the generic name and with the word certain at the end SAR ta n so when you're looking at a patient's medication list you'll be able to recognize it a lot easier so examples of arms would be like losartan valsartan almost Sartain just to name a few now let's talk about how these ARBs work and let the name the family name of any drug you're studying always help you because it's going to give you clues of how it works and if you can connect which system it's manipulating it makes it so much easier to understand side-effects and really your responsibilities as a nurse and what you teach the patient so we're talking about angiotensin ii receptor blockers so that's telling us that this drug is going to block the receptors that deal with angiotensin ii so since we're dealing with angiotensin ii what system are we're going to be dealing with the wrath the renin-angiotensin-aldosterone system and this system deals with managing our blood pressure especially when it drops too low so ARBs they affect the end result of wrath what's the in result of rass well we talked about in a review over the RAF system that its whole goal is to activate angiotensin 2 to get it on board so we can have vasoconstriction of vessels and help increase blood volume there like the release of aldosterone so that system increases blood pressure when we need it to because blood pressure has dropped so low that the patient is when it be perfused very well so they need that system now what an art is gonna do it's going to block that from really happening because the blood pressure needs to be decrease so how arms work is that they block the activation of certain receptor sites that would accept that angiotensin ii once it's activated by the system and we're specifically talking about receptor sites called angiotensin ii receptor type 1 and these type 1 receptors are found mainly in the vessels of smooth muscle and the adrenal glands so if we can block these type ones from accepting this angiotensin 2 what are we going to do well instead of vaso constricting we're going to vasodilate when we vasodilate we decrease assuming vascular resistance and decrease the blood pressure well one thing that angiotensin 2 normally does is it triggers the release of aldosterone which is going to cause the kidneys to conserve sodium and water that excrete potassium in hopes of increasing the blood volume so we increased blood volume we increase blood pressure well that's not gonna happen if we block this receptor site because that receptor site is really what deals with that so in a sense we're gonna decrease the blood volume because we're going to excrete sodium in water and keep some potassium now let's do a quick review over wrasse and throw in an angiotensin ii receptor blocker and see how the system changes and if you want a more in-depth look at the RAF's i have a video where i go over it in detail but right here i'm just going to quickly review it so the whole point of wrasse is to manage ur blood pressure especially Everett drops it need sit back up so the blood pressure drops this will cause the kidneys to release renin whenever renan's present in the circulation and activates a substance in the liver called angiotensinogen angiotensinogen is going to turn into angiotensin 1 now we need angiotensin 1 to get to angiotensin 2 and in order to do that we need a special substance called ace ace stands for angiotensin converting enzyme and then that turns it into angiotensin 2 so we're there this is the goal of wrasses the yet angiotensin 2 on board now we have angiotensin 2 floating in the system it needs to attach to some receptor sites so we can get the job done you have angiotensin 2 receptors type 1 and you also have angiotensin 2 receptor type 2 but we're not dealing with these type 2 so don't even think about those for ARBs because ARBs work on the angiotensin ii receptor type one side so it's what we care about for this lecture so angiotensin 2 goes and binds with these receptor sites the type 1 and whenever that occurs you're going to get vasoconstriction of the vessels which is going to increase systemic vascular resistance and increase blood pressure and it's also going to trigger the adrenal cortex to release aldosterone and when aldosterone is present it's going to cause the kidneys to keep sodium and water but will excrete potassium so will increase blood volume and remember it's that same concept if you increase with the water hose you increase the amount of water that's going through that water hose and constrict that hose down that's majorly going to increase the pressure of the water coming out of the hose same concept really applies to the vessels in our body so that is what it's doing so now let's throw in an angiotensin ii receptor blocker what's it going to do what's it going to effect well we have these angiotensin ii receptor type ones hanging out and they're ready to receive this Jennsen - but this patient has taken and our well this connection is not going to happen this angiotensin ii is not going to be able to go to these type 1 receptors so we don't have that occurring we have blocked that so the result is going to be we get vasodilation of the vessels whenever that occurs we're going to decrease - semuc vascular resistance we're going to decrease blood pressure it's going to make it a lot easier for that heart to pump blood through the body because it's not hitting that resistance so it's gonna decrease afterload also you're gonna get a decrease in preload and we're going to excrete sodium and water instead of keeping it but we can keep some potassium so it has like the opposite effects so some things you need to watch out both with ACE inhibitors and ARBs is that increasing potassium level so hyperkalemia so we see that ARBs effect rafts just like ACE inhibitors but they do in a little bit different way ACE inhibitors and said of blocking these receptor sites they inhibit ACE hence why we call them ACE inhibitors so they prevent this ace from converting angiotensin one to angiotensin 2 now remember whenever we talked about our ACE inhibitors we talked about that some patients not all but some patients can get this persistent dry cough and they just can't take the medication so a lot of physicians will put them on an ARB instead of an ACE inhibitor now why do they get a dry persistent cough with ace inhibitors but not with ARBs well a so let's talk about that substance ace what it does is it will inactivate a substance called Brady Kannan Brady Conan is like an inflammatory substance so it activates it by breaking it down normally so you're breaking down Brady Khan and you don't have all this Brady Khan and hanging out causing issues but if we throw in an ACE inhibitor that inhibits this ACE you no longer have the enact Batian of Brady Kannan with it being broke down so now you'll have increased levels of Brady Conant which in some patients can cause that dry persistent call so if we switch them to an armed arms don't inhibit ace so this ace phenomenon will occur you'll have angiotensin 1 to angiotensin 2 so we're not going to be increasing our ad können levels because ace is going to be able to activate the Brady können by breaking it down so that is why a dry persistent coffee is lot less likely with an ARB now I'll talk about what ARBs are used for well we've already established the fact that args help lower the blood pressure so people who struggle with high blood pressure they have hypertension this medication can be prescribed along with the patient also making lifestyle changes because these blood pressure medicines are not a cure they help bring the blood pressure down but the patient needs to if they smoke to quit smoking exercise diet etc another thing that ARBs can treat is in these type 2 diabetic patients who have diabetic nephropathy and this is a fancy word of saying they have kidney disease related to diabetes and how an arm will work is that it will slow down the progression of the disease now ACE inhibitors also do this as well so keep that in mind they both can help with diabetic nephropathy in type 2 diabetics and how it does this is that herbs lower the blood pressure well patients who have kidney disease they are able to really filter the protein like they should so protein will leak into the urine and the higher the blood pressure the more protein that's gonna leak into the urine which can cause even more problems so if we throw an ARB on ACE inhibitor it will lower the blood pressure which will decrease the amount of protein in the urine which is going to over time slow down the progression of this kidney disease another condition that cards are used for is heart failure and remember with heart failure the heart is so weak that it can't really pump blood out of it so cardiac output diminishes and blood can even backflow into the lungs leading to pulmonary edema and causing swelling and back flowing and blood throughout the body so how an arm can help once you throw that on board is that remember an arm vaso dilates so when we vasodilator CIL's that decreases systemic vascular resistance and this is really the resistance that this heart must pumping it to get blood out of it so if we decrease the resistance we're going to make it a lot easier for the heart to squeeze blood out of it so we're decreasing the afterload so afterload again was the male of resistance that the ventricles must overcome to pop open those valves so blood can leave it in addition the way that arms work and how it manipulates the sodium and the water with the kidneys is that we can decrease preload which is the male of blood that fills in that ventricle at the end of diastole so if we can decrease preload afterload make it a lot easier on the heart to pump in a patient who has heart failure now let's talk about the responsibilities of the nurse so we're giving our patient and ARB and ARBs lower the blood pressure so a big thing what we want to do is we want to assess that blood pressure routinely along with their pulse and what we're watching out for is hypotension where that systolic that top number is getting less than 90 and some patients are going to have a more increased risk of developing hypotension especially if they're taking diuretics along with taking an ARB because if we're diary seing them where they're urinating out their extra fluid volume we can bottom out their blood volume which can cause even more hypotension in addition let's say that they're started on some new cardiac meds with their arm you really want to monitor them closely because we could drop their blood pressure too low or if the patient is dehydrated they already have low fluid volume and how this medication works remember with the wrasse it affects how the kidneys deal with sodium water so you also want to watch out for this hypotension next you want to monitor their potassium levels because remember we are at the end with the aldosterone what's happening is we're really reversing how aldosterone works so the kidneys are going to excrete sodium and water but it's going to keep potassium so in some patients they're batao seen levels can become elevated and you really want to watch that in those patients who have the diabetic nephropathy their kidney function is already compromised so closely monitor that potassium level a normal level is 3 point 5 to 5 milli equivalents per liter another thing to monitor for is renal failure and you may be thinking okay how can this cause renal failure since you talked about in the treatment part what it's used for it can actually help slow down the progression of kidney disease and type 2 diabetics well renal failure can occur in some patients here at risk and patients who are at risk are patients who have severe heart failure because remember what I talked about with heart failure their cardiac output isn't that great so they really depend on rafts the renin-angiotensin-aldosterone system to help them maintain their cardiac output so they're very dependent on that and if we go and throw this medication on them it can lead to renal failure so keep that in mind and what are some signs and symptoms that they may be having renal failure well you want to look at their kidney function with their bu in and creatinine it's increasing a normal bu n is about 5 to 20 a normal creatinine is 0.6 1.2 milligrams per deciliter in addition you can look at their urinary output how much have they put out of urine on your ship if you wanted at least 30 CC's per hour and are they retaining fluid where those kidneys aren't able to excrete the water because they're failing so look at their daily weights and just look on their body are they retaining extra fluid in their tissues also monitor liver enzymes especially patients who are at risk with for liver disease this drug can actually increase the level so looking at and lastly I wanted to mention this angioedema this is very rare to occur in a patient who is taking an ARB compared to an ACE inhibitor so it's not likely to occur in a patient taking are but it can it has occurred in some patients so I just wanted you to be aware of it and this is where you get swelling and those deep tissues and it can be swelling of the face the lips the tongue and it can cause them difficulty breathing so always look at that with your patient who is taking this now let's wrap up this lecture and let's talk about some side effects and education pieces for the patient who's taken an art so some quick side effects would be you want to tell the patient that they could experience dizziness because you know we're altering the blood pressure so when they change positions or stand up they need to do this slowly they want to be on the lookout for hypotension that blood pressure dropping too low high potassium level and GI upset now education pieces which actually tie in with some of those signs and symptoms we want to teach the patient to regularly monitor their blood pressure at home show them how to do this where they can buy a device the importance of recording those numbers and notifying the physician of anything abnormal what's abnormal versus normal so educate them the importance on that also to avoid salt substitutes with potassium in them or consuming a diet really rich in potassium especially if they're taking diuretics that conserve or spare potassium like Spyro no act alone and because this can increase your potassium levels really high and ARBs already have that effect where they can increase potassium so let them know that next who never abruptly just quit taking the medication they just don't want to take it anymore or they have literally just forgot for a long time to take their medication because ARBs and aces they have this thing that they can cause called rebound hypertension where the blood pressure can just get so high and it's really hard to control I have this and patients who haven't been compliant with their medications that it can occur so tell them about the risk the best way to prevent it is to never just abruptly quit taking the medication also missing a dose so they missed a dose what are they supposed to do because they're at risk for this well if they miss the dose if they remember it the same day go ahead and take the dose though they don't remember it to the next day don't take that misto so they miss on the previous day but just take the scheduled dose for that day and the importance of lifestyle changes these hyper anti hypertensive medications do not cure their hypertension they need to if they smoke to quit smoking they need to follow a healthy diet and exercise which can help with these medications okay so that wraps up this review / angiotensin 2 receptor blockers thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Incentive_Spirometry_Spirometer_Demonstration_Instruction_Incentive_Spirometer_Procedure.txt	okay first let's go over some wrong ways to use in some spirometer a lot of times if patients haven't been properly they will do what they think you're supposed to do naturally with it by blowing into the device rather than actually inhaling from the device another wrong way patients may try to use in sims from--it ER is by quickly inhaling and exhaling off the device like this now let's look at the right way to use incentive spirometer okay first what you want to do is you want to set the goal for the patient with the yellow marker so they know where they need to get whenever using this instead of spirometer then you're going to have the patient set up and exhale completely then have them seal their mouth around the mouthpiece tightly and they will inhale slowly and deeply making sure to keep the yellow indicator on the side within normal range they don't want that little yellow piece to go too high or too low and as they do this the piston will rise up and have the patient keep inhaling as deep as possible until they can't inhale anymore and then they'll need to hold the breath for six seconds and then exhale slowly and allow the piston to fall before repeating again and record the amount that they were able to get on incentive spirometer and they will perform this at least ten times every hour to wile away so this is what it looks like in action
Medical_Surgical_Nursing	ABGs_Made_Easy_for_Nurses_w_Tic_Tac_Toe_Method_for_Arterial_Blood_Gas_Interpretation.txt	hey everyone this is sarah with register nurse RN comm and today i want to be talking to you about the tic-tac-toe method and how to use it when solving arterial blood gas problems in nursing school you'll be required to learn arterial blood gas values and how to interpret that based on those values for instance is a patient having respiratory alkalosis or they have a metabolic alkalosis and you have to be able to differentiate between those two and also you'll have to know whether the patient's trying to compensate or if they're partially compensated so in nursing school i remember having to solve these problems and these problems gave me a lot of difficulty but then someone showed me how to use the tic-tac-toe method so in this video i want to show you what the tic-tac-toe methods about how they actually set up a problem with it and talk to you a little bit about pH levels H c3o levels and things like that in the next video video we're actually going to work these ABG problems so be sure to check out that next video and work the videos along with me and then after that check out the free quiz we have on our website register nurse orange comm and test your knowledge on ABG's along with other in clicks quizzes and personality quizzes that we have so first let's talk about the tic-tac-toe method and how to use it with ABG's first the very first thing you want to learn before you start solving ADG problems is you need to learn the normal values because in a problem you'll be given the pH level you'll be given the pco2 level and you'll be giving given the hco3 level so you need to know what the normal ranges are for people so here are the normal ranges I would write this down pH level the normal is 7.35 to 7.45 anything over seven point four five is a base another word for base is alkalotic which is alkalosis anything less than seven point three five is an acid so it'd be acidotic I'm going to skip two hco3 because it's the same um 22 to 26 is your normal range for that and that represents metabolic so anything Oh 26 would be basic it would be alkalotic just like with the pH and anything less than 22 would be an acid so be alcoholic so they would be having a metabolic problem and they would be alcoholic I mean acidotic okay for the pco2 this represents your respiratory level and it's the opposite for what the pH and the hco3 are this a lot of times throws people off so just remember pco2 is opposite in a represent your respiratory so for instance anything less than 35 is basic so it's alkalotic anything over 45 is acidotic so it's an acid so you'll want to memorize these values because this is your baseline for whenever you're comparing your problem that you're given to how to set up the problem so I would write that down like I said before you actually start working your problems next let's go over the actual setting up for the tic-tac-toe method as you see this looks like a basic little tic-tac-toe you know whenever you used to play with your friends you would set up the tic-tac-toe like that and someone would be OHS another person would be exes and you would play like this and oh you got chick tac toe we're not really using the X's and O's we're going to throw that concept out but we are keeping the concept of lining something up with threes and in a row of threes so for a grid for the tic-tac-toe grid we've automatically going to put acid normal base and this is easy how it set up anything for the pH or the hco3 and remember anything that's less than the normal value is an acid and anything greater than that value is a base except for respiratory remember paco2 is the opposite so let's just work a problem so you can see exactly what I'm talking about okay in this problem the patient's pH is seven point two three there paco2 which represents respiratory is 50 and their hco3 is 30 and remember hco3 represents metabolic okay after you've set up your tic-tac-toe you wrote acid normal and base up at the top you're going to look at your ph it's 7.3 so remember normal pH is 7.35 to 7.45 so it's seven point two three so that would make it an acid so under acid we're going to write pH okay now we're going to look at paco2 and remember that represents respiratory it's fifty and looking at our normal paco2 if normals are thirty-five to forty five so since it's fifty remember it's the opposite for a respiratory it is an ass it's going to be an acid not a base it's an acid so our paco2 is f it ik so under that we're going to put paco2 and always solve your problem before you start doing your crosses because we need to know how our metabolic fits into this because this is going to tell us if we're compensating or not so always put all your values in before you cross down in your three letters so the hco3 is 30 normal hco3 is 22 to 26 so it's 30 so because it's greater than 26 its basic so there alkalotic so under base we're going to write HC 0 3 now we already have our tic-tac-toe and looking at this you know that this patient because we have three in a row this is where you're going to interpret if it's respiratory or metabolic paco2 what does it represent respiratory so we know that we have a respiratory issue now for instance let me just throw this out here if these two values were switched say hco3 was over here and paco2 was under base because we got the cross underneath here that would be a metabolic problem instead of a respiratory problem so we have respiratory problem now we have to decide are we alkalotic or acidotic very easy underneath on our grid we know it's an acid we have respiratory acidosis next thing we have to determine is this patient compensating or are they uncompensated they are partially compensated and this is how I know that because the body is trying to compensate the metabolic value is thrown off so it's not normal so they're partially compensating now if her hco3 was normal say it was 25 because remember 22 to 26 is normal this 25 would be under the normal range the body's not doing anything to try to help balance it out out because your body's always trying to do homeostasis and do a balancing act because if it was under normal it would be and it would be uncompensated but because the body's trying to correct itself and throw the metabolic rate off its partially compensated so your answer to that question would be respiratory acidosis partially compensated now in my next video on how to actually work these problems we get a little bit more in depth we talk about all the disorders and if they're compensated uncompensated using the tic-tac-toe method it's very easy and will help you on NCLEX help you on how to see your eighty eyes on how to just solve these problems so thank you so much for watching I hope you liked this video if you did please give it a thumbs up and be sure to visit registered nurse or en comm we have a lot of free in clicks and quizzes personality quizzes abd quizzes care plans everything you need to help you in nursing school and after nursing school so thank you so much for watching and have a great day
Medical_Surgical_Nursing	Congestive_Heart_Failure_CHF_Pathophysiology_Nursing_Treatment_Symptoms_Heart_Failure_Part_1.txt	hey everyone it's Sarah register nurse rn.com and in this video I'm going to be going over an inlex review of heart failure this video is part of an inlex series over the cardiovascular system and in this specific video it's going to be part one I'm going to be covering the pathophysiology of heart failure the causes the signs and symptoms the different types what triggers it how it's diagnosed and things like that and I'm going to be giving you some clever pneumonics on how to remember this material for inlex and your nursing lecture exams and in the next video which will be part two I want to be covering specifically the nursing interventions and the pharmacological aspect of heart failure which is another important part that inlex will test you on and then after you watch this video be sure to go to my website register nurse rn.com and take the free inlex quiz that will test you on this material and a card should be popping up so you can access that so let's get started Ed first let's start out talking about what is heart failure heart failure is where the heart is too weak to pump efficiently and because it can't pump efficiently what happens it can't provide the proper cardiac output that your body needs to maintain its metabolic needs so what's really happening with heart failure is that that heart muscle has either messed up with how it can contract and pump that blood up through those valves out through your heart out through the other side of the heart or it's become too stiff and we're mainly talking about the ventricles of the heart we're going to be talking about mainly our right ventricle and our left ventricle and I'll go over that in depth whenever we cover the different types now what are the causes of heart failure to help you remember this remember the pneumonic failure we're talking about heart failure so it's easy to remember failure whenever we're trying to think about what causes this condition so first F heart faulty heart valves what does this mean well you have four different valves in your heart you have your tricuspid and your bicuspid valve also called your mital valve which are your avov ventricular Valves and then you have your pulmonic valve and your adoric valve which are your semi lunar valves now your tricuspid Valves and your tricuspid valve and your bicuspid valve can becom stenos or it can become regurgitated and whenever it becomes stenos it's too narrow and whenever it becomes regurgitated it means it leaks and this can lead to heart failure I have seen this as a nurse in the clinical study patient comes in they have messed up heart valves maybe from endocarditis and they need their heart valves replaced because whenever those heart valves are messed up it causes your heart to overwork and they enter into heart failure but whenever they get those valves replaced it fixes the problem and they're much better okay next a arhythmia um arhythmia like atrial fibrillation or tacac cardia can send you into heart failure and this is where for instance let's talk about atrial fibrillation atrial fibrillation is where your atriums are quivering they're not pumping efficiently so blood is like pulling in there and this can send a patient into heart failure a lot of times I have seen patients come in they didn't even know they were an aib and they had the sign of heart failure and also tacac cardia this is where you have a really fast heart rate patient may not know it it's elevator for a long time that puts a lot of strain on that heart makes that muscle weak and they enter into heart failure all right infarction such as mardial infarction and you will get this with coronary artery disease mardial infarction heart attack what happens is that they have a plaque build up in one of those arteries that feeds that heart muscle all that that nutrients it blocks the all that nutrients go into that heart muscle that heart muscle becomes es schic and dies and it becomes weak so um for instance like left ventricle this happens a lot whenever people get left-sided heart failure the arteries that feed that ventricle become blocked that muscle dies sends them into heart failure L for lineage um this is genetic family history Mom Dad grandmother had it so you're more at risk for developing it congenital you're born with it family history so that can run in families next you uncontrolled hypertension we talked about in the inle review video of hypertension hypertension is a number one it's a silent killer because patients don't know that they have it they don't have signs and symptoms until it's too late till it's affected the organs and what happens is whenever you have such that high pressure beating on that heart it can cause those ventricles to become stiffen so whenever they become stiffen they can that those ventricles will not fill properly with blood and you can enter into heart failure are recreational drug use such as cocaine or alcohol abuse patients who um do cocaine or have alcohol abuse are more susceptible for developing heart failure e evaders such as viruses infections that get in and attack the heart have seen this again a patient will come in um they're relatively healthy some of them are young but they've got some type of virus or infection that has attacked that heart muscle made it weak and now they are in heart failure now let's look at the different types of heart failure you can have you can have left or right-sided or both now to help you understand the different types of heart failure because this is a big thing the inux likes to ask and especially your nursing lecture exams because you need to know those different signs and symptoms that a patient with left-sided heart failure may be presenting with that someone with right-sided May so you need to know the different ones and let's look at the blood flow how the blood flow FL flows through the heart and the pathophysiology of it okay first let's get familiar with which side of the heart is which because that is very important when determining if you're in left-sided or right-sided heart failure so this right here is the right side of the heart where the blue unoxygenated blood is draining down into the heart this side is the left side of the heart where the nice rich red oxygenated blood it's went through the lungs it's going to be pumped up through the body and we're specifically remember looking at these ventricles because that's where our problem is with heart failure they're either too stiff or they're not Contracting properly so first let's look at how the blood normally flows through the heart and then we'll go through how it can back up and cause all those signs and symptoms okay so you have your Superior Vena and you have your inferior vena and what these do is they drain all that blood that your body has used to become re oxygenated it wants to send it through the lung lungs that's the goal of your right side to get that blood to the lungs to become oxygenated so it can go back to your body so it does that now note this is important later in your inferior venne it's also connected through those htic veins to the liver so whenever you start getting congestion in your right side of the heart the liver is going to be affected which we'll go over here in a second so it drains down into your right atrium then it flows down through the tricuspid valve then to your right ventricle the right ventricle squeezes it up through your pulmonic valve up through your pulmonary artery and out through your lungs and then it goes through gas exchange through those little sacks it becomes replenished then it's not nice and oxygenated and it shoots through the heart down through the left atrium down through the bicuspid valve which is also called your mital valve then down into that left ventricle and remember the left ventricle has the most pumping power of all four chambers because it has to in order to shoot that blood up through the body so that left ventricle will squeeze that blood shoot it up through your aortic valve up through your aorta and then through your whole body and then the cycle starts all over again now with heart failure like I've said there's either a contraction problem with these ventricles they're not Contracting properly maybe the muscles die become ischemic or they're not feeling properly and this could be due to um uncontrolled hypertension where that ventricle has just become too stiff first let's talk about left-sided heart failure so what's happening in left-sided heart failure why do you get pulmonary symptoms well with left-sided heart failure The ventricle either it's too stiff or it's not Contracting properly and you can have diastolic or systolic left ventrical dysfunction which we'll go over here in a second and what happens is that the blood will back flow up through your Atrium and up into your lungs so the patient will start presenting with pulmonary symptoms because that blood is back back flowing into there so they may um have crackles U shortness of breath uh oropa where they can't even lay down and sleep so they're going to get pulmonary signs and symptoms with left-sided heart failure now with right sided as a side note remember this Left sided because it's over here it can increase the pressure in the right ventricle because of all this back flowing of blood up through here and it can actually cause a patient to go into right um sighted heart failure as well so remember that so you can have both going on at the same times but sometime you can sometimes you can just have right-sided heart failure and whenever that happens on your right side watch where the blood would backf flow where you have too much blood back flowing because your ventricles aren't pumping out properly where is that blood going to go it's going to go up into those Superior and inferior venas out through the peripheral areas so you're going to be seen um peripheral edema um excessive weight gain um they may have increased abdominal girth in their belly acies and again back to the hepatic veins because all this blood is going to congest into the inferior vena it's going to cause hepatomegaly and cause your liver to become enlarged and then you'll get the large abdomen and just really uncomfortable so that is why you would see the certain signs and symptoms with each side so again just to recap your left side you are going to see pulmonary issues because it's back flowing into your lungs on the right side you're going to see peripheral edema and issues like that okay as I was talking about before you can have left-sided systolic dysfunction or you can have left-sided diastolic dysfunction and we're talking about the left side of the heart the left ventricle so let's go over systolic and you can also see it as left ventricular systolic dysfunction okay now let's think about to what systolic is we talked about this in the other video where we went in depth about blood flow what is syy systolic is the squeezing phase of your heart remember s systolic squeezing so it's the Contracting phase of your heart so there is an issue with the left ventricle Contracting and squeezing that blood up through the heart now with this patients are going to have a low ejection fraction usually less than 40% a less than 40% ejection fraction is a diagnosis for heart failure and whenever that happens the heart cannot squeeze that nice fresh oxygenated blood up through all those um tissues everything that needs it those vital organs so they don't get it and it backs up into the lungs as you just seen now what is ejection fraction what does it mean it's a calculation tool that is used to D agnos the Contracting ability of your left ventricle so it's the amount of blood that fills inside the left ventricle that is actually being contracted out of that ventricle now for instance say that you seen that a patient had an echo cardiogram because that's one of the tools used to diagnose ejection fraction and it said an EF of 38% what does that mean that means that only 38% of the blood that filled inside the left ventricle is being pumped out that is bad so they are in heart failure now a normal EF is an ejection fraction of greater than 50% that's a normal healthy heart and um like I said it can be diagnosed with an echocardiogram remember this this is really important not only for inlex but whenever you work as a nurse whenever you're reading test results so an echocardiogram can give you an ejection fraction a heart catherization can give you an ejection fraction and a nuclear stress test can as well give you that now let's look at left-sided diastolic dysfunction we just looked at systolic and that was the squeezing part of the heart there was an issue with the left ventricle being able to squeeze properly with diastolic dysfunction it is an issue with the ventricle being able to F properly because the diastolic diaso is the filling SL resting phase of the heart so The ventricle this left ventricle has probably became too stiff to fill with blood so not all the blood that's supposed to get in there gets in there but it contracts normally so it gets just a little bit of blood and it contracts beautifully so because it's not an issue with contraction it's an issue with it actually feeling your ejection fraction is usually going to be normal on these patients so they'll go over an echocardiogram and their EF comes back normal because there's not an issue with contraction just feeling now with your left-sided heart failure just because of where that left ventricle is you are going to have pulmonary symptoms with your left-sided heart failures now let's look at right-sided the other type of heart failure right-sided heart failure is not as common as left-sided heart failure funny enough left-sided heart failure is one of the main causes of why people would enter into to right-sided heart failure along with it's also caused by a pulmonary heart disease coal called core pulmonol as a complication of the patient either has pulmonary hypertension or COPD so that can be other causes of it now just the recap with the right side remember on the right ventricle just where it's located and where the anatomy is and everything that's going to be affected it just Mak sense if that if this ventricle is not Contracting properly blood is back flowing it's going to go peripherally so you're going to see peripheral signs and symptoms with this with Left sided you're going to see pulmonary so now let's look at the signs and symptoms side by side and let me give you some clever pneumonics on how to remember them okay for rided heart failure let's remember the pneumonic swelling and why swelling because remember these patients are going to have peripheral swelling everywhere so it's just an easy pneumonic to help you remember the typical signs and symptoms and then for left ided heart failure we're going to remember the word drowning because remember our lungs the pulmonary system is majorly involved in this and they are literally drowning in their own fluid so let's remember the word drowning okay so let's start with right sided for the s in swelling we're going to remember swelling of the hands the legs the liver they're going to have a lot of congestion lot of fluid going on with that W weight gain this is going to be present with both of them but especially with right-sided heart failure um you want to tell the patients to monitor their weights daily any fluctuation between 2 to three pounds in one day or 5 lounds in a week is something to be alarmed about because they could be going into heart failure exacerbation edema these patients not only will have swelling but they could have pitting edema in their legs and um this is where you can press on the tibia of the leg and it will actually pit in I have seen three four plus pitting edema it's very very interesting how much swelling these patients can have L for large neck veins this is um the jugular veins if you have a video on how to do this but if you turn the patient's neck to the right side they're setting up you or laying back a little bit you can actually see um jugular Venus distension L for lethargic these patients are going to be extremely tired extremely they can't tolerate it's hard for them to even get up from the bed to the bedside chair they get very winded because of all this extra fluid they're carrying and their heart is just so weak it can't pump efficiently to get that blood going everywhere I for irregular heart rate a lot of times whenever patients come in with congestive heart failure they can flip into um a regular heart rate like atrial fibrillation another thing is no Noca the n and this is very interesting this is where they have all of a sudden frequent urination in the middle of the night at the time they don't want to have it and this is because normally a patient people are up moving around but at night whenever you're laying down your legs are elevated it allows that fluid to enter back into the vascular system goes to the kidneys so your kidneys try to start putting out that fluid so that's why they may have excessive urination at night with this and G for girth the abdominal girth of their belly can be increased and this is because remember of the hepatomegaly where all this congested fluid is going to the liver so they can have that whenever they have that they have this big belly of extra fluid it can cause them not to breathe very well they'll have difficulty breathing because it's pushing on those lungs um it's also going to be pushing on the stomach so they could have anorexia just don't feel like eating and they can feel nauseous with this now left-sided heart failure we're drowning because we got pulmonary issues going on first D remember dpia this is because of all that fluid backing up into that lungs causing that patient not to breathe very well R for rails this is another word for crackles this is when you listen with your stethoscope and you can hear in the lungs this crackling noise how I like to do is take your hair and take it by your ear and that's what it sounds like o for oropa this is one of the telltale signs if a patient tells you and they have a mystry of congestive heart failure at night I've been having to use some pillows to set up to sleep and breathe because I just can't breathe that is a warning find them they may be going into SE to heart failure exacerbation so that's um what that is and then W for weakness again just like with right-sided heart failure they're going to be extremely weak just because that heart cannot put out the cardiac output it needs to to me meet your body's metabolic needs and for nocturnal proximal dispan this is where at night they will just wake up all of a sudden with extreme breathing difficulty just can't breathe at all it's very frightening for them and this is one of the things that can happen left-sided heart failure because you're having those pulmonary issues I for increased heart rate and the reason they have increased heart rate is because they have the heart the body sense is hey we have all this blood in the heart but we need to get out to the organs so it's just staying there so that heart will increase that heart rate and make it become tacky so it can p pump it out to get to those bottle organs and for nagging cough again that's you have the lung issues going on they'll have this persistent nagging cough and sometimes it can become frothy or blood tinged sputum and if this happens this is a really really bad sign that um something horrible is going on and you need to get them diares fast because they have some major fluid overload so if you see that that's usually a late sign G for gaining weight again just with right sided heart failure um they if they gain more than 2 to three pounds in a day or 5 lbs in a week that is a red flag okay let's look at real fast how heart failure is diagnosed in the hospital setting okay A lot of times Physicians will order a lab result called a BNP it stands for B type natur remic peptide we call it BMP and what it is it's a biomarker that's released by your ventricle when there's excessive pressure pressure on the heart due to heart failure and um typical readings if you have less than 100 there's no heart failure going on um if you have a 100 to 300 reading it's present greater than 300 it's mild greater than 600 it's moderate and greater than 900 it's severe and I have seen these in the 2000s with heart failure patients other things that are used to diagnose this a chest x-ray looking to see if there's any congestion in in those lungs looking at the heart to see if it's enlarged um an echo cardiogram a heart cath and a nuclear stress test which is what we talked about earlier with ejection fraction now heart failure can be maintained for patients um they can take medications they can do diet regimen and um other treatments so they can maintain it however um heart failure can go into exacerbation where it comes out in full force and some things that can trigger that are um maybe the patient isn't compliant with their diet they eat a lot of fast food a lot of sodium they don't restrict their fluids they drink a lot of soda a lot of water that can trigger them to go into heart failure infection they get really sick stresses the heart out go to heart failure uncontrolled atrial fibrillation or renal failure because renal patients have issues with fluid overload already and that can put more stress on the heart that already is more susceptible to heart failure so in the next video be sure to check out part two because I'm going to be going over nursing interventions and all those medications to use to treat heart failure so thank you so much for watching this video and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Kidney_and_Nephron_Anatomy_Structure_Function_Renal_Function_System.txt	hey everyone it's s Earth register nurse rn.com and in this video I'm going to be going over kidney and nefron Anatomy this video will start our inlex review series over the renal system and at the end of this video don't forget to access the free quiz so let's get started first let's start out talking about the kidneys okay you have two kidneys you have a right kidney and a left kidney and your right kidney sets a little bit lower than the left kidney and the reason for this is because above the right kidney is the liver and to help accommodate the size of the liver that kidney has to be just a little bit down when you compare it to the left one now what do our kidneys do they are very very important in our survival just like with the heart we've learned that the heart will take our blood and pump that fresh oxygenated blood that it received through the lungs throughout the body well the kidneys receive that fresh blood through the renal artery and it will take that blood and it will filter that and after it filters it takes what it needs it will send it back through the renal vein so inside the kidneys you have filtration absorption and secretion and excretion going on and what will happen is that the kidneys will produce filtrate which is a liquid that will turn into urine it will go down through your urur you have one you have two that connect to each kidney then it will go down into the bladder to be stored and as the bladder becomes full you will feel the urged void and then it will exit through the urethra now let's look at the inside of the kidney if you took a kidney which um look is like a little bean shape if you've ever seen kidney beans they look like that but they're a lot bigger and you took it and you just cut it in half this is what it would look like on the inside so let's cover the basic anatomy of the kidney okay around the kidney is this outer capsule and it's called the renal capsule and this capsule what it does is that it gives the kidney its shape but it also helps protect the kidney from any infection that may be present in other organs because we don't want our kidneys to become infected if they become infected we can die now now inside the kidney this is what we are interested in because this is where things get done this is where our urine is going to be created so you have this outer part of this layer this is called the renal cortex then you have this little inner layer and this is called the renal medulla and please note where these layers are because it's going to be really important when we're talking about the nefron CU certain parts of the nefron are in the cortex versus the medulla and it'll all makees sense in the next video when we talk about the nefron physiology okay so we have that structure then inside where the medulla is we have these areas and I think they look like little seashells they're called renal pyramids and they have these striped areas why do they have these striped areas well inside the renal pyramid you have part of the nefron and the nefron is running straight parallel in these pyramids and it gives us this striped look to it then if you took away your renal artery and your renal vein and you looked behind it we would have this area right here and this is where the urine is really draining down through the uror into the bladder this is where once it's created in this area up in here it will drain down through these areas so let's go over these areas again you have your renal pyramids you have your renal papilla which um is the tip of the point of the pyramid then when your urine comes down through the renal pipila it will go into the kexes and you have the minor KX and you have the major KX then the urine will progress down through the renal pelvis which will go down into your urer then into the bladder and then the urethra now um in between your renal pyramids are renal columns and the renal columns contain a network of where your renal artery and your renal vein Branch off into these um capillaries and um arterials now let's look at the nefron okay if you're going to remember anything about the kidney the nefron is what you need to remember because this is the functional part of the kidney that um allows it to filter reabsorb and secrete um waste and things we don't need and turns into urine and each kidney contains millions of these little nephrons and they run in this area right here so let's dissect a nephron so here is a basic structure of a nephron and if you took a nefron and just stretched it out it would allow you to see these different Parts but in reality because you have millions of these just throughout here if you look at them they're all like twisted and they look convoluted and everything and they're all squeezed together and it would be really hard to tell what's what so um with nefron let's talk about this you have two I like to think of it as two different sections you have the section which is known as the renal cor pusle that is responsible for filtration and it is the Bowman's capsule and the glomus this is where filtration happens your blood's being filtered um things that are being pulled out or like water ions and waste and then you have the second section called the renal tubal and th it's this section and this is where reabsorption and secretion are happening what's happening is that you have this filtrate that's been created in by the renal cor pusle and you have these substances and water that's constantly flowing in and out of these tubules back into circulation which would be reabsorption or um it's moving out of circulation into the tubules which is called secretion so let's break this nefron down okay so going to the nefron remember um we just receive fresh blood from our hearts nice and oxygenated but it needs to be filtered so um urinal artery breaks off and it will break off into What's called the afron arterial and this is going to the first part of the Nephron the glomus afren means towards something so it hits the Glarus and the Glarus is this really unique structure if you ever look at a nefron look for the red part with all these squiggled up capillary looking areas and that's your glomus and so that's what it is is a bunch of capillaries just Twisted in this circular um shape and because of that the way it's formed um as that blood flows through there it creates this ultra filtration process which allows that blood as it's in a sense spinning through there to be filtered and to um release what's called filtrate down into this collection capsule called Bowman's capsule so you have this filtrate coming out of there and this filtrate will include like water um your electrolytes like pottassium chloride sodium magnesium calcium phosphate and waste like Ura and creatinin and it collects in there and it's called filtrate then um your glarius will go after the blood has filtered through there and it'll Branch off into What's called the ephant arterial ephant means away so it's leaving the Glarus and then the E arterial ghost just doesn't stop it still has a very important job to do it goes down and starts forming and twisting around those tubies and hanging out around there because it has a very important job as well the what it forms is called peritubal capillaries and um these are up here on these ducks and then when they go down and they form down where the loop of Henley is it's called the vastera which is a type of paru or capillary now what do these capillaries do okay so we have this filtrate going down through these tubules and remember what I said the renal tubules are responsible mainly for reabsorption and secretion so um in order for things to be reabsorbed and secreted so you can get rid of it you need something to help with that process so that's where those peritubal capillaries come into play so let's talk about these two terms cuz um in order to understand the physiology of the nefron which we're going to talk about in the next video in step you have to really understand these two terms reabsorption and secretion so reabsorption okay number one we call it reabsorption why not absorption well because we've already absorbed these substances that's how they've gotten our blood because remember it's went through the hearts came here been filtered and we got it where did we already absorb most of this nutrients out when we ate food through our GI tract because we eat your small intestine does most of the absorption so those specialized cells in there took the glucose the amino acids the potassium the calcium the sodium and took it and transported it where it needed to go and put it in the bloodstream and the heart now pumps it out and says kidneys do your job you filter this out choose what the body needs because the body likes homeostasis it likes a balance of water balance of electrolytes and a nice balance of waste specifically Ura and creatinin so as this filtrate has all of this nutrients in it it needs to be reabsorbed so that's what's going to happen it's going to flow through here and based on where it's at in these tubules because certain tubules absorb more here and more there it will be reabsorbed because we've already absorbed it once so it'll be reabsorbed and will flow through those peritubal capillaries which will eventually go to the renal vein which will eventually go back to the heart it'll get reoxygenated and the Beautiful Cy will just keep going and going now let's talk about secretion okay secretion the parital capillary is helping that because um these capillaries will carry like any um waste like Ura creatinin um or any drugs you've taken like antibiotics diuretics and will secrete their substances into the filate um and it will be taken and transported out and excreted as urine so that's how those two go hand inand okay now back to the nefron okay so all that filtrate is there in Bowman's capsule it's ready to go down in through these tubules to be reabsorbed or secreted so filtrate goes down the first part it hits is called the proximal convoluted tual and um this area is where a lot where actually most of your reabsorption is going to occur like um pretty much all of your glucose your amino acids um a lot of sodium and chloride and things like that things that are essential that your body really needs right away then the filtrate is going to travel down into the loop of Henley and this is really one of the most important parts and interesting parts of the nefron and remember what I said about these cortexes and the medulla the loop of Henley has a descending limb and an as ascending limb and they really each do their own different things and they're located the loop of Henley is mainly located in your renal medulla and the renal medulla is a very very salty area it's um hypertonic the interstial fluid that is in the renal medulla is hypertonic and this is very important animportant because this area is where most of your water absorption is going to occur and this is where your urine's really going to get concentrated then it's going the filtrat is going to go up through the distal convoluted tubal where some more absorption a little bit of secretion is going to occur then it's going to go down through your collecting ducts where everything's just going to be brushed up the last part of secretion and reabsorption is going to occur then it's ready to exit the body it's going to go down through the renal Pila which eventually will go into your KX your minor and major KX through your renal pelvis down through your Ur into the bladder and into the urethra so that is how urine is made through your nefron now don't forget to check out the next video about nefron physiology thank you so much for watch watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	How_to_Count_Respirations_Counting_Respiratory_Rate_Nursing_Skills_Video.txt	hey everyone it's Sarah with registered nurse rn.com and in this video I want to demonstrate for you how to count a respiratory rate this is one of those very important bottle sign skills that you have to do as a nurse or a nursing assistant so in this video what I'm going to do is I'm going to go over the basics of counting a respiratory rate and then I'm going to show you how to do it on a real person so first let's cover the basics whenever you are looking at the respiratory rate on a patient you're looking for several things first thing you're going to be looking at is the Rhythm and you're going to look at the breathing effort of the patient whenever you're looking at the rhythm you're looking at to see if it's regular or irregular and what you're paying attention to is that inspiratory phase and that expiratory phase the inspiratory phase is whenever they inhale take a breath in an expiratory phase is whenever they exhale take a breath out and watch your looking at is to make sure that they are equal because in some patients for instance patients with chronic obstructive pulmonary disease copy the expiratory phase will be a little bit longer than the inspiratory phase so they'll take a breath in and then they'll breathe out and it'll be a lot longer now next thing you're going to look for is how's the patient breathing are they having difficulty moving air are they having dmia where they're going or is it just effortless for them they're not really even aware that they're breathing just like how you're blinking so you want to pay attention to that next you want to count that breathing rate you want to make sure that it is within the normal range for an adult a normal range is 12 to 20 breaths per minute so we're making sure that they meet that criteria so to do this typically what you do is whenever you go in to do your botal signs you'll collect them and you'll count a radial pul by feeling on the radial artery and you'll count that for 30 seconds if it's regular and then while you're still holding the radial pulse site you are going to look at the chest of the patient and you are looking to see how that chest is rising and falling and you're counting those Rising the rising and the falling as one breath because one inspiration and one expiration equals one breath and you're going to do that for 30 seconds and after 30 seconds you'll take that number multiply it by two and that is your respiratory rate so the reason you want to hold the radial pulse why you're counting the patient's respirations is because if a patient knows that you're counting the respirations they're going to throw them off and it's just like blinking if you tell someone I'm going to measure how much you blink the person's going to be aware of how much they're blinking and they're going to be conscious of it and it's going to throw what the normal rate would be so after you get done done counting the respirations let them know that you were counting the respirations now let me show you how to count respirations on a person hi my name is Sarah and I'm going to be your nurse today and I'm going to take your Vital Signs is that okay with you absolutely okay so I've performed hand hygiene and we're going to get his Vital Signs so let me see your wrist and I'm going to feel your pulse e okay so your pulse rate was 70 and your respiration rate was 20 so that is how you count a respiratory rate now be sure to check out my other videos on how to do other nursing skills and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Preload_and_Afterload_Nursing_Stroke_Volume_Cardiac_Output_Explained.txt	hey everyone it's sarah thread sterner sorry and calm and in this video we're going to be talking about cardiac preload versus after lobe and when you get done watching this youtube video don't forget to access the free quiz that will test you on preload and afterload so let's get started what is preload and afterload well these two terms play an important role in influencing cardiac output and cardiac output is the amount of blood that this heart pumps throughout the body per minute and it plays a very important role in maintaining tissue perfusion so your heart takes the blood it's received it's nice and fresh and oxygen and it provides that to the cells that make up our tissues and organs and our cells are very specific about their oxygen and if they don't get a lot of it they start to die and the patient starts going through those stages of shock now cardiac output is calculated by taking the heart rate and multiplying it by the stroke volume now this is where preload and afterload come into play and stroke volume is the male a blood pumped by a ventricle with each beat because stroke volume is affected by three things one thing is affected by is contractility and contractility is the strength of cardiac cells to contract / shorten now we're not really going to concentrate on contractility main thing we're gonna concentrate on are the other two factors that affect stroke volume and that is preload and afterload so let's talk about preload first now preload is the mount the ventricles stretch at the end of diastole now what phase of the cardiac cycle is vastly what's going on during this faith this is that relaxation filling phase and we're talking about the filling phase of these ventricles are being filled with blood so blood is draining down from either the right or left atrium your AV valves your tricuspid mitral / bicuspid valves are nice and open and blood is flowing down and once the have filled that is the part that we are talking about the preload so you can also refer to the preload as the in diastolic volume it's that volume amount that isn't that ventricle once it is filled at that end of that diastolic phase so now let me illustrate preload for you and to do that let's use a balloon so let's pretend the end of this balloon is our ventricle and our vin Terkel is in the diastolic phase so it's filling with blood ok now we're at the end of dice Lea once it's filled with blood and preload is the amount that this ventricle stretched once it was filled at the end of - Lea so it's the end diastolic volume now let's talk about how we can increase preload and how we can decrease preload because if we increase preload we can play a role in increasing stroke volume and this will help increase cardiac output and some cases you might want to do that like with hypovolemic shock your patient doesn't have a lot of fluid in the body so we want to increase that preload to increase stroke going to increase cardiac output so one way we can increase preload is through the administration of IV fluids and how that's given is that you stick a patient's vein with a needle you leave a cannula inside of it and it will drip fluids into the venous system now what that's going to do is that's going to increase the blood return the venous blood return to the heart so for increasing blood volume that's returning to the heart the male of volume that is filling in these ventricles at the end of astley is going to be high so we're going to have an increase preload another way we can do that is through the sympathetic nervous system stimulating that and the body can do that naturally on its own or we can give drugs to do that like vasopressors and what happens in a nutshell is you have vasoconstriction where those vessels are gonna clamp down they're gonna narrow and this is going to increase venous return to the heart so it's the same concept we're going to have more blood returned to that heart so that's going to increase the amount of volume that's going to be in that ventricle at the end of its filling face so we're increasing our preload now how can we decrease this preload where these ventricles aren't going to stretch as much at the end of dice Leiby cuz sometimes we need to do that if a patient is in fluid overload like with heart failure we want to decrease their preload in one way we can do that is through the administration of diuretics and how diuretics work is that they will use the renal system and they will remove extra fluid from the blood line and the patient will urinate that out and a type a diuretic that comes to mind is like furosemide lasix so when we give that drug that's going to pull fluid out of that blood volume and it's gonna decrease the male a blood return coming to that heart so if you don't have a lot of blood volume coming to the heart that's gonna decrease how much these ventricles are gonna stretch once they're filled hence decreasing preload another way is through vasodilation so it'll have the opposite effect of what vasoconstriction have and a drug that can do that is like nitroglycerin and what happens is instead of having the narrowing of the vessels you're gonna have dilate and they're gonna wanna and when they widened that's gonna increase blood pulling and it's gonna decrease the male and venous return coming to that heart so you're gonna decrease the amount that these ventricles are going to stretch once they have filled now let's talk about cardiac afterload okay this is the pressure that the ventricles must work against in order to get the semilunar valves open so blood can leave the ventricle and go either to the lungs or to the body and cardiac afterload is really affected by vascular resistance so if you have a high vascular resistance that that ventricle is having to pump again that's going to increase its afterload and let me illustrate this for you and explain a little bit further okay so we have our right ventricle and our left ventricle and the goal of the right side of the heart is to get blood to the lungs and in order to do that this right ventricle is coming up against pulmonary vascular resistance this is that vascular resistance I was talking about that it's gonna affect our afterload so you have the right ventricle it has to open up this pulmonic valve which is a semilunar valve and once it's open blood is gonna be shot through the pulmonary artery go to the lungs where gas exchange is going to occur and very similar over here on the left side left side has to get this a Orting valve open once it's open it's going to go up through the aorta into systemic circulation but here we have systemic vascular resistance that this led ventricle must overcome in order to get this aortic valve open so let's pretend we have our ventricle again and this is our left ventricle and my fingers that are clamping this shut is the aortic valve it's closed and this part right here is the aorta and it has vascular resistance in it systemic vascular resistance and the pressure of this is really keeping this aortic valve closed and to this ventricle can overcome this systemic vascular resistance to open it up to pump blood out so this ventricle it must overcome that vascular resistance here that's our afterload so if we have high systemic vascular resistance increase this is going to increase our afterload it's going to increase the amount of pressure that this ventricle has to overcome in order to get this a or DIC valve open so blood can be shot out through the body so let's talk about things that can increase after load and decrease after load so increase after load when you have vaso striction going on again that's a narrowing of those arteries so if we have narrowing of the arteries that it's affecting our systemic vascular resistance or if we even have narrowly faced of constriction that's affecting our pulmonary vascular resistance that's going to increase the pressure that these ventricles must overcome to get these semilunar valves open so blood can go either to the lungs or throughout the body and one thing that can increase afterload is pulmonary hypertension and we talked about this with our congenital heart defects where they have increased blood flow that keeps going to those lungs it damages the arteries that feed the lungs they narrow and you get pulmonary hypertension so if we have pulmonary hypertension this is going to increase the pulmonary vascular resistance so that's going to increase really that workload on that rot ventricle it's gonna increase the afterload because you have such a high pressure here and it's keeping this pulmonic valve closed so it's going to increase the after load the amount of pressure that this ventricle must overcome to get that semilunar valve open so blood can go throughout this system if you have a really high pressure blood pressure going on with like vasoconstriction with systemic vascular resistance that's when it increase that workload on that left ventricle and increase it's after load the pressure it must overcome to get by or to valve open to get blood to systemic circulation so after low and vascular resistance really go hand in hand now another thing that can increase after load is a valve problem so let's say we have our aortic valve it's narrowed we have a or txt enosis narrowing of a valve so we have issues an obstruction of outflow of that blood that's leaving that left ventricle so it's really this left ventricle just having to work really hard to even get blood through this aortic valve because it's narrow so that's when it increased the pressure that this the left integral has to overcome due to that narrowing of aortic valve to get blood throughout the body so a or --tx enosis can ink our afterload now what's something that can decrease after load well a lot of times we need to give drugs to patients to decrease their after code because their ventricles are exhausted so we can give them like vaso dilators dilate that it's gonna dilate the vessels out it's going to decrease vascular resistance so we decrease vascular resistance due to why mean of those vessels it's gonna decrease pressure and it's going to decrease the after load because it's gonna decrease the pressure that that ventricle must work against the gift that semilunar valve open so blood can flow out of the heart okay so that wraps up this review over preload versus after load thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Lung_Assessment_Nursing_Lung_Auscultation_Assessing_Lung_Sounds_Part_2.txt	hey everyone it's sarah thread sterner sorry and calm and in this video I want to demonstrate for you on a patient how to auscultate the lungs anteriorly and posteriorly in the previous video I went over an in-depth lecture about how to do this along with normal breath sounds and abnormal breath sounds so be sure to check out that video after you watch this so let's get started first I want to start out showing you the auscultation side so I wanted to use these stickers so you can see about where I'm going to go with the stethoscope and let me get over these real fast for you because these are the little landmarks of where you're going we have our right leg over here and our left leg over here and what we're doing is we're assessing the lungs the right lung has three lobes the right up or the right middle and the right lower the left lobe only half of the left lung only has two lobes the left upper and the left lower so whenever you're listening you want to start out at your apex up at the top of the lungs right above the clavicle just slightly above it right here where you see these pink stickers then you're going to go down to the second intercostal space a little bit over from where your breastbone is the sternum and this is where you're gonna start assessing the upper lobes of the lung then you're just gonna inch down a little bit and you wolf this is about the third intercostal space and you're gonna listen here then go down to the fourth intercostal space and this is one of the landmarks for the right middle lobe your fourth intercostal space so right here well listen I'm here here a right middle lobe and then we'll listen to our left upper lobe then we'll inch down a little bit and we'll listen a little bit more to that right middle lobe and then we're going to be listening to our left lobe and then we're gonna go mid-axillary over here to the side where the armpit is mid axillary axillary sixth intercostal space and we're going to be assessing our lower lobe so it's right here on him and then it's again right here and you'll listen there and then um you'll just inch down a little bit and listen at the bottom just to assess those lower lobes a little bit now let's listen to the lungs with a stethoscope okay before you begin what you want to do is you want to perform here hi Dean introduce yourself to the patient and tell them what you're going to be doing and what whenever I listen to lung sounds I like to listen directly on the skin with my stethoscope not over the gown or over their clothing because you can pick up other sounds that may sound adventitious when it's really not and you just get the best acoustic sound whenever you listen directly on the patient so you want to get your stethoscope and you want to listen with the diaphragm of your set the scope because that's what picks up the best sounds and what we're listening for is we're listening for that full cycle of inspiration and expiration and we're paying attention to what type of breath sound is it is it bronchial vesicular Branko vesicular if you're not familiar with those sounds check out my other videos because I have audio clips where you can listen to those and we're also listening for any extra sounds on top of those sounds like crackles wheezes Strider anything like that that we may be picking up and another kids this skill takes getting used to you have to practice it over and over especially when you're listening over these areas because you're gonna hear the heartbeat at the same time so you got to train your ears to listen for those correct sounds like you're the heart versus lungs so practice this on yourself and others so you can get comfortable with it so what we're gonna do is we're gonna start at the top and we're gonna work our way down and we're going to start on one side and then compare that side because we want to say say see if we're hearing the same thing on this side as we are that side so let's get started okay what I'm gonna have you do is take one breath in through your mouth and out through your mouth and if you start to get dizzy or anything let me know and we can slow down okay we're starting up at the apex right above the clavicle now we're gonna inch down to the second intercostal space and this is where we're gonna start listening to our upper lobes of our lungs so about right there then we're just gonna inch down a little bit to about the third intercostal space and listen there and we're gonna go over and compare it now we're going to go down into the fourth intercostal space and we're still gonna be in the upper lobe of the left lung but now we're gonna be in the middle lobe of the right lung so let's just go down just a little bit and then we're gonna go over here and compare and then we'll just go a little bit do maybe the fifth intercostal space just still assessing that middle lobe and I go over here and compare now we're gonna go mid axillary and we're gonna be down in our lower lobes now and this will be at the six intercostal space okay we're going to compare sides so if you just want to turn over here we're gonna go mid acts like a parasite then we're just going to go down just a little bit to say in that lower lobe and then we're going to compare sides now let's look at the posterior view of the back here over on this side we have the left lung and over here we have the right lung it's flip compared to the anterior view and what we'll do is we'll start listening up at the apex of the lungs again and that's right above slightly above that shoulder blade in this area where the green stickers are then we're going to go and we're gonna listen between c7 to t3 and c7 is where you're prominent starts so right here and we'll go a little bit below it because c7 to t3 is going to assess the upper lobes of the posterior side of the lungs so we'll go here and here then we'll go down just bed.this is about where t3 is and then we'll jump down to round t4 and from t3 to t10 we'll be assessing the lower lobes in your posterior view you have more ability to auscultate the lower lobes then compared to the anterior view where you're gonna really be assessing the upper lips so then we'll just go down listen here listen there we'll go there and then we'll just go a little bit mid-axillary almost mid-axillary and listen over on these sides and then down at the bottom and over here now let's do it with a stethoscope now we're going to listen posterior lis okay let me tell you a trick with this whenever you're listening back here as you've learned if you watch the other lectures you have the scapula back here and you have the vertebrae and what you're trying to do is to get in between that scapula and vertebra to listen to those lungs and you don't want to go over the shoulder blades of scapula while you're listening to lungs because it's really gonna muffle out your sound and you're not gonna hear a lot so what you need to do is have the patient sort of just move their arms like this to separate those shoulder blades from one another so you have some space to work with so what we're gonna do again we're gonna start from top and work our way to the bottom and we're going to compare side so we're gonna go slightly above the scapula listen to the apex then we're gonna go down in the area where c7 is which is where your prominence is then we'll work our way down to where t3 and remember this is assessing the upper lobe and then we'll go down from t3 to about t10 and assess those lower lobes so here we go and again just take a deep breath for me in and out okay and we are done with posterior okay so that is how you assess the lungs with a stethoscope now be sure to check out the other videos in this lung series like the audio files of the normal breast films vs. abnormal and the lecture that covers this material in depth and thank you so much for watching and please consider subscribing to this YouTube channel
Medical_Surgical_Nursing	Nitropaste_Ointment_Application_Nitroglycerin_Nitro_Bid_Medication_Administration_Nursing.txt	hey everyone it's sarah stanner sorry end comm and in this video i'm gonna demonstrate for you how to administer nitro bid which is not your glycerine appointment first what you want to do is you want to gather your supplies so you'll need to get your nitro bid nitro glycerine pointment and a lot of them come in tubes like this or they come in like little foil packages so get whatever your facility has you will definitely need to get an application paper this is so important because this allows you to measure how many inches of ointment you're going to get like half an inch an inch and they come in like a little booklet like this you can tear off in your Omni cell whatever you have that dispenses medication and get one of these papers you also need to get some gloves to protect yourself from this ointment because if you get nitroglycerin on you this ointment it will cause a headache and cause you to feel flushing and things like that and you don't want to experience that you need some tape to secure down the application papers along with some Tegaderm or plastic wrap to cover the application site because nitroglycerin can stain the clothing along with a cloth for whenever you remove the old application paper from the skin just to clean off that excessive amount of nitroglycerin that will be left behind after you gather your supplies you'll want to do the patient's five right so make sure you have the right patient you have the right drug the right dose the right time and the right route now whenever you're giving nitroglycerin appointment you want to watch out for some things number one you want to make sure the patient's blood pressure is good they don't have hypotension and you want to warn your patient that you know this may cause a headache if this is really the first time receiving it it can also cause warmness and flushing in the space another thing is you need to know what nitroglycerin pointment is used for it's typically used to prevent chest pain in patients with coronary artery disease so if you're working on a cardiac floor you'll probably be giving a lot of nitro Paste so the first thing what you want to do is you want to remove the old application paper first that contains the nitroglycerin before we actually put on the new one so you want to wash your hands and you want to wear gloves very important never do this without gloves because there's still nitroglycerin on the skin and if you get this on you you will get some side effects of nitroglycerin and you don't want that so we are going to take it off and gently just remove the tape from the site and if you have trouble finding where the the applicator pad is just ask the patient and just look everywhere you can find them on the arm on the chest on the back sometimes maybe the patient's bed if they've came off so just always try to look for it and then you're just gonna take it off notice there's still some nitro and then just gently fold this together and discard then take your cloth and gently just wipe off the area of the excessive nitroglycerin now we're going to place a new applicator pad somewhere else and again we can use the arm the chest the back but you always want to rotate sites after doing that you want to perform hand hygiene then you want to prep your application paper and what we're gonna do is we're going to date and time it and initial it and then we're going to square the ointment on to the scale so where we're going to write our date and time and initials is on the printed side because on this opposite side without the print is where we are going to measure the pointment and you can see through the onto the other side because it's paper so thin so you can measure it a lot of people ask well why don't we just measure it on the side with the scale it's because whenever the pointment comes into contact with this print it can cause the print to leak into the ointment and we don't want to get that on the patient so we're gonna go ahead and date time and initial it and don't date in time over the scale because when you flip it over you won't be able to see the scale whenever you're measuring out the pointman so right somewhere where you have access to it and it's best to use one of these markers if you can because it shows up better than a pen okay now we're going to flip it over and we're going to measure out our point Minh and the doctors order says one inch of Nitra bid point Minh so to do that we are going to daughter gloves now let's open our pointment tubing okay if this is the first time you're opening up this point mandir is a special way you have to open it and for this video this is a demo dose of nitroglycerin pointment it's not the real thing in there we're just using this for teaching purposes so what you want to do is you want to unscrew this cap and on this side of the cab is like this beveled area that's sort of pointy it's going to screw into the top of this tubing and it'll poke a hole in it so you can squirt out the ointment so take that and just insert it in there and just screw it on a little bit like that and see it allows your ointment to come out now we're going to squirt out one inch of paste okay so looking at your scale from here to here is half an inch and from here to here is an inch and so we're going to squirt the ointment from here to there so let's do that okay and we have an inch so we picked the other arm to place our new application paper with appointment and I made sure that it was intact there's no areas that are open and there it's free from hair if it had a lot of hair we want to trim it not shave it and I wanted to make sure that the site was clean so now we're just going to apply our paper to it and to do that we are going to put the ointment side on to the skin and we're just going to thinly spread it at the side don't rub it in don't massage it just thinly spread it so it's evenly dispersed like that now we're going to secure it to keep it in place so you can use a Tegaderm plastic wrap whatever you have access to and just cover the site and then tape it into place okay and then the patient is ready to go until their next dose after you're done with that discards your gloves perform hand hygiene and then chart that you gave them medication and where you place that applicator pad so the next nurse can find it and just a quick tip I wanted to go over real quick with you is about this nitro pointment and some places keep it in the tubing like here and if this is the case with your facility because it's multi patient use you can use it for your patient several times in the tube you'll put like their patient label on it you want to keep this in the designated area that your hospital wants you to keep it not in the patient's room and their drawer or something like that because one time this nurse told me that she had a patient and she walked into the room and the wife was giving the patient a massage a back massage and she was using this ointment because she found the women in the patient's drawer and thought it was just some type of lotion she could use and both her both the patient and the patient's wife had an adverse reaction to it so just to protect your patient their family members and yourself always keep this in the designated place set by your Hospital okay so that wraps up how to administer nitroglycerin thank you so much for watching and don't forget to subscribe to our channel for more videos
Medical_Surgical_Nursing	Septic_Shock_Nursing_Sepsis_Treatment_Pathophysiology_Symptoms_Distributive.txt	this is Sarah Fred sterner sorry and calm and in this video we're going to continue our series on shock by talking about septic shock and as always after you watch this YouTube video you can access the free quiz that will test you on this condition so let's get started septic shock occurs due to sepsis and this leads to a major decrease in tissue perfusion so what happens is that the cells that make up our tissues and organs for some reason do not receive enough oxygen hence blood flow so they will start to experience what's called hypoxic injury and if this continues the cells will actually die and when cells die they take organs with them because organs are made up of cells so whenever we've talked about all these types of shock we have learned that depending on the type of shock will depend on why we are actually having this altered tissue perfusion and for instance with cardiogenic shock why were these cells being deprived of blood flow of oxygen because with that type of shock there was an issue with this heart most commonly my cardio infarction has damaged that heart and it can no longer maintain cardiac output so the blood flow going to those cells is altered now with septic shock it's a little bit different of why we had an issue with blood flowing not flowing to those cells tissues and the reason is because we have issues with how these small vessels are able to distribute blood flow and it's going to come from some type of invasion from a microorganism which is where the word septic comes from so Senate beginning of the lecture septic shock occurs due to sepsis on what is sepsis well sepsis is where you've had that invasion of that microorganism in the body and the microorganism can vary it can be bacteria which is the main cause of sepsis it can be grand positive or gram-negative you can have a fungus a virus or a parasite but regardless whatever it is the immune system is going to respond but insects this that response is amplified system why it sets off this inflammatory response system that's going to majorly damage these small vessels that actually deliver blood flow hence oxygen to these cells that make up our tissues and organs so think of sepsis as sepsis progresses it leads to septic shock so septic shock is really the end result of sepsis so we've really got to monitor a patient for this and listen to this statistic by cdc.gov one in three who died in hospital have sepsis so as a nurse we need to be able to recognize the early signs and symptoms of sepsis so they don't actually get to this point and be aware of which patients that we have that are actually at risk for developing sepsis now what are the characteristics of septic shock how do we know if we have this patient in sepsis that they're actually entering into shock territory well we want to look for things that indicate that we have this decrease in tissue perfusion that's going to cause cell problems where they're not going to receive enough oxygen one thing we can see of course you're going to see hypotension with sepsis but this hypotension is going to be different when we're starting entering into shock territory it will be persistent hypotension where that systolic is less than 90 will not go up even when they've had large amounts of fluid replacement in addition in order to keep their mean arterial pressure their map greater than 65 they need vasopressors to achieve that like norepinephrine and arm at what it does is it tells us how well those vital organs are being perfused if it's less than 65 that pressure going to those organs really isn't maintaining them plus they will have a serum lactate if that is measured greater than 2 million moles per liter and think back to our stages of shock video why do we care about that serum take level well remember when cells are struggling when they're not receiving enough oxygen they will switch from aerobic metabolism to anaerobic metabolism because they don't have any oxygen so they're gonna metabolize without it and because of that that is going to produce lactic acid and as it accumulates in the blood your serum lactate will accumulate and that tells us we have altered tissue perfusion now let's talk about the pathophysiology of septic shock and while we're having persistent hypotension and what is leading these small vessels to not be able to actually deliver that oxygen to those cells well septic shock is like I said earlier a distributive form of shock the other types of shock that are distributed are neurogenic and anaphylactic which we'll also be talking about in this series so what that means again is that there is issues with these small vessels being able to distribute blood flow to those cells so they can't get oxygen now that is occurring not due to a cardiac output issue it's not because our cardiac output is so low it can't profuse to those small vessels because in the early stages of septic shock you actually have a high or a normal cardiac output it's fine but it's coming from a decrease in systemic vascular resistance which is due to this major vasodilation that is occurring throughout the body in these vessels so these vessels have a button and whenever it ones it decreases systemic vascular resistance so one the world is that occurring okay well let's talk about what's going on we have this micro organism that has invaded our body the immune system in sepsis has responded in this like exaggerated way so it thinks it's going to take care of it but it's actually going to make things worse for a patient and progress them to septic shock if we can't take care of it so these chemicals are being released by the micro organism toxins it's damaging the Saran into issues with its toxins and the immune system sees this and it's like okay we've got to respond but he responds in an amplified way and it releases cytokines and Pro inflammatory mediators that's what's going to make our vessels and what's happening in septic shock a lot worse so these chemicals right here are going to lead to the following you're going to get vasodilation so these vessels system-wide are going to open up and whenever that happens blood as it really flows it's not really going to flow it's going to pull so you're gonna limit the mail of blood flow that's going to those cells and that's leading to our decreased systemic vascular resistance in addition these chemicals are going to change the permeability of these vessels it's gonna make them leak so the fluid that's in our circulatory system is going to start leaving it's gonna leave the inter vascular system and that fluids gonna move out into the interstitial tissue what's this going to do this is going to lead to hypovolemia specifically relative hypovolemia and that's going to lead limit even more blood flow hence oxygen being able to travel to those cells because they are depending on that blood flow to come to them but and we have vasodilation and we're losing our flu and due to leaky vessels that's not happening very well in addition to make things worse what's also going to be released is called platelet activating factor and what this does a substance is it causes platelet aggregation because in these vessels were having inflammation we're having damage so all these small little clots are gonna start forming in these vessels and we're talking system-wide now if we're forming clots system-wide what's that going to do to our clotting factors it's gonna use them up so the patient is at risk for di C or they can bleed out of every orifice of their body so watch for using of blood and these clots are gonna create an even more of an obstacle for blood flow we have all these clots in our micro circulation house blood when a flow who those cells it's not it's gonna decrease the ability of that to occur so if you have vasodilation increased permeability clot formation in vessels system-wide you can see how those cells are being deprived of oxygen and we're having decreased tissue perfusion so when we talk about treatment here in a moment nursing interventions you're gonna see Y is going to try to undo this phaser dilation and undo the clots and all this system-wide inflammation that is going on in the body and then later on what's also going to occur because of this process taking place you have those cytokines that are present well if you have abundance of these cytokines present throughout the body it can affect the myocardial function your heart's function and specifically we're talking about tumor necrosis factor and interleukin 1 and what this can do it can decrease ejection fraction which is the percentage of blood ejected by your heart with each contraction now let's talk about the risk factors for septic shock because the chances are if you're taking an exam over this topic there may be a question that says which of the following patients is at risk for developing sepsis and we know that the patient develops sepsis they are definitely at risk for entering into septic shock so remember these risk factors and to help us remember that we're going to remember the pneumonic sepsis okay our first s is suppressed immune system so any patients who have HIV AIDS or they're on immunosuppressive therapy they're taking steroids chemo they're pregnant have malnutrition issues they're all at risk for an altered immune system and then e for extreme age this can be your really young patients like your infants and elderly or at risk for developing sepsis and then P for people who've received an organ transplant at risk and then s for surgical procedures anything invasive anything that's going to go in there and possibly introduce a microorganism into the body that normally shouldn't be there and then I for indwelling devices anything that's inside your patient puts them at risk for a microorganism so if the option says that a patient has something inside of them like it Foley a central line trach think how risks they have that risk factor for introducing a microorganism and then our last s is sickness and these are chronic conditions and it can be anything from diabetes mellitus to hepatitis alcoholism renal insufficiency etc that can alter a patient's ability to fight infection and another thing to consider would be the most common sites of sepsis so be thinking about the GI system specifically the abdomen or the respiratory system the lungs or the urinary tract all these are common sites where sepsis develops now let's talk about the signs and symptoms of septic shock and to do that we're going to look at the early signs and symptoms versus the late signs and symptoms because as a patient is in shock signs and symptoms are going to vary depending on what stage they're in especially septic shock because it's a little bit different than those other types of shock we've talked about in their stages because we had this massive vasodilation so early on we're gonna have some signs and symptoms that are a little bit different than what may let's say occur in cardiogenic shock so let's look at the early signs and symptoms first okay this is sometimes referred to as the warm stage of septic shock it's where we have compensation going on and the patients in this hyper dynamic state because of this phase OH dilation and what you're gonna see is warm / flushed skin when you feel that skin it's going to be warm and it can be flushed now later on once we're in the late stages it's gonna be cold and clammy so remember that difference in addition their blood pressure is going to be low their heart rate is going to be up and their respirations are going to be up in addition they're going to have a fever so if you're looking at this patient they have a fever their blood pressure is low their heart rate is up there breathing fast and they have warm flesh skin hmm they're probably septic sepsis septic shock we have that going on in addition they can have the high cardiac output so either that can be normal or high later on it will be low because that's where we have the failing of our heart and our organs mental status wise they'll be restless anxiety now as the septic shock progresses we're going to go out of compensation we're going to go where we're uncompensated so this is like the late stage we consider this the cold stage of septic shock they're hypo dynamic and what's going on is all the systems are really failing so you're gonna see signs and symptoms that are going on with that we really don't want to get our patient here so skin instead of being warm and flushed it's gonna be cold and clammy we have vasoconstriction going on things are just not being perfused because our heart is failing now at this point so her cardiac output is decrease they will have severe hypotension heart rate can be high respirations high respiratory failure everything going on urinary output Osler ik that is one thing that's so simple to look at to tell us if we're getting enough blood flow to those kidneys if it's not at least 30 MLS per hour or more our kidneys are not being perfused very well and they're starting to shut down so we're gonna get renal failure another easy thing to look at is Mental Status are they in a coma not responding at all that's telling us that our brain is not being perfused and they can have hypothermia and again they just can't regulate their body temperature because every system of the body is failing now let's wrap up this lecture and let's talk about nursing interventions and treatments and to help us understand why we're doing these certain nursing interventions and implementing these certain treatments we have to understand our goals for these patients and those goals are really going to be around what is going on in these small vessels that are disrupting blood flow to those cells we want to read that so we can increase perfusion so some goals would be of course the increased tissue perfusion this can be done several ways by giving them large amounts of fluid replacements if that doesn't work vasopressors like norepinephrine to help constrict the vessels instead of having major vasodilation cause vasoconstriction that can increase our pressures then we want to make sure they are oxygenated if that patient is being perfused but there's not enough oxygen in that blood we're not really doing a great job so we want to make sure that we're keeping the oxygen oxygen saturation greater than 95% the problem with patients in septic shock is that they are at risk for developing respiratory failure due to acute respiratory distress syndrome and remember with that disease we talked about this in depth what's going on is that whenever you have increased capillary permeability going on in the body like how we do a septic shock that's going to affect the vessels in the lungs especially run those alveoli sacs so fluid is going to leak into those sacs and cause them to collapse and the patient's gonna be in respiratory failure so a lot of times these patients have to be intubated and have mechanical ventilation to breathe so we'll be looking at that in addition we want to fight that microorganism so we want to obtain cultures as soon as we can to see what we are fighting against so they can receive the appropriate treatment and start antibiotic therapy if this is a bacteria so we can get rid of that microorganism in addition decreasing that system-wide inflammation that's going on sometimes that has to be done and to help increase perfusion so they may be started on like low dose corticosteroids or on activated protein C to help that which has anti-inflammatory and anti-roll badhak effects because remember we have claw issues as well and we'll talk about that here more in a second and nutrition we want to make sure that they get early nutrition because when we have decreased tissue perfusion especially going to our gut that can alter gut integrity so we can start nutrition early through those feedings we can increase got integrity help prevent those stress ulcers that can happen and improve our patients outcomes and in addition we want to control blood glucose this is really a big thing today because hyperglycemia alters the way that the immune system can work so we want to make sure that we're keeping their blood glucose controlled they may need to be on an insulin drip to help achieve that now let's take all that information let's put it into an easy to remember mnemonic septic shock so whenever you're trying to pull for your exams what you're gonna do for this patient think of this word so s first s is start antibiotics this will be administered within the first hour of septic shock this helps improve the patient's outcomes and typically a broad-spectrum antibiotic is used until that micro organism is identified and you will want to collect cultures before actually starting the antibiotic however don't delay antibiotic therapy next is e internal nutrition this will need to be started early by starting it early it helps preserve GI integrity because there can be a risk of altered tissue perfusion to that gut and plus nutrition is going to help play a role with immune health helping it to work as optimally as possible helps with healing and with the prevention of stress ulcers now to help prevent stress ulcers the patient may be order some GI drugs like famotidine to help with ulcer prevention and that is the brand name pepsin then P for protein activated C and this is what I was talking about that has that anti-inflammatory and anti-prom badhak effects because we need that with what's going on we have massive inflammation and we have these small little clots forming throughout our body and medication that does that is Dro trea Cogan alpha and this is most effective if it started within 24 to 48 hours of septic shock now because it has the anti thrombotic effect you'll want to monitor for bleeding t for tight vasopressors to keep that mean arterial pressure greater than 65 millimeters of mercury an example and first-choice drug is norepinephrine so what this will be used for is when fluid replacement is unsuccessful so fluid replacement is first we can't get that blood pressure up they're gonna switch to vasopressors and what these oppressors are going to do is they are going to cause major vasoconstriction because may we have vasodilation going on and this is going to increase systemic vascular resistance which we majorly need because we in septic shock we have decreased systemic vascular resistance and by titrating this to keep our mean arterial pressure greater than 65 that's gonna help perfuse our organs and again that map is the amount of pressure in the arteries during one cardiac cycle and what it does is it shows us how well our vital organs are being perfused then i for init robux an example of a drug that can be used in septic shock that can provide this type of effect is called dobutamine and this drug may be added if there's still low to perf using going on so they can add this with the presser and it helps increase the strength of the heart's contractions see for crystalloids or colloid solutions these are used with that first initial treatment to help get that blood pressure up but if it's not working then vasopressors are added to treatment now how can you evaluate if your IV solutions are being successful well you can look see is blood pressure going up is their systolic getting higher while it's working and if the patient has hemodynamic monitoring because when these patients are in septic shock they're going to be in the ICU and they're gonna have these special devices that can monitor for instance the CVP which is a central venous pressure and we talked about this a lot in cardiogenic shock but just to recap central venous pressure is that filling pressure on the right side of the heart so it's how much blood is really returning to that heart and septic shock we have hypovolemia relative hypovolemia so remember a lot of fluid left that vessel and went into the interstitial tissue so we depleted our circulatory system and if we're giving them fluids we should be replacing that fluid that has left that vessel and we're gonna increase the venous return to the heart so as that blood is flowing into the right side our central venous pressure should be going within normal range and a normal CVP is eight to 12 millimeters of mercury now if it was unsuccessful these fluids just really aren't doing the job you would be seeing persistent hypotension it's totally changing that blood pressure there hypotensive still and that CVP is less than eight millimeters of mercury so there isn't a lot of filling pressure occurring in that right side of the heart because our circulatory system is depleted of fluid as for steroids what can be used as like low dose corticosteroids and this is used in some patients to help decrease that amplified inflammation that's occurring due to that immune system remember it's occurring system-wide and if that patient isn't we're really responding to those vasopressors that baby's oppressor isn't really helping get that response that we need so they may be started on this as well h4 hemodynamic monitoring they're gonna have that like I said they're gonna be treated in the ICU they will have a central venous / arterial catheter to help assess tissue perfusion and those filling pressures in the heart that tells us a lot of what's going on with our patient example that CVP was that filling pressure in the right side and then you can look at what's called a pulmonary arterial wedge pressure and this is a filling pressure in that left side of the heart o for oxygen a you want to keep that oxygen saturation greater than 95 percent because those tissues need oxygen if we're making sure the blood is getting there if we don't have oxygen in it then it's not really doing great so we want to make sure that they're having plenty of oxygen in their blood and again they're at risk for a RDS and they may need to be intubated with mechanical ventilation to help assist them with breathing see four cultures this will need to be collected before starting the antibiotics but of course do not delay antibiotic therapy and this will help identify the microorganism that's causing the infection so appropriate antibiotics can be ordered and target that micro organism and then last k-keep glucose less than a hundred and eighty we want to prevent hyperglycemia because hyperglycemia affects the immune system and how I can heal so patient can be started on an insulin drip to control blood sugars other interventions that will be initiated of course is monitoring that serum lactate level level is greater than 2 to 4 millimoles per liter are abnormal and this again shows that cells are struggling for oxygen and have switched to anaerobic metabolism because they don't have any oxygen to metabolize and of course you want to monitor their urinary output Foley insertion we're gonna have that and you want to make sure that the kidneys are putting out at least 30 MLS per hour of urine and if it's low that tells us that our kidneys are failing due to decreased tissue perfusion okay so that wraps up this review over septic shock thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Medical_Surgical_Nursing	Tetralogy_of_Fallot_Nursing_NCLEX_Congenital_Heart_Disease_Defects.txt	hey everyone it's sarah thread sterner sorry and comment in this video i'm going to be going over tetralogy of below in this video is part of an ink lex review series over pediatric nursing and as always after you watch this youtube video you can access the free quiz that will test you on this condition so let's get started what is tetralogy of below it is a congenital heart defect that is characterized by four structural defects of the heart now some quick facts about tetralogy of flow is that it is one of the most common complex congenital heart defects and it occurs whenever the baby is developing in its mother's womb so some parts of the heart do not form correctly and according to the cdc gov in every 2518 births one baby in the US will be born with this condition and it's known as a cyanotic heart defect which means that there is going to be decreased pulmonary blood flow going to the lungs so that blood can become oxygenated so in other words that baby or child is not going to be receiving nice oxygenated blood which is going to cause the organs the tissues to suffer so they can have this bluish type tint to them called cyanosis now to easily understand tetralogy of flow you'll want to know the basic anatomy of the heart and how the blood normally flows through it because as you're studying all those other congenital heart defects it's just gonna make sense and there's really not a lot of memorizing you have to do it because once you can see how that blood flows you're gonna see okay I see why this person's having these signs and symptoms and what's going on so first let me cover the normal blood flow through the heart and then we're gonna compare it to a person who has tetralogy of flow and talk about these different structural defects okay so how I like to look at blood flow is I like to divide it up into two parts we have the right side of the heart and we have the left side of the heart and everything starts in the right side of the heart now the goal of the right side of the heart is to take that an oxygenated blood that exhausts of blood that your body just used up and get it to the lungs so we can get oxygenated and then it'll come to the left side of the heart and the goal the left side of the heart is to take that nice rich oxygenated blood and get it to your organs in your tissues because your body wants real oxygenated blood it doesn't want this mixing of an oxygenated with oxygenated just doesn't work and it doesn't like that okay so your body's used up this blood it's gonna drain it back through the superior and inferior vena cava hence it's represented in blue it's uh Knox agente 'td at first it's gonna flow down through the right atrium then the blood as this valve right here which is called the tricuspid valve it's gonna open up and let it flow down through the right ventricle now you have the tricuspid valve in the bicuspid valve tricuspid valve is on the right side of the heart and the bicuspid valve which is also called the mitral valve it's on the left side of the heart don't let the to confuse you how I remember it is a little saying try before you buy so try tricuspid by bicuspid over here so the right ventricle hearts going to contract it's going to squeeze and pump that an oxygenated blood up through the pulmonic valve then through the pulmonary artery which is going to go to the lungs and you have capillary beds on your alveoli sacs and oxygen that you just inhaled is going to cross over into this blood and carbon dioxide is going to cross over for you to exhale and that blood is going to be replenished again with oxygen so nice oxygenated blood then is going to go into the left side of the heart through the pulmonary vein then it's going to go down through the left atrium down through the bicuspid valve which is the mitral valve then to the left ventricle it's almost to the body then it's going to get squeezed up and if we could see behind this area you would see part of that a wordham it's going to go up through the aortic valve be squeezed up through there and then into the aorta and then shot throughout the body and it's going to replenish those organs and shoes however with tetralogy of flow this is not how the heart is set up there structural defects which is going to alter the way that the blood flows and like I said at the beginning the lecture that how many structural defects are there there's going to be four and to help us remember those let's remember the word wraps okay this person is going to have r4 right ventricular hypertrophy they're gonna have a 4a organ displacement p4 pulmonary stenosis and then s4 a septal defect specifically a ventricular septal defect so let's look at it okay here we have our heart let's go through just like how the blood should flow and talk about what's happening okay so with these patients what's going to flow in the normal way everything starts at the right side so superior inferior vena cava is bringing that exhausted enough oxygenated blood to the right side of the heart which it's trying to get it to the lungs to get oxygenated so it's going to go down through the right atrium down through the tricuspid valve and then down through the right ventricle this is where our problem begins okay normally and our last picture if you notice the right and left ventricle was separated by like a septal wall because we should have our blood that goes into a right ventricle and our left ventricle to mix but unfortunately we have a septal wall defect so there's gonna be this big hole right here allowing this blood to mix together now our problem continues what did I say that the right ventricle would does and whenever it receives its blood it squeezes it up through the pulmonic valve through the pulmonary artery to get to the lungs ain't happenin here because our pulmonic valve is going to be stenosis it's gonna be real narrow and that arteries gonna be really narrow so the right ventricle isn't going to be able to successfully pump that uh Knox generated blood to the lungs so you're gonna have decreased pulmonary blood flow so you're not gonna get a lot of blood that's becoming oxygenated so we have pulmonary stenosis now that's going to lead to another issue that right Interpol has to pump against so much resistance against that narrow pulmonary valve artery what happens to a muscle when you give it so much resistance it starts to enlarge so that's what happens right ventricular hypertrophy so a right ventricle is going to enlarge instead of being normal-sized so another thing because we have four problems this a or de we're gonna have a or de displacement so here we have a Orting valve on our other drawing it was nice up here wasn't enlarged but here with these patients it's enlarged and what happens is that this moves the aorta and unfortunately what happens is that it moves the aorta right over this septal wall defect opening so as you can see you have this uh Noxon aidid blood that's mixing with this oxygenated blood together and it's getting an ascent sucked up through the aorta is going throughout the body so this person's receiving all this uh Knox native blood that way and the right side of the heart is limited in how much blood it can get to the lungs to become oxygenated because this Pullman pulmonic artim artery and valve is so narrow so really it's all just going up through this area so you have what's called a right-to-left shunt all the blood from the right is being shunted over here and just going up through the aorta and it's an oxygenated blood now let's talk about the signs and symptoms that you can see in these patients who have tetralogy up below and to help us remember those signs and symptoms let's remember the word afflict now we know all these signs and symptoms are gonna go along with that decrease pulmonary blood flow because that blood is not being able to be oxygenated and go to the organs and tissues so our signs and symptoms are really going to correlate with so be thinking in that realm so a for activity any activity that this patient does we're talking about children babies like crying there ceding their plane it's gonna put a lot of stress and demand on that heart and as we just seen the structural defects don't allow the heart to be able to work correctly under those type of conditions so it can't replenish the blood with oxygen so any type of activity can stress the heart out leading to what's called a Tet spell if you can't remember anything about tetralogy of flow remember Tet spell and need a chest position or squatting just remember that because it's a big takeaways from this lecture for your exams so they have these Tet spells and this is where they start to become cyanotic that skin will have a bluish tint shortness of breath increased respiratory right and here in a moment we'll talk about your role during a test spell for fingernail changes which will represent clubbing of the nails and this is from where they have chronic hypoxia that chronic low oxygen in the blood causes those nails to have an abnormal appearance which is similar to these image this image right here and as the nurse you may notice this around six months of age in your patients our next F for fatigue slash faints easily and again this is related to those chronic low oxygen levels and especially during a tent spell the patient can feign so you'll want to be aware that we don't really want them to get to that point so whenever you're thinking of your plan of care for this patient nursing diagnosis a great one would be activity intolerance patients who have this can't do the normal things like other children can so in your plan of care you would want to make sure your nursing interventions and your goal goals for those patients are appropriate okay l4 lift knee to chest position or squat squatting and notice I have three asterisks by that because I really want you to remember this so anytime a patient is having a Tet spell what you want to do say you get a test question that says you're feeding an infant with tetralogy of flow you notice while you're feeding the infant they start their skin starts to turn like a bluish color and the respiratory rate has increase what your nest next nursing action well this is a tat spell so you'll be thinking in that realm what you want to do is stop feeding that infant and put them in the need to chest position give them oxygen and calm them some physicians may order medications to help keep the infant calm or IV fluids now why IV fluids well IV fluids can help decrease that right-to-left shunt which ties it in with the squatting some parents may ask you you know my kid to one and a half they noticed whenever they're playing with others all of a sudden they'll just squat why are they squatting what's the purpose of that well it goes along with the knee to chest position and the squatting IV fluids it helps what it does is it increases systemic vascular resistance and whenever you have that what that's going to do is that's going to decrease that right to left shunting which is going to help improve blood flow and help increase the oxygen level so that is what that is doing which is really need that the child just in a sense naturally knows just a squat to do that so that's the purpose of that and if you see that again you'll know okay i-4 inability to grow these patients will usually be smaller for their age and again it's just tying back to our body whenever a child is growing they need oxygen to grow to their tissues their bones everything like that so they'll have the inability to grow right see for cardiac sounds these patients are going to have abnormal cardiac sounds what are you gonna hear when they you in here is a harsh systolic murmur and you could feel a systolic thrill now where are you going to hear this murmur well where is it coming from what's causing it remember the pulmonic valve is stenosis it's narrow so you're gonna hear it where you would hear your pulmonic valve which think back to health assessment where do you hear that pulmonic valve you hear it at the left of the sternal border and that second intercostal space so a harsh systolic murmur and is from pulmonary stenosis and then tea or last part of our mnemonic trouble feeding and thriving so these patients another nursing diagnosis some of these patients could have is failure to thrive because of what's going on with oxygen levels so they can have low weights because they're not growing they'll be small for their age and they will have a decrease in meeting their developmental milestones compared to their peers now let's quickly go over the treatment for this condition okay this condition requires surgery to fix these structural defects now cases vary of tetralogy of blow some patients have very severe cases with worst-case-scenario so it'll vary on why each patient will get but they can have a temporary surgery which is like a palliative surgery until they can have complete surgery whenever they're really young and a shunt can be placed to shunt blood so you're increasing the pulmonary blood flow to the lungs or a stick can be placed to open up that narrowing of the pulmonary artery in the pulmonic valve to help increase the pulmonary blood flow then a complete repair can be done this is usually around six to twelve months of age whenever the child is a little bit older and they can place a patch to correct the VSD that ventricular septal defect because remember we don't want the blood mixing here so they can place a patch here to prevent that blood from mixing together now one drug I want to point out to you just so you can be familiar with it it's called our prosody which is a prostaglandin a medication and what this medication does is it keeps the ductus arteriosus um open and we're talking about newborn babies here a lot of times babies who are born with tetralogy of flow if they have a major defect to that pulmonary valve where they are literally just not getting any blood flow to those lungs we're gonna have issues they're gonna have like major cyanosis at birth and that can be started on this and food infusion and what it's going to do is it's going to keep this ductus arteriosus I'm open because after birth normally that will close shortly after birth so we don't want to close in this condition because what it can do it's normally about right here it allow blood to flow into this pulmonary artery which is going to increase blood flow to the lungs and we can get more hopefully oxygenated blood throughout the body so just be familiar with that drug and patients who receive that will get that it as an infusion and then they can have a temporary surgery until they're old enough to have complete repair okay so that wraps up this review over tetrology of below thank you so much for watching don't forget to take the free quiz and to subscribe to our channel for more videos
Quantitative_Finance_by_Yale_University	10_Dynamic_Present_Value.txt	So this class and the next class and a half are going to be about Fisher's theory of present value and the interest rate, and then we're going to move to uncertainty. So up until now what we've done is we found out first, if you know the whole economic system, how to solve for equilibrium. To figure out from the primitives of people's tastes, their impatience, the technology, the economy, how to figure out the real rate of interest if provided there is no uncertainty in the world and people can forecast what is going to happen later. We've found that once you've done that, the price of every asset, if people are rational and looking forward to the future, the price of every asset is going to be the present value of the future payments of the asset. So if you think of the payments as real payments, which is what Fisher always recommended, you discount by the real interest rate. If you think of them as cash payments then you discount by the nominal interest rate. So every asset corresponds to its present value of its dividends either discounted by the real rate or the nominal rate. Now, this thinking is surprisingly powerful and leads you to unexpected conclusions. So the next two classes is about that. Mostly I'm going to talk about Social Security, but I'm going to begin today by finishing off a subject we didn't quite get through last time. So you see, if you realize that the price of every asset is just the present value of its dividends, and you also suppose you know what the dividends are going to be and what the future interest rates are going to be, then it follows that you know what the price of the asset is going to be, not just today, but next year, and the year after and the year after that. So your theory of asset pricing today, which was based on the assumption that you can forecast the future, necessarily implies the theory of asset pricing in the future. So you can tell something about how asset prices are going to change, and of course you can also test the theory because the theory implicitly is forecasting something about the future, and therefore you can test the theory. So let's just take a couple examples that are in the notes. So we said at the top, if you can read it, I hope it's not too small--I want to move a little quickly so I could be writing this on the board, but if you can see it and you look at the top line it says that the present value of the assets is just the discount of future dividends. So maybe I'll start one line up, actually, in these notes. So if you look in the middle here the present value today, suppose you have an asset, maybe I'm going to write on the board after all. Present value of an asset, suppose you know the dividends are going to be paying C (1), C (2), and maybe C (T) at the end. Those are the dividends that are going to be paid, and you can ask what the present value of the asset is today, PV_0 today, 0. Well, Fisher would say if you think of these as nominal cash flows he would say what you need to do is you need to find out the price of zeros. So you recall that Fisher said that you could let pi_1 = the price today of 1 dollar at time 1, and the price today pi_T = the price today of 1 dollar time T. It's the price today of 1 dollar in the future. These were the crucial prices that Fisher said that you should always look for. He said that you can always find these prices, pi_1 through pi_T by deriving them from the yield curve. So every morning everybody looks at the yield curve, all financial analysts, they look at the prices of bonds traded in the market. The simplest form is you get a yield curve in the newspapers. You deduce from the yield curve what these present values pi_1, pi_T are, and that allows you to price any asset like this one simply by multiplying by pi_1, pi_2 and at the end by pi_T. So that's step 1. But then step 2, we said, was that once you've got these prices you can figure out the forwards. So the forwards are going to be 1 i_t, so 1 i_t that's by definition the interest from t to t 1 that would be agreed today. It's not the interest rate that's going to prevail from time t, it's the interest rate that people today at time 0 would agree to pay between time t and time t 1. So that, of course, has to just equal pi_t over pi_t 1, because everybody today recognizes that the cost of a dollar time t is pi_t, and the cost of a dollar at time t 1 is pi_t 1. So the tradeoff between t and t 1 that's effectively what an interest rate does is it trades off money at one time for another time. It has to be this ratio. So today people would agree on 1 i_t^(F), forward, as the forward rate. Now, you add to that the assumption that everybody is certain about the future, assume perfect forecasting. So I don't have to actually assume people are right in their forecasting. I have to assume that they are completely sure of their forecasting. So if they're completely sure of their forecasting then everybody must foresee that they think they're sure that the future interest rate that will prevail at time t is also equal to this number. So we can then rewrite this price. Hello. We can rewrite this price as 1 i_0^(F), forward; instead of pi_2, pi_2 is just going to be 1 over (1 i_0^(F)) times (1 i_1^(F)), and time pi_T is just going to be 1 over (1 i_0^(F)) times (1 i_1^(F)) ... times (1 i_t 1^(F)). Because using the fact that (1 i_t) is pi_t divided by pi_t 1 I just multiply pi_1 divided by pi_2 times pi_2 divided by pi_0 etcetera. If I take pi_1 divided by pi_0 times etcetera I'm going to get exactly this formula. So pi_0 is always 1, by the way. So if I want to take pi_1 it's just going to be 1 over (1 i_0^(F)). If I want to take pi_2 I can always do this, pi_2, and so this is going to equal pi_2, so pi_2 is going to be 1 over (1 i^(F)_0) times 1 over (1 i^(F)_1) etcetera. And pi_3, if I want to do pi_3, I just multiply by pi_3 over pi_2 and so that's equal to 1 over (1 i^(F)_0) times 1 over (1 i^(F)_1) times 1 over (1 i^(F)_2). So instead of multiplying by the pis I may as well take the product of the forwards. It's exactly the same thing. So the present value has this simple formula, but this is a formula that holds at every time t if you're totally confident of your predictions of the Cs and of the future interest rates. This is where we ended last time, basically with this formula. The key that you had to use in the problem set was to realize if you're totally confident now about the future you have to be totally confident about doing this calculation in the future. So PV_1 is going to be basically the same calculation. So what's going to happen at time 1? After you've gone down 1 year you've finished with this interest rate and you're looking at everything 1 year later. So I may as well write the PV_1 here and that's going to equal C (2)-- let's put it a little bit lower--PV_1 is going to equal the same C (2) as before, but now a year later. So it's just going to be 1 i^(F)_1 C (T), and I don't need the 1 i^(F)_0 anymore. (1 i^(F)_1) times ... (1 i^(F)_T-1). So it's exactly the same formula 1 year later, and 1 year later you no longer have to worry about the interest rate. That time already passed. So you just drop this at every time and you write the same formula, and of course you drop C (1) because that's all finished. So the price at time 1 is just what's left except you've chopped off the 1 i^(F)_0 everywhere. So to write that the same way, so PV_0 (I can write it the same way) =, PV_0 = what? It's going to equal the interest payment you get, C (1), not the interest, the dividend you get, the cash flow you get plus PV_1 divided by 1 i^(F)_0. So this is a very important formula. So why is that? Well, it's a proof by formula, but another way of saying it is that PV_0, when you get the asset at time 0 it gives you a cash flow at time 1, and then of course looked at from the point of view of time 1 you've got all the future cash flows, but that's just what PV_1 is. So basically the bond is going to give you a cash flow at time 1, and then the right to cash flows in the future, but this right to cash flows in the future at time 1 is worth PV_1. So it's like you've got all this money at time 1 and so to get the value at time 0 you have to discount it back again. So this is a very famous and important formula which I want to pause a second and think about. So there's a controversy today called marking to market. Does anybody know what that controversy is about? What does marking to market mean? Yep? Student: I believe that it means that corporations and their accounting rules are currently required to value their assets at what they would fetch in the market if they were to sell them. Prof: Right, but you know that they've been relieved of this responsibility recently. Student: No, I didn't know that. Prof: Well, so they've been relieved of this responsibility lately. Now, why have they been relieved of it? Because the thought was that the market was so panicked in the crisis that the price that they could fetch by selling their things really had nothing to do with the value. So we're going to come back to whether that was a good idea that Congress passed under tremendous pressure. What is the point of marking to market? So let's suppose that you really could anticipate the future and everybody was right about it. The market price then would really be PV_0 today, and it really would be PV_1 tomorrow, because if the interest rate's do actually turn out to be what everybody expects, and everybody's completely confident of their expectation, then as we saw the prices would have to be this today and this tomorrow, otherwise there'd be an arbitrage. You could make money for sure, or think you could make money for sure. So if you're marking to market what are you going to mark as the profits? Are you going to say the profit at time 1 is--so what is profit? If I had some room I'd put this somewhere. How would you define profit? I'll get rid of this. I think we've got this straight. So how would you define profit at time 1? What would you write? So let's say that this isn't a bond. It's an investment. You paid a bunch of money at time 0, maybe PV_0 and in the future your investment is going to pay off some money. Maybe it was a project you invested in. Maybe you bought a bunch of stuff and you're selling it in the future and getting this money. Maybe you bought a bond which is paying these coupons. Whatever it is these are the cash flows of the project, and now of course your investors are very curious. In year 1, they want to know what profit have you made, how are you doing? So what's a number that you'd think of giving? What's the first number you'd think of telling them? Yep? Student: Maybe the first cash flow payout. Prof: So you might think of saying, C (1). That's the cash you've gotten. So all these people could see you've gotten C (1). That's your revenue, and I'm assuming this cash flow is net of expenses. So you could say here's your revenue you got at time 1, C (1). Is that your profit? If it were, people would then look and they'd say, "Well, we got profit of C (1) and we put an investment in of PV_0 so is that the rate of return? Is that my rate of return?" Yeah? Student: Can we do PV_1 - PV_0 and add it here? Prof: So he's exactly right. I'm going to repeat what he said, but I'm going to take longer to say it. This idea of writing C (1) over PV_0 is actually what many people try to say is their profit, but it's a bad number for profit. Now, if in period 1 you stopped marking to market, and you had no idea, you didn't have to report this number PV_1, I mean, you didn't know what it was or you didn't have to report it, what else could you report but C (1) over PV_0 as the profit? So marking to market, you see, is intimately connected to how you report profit. So if you don't mark to market you don't know, you don't have to declare what the value of the assets are that are left. All you would do when you describe your profits is you'd say C (1) and people would, of course, in their heads, in fact they wouldn't do it in their heads, you'd tell them, "Our rate of return was C (1) over PV_0," but why might that be a very misleading number? Well, his point is it could well be that C (1) is a very high number. You've got a lot of cash flow this period, but he said it may turn out that PV_1 is a terrible number. You may have gotten a lot of cash flow, but there's nothing left going forward. So he doesn't think that's a very good measure of profit. So he's suggesting why not report profit as C (1) PV_1 - PV_0. Now, suppose you did that? So he's saying, look, you've got a certain amount of cash but the assets that you had also changed value and you ought to include that in your profit. So what if you did that? What would your rate of return be? And suppose PV_0 and PV_1 were calculated as this? And so you divided this by PV_0 what would that equal? What number would I get if I did that? I can't hear. What? Somebody speak up. Student: i^(F)_0. Prof: Yes. This would just be i^(F)_0, and you get the rate of return that you're expecting to get. Now, how do I know that's i^(F)_0? Because I multiplied by PV_0 to this side, then I moved that PV_0 to the other side. That gives me 1 i_0^(F) PV_0, then I divide by that 1 i^(F)_0 and put it down here, and that's this formula. So that is what you would get, i^(F)_0. And you see that's what you should expect to get because you haven't done anything great. You've got a cash flow. You've got these cash flows at the beginning. You paid a fair price for them and next period everybody forecast that the values were going to go to PV_1, and so it can't be that you're, you know-- this was an investment you made. You put your money in. You bought this bond. You could sell the bond now at time 1 after having obtained the cash flows. It better be that your rate of return is the market interest rate of return otherwise there'd be some arbitrage, and in fact it is. So if you can compute all the present values properly, the only fair thing to do--this is not a great investment. Even if C (1) is a huge amount of money it's only huge because PV_1 is a low amount of money. Because it has to be that the profit every period, the rate of profit, is exactly equal to the interest rate, because everything is always priced at its present value. So it's a simple concept which somehow takes a long time to grasp. It just seems to people that--here's the money that's come in. That's the cash you can count in your hands. You've got it in your hands. That's the number you should talk about as profit, but of course of the money coming into your hands--there's this other hidden thing. The stuff that you own has suddenly fallen in value compared to what it was before. You're really not putting the firm in any better position than it was before. You just earned your normal rate of return. So you can see why, to give a fair description of how people are doing, the law was written, evolved to the point where people were forced not to just say C (1), they were forced to declare--mark to market, and add PV_1 - PV_0 to their profit to get a real rate of return, to get a more revealing rate of return. And so what happened in the crisis is this PV_1 became such a horribly low number that if you plug that into this formula you get PV_1 is a really low number compared to PV_0. You get a giant negative here. It would look like the rate of return was terrible. Everyone would panic and think the firms had fallen apart. So especially the banks were the ones who didn't want to do this, and so Congress didn't want the public to be panicked so it simply said, "Okay, forget about it. We're going to not hold you to writing PV_1 anymore because we can't count anybody figuring out what it is, and so you don't have to tell us that. You just have to tell us this," which happens to be a good number for the banks, but that doesn't mean the banks are actually doing well because the assets they hold have been collapsing in value. Yeah? Student: Does that > say that assuming there's no arbitrage opportunity if a firm pays out a high dividend its stock should go down? Prof: Yes, right. That's exactly what it says and that's what does happen. So you always talk about the price, ex-dividend and stuff like that, precisely that. So if a firm pays a bigger than usual dividend, if it suddenly decides it's going to pay itself a gigantic dividend then the price of the firm is going to go down, exactly, because there's less value in the firm. You've paid it out here instead of keeping it into the firm. So this is a very simple idea, but it's very easy to get confused about. Are there any questions about it? So let's do an example of it. The most basic example of it is the premium bond. So we talked about this before, the premium bond. So let's say you have PV_0 = 5 divided by 1.10 5 divided by 1.10 [correction: squared] (maybe this was exactly the problem set, I can't remember) 105 divided by 1.10 [correction: to the T]. So in other words the interest rate--I did that wrong--squared and T. So the forwards, in other words, 1 i^(F)_t (small t) = 1 .10 for all t, so all the forwards are 10 percent. The bond is paying--I can't remember which one I did. Let's do 20 here. I'm going to make it a premium bond, so it's paying 20. So what's going to be the price of the bond? Well, in the first period it looks like you get this incredible profit. The interest rate is 10 percent. You've paid some present value and you've made 20. You've made a number much bigger--so the price of this thing, by the way what was the home work problem? What were the numbers? What was the interest rate? Did somebody do the homework? I did assign a homework on a premium bond, right? The interest rate was 5 percent and the coupon was 10, was that what it was? What? What was it? What was the homework problem? Student: 8 and 6. Prof: 8 and 6. So this was 8 percent. Might as well do this one, 6 here, yeah, 6 percent, and this one was 8. So what was the price PV_0? What was PV_0? You've done this homework problem, right? Does anyone remember what number they got? Ben, do you remember the number? No. I'm counting on my trusty class here to provide me all the numbers. It was what? Student: 108.4. Prof: Was that what it was, 108.4? That's all? This was the price just 108.4? So 108.4, right. That's a high price. So it's way above par. This is a bond that's worth much more than 100. Why? Because the interest rate is 6 percent, but the coupon is 8 so this is called a premium bond. So if you look at the first year the rate of return on the first year is 8 over 108.4. Now, is that more than 6 percent? It is way more than 6 percent, 8 over 108.4. It is way more than 6 percent because 7 percent of this is going to be less than 8. So it's more than 7 percent, so this is greater than 7 percent, and so it's certainly bigger than 6 percent. So it sure looks like at the end of the first year like this bond was an ace bond. That's the kind of calls you used to get. You still sometimes do get them if you're a wealthy person and you actually answer calls like this, which you don't of course, but you can get some cold call from a sales person saying, "We've got a fund and look how well it's doing. On this much investment last year we got payments of 8 dollars. That's more than 7 percent, and look, everybody can see the interest rate is only 6 percent and we did better than 7 percent. We're doing great. Why don't you invest in our fund?" But actually, what the salesman hasn't told you is that the value of his assets has gone down. So the present value PV_1 must be less than PV_0, because we know from this formula, the formula right up here, that 6 percent is going to be the cash flow over PV_0 which is more than 7 percent plus this difference, and this difference, therefore, is going to have to be negative. So what he didn't tell you was that the fund lost value even though the first payment was better than 6 percent, the market rate of interest. So that's the first example. Now, let's do another example. Suppose you have a--let's see if I can write on this board. There's a famous trade called the carry trade. Now, suppose the forwards--suppose 1 i^(F)_0 is 2 percent, sort of like now, the 1 year yield, and 1 i^(F)_t is 5 percent, for t greater than 1? So if you have a 1 year bond it's going to pay--well, let's say it's 2 percent and this is equal to 1 --can you see this or it's disappearing. So let's make the first two of them be 2 percent, and this is for t greater than or equal to 3. So the interest rate is 2 percent and then it's going to jump to 5 percent. All right, so if you have a 2-year bond, a 2-year Treasury, a 2-year bond might pay 2 and 102 and the present value of this equals 100, the present value of the 2-year bond. But now maybe you've got a longer bond that's a 5-year bond which pays coupons 4, 4,4, 104, so this is a 5-year bond, and maybe its price is close to 100. Actually, I haven't worked out the number so you're going to have to do that in the next problem set. So is it possible, so I'll ask it this way, is it possible for this coupon to be higher 4, 4,4, 4,4 and yet still have a present value of 100 than this one which is 2 and 102? Could you have a higher coupon and yet the same present value of 100 on a longer bond than on a shorter bond? How could this bond have a higher coupon and sell for the same price as this bond? Yep? Student: You're losing money on the assets you put on the principal value because you get it in a later period > Prof: So the point is you're discounting the first two payments by 2 percent a year, but you're discounting these payments by 5 percent a year. So these things are going to be much worse than they look. And so even though the 4s are all better, this 100, you know, it's 4,4, 4,4, 4 100, that 100, not to mention these three last 4s are getting discounted by a lot. So that 104 is going to be worth less than 100 back, you know, it's going to be worth less. So that's why these things are going to go down a lot more than you think. They're going to be worth less than 100. So even though these things are better than the 2 percent rate of return-- this bond does great at the beginning, but does poorly thereafter, because in the beginning it's paying 4 percent when the interest rate is 2 percent, but later it's paying 4 when the interest rate is 5 percent, so clearly you could have some situation like that. So what's the carry trade? The carry trade is you buy the long bond and sell short the short bond, so the lower maturity--too many shorts--the lower maturity bond. So this is the, let's say, 5 year and 2 year. Buy the 5-year bond and sell short the 2-year. The word, sell short, is different from the word, short bond. So you buy the 5-year bond and you sell the 2-year bond. They both cost you 100, so what's happening at the beginning? You're making 4 dollars and you're only having to pay 2 dollars. It looks like you're making a profit for nothing, right? So that's the carry trade. You buy long bonds with a high rate of interest. You sell short bonds with low coupons and it looks like you're making a profit. But in fact, what's really happening? So just repeat what you were saying before, but now in this context. What's really happening? Student: You're paying off that difference, the loss of the value of your assets. You're not getting back as much as you would if you had just bought the 2-year bond. Prof: Right. So the long bond you got a cash flow of 4 the first year. You had to pay 2 because you sold the 2-year short, right? So you're up 2 dollars, but the thing that you owe now at the end of the first year, since the interest rate is 2 percent, the next interest rate is 2 percent, the 2-year bond is still worth 100. So your negative position is still worth 100, but this positive position now, these 4, 4s and 4s it looks worse than it did before because you've moved up the yield curve. Instead of having two 2 percent years you only got one 2 percent year before you shift into the 5 percents which is worse and worse. So what's going to happen is you're going to get a positive cash flow at the beginning, it looks like positive profits right at the beginning. That C (1), the net C (1) looks really good, but right after that, the value of your assets is going to plummet compared to your liabilities, because now all of a sudden you're discounting this at 5 percent and this thing is still, you know, it's only got 1 year left where the interest rate is still 2 percent and the rest of this is discounted at 5 percent so it's starting to go down in value. So if you didn't have to mark to market what would you do? If you didn't have to declare to the world what your present value of your remaining assets are, because you could say, "Oh, it's so hard to figure out. I don't know what the stuff is worth, the present value of what's going forward. I just know the cash that's coming in." This carry trade would look like a really good trade, wouldn't it, and a lot of people would do it because then they would look-- the public would think that they're doing really well because they're getting positive value, but in the future that positive value they're getting is just disguising losses that are happening in their portfolios going forward. So any questions about that? Yeah? Student: Can you explain where their losses >? Prof: I want you to explain it. So I didn't calculate the numbers. It would have been better to do actual numbers. If we do 4,4, 4 at 5 percent interest, or maybe I can do a--let's just do a real number. Well, let's just do the one over here. So this one is--no, I can't do it, because we've got 2 percent and then 4 percent. So we take a minute to do it on Excel and we've seen how great I am doing those on the fly. So the point is that you agree that this payment 4 is bigger than 2. So the first year if you buy this bond and you sell that bond you're going to have a positive net 2 dollars. However, it's perfectly possible for this whole bond at the beginning to be worth 100 the same as this bond at the beginning. Now, how could that be? Well, the payments--4 is bigger than 2 so how could this whole thing have a higher present value than this thing? It has to be that starting at period 1 the present value of this 5 year bond (let's call it this) in period 1 - the present value of the 2 year bond staring in period 1 has to be what? If this present value of the 5 year bond, this is the 5 year bond at time 0, equals 100, and that's exactly the same as this present value at time 0 of the 2 year bond, if that equals 100, so the present value from the beginning of this thing is the same as the present value of this thing from the beginning. How could this thing have value 100? Well, it's because it makes lots of high coupon payments, but the interest rate is going to jump up in the future so you're discounting all these future cash flows at a big number. So all these things present-valued could well equal 100. So this could be 100 and this could be 100 even though this is paying off more at the beginning than this thing is. But what does that formula that we just wrote down over there, what does this formula tell us? Where was this formula that I wrote down? This formula over here tells us if the present values of two instruments-- I see I wrote it for 1 bond, but if you take 2 bonds with the same present value, one of which has a higher cash flow in the first period than the other, then that formula tells you the bond with the higher cash flow at the beginning has to have a bigger drop in the present value than the other bond, otherwise you can't get them both equal to the same 100. So this bond and this bond have the same present value of 100. Because this payment is bigger than this payment, but the present values are the same, 100, it has to be that starting from this point on, this bond is worth less than that bond. So what happens? You go long this bond, you short that bond, you say to the world, "Ah ha! I've made 2 dollars. I'm a genius," and then you hide from them, you might hide from them if you didn't have to tell them, they wouldn't know that the present value of the bond you're long going forward is actually lower by 2 dollars than the present value going forward-- this is right after this period--the present value starting at this point of this bond going forward has actually dropped 2 dollars below the present value of this bond going forward, and it has to have dropped otherwise the present values wouldn't be the same. So to just say it much more simply, if you take 2 bonds with the same present value you could well have that situation where they have the same present value because one of the bonds pays a lot of stuff early and terrible stuff late. So in the beginning it looks like this bond is paying you more money than the other bond, but since they have the same present value it must mean that this bond is going to pay you more money at the tail than this bond is. That's why they had the same present value. So if one of them gets ahead at the beginning it has to be it's going to fall behind the rest of the time. So this one got ahead at the beginning, it has to fall behind the rest of the time. That's hard to see because it looks like this bond it's paying a coupon that's always bigger than that bond. So it's easy to lose track of the fact that this bond, because its coupon is higher than this bond, how could it possibly ever fall below this bond? Well, it falls below because it's longer and the cash flows towards the end of it are being discounted by an interest rate-- because everybody knows the interest rate's going to go up. And remember we saw last time the yield curve. The yield curve, remember today's yield curve is practically 0 now because the government's held it at 0 and it's going to go way up to 4 percent or something in a couple years. So that's the yield curve today. So everybody knows the interest rates are really low now and they're going to get much higher later. So what it means is that every long bond that's being issued now is going to be issued with a higher coupon than the short bonds, and if you go long the long bond and short the short bond you're going to make money at the beginning but lose it back later. But if you don't have to report mark to market, you don't have to say the value of what's left over, the public's just going to see that you're making money at the beginning. It's clear now? Any other questions about this? So a lot of this is going on right now. So let's do one more application of this. Let's explain how mortgages work, one more idea. Since the present value is = to the cash flow the present value at 1 times that, given this formula, that tells you one more thing, very important idea. How do you compute present value 0? Well, the way we've always computed present value at 0 is to do this calculation, this long calculation discounting all the future cash flows, but this formula tells you that there's actually a more efficient way of calculating it by backward induction. If I knew what the present value was at time 1 then I could get the present value at time 0 just by this formula. I'd add the present value at time 1 to the cash at time 1 and discount it. So in fact I don't have to--now, I don't know the present value at time 1, but if I go to the end, at the end of time, I know the present value of the bond is 0. There's nothing coming up later. At time T - 1 I know the present value's very easy to calculate. It's C (T) divided by 1 i^(F)_T - 1. So I can go backwards by present value and compute. I can do backward induction. So that's the word I want to describe which is going to play a very important role in the future of the class, backward induction. It says if this formula is correct then a good way to do the computation is by working backwards from the end. Don't just blindly take the present value. If you blindly take the present value all you've got is PV_0. If I calculate by backward induction I start to the end and say, what would PV_T-1 be? That's a really simple thing. Then I can very simply find out what PV_T-2 is etcetera back to the beginning. I do basically the same calculation without having to take powers of-- it's a shorter calculation because here I've got exponents of interest rates multiplying each other. So it's actually a shorter calculation, and on top of that I get much more information because now I've calculated out what the present value's going to be at every time period. So a much more efficient way of calculating things is to do it by backward induction because it also tells me more. It tells me what the future path of the bond is going to be. So let's just see how that works on an example that I hope I worked out properly before. Of course, I did it last year, but let's assume I did it right. So let's take a mortgage, if you can see this. So this is something you have in your notes. So there's a mortgage. Now, how does a--all right, well pay no attention to that. So let's just say that--oh no, why did this happen? Let's say that the payment is 8. So I've made payments of 8 everywhere. I hope I haven't screwed this up. So here's the mortgage. It's a 30-year mortgage. So these are the years 1,2, 3,4, 5,6, 7, blah, blah, blah, blah, blah, blah up to year 30. Now, suppose I happen to have a bond that pays a coupon of 8 dollars every year, and the interest rate, let's say, is 7 percent. So it would be the interest rate on the mortgage, but let's say the interest rate in the economy is 7 percent and the bond, however, is a premium bond. The bond is paying 8 percent every year. Now, this is a mortgage so what does this mean? See the mortgage pays 8 every year until the very last year where it's still paying 8. So it's not paying 108, it's just paying 8 every year. So it's not a coupon bond. It's a mortgage. A mortgage pays the same amount every year until the end. So if this were a coupon bond the last payment would be 108 and of course the thing would be a tremendous-- it would be a premium bond because the interest rate's only 7 because it would pay a higher coupon of 8 and 108 at the end. But you see I'm not paying 108 at the end. I'm only paying 8 at the end. So the first question is, what is the present value of this bond? So I could take 8 divided by 1.07 8 divided by 1.07 squared (all the way) 8 over 1.07 to the thirtieth power and figure out that number. But a much better way of doing it is by backward induction. So what do I do? I go to the end and I say this line is the remaining balance. Well, at year 30 there'd be no more payments of the bond so the present value of what's left is obviously 0. Now, what is the present value of what's left at time 29? Well, the only thing I'm going to get is I'm going to get this payment at time 8 right over there. Sorry. I'm going to get this 8 right there and so the present value of 8 at 7 percent interest is 7.47, I mean, 7 percent interest. So how did I figure that out? I just said, take that payment on the right and discount it by 7 percent, so it's 7.47. Now, what's the present value here? Well, here you're going to get two things. What are you going to get? You're going to get a coupon payment. Just after the payment in year 28 what's the present value of what's left? You're going to get a payment in year 29 of 8 dollars. You're also going to get one in year 30, but you don't care about that. You just know that the value in year 29 is the coupon you get in year 29 plus the present value in year 29 of what's left. The PV at time t, I can just put a t here, PV at time t is the coupon you get at time t 1, the present value at time t 1 divided by the interest rate at time t. So all I have to do is take 8 7.47 and discount that by 7 percent, and that gives me the present value as of time 28. So if I go back to time 26 I say, well, how do I figure out the present value at time 27? It's time 27. I say, well, I'm going to get 8 at time 28, but the present value at that time, just after that payment, is 14.4. So I take 22.4 and discount it by 7 percent and I get about 21. So that's how I can work backwards and figure out the present value today. Now, in mortgages this number is very interesting. It's called the remaining balance, which we'll see in a second. But anyway, that number you can calculate it every t. It's just the PV_t worked backward from the end. So it's a very simple calculation and it tells you the present value of the bond, of that 8 percent coupon, until year 30 and no principal at the end. Well, a mortgage has to pay a coupon of 8 percent that gives 100 because if there were no uncertainty and there are no prepayments or anything, no uncertainty, the bank giving the coupon is not going to give you money unless its present value is equal to 100. So they're going to ask you to pay a coupon. So now you see what have I done over here? This is B 26 - B 30, so the original face it was supposed to be 100, but the present value of all those payments is only 99, so there's a gap here of .72 and the square of the gap is that. The square of the gap is there, and we want to minimize that. So we're going to find the payment every period, Solver. So I want to minimize B 32, minimize by choosing B 29 which looks good. That's the first payment, and all the other payments are set to be equal to that, to minimize that difference. B 29 is the first payment, so why didn't this work? Student: You hardwired in C 29 and D 29 > Prof: Is that what I did? So here's 8 and then this over here. I hardwired that in, so I didn't want to do that. So that's got to be equal to what's left, equal, left. So here I got--when I hardwire this then, okay, so that's good. So let's try the same thing now. Tools, glad I have you guys, Tools, so B 32 is what I'm minimizing. B 29 is the first payment and all the others have been set equal to it, and if I solve... Student: C 29. Prof: All right, let's try. The first payment is year 1, right, so it should be--oh, C 29, thank you. Yeah, that's why I'm confused, C 29, thanks. Tools, so let's just look at this a second. So that's what I've hardwired in. So Format, no Tools, Solver. Minimize B 32 subject to C 29 as you've told me 20 times, C 29 and now solve. So now we did it. So we got the right payment to make the balance exactly equal to 100. So that's how a mortgage works. You have to find the coupon payment such that if you take the present value of that same coupon payment forever it's just going to be worth 100 which is that number. And how do you figure out the coupon payment? Well, you do it by backward inductions. Figure out the present value. Do it by backward induction just as we did. But we've gotten a lot of information. We've gotten this number at every period. So by doing it by backward induction instead of just doing the long exponential calculation, by doing it by backward induction we've produced the present value at every time in the future. Now, that's an incredibly important number in mortgages. It's called the remaining balance. Why is that such an important number in mortgages? This will play a very key role in the rest of the course. What is the remaining balance and why is it so important? Does anyone know how a mortgage works? Yep? Student: Is that the mark to market value or just whatever you'd be able to sell that mortgage for to someone? Prof: Not what you'd be able to sell it for, but close. So when the bank gives you a mortgage it says--so how did mortgages work? It used to be in the old days that the mortgages were coupon bonds. They'd pay 8,8, 8,8, 8,108, and then what would happen is just before the 108 payment everyone would default. So in the Depression the people who defaulted were people who defaulted just before their big principal payment, so bankers got wise after the Depression. They said, "Well, that's a terrible thing to do. We should make the payment be constant and that way there's no reason for the guy to default right at the end and we're not going to get stuck with 100 dollars that's not paid." So it's constant. But of course if it's constant that means the present value of what's left is going down all the time, so that's why this number is going down all the time. If it's 108 at the end, that's why the present value would stay the same. So it's going down all the time, so that's why it's called an amortizing mortgage. It's because what's left in the mortgage is getting smaller all the time. So a fixed rate mortgage pays the same coupon every year. The present value of what's left, therefore, must be going down every year and that's why it's called amortizing. And bankers wanted that to happen because that way their risk is going down every year. Every year the house is presumably still worth 120 or whatever it was at the beginning and the amount owed is getting lower and lower. So the bankers are feeling more and more secure every year because the house is backing a smaller and smaller loan, or to put it another way, if you're uncertain about what the price of the house will be in the future, you want to make sure that what is owed is going down in the future. If the price gradually goes down of the house what's owed is gradually going to go down. But the main reason why the number is so important is you have to realize the purpose of a mortgage is you take out a loan using the house as collateral. If you don't make your payment they can take your house. Well, what happens if you want to move? If you want to move you're going to sell the house. The house is no longer collateral, so if you want to move you have to undo the promise to the bank. So if in year 5 just after you're making your payment of 8 dollars and 5 cents in year 5 you decide to move, you say to the bank, "I want to cancel the mortgage." How much will they ask you to pay? Well, the remaining balance, 93.91. So that's why this remaining balance is such an important number. So it allows people to leave their house and pay off their mortgage by paying off the remaining balance. You wouldn't want them to pay 100 if they left because they've made payments. You notice that the payment here is 8 dollars. That's bigger than 7 percent, right, because if it's a coupon bond you'd pay 7 all the way to the end and pay 107. That would have a present value of 100. If you're not paying the 100 at the end, but just making a level payment all the way through, the payment you have to make every year better be more than 7, so it's 8. So this 8 - 7 is sort of what you're paying down of your mortgage, right? The interest is only 7. You've paid 8. That's why you owe less than 100. You've paid 1 dollar 6 extra. That's why you only owe 98.94. So every year you're paying part of your principal down. That means it's amortizing, and that means if you want to get out of the mortgage you can get out of it by paying less and less. It means the lender, the mortgage lender, is more and more protected by the house every year because what you owe is less and less. So that's how a mortgage works. Any questions about that? All right, so what's the point? The point is that by simple present value thinking you can start to understand the main instruments in the economy, how mortgages work, why they're called amortizing, why the amount you have to pay to get out of your mortgage goes down every year, and exactly how much it goes down every year etcetera. So we can do a lot more examples like that, but I want to change, shift the discussion now to a much bigger subject, a subject of tremendous policy interest in the country, namely Social Security. What should we do about Social Security? Now, it will turn out that you can analyze the situation the same way we've just analyzed these bonds. It's very simple to figure out what the problem is and what went wrong, yet very few people understand it, including most of our politicians and, I'm sorry to say, a lot of our economists. So I want to describe now in the next class and a half the Social Security problem and how to solve the problem, but also how to understand the problem. You can't figure out the right solution until you've understood what the problem is. So were there any questions? Before I start this, were there any questions? I should have paused. Are there any questions about the mortgage, or present value, or how present value changes through time? So those ideas, and marking to market, those are very important ideas I think once you think about them not so hard. I'm now going to take exactly those ideas and apply it to Social Security where the public is totally baffled, but all you have to do is apply the same thinking. So Social Security is supposed to be in a terrible crisis. That's what they always tell you. It was a big campaign issue in 2000, you probably were too young to remember that, but there were three debates between Gore and Bush in which Gore grimaced and everybody thought he wasn't a good guy and so they voted for Bush. He was mostly grimacing about Social Security. And then in 2000--well, I'll get to the future. So anyway, in those debates three mistakes were made. So Bush argued that the returns on Social Security were disastrously low. He said the whole program is in a terrible crisis and we've got to privatize to save the system. How did it get into the crisis? Well, it wasn't clear exactly how it got into the crisis, but it seems like the baby boomers had something to do with it. They're all getting old and they're going to have to get these huge Social Security payments, and that's why we're in the crisis because the baby boomers are getting old. It's all my fault, or my generation's fault. Then the third mistake was Gore said, "Well, it's impossible to privatize." Privatize means take the money that your parents are paying in Social Security and that you'll start to pay; instead of putting it into the fund that's being used somehow, you don't probably know exactly how, instead of doing that, take that money and say it's the taxpayer's money. It's your money. You can put it in the stock market if you want. So that's what Bush wanted to do, privatize Social Security, say your tax contributions should go into a stock market with your name on them. And Gore said, "Well, that's impossible. If you privatize, what are the old people today going to do? Where are they going to get the payments? You can't privatize Social Security and take today's young tax contributions to Social Security and say, 'You young guys, there's your money. You can keep them in the stock market,' and at the same time pay the old retirees, so Bush must not know what he's talking about." So that also was wrong. So those three things, that Social Security is going to give terrible returns, it must be it's wasting money, something's horribly wrong with it and the only way to save it is to privatize it. That's Bush's main claim. Blame it all on the baby generation, that's everybody's claim, and Gore saying you can't privatize without screwing today's young [correction: today's retirees]. All three of those things sound pretty convincing and yet they're all three wrong. So I want to explain the system to you and help you understand it, and then I have a policy recommendation you'll get next class which most people don't agree with, so you probably won't either, but I'll warn you when we get to a point that's controversial. So everything I'm going to say in the first 90 minutes is going to be uncontroversial. Not everybody knows it, but I think it's obviously just a matter of logic. And then my conclusion about what to do, you can criticize it. I think it's a matter of logic too, but I admit most people don't agree with it. So now, in 2005 if nothing else Bush was tremendously consistent. So whatever he told you he was going to do no matter how wrong-handed it was he did it. So he said in the debates that he wanted to privatize Social Security and sure enough he kept his word. He launched a huge program. That's how he started right after the 2004 election. His first initiative, you might remember, was we've got to privatize Social Security. He went on a 60-day, 60-city tour to kick off his second term. So after the 2004 election privatizing Social Security was a huge issue. In the 2008 election it was still a big issue. McCain said sort of what Bush said. "I want young workers to be able to if they choose, to take part of their own money which is their taxes, their money that's getting taxed and getting put into Social Security, I want them to have their own account and put it into the stock market with their name on it." And Obama said he's totally against that. That was 2008. Recently, of course, the public has made another mistake. So everybody is saying now, "Oh, the financial crisis. We better not talk about Social Security anymore." Nobody's talking about Social Security. They're saying, "Well, could you have imagined what would have happened had we privatized as Bush wanted us to do and the stock market collapsed? Everybody would have lost all their money. What a disaster that would have been, and it would have ruined the old." This sounds pretty persuasive. So Krugman wrote a column saying, "A bullet dodged. What would have happened if Bush had succeeded? All the old people would be broke now." And Robert Reich who was in the Clinton Administration sort of more or less said the same thing that it'd be a disaster. Now, the Obama Administration, by the way, hasn't stopped talking about Social Security. So their director, he's the Director of the White House Office of the Budget, so this is an incredibly important position, Peter Orszag. He's the son of--there's a math professor here, Orszag, his father. So he's a friend of mine, the son. He said once healthcare reform is in place the U.S. can then focus on other important things, especially Social Security. So Obama wants to do something about it, but he just doesn't want to privatize. So it's a big problem and everything everybody says about it seems plausible. Now, just to continue along the plausibility of it, so Bush says what he really wants to do is-- why private accounts are a better thing is that if you put the money in private accounts it can grow. You can get a greater rate of return than the current system which is terrible. If you were a young person by putting your Social Security tax money aside in a private account you'll be able to get a better rate of return on your money than the government could get you on your money. So why would you just want to give it to the government? It's for your retirement and you'll be able to pass that money along to your children and grandchildren if you want at the end. And best of all the money's yours and the government can't take it away. So that's what Bush says and he's said many times. So there's one sense in which he's right. So let's look at the returns people got on Social Security. Now, what is a return? We know what the rate of return is. How do they calculate it? You can go back to people born starting in 1878. Social Security, as you'll see in a second, I'm going to give you the history, began 1939. So these people in 1878 they're 60 when Social Security's beginning, if my arithmetic is right. So they're 60 at that point. So you can look at all these people and you can say, for every generation in the past, you can say how much money did they pay when they were young? They paid taxes. So they got negative 12.4, that's the tax rate. Negative 12.4, they did that a bunch of years when they were young and then they started getting payments when they were old, 24,24, 20 something like that. Those are the payments when they're old. So there are negative ones at the beginning and positive ones at the end. You can calculate the internal rate of return, the yield, the thing that makes this present value 0. We know how to do that. We've done it. So people have done this. So there's a guy named Limmer, Limmer or Leemer from the Social Security Administration who did these calculations, prompted a little bit by me. So I should say that a lot of the reason I got started thinking about this is I got put on a Presidential Panel to study Social Security Reform in the Clinton Administration and every Democrat was matched with a Republican. So the two chairmen, one Democrat, one Republican, all the way along there was Democrat and Republican, and after Bush got elected all the Democrats got kicked off the committee. But anyway, so in any case here are the rates of return. For people who are old when the program began, they got sensational rates of returns, 40 percent, 30 percent, incredible rates of return. As the generations get younger and younger the returns go lower and lower and they're down now to 2 percent. These are a forecast of these rates of returns. And so let's see, you're 20, say, something on average. You were born in 1990, something like that or around there. So here's your rate of return. It's down here, right? It's 2 percent, and there it is blown up. It's under 2 percent. So these are the people from 1924 to 2002, so you're right at the end here. That's your rate of return blown up. You can only expect 1 and a half or 2 percent. So George Bush is right. The rate of return on Social Security is terrible. If you look at the taxes that you put in, and you look at the benefits that you can expect to get your generation is getting totally screwed. So now if you look historically--this was done in 1994, so the number's a little bit--it's not quite as dramatic, but it hasn't changed as much as you think. From money put in the stock market between '26 and 2004, that's before the crash of '29, so I should have gotten the number after the recent crash. It doesn't change that much. Before the crash of '29 you looked at keeping your money in the stock market, just leaving it there for all that time, after inflation you'd get 9.1 percent return. On treasury bonds you get 2.7 percent return and yet on Social Security you're going to get under 2 percent. So George Bush says, "Look, put it in the stock market. Get 9 percent." We had a little disaster here, so maybe it's 7 percent. "Put it in the stock market and get 7 percent. Why be satisfied with 2 percent? There's something wrong. We've got to privatize, put an end to this." So there seems to be something to what he is saying. So now you look at what's going on with Social Security. So what happens in Social Security? I'm going to explain the whole history and how it works here. What happens is you pay taxes, 12.4 percent tax. You probably know that. Everybody's paying taxes on the money they make and then there are benefits that are being paid. Now, the benefits are not--there's a formula for benefits which doesn't have anything to do with the amount of taxes being paid, so at the present time the taxes are bigger than the benefits. So where does the extra money go? It goes into the Social Security Trust Fund. So here's the Social Security Trust Fund which is now around 2 trillion, which is going to keep growing because contributions are going to be bigger than benefits until 2020 or so, and at that point contributions--that's the baby boom generation, that's me retiring, or a little later in my case, but anyway the baby boom generation-- in fact since I'm a Yale professor it's out here somewhere. So anyway, my generation's going to start retiring here and then the benefits-- so we're going to be not working, not paying taxes but we're collecting benefits and there are so many of us that the benefits are going to be less than the taxes and the trust fund's going to go down, and down, and down. And then the year 2030, at a little bit more than 2030, the trust fund's going to go to 0, and then after that the taxes are still going to be smaller than the benefits. And so what's going to happen? They'll be no money to pay these people and there's going to have to be a big drop in what people are getting. So it looks like the system is not only paying a horrible rate of return, it's not even going to pay. It's going to run out of money and go broke in 2040. So it seems like a total disaster. So that's the setting of the question. George Bush said it's a disaster. It looks, at first glance, like a disaster. The newspapers tell you all the time it's a disaster. How did it get to be so bad and what should we do about it? All right, now it's going to turn out that by using the concept of present value it can be very simple and straightforward to understand, and it's going to be the exact opposite of what everybody seems to be saying. So I'm going to play you a clip next time of Roosevelt announcing the Social Security program and this lady behind him is Frances Perkins, the first woman to ever be in the Cabinet, and she played a tremendous role in shaping Social Security. So after Roosevelt started Social Security in 2004--I'm wondering whether I really have time to do this, so I'll just say this. So Roosevelt started the program in 1938-'39. He started the program in '38-'39. It was one of the cornerstones of the New Deal. It's an incredibly famous program and it seems to be in incredible trouble. So we need to find out and get to the bottom of why that is and we'll start doing that next class.
Quantitative_Finance_by_Yale_University	20_Dynamic_Hedging.txt	Prof: The subject of today's lecture is hedging. So this is what hedge funds do. It's what almost everyone on Wall Street does nowadays, at least to some extent, say half the people on Wall Street nowadays. It was hardly done at all in the past. So first of all, just to mention what a hedge fund is, a hedge fund is a firm that manages money. And why is it different from any other firm that manages money? Well, the definition of hedge fund basically has three parts. One is that hedge funds hedge. Now I'll say what that is in a second. Secondly, hedge funds use borrowed money in addition to their investors' money to buy assets. So they do what's called leveraging, which is going to be an important subject for the last few lectures of the course. And thirdly, they charge their investors very high fees. That's basically the definition of a hedge fund, because they're supposed to be so good at what they do, they can charge high fees and still get the investors. So what is hedging? Hedging is the idea that you want to cancel out some of your risks. So for instance, you might know that a company's not going to default, whereas the rest of the market thinks it is going to default. So you know the company's worth more than the rest of the market thinks, so you might be tempted to buy the company. But if the interest rate were to change, say go way up and the company's paying, has constant cash payments, if the interest rate goes way up and the company has constant cash payments, you could end up losing money anyway, because the present value's going to go down, just because the interest rate has gone up. So what a hedger would do is, the hedger would say, "Look, I'm relying on my expertise as an evaluator to realize there's no default risk. I want to bet that there's no default risk in this company. It's not going to default. I don't want to bet on which way interest rates are going to go, because I don't know which way interest rates are going to go, so I want to hedge myself against that." So to take-- sorry, I'm just starting here. Hello. Sorry, hard to talk when everyone else is talking. So what does hedging a risk means? It means no matter which way the risk factor goes, you're going to still end up with the same amount of money. So the first person to do this and call himself a hedge fund was somebody named Jones in the 1940s and he was a stock picker who would try to find the best possible stock to buy. So before him, people would say, "Okay, Ford is a great auto company. We're going to buy Ford." The trouble is that Ford may in fact turn out to be the best auto company, but because the whole economy collapsed, it may be that Ford collapsed with the rest of the economy, even though it did better than all the other auto companies. So what Jones said is, "I'm not going to just buy Ford. What I'm going to do is, I'm going to buy Ford and I'm going to sell General Motors, so that way I'm going to be betting not on whether Ford is better than General Motors, and in addition, whether the whole economy's going to go up. I only want to bet on whether Ford is better than General Motors." So if the whole economy goes down, Ford and General Motors will go down together. So what you own in Ford, you won't own something as valuable any more, but what you owe by having sold General Motors short also won't be as valuable. So what you've bought and what you've sold will cancel each other out and you won't have lost any money. On the other hand, if Ford ends up doing better than General Motors, you'll have gained more with Ford than you'll have lost with General Motors. So whether the economy goes up or down, if the gap between Ford and General Motors stays the same, you won't lose or win money, so you're hedged against general changes in the economy. You're only going to make or lose money depending on the spread between Ford and General Motors. So you've canceled out the economy wide risk and you're only holding one risk, which you really think that you've understood. So that's what hedging is. So I'm going to now show you that hedging is actually a slightly delicate thing. It's quite complicated and we're going to learn the technique of dynamic hedging. Now why is dynamic hedging so important? Dynamic hedging is so important because there are so many things that can happen in the future, and as I said, for example, if you hold a mortgage, you may think the mortgage is more valuable, because you know people aren't going to default, and the rest of the economy thinks they're going to default. On the other hand, the value of the mortgage will change with the interest rate, so you want to protect yourself against the interest rate change. But it's not just the interest rate change. Over ten years or 30 years, the life of the mortgage, there are going to be a huge number of interest rate changes. There'll be a whole path of interest rate changes, and the mortgage will be paying different cash flows along the whole path. In over 30 years, even if you think of only one change a day, there's an exponentially growing set of changes, so there's an exponential number of paths. You'll never be able to equalize your cash flows, you would think, over every single path. There are just too many of them. But dynamic hedging says you don't have to equalize over every path from the very beginning. That is, you don't have to hold a portfolio at the very beginning that equalizes your cash flows by the end of every path. You only have to equalize your cash flow one step at a time and then dynamically change your hedge, so it's a much easier thing to hedge than it sounds at first glance. So I want to illustrate that, because you can't know what that means yet until we see an example. So let's start with a very easy thing to understand, the World Series, where we started before. So you have some expertise, in fact, there are other people besides you who have the same expertise, these other bookies. You all know the Yankees have a 60 percent chance of winning every game against the Phillies, and let's just assume for simplicity that the World Series is only going to take a couple of weeks. The interest rate is 0 over such a short period of time. You don't care whether you get the money now or at the end of 2 weeks, just so long as you get it. You can borrow or lend at 0 interest over those short number of days. And secondly, you know that the probability of winning is 60 percent. Now suppose that some naive person comes to you and says, "I'm a Phillies fan. I want to bet at even odds that the Phillies are going to win for 100 dollars." So you're going to now get a payoff that's -100 dollars at the end of game 7, assuming I counted right. So this is the start. This would be game 1 here, so it's 1,2, 3,4, 5,6, 7. So by the end of game 7, if you played it to the end, you would have made 100 dollars if the Yankees won a majority of the games, and you'd have lost 100 dollars if the Yankees didn't win a majority of the games. So how much is that worth to you? Well obviously it's worth a lot more than 20 dollars, because if they only played 1 game and the Yankees had a 60 percent chance of winning, the expected payoff for the Yankees, that bet for 1 game would be 20 dollars, because you know in 1 game a .6 chance of 100 and a .4 chance of - 100, that gives you an expectation of 20. 60 - 40 is 20. However, we're playing a seven game series. The whole point of playing a long series is that the Yankees are more likely to win. The better team is more likely to win, and in fact, we know that by doing this backward induction calculation, we know that the expected winnings for the Yankees is 42 dollars. However, the Yankees--you could lose 100 dollars. If the Phillies just got lucky, you could lose as well as win 100 dollars. You don't want to face that risk, so what could you do? Well, the simplest thing to do is to go to another bookie and say, "I want to bet on the World Series," with this other bookie. So if the bookie is willing to make a bet with you for the whole series, so the bookie has to be pretty sophisticated and do the same calculation, the bookie is going to let you bet however you want to at the right odds. So what would you do? So here you can win 100. There are only two outcomes. You can win 100 or you can lose 100. Now the odds of winning the series, I forgot to say, we figured this out before. Oh dear, what were the odds? Hope I have another one of these World Series things. Okay, so what are the odds that the Yankees are going to win the World Series? We calculated this before. Do you remember what it was? Well, we know some probability P times 100 some probability (1 - P), -100 gives you 42. So P times 100 (1 - P) times - 100 = 42 approximately. That's 42, right? So we know that therefore, 2P times 100 = 142, so P = 142 over 100 times 2, which equals about .71. Okay, so this other bookie would have calculated the odds are 71 percent that the Yankees are going to win the World Series. We calculated this a few classes ago. The Yankees have a 71 percent chance of winning the World Series. So if you went to another bookie who could do this calculation, the other bookie would be willing to give you odds of 71 percent Yankees versus 39 percent [correction: 29 percent] Phillies, so you could just unload this whole bet and get 42 dollars for sure. In fact, what would you bet with the other guy? What would you bet with the other bookie? What would you do if you could bet on the whole World Series? Somebody suggested that. He was sitting over there at the end of the last class. What would you do if you could bet on the whole World Series with the other bookie? What bet would you make? You know that the bet is giving you 42 dollars on expectation. The trouble is, some of the time it's giving you 100, some of the time it's giving you -100. You don't want to fix this risk. You want to end up with 42 dollars for sure. Now how can you do that? Well, if you did -68 [correction: -58] here, that would = 42, and if you did 142 here, that would also = 42. So could you figure out a way of betting with the other bookies 142 versus 58? You win 142 if the Phillies win, and you lose 58 if the Yankees win? Student: > Prof: That's not 42 by the way. Okay, would another bookie be willing to give you this bet? What's the answer? The answer is yes. How do you know the other bookie would be willing to give you this bet? What is P times 42 (1 - P) times 42? It's 42. What's P times 100 (1 - P) times -100. It's also 42. So therefore, what's P times this (1 - P) times that? Student: 0. Prof: 0. So at the odds, P and 1 - P, this bet is perfectly fair. So the other bookie would say that's the odds, 71 percent to 39 [29] percent. That's exactly what these odds are. So if P times this (1 - P) times that is 42, and P times this (1 - P) times that, that's obviously 42, must be P times this (1 - P) times that is 0. In other words, at the odds, P and 1 - P, this is a fair bet, so the other bookie would give you those odds. So that's what's hedging is in its simplest form. We haven't had to do anything dynamic. Some guy is willing to bet on the World Series with you, so you know that he's done something wrong in his calculations. He's got the wrong P, so you can take advantage of the situation. You know that P is higher than he does. On the other hand, there's still God in the background and luck, which might make the Phillies win, and so you don't want to subject yourself to that risk. So what do you do? You take the bet, the advantageous bet, but you put together with the advantageous bet a hedging bet, where you're betting on the wrong team, the team you think is going to lose. But you're betting on the wrong team, but this time, at fair odds on the wrong team, and so you're transforming your risky payoff, albeit with very favorable odds--P we just said was .71-- you're taking your risky payoff and turning it into a safe payoff of 42, no matter what. That's the essence of hedging. In order to do that, you might have to bet the opposite way that you think is going to turn out. So there's principle number one. So let me pause and see if there are any questions for that, about that. The idea is that there's something you know that you can take advantage of, but life is more complicated than knowing one thing, namely what P is. Life also involves all kinds of other things that might happen. You want to insulate yourself from those other things and concentrate entirely on what you know about P and 1 - P and therefore assure yourself of a bet of 42, no matter what. And you're taking advantage of the fact that other people will also be able to bet at P with you. This one outsider doesn't understand that all the bookies are willing to take odds of P, he's offering odds of 1 half, which is crazy. It's a big gap, 71,29 to P. So you can take 42 of his dollars for sure. Okay, so now let's go to--okay, this is hedging. It's also an arbitrage. This is--hedging created a pure arbitrage. In this case, it's done even better than in my example with Ford, because you've taken now a bet and transformed it with an expectation you're going to win, into a bet where you can't possibly lose. Okay, now suppose that these other brokers weren't as clever as you. Suppose that the other brokers--okay, so that's hedging. Now we're going to do dynamic hedging. Suppose the other brokers, they're not as smart as you. They don't know how to build these trees. They can't do backward induction. They just know the odds are 60 percent that the Yankees are going to win any game against the Phillies. Now what would you do? Okay, you can't go to another broker and say, "I want to bet on the whole 7 game series." The guy's going to say, "It's just too complicated for me. I'm a simple man. I make a simple living. I just do 1 game bets. I'll let you bet any game you want. You tell me what you want to bet, we'll bet one game at a time, 60/40 odds. The whole series, it's much more complicated for me." So is there anything you can do now? What can you do now? So now you have to do something more complicated, which is called dynamic hedging. So we started to talk about this last time, so what would you do? You only now have the opportunity of protecting yourself against bad luck by betting one game at a time with these other brokers. So what should you do? Well, let's look at this picture here. You know that this bet of ( 100, -100) by doing backward induction is worth 42. So if you were a trader, a hedge fund manager, you would be marking your position at 42. You're expecting now--you've just made a trade which you know on average is going to make you 42 dollars. Of course, if you had bad luck, you could end up losing 100 dollars, which means you're going to go out of business, you're going to be fired, your name's going to be in the newspaper, you're going to be probably sued by your investors. Or you can--we haven't been sued by any investors. Or you might make 100 dollars. Now you don't want to face that. You want to hedge yourself, protect yourself, so you're going to make the money for sure. Now some people don't hedge. They say when you hedge, you're betting against yourself, and something bad can happen. The hedge might go negative, right? It may be that the Yankees win, just as you think, but because you've hedged, you're not going to get 100 dollars. You're only going to get 42 dollars. So the essence of hedging is you give something up on the upside to get something on the downside. So people don't like hedging because they're giving something up. Okay, so you're giving something up. The point is, you're getting something back on the downside, and you're making it so you're locking in your profit. So hedging is a good thing. So people who don't hedge I think they're just very simple minded. So there are a lot of people who still don't hedge, but anyway, there's a revolution in financial thought in the last 30 years, anticipated by Ford [correction: Jones], but it didn't really get--people didn't really catch on until the '70s that you should hedge. So how can you hedge this if you can only bet 1 time, 1 game at a time? That was the question we dealt with last time. What should you do? Well, you see the principles we've learned so far tell us what to do. You started here thinking on average you're going to make 42 dollars. You should be marking your position correctly that it's worth 42 dollars. Now if you win the first game, you're at a big advantage. The Yankees are up a game and by backward induction we know that then your position will be worth 64 dollars. If you lose, your position will be worth 8 [correction: 9] dollars. Now what is 60 percent of 64 plus 40 percent of 9? It's 42. 60 percent of 64 is 38.4. So you're at 42 and you could go with 60 percent probability to 60-- I can't even remember the number--64, or down to .9,40 percent. Sorry, I'm getting senile, 9 with 40 percent probability. So 60 percent times that is 38.4 40 percent of 9 is 3.6 and the two add up to 42. So that's why--so to say the value's worth 42, how did you get the 42? We were doing backward induction. We took 60 percent of that 40 percent of that and we got 42. So if you're marking yourself to market, after the first game of the series, you'll have to admit to the world that you're either now worth 64 dollars, or you've gotten crushed, and you're down to 8 [correction: 9] dollars. That already might get you fired. Going from 42 to 8 [correction: 9], that's a pretty drastic loss. So even the first day, if you have to mark to market, you're going to be revealing to the world that you've screwed up and now your position's only 8 [correction: 9]. You've told all your investors, you've done this brilliant thing. They're up 42 dollars. The next day, you're going to have to tell them, "Well, I'm sorry, you're only up 8 [correction: 9] dollars." They're going to be very upset. So what would you do? You know what to do. What would you do? Student: Hedge. Prof: Hedge. Good answer. How would you hedge? Student: > Prof: Right. So what do you say? This is 9, so you'd go ( 33, -22). So that's equal to 42 and that's also equal to 42. Can you do this? Is it fair odds to do this? Well, yes, it has to be fair odds to do this, because 60 percent of 64 40 percent of 9 is indeed 42. 60 percent of 42 40 percent of 42 obviously is 42. So therefore the difference, 60 percent of this 40 percent of that must be 0, so in other words, it's fair odds. And sure enough, this is obviously 3 to 2 odds, right? 60/40 means you're betting at 3 to 2 odds. That's 3 to 2 odds. So it is a fair bet, so the other bookie who's willing to bet at 3 to 2 odds is going to give you this bet. So again, you think the Yankees are going to win, you make a bet with the naive Philly fan, you're betting the Yankees are going to win. You go to your broker friend and you bet against your Yankees. You're going to lose 22 dollars if the Yankees win, and win 33 if the Phillies win. You're betting against yourself, but of course you're betting against yourself to a smaller extent than you're betting against the other guy, and therefore you still locked in 42 dollars. So now we don't have to go any further. It would only be confusing to go further. I usually go further, so it would just be complicated. If you can do something once, you can do it many times. So by making the right hedging bet, you can lock in a profit up here and up here. But that means you can lock it in going forward to the very end, because you can keep repeating that hedge over and over again. Maybe I'd better go one step further. You don't really believe me. So what could you do going from here to here? Well, the average of here and here is about 9. You've collected 33 dollars, don't forget, from your hedging bet. So although this says 9, you've got the 33 in the background, so it's 42. But it's 9. So what you want to do, this is 9, you just want to transform this and this into 9. Once you've transformed this and this into 9, which you can do because 60 percent of this 40 percent of that is 9, so the other broker--you can do an offloading hedging bet with another broker at 60/40 odds to get 9 for sure here. Why is that? Because 60 percent of this 40 percent of that is 9, so therefore there must be offsetting-- a bet he'd take that gave you 9 for sure in both cases, because the offsetting bet would also be valued at 0 according to 60/40 odds. So you can transform this and this into 9s but don't forget, you've been paid the 33, so actually this is 42 and 42. So you can keep 42 and 42 going forever and by the end, you'll have 42 forever. So that's what dynamic hedging is. It's as simple as that. Yes. Student: In order to make money with hedging, wouldn't you have to have someone who would bet against you with different odds? Prof: Yes. So how do you make money in hedging? You effectively were betting against the Phillies fan at 50 percent odds, and you've got your broker who's willing to give you 60 percent odds, and you're exploiting that gap. So let's do another--excellent question you're asking. I haven't answered his question yet. I want to give another example to answer his question. What is really going on with the hedging? What am I relying on? How many brokers do I have to deal with to hedge? What's going on here? I've given an example of a World Series where it's very simple to figure out what to do. So now I want to give an example of a bond. It doesn't matter what bond. I have to confess, I haven't done this in advance. Here we have a 30-year bond, 8 percent 30-year bond. It's an 8 percent 30-year bond. So we know what its payment is. Homeowners are all perfectly not paying attention, the bond is going to be worth some amount of money. So here are the interest rates, I forgot to say. So we have to assume what the risk is. So in fact, what does this mean? We know that the risk is 6--the interest rate starts at 6 percent and it has a 20 percent volatility. So what does that tell us? It tells us that the interest rates could go up or down by this amount. Now, we've assumed that the odds that it can go up or down are 50/50. So we've assumed that everybody thinks the odds are 50/50 that the interest rate could go up or down. That's an assumption, and so now I'm going to make--we've assumed that the odds are 50/50. Let's assume that everybody is willing to trade you 50/50 odds. So what does that mean? This is like your other broker. So the interest rate is here, r_0. It can go up to r_0 times up, or it can go down to r_0 times some down. Up remember, is--up, by the way, this = r_0 e to the volatility times e to the drift, and down = r_0 e to the - volatility e to the drift. It doesn't matter. r_0 can go up or it can go down. So U is bigger than 1, D is less than 1 probably. So we see examples of that. Now I'm making an assumption here that the odds are 1 half and 1 half and that everybody understands and is willing to bet on these odds of 1 half and 1 half. So betting on an interest rate move is called--that kind of betting on interest rates means trading interest rate derivatives. So there are a bunch of ways that you can trade in the interest rate market to get 1 dollar if the interest rate goes up to this number, in exchange for losing 1 dollar if it goes down to this number. And these things are called swaps and they're called interest rate derivatives and they're called a whole bunch of other things, which it's going to take too long to explain. So let's suppose that you can go out into the interest rate derivative market and simply trade a security that'll pay 1 dollar if things go up or you can buy another security that will pay 1 dollar if things go down. Now what is the price of this security that pays a dollar if the interest rates go up? Let's say they can only go up or down to one of two values. So what would be the cost if everyone agrees the odds are 50 percent of getting up here? What is the price today going to be of getting 1 dollar if the interest rate goes up? Student: X divided by the interest rate. Prof: Excellent. Who said that? Perfect. I didn't expect anyone to say that so fast, so right. So the price here, we could write is .5 divided by (1 r_0), and this price going down is going to be .5 divided by (1 r_0). How did he figure that out? Well, the odds are 50 percent of going up here and 50 percent of going down here, but don't forget, you're getting the money later and this is a 1 period interest rate, 1 r_0. So therefore, what you'd be willing to pay here is 50 percent of the dollar that you'll get, discounted by 1 r_0. What you paid here for that is 50 percent of the dollar you'd be paid, discounted by 1 r_0. So, exactly right. But now these are like the World Series, game by game odds. They're going to change depending on where you are in the tree, because if you go here in the tree, you've got a higher interest rate, so it's going to be .5 divided by (1 r_U) or something, which is a bigger number. So the price of betting on 1 dollar-- what you have to pay to get 1 dollar if interest rates go up is going to be more [correction: less] here than it is here, say, because you're going to still have 50 percent chance of getting here, but you're discounting by a higher interest rate. So it's slightly subtler, but not much. It's like the broker in the World Series who game by game, day by day, there's the interest rate derivative market, and they're willing to trade you, they're willing to let you bet on which way the interest rates are going to go. So what have we got now? We've got this mortgage that's sitting there. So let's say that you know that the mortgage is owned by a very rational guy. The homeowner--he's not the owner of the mortgage--the homeowners are very rational people. The market is very foolish. This is an exaggeration. The market might think the homeowner never does anything, so they think the bond is worth 120. You've studied prepayments much more than the market does. You realize that the homeowners aren't going to just sit there, dumbly paying whatever they owe if the interest rates go down. They're going to prepay, so in fact the mortgage is only worth 98. So the market thinks it's worth 100. The market understands the interest rate probabilities and is willing to give interest rate risk. They agree with you about that. You don't know anything more about interest rates than the market does. What you do know is you know something about the prepayments that the market doesn't know, and so you know the bond is really worth 98 instead of 120. So what should you do? Let's suppose that the market is actually treating-- so what the market thinks, mortgage is = to a 30 year bond-- well, it's not actually a bond because it doesn't have a principal at the end, so I'm going to have to do a different sheet here to get it together. The market thinks mortgage never prepays. Let's suppose that what you can trade in the market is these interest rate derivatives. So what should you do now? You can trade the mortgage, you can buy it, you can sell it short, you can buy or sell these interest rate derivatives. What would you do? Let's say you can only buy or sell 1 unit of the mortgage. There's only 1 mortgage that is trading, and since you know there's a mistake being made, you're going to use all of it. So what would you do? Do you think the mortgage is overvalued or undervalued? Student: Overvalued. Prof: It's overvalued, so therefore what should you do? Student: Sell it. Prof: Sell all you're allowed to sell. I've assumed a little artificially. All you can do is sell 1 unit of the mortgage short. So you're going to sell it for 120 dollars. But what does it mean to sell it short? It means you have to make the payments that the mortgage is making. So you know those payments are only worth 98 dollars? So what does that mean? It means that you know you're going to get a profit of 22 dollars. However, you could get completely crushed if things don't turn out exactly the way you thought, so you want to lock in a constant profit for sure. So you don't want to get a huge profit more than 20 and no profit in some other cases, or even a negative profit and a huge profit. You want your 22 dollars for sure. So how would you do that? What would you do? Yes. Student: > Prof: Okay, so let's be more precise. It's exactly right, but let's just see what this really means. So I'm going to copy these numbers down which I can't see yet. You have a mortgage that's 98. You know it's 98 something, .8 and it could go in the up state to 92.6 or in the down state it could go to 99.11. Now on the other hand, the market thinks that this mortgage, this other instrument, you're selling at the same time something that's worth 120. You're selling it for 120. It doesn't matter what the mistake is the market makes. That's the reason why the market made its mistake. You don't care why they made their mistake. You know they're just willing to give you 120 for it. So you're making a 22 dollar profit, so what should you do? If you were marking yourself to market, what would you do? What would you mark yourself to market here? Well, you've gotten 122 dollars so you've marked yourself to market. Here you'd say you're 21.16 dollars up. Here you'd have to say you're not up so much money anymore, because you've just lost some of the value of your mortgage, you've lost 6 bucks. So you'd have to say you're only up 15 dollars now. And here you'd have to say you made a little bit of money, so you're up 22 dollars now. But you want to lock in this profit, 21.16 for sure. So what should you do? If you're marking yourself to market, you want to turn this money into 21.16, but more than 21.16. You want to turn this into 21.16 times (1 r_0). You want to turn this into 21.16 times (1 r_0). Because then, having locked in 21.16 times (1 r_0), that's no risk and it's got the same present value as this and so every period, you want to keep locking your money into 21.16. That's the gap between that and up there. Maybe 16 wasn't the right number, by the way. What was this price up here that they were willing to pay? They were willing to pay 120.58. So that's a little bit more. 21.7 or something. So it's 21.7, that was the gap. So it's 120.58, so the gap here is 21.7. So you want to turn this into 21.7 and this into 21.7. So 21.7 here, you want to ensure that that's where you're marking yourself to position. You want to know by the end of the next year, you could turn this into 21.7 discounted up and then keep it discounting till the very end. So whether you take your money now, you take your money later, it's always a sure thing with exactly the same present value. So how would you turn 21.7, knowing that you're going to run this risk if you're marking yourself to market, how would you do that? Well, you know the value of this this at this interest rate, in the mortgage derivative market, it's worth 98.84. So you can always transform this into exactly 91.84. By doing a fair bet you can get this to go up to 91.84 and this to go down to 91.--oh, there's also a payment here. Don't forget the payment. So sorry, we've forgotten a payment. The mortgage is much subtler because you've actually gotten 8 dollars here 8, and this is 8. So we forgot about this. So you got an 8 dollar coupon what was left was 92.6. this is 99.1 8. So actually, the total value here is 100.6 and the total value here is 107.11. You discount this by this 6 percent interest and you get 98.84. So I left out a crucial step. Remember, the cash flows here are the coupon the value of the mortgage that's left. So the value of the mortgage that's left is 92.65, the 8 dollar coupon. So over here, you're going to have a value of 100.6. Down here, you're going to have a value of 107.11. So how can you--you want that to equal, locked in forever--so you've just sold this mortgage for 120, so you've got 21.7 dollars sitting here. So now what can you do with this 21.7 dollars? You can cancel your cash flows so what you owe on the mortgage is always exactly the same thing, 98.84. So you want to make this 98.84, so you have to subtract something off from here, 100.6. You want this to be equal to--let's do it this way. Let's make this 98.--this is a simpler way of saying it, I think--98.84. Let's turn this thing, the present value of this and this is 98.84. Therefore you know there must be some fair trade in the derivatives market that turns this thing and this thing into 98.84 times (1 r_0), and this into the same thing, 98.84 times (1 r_0). How do you know you can do this? Because the present value of 98.84 times (1 r_0) and 98.84 times (1 r_0), 1 half of that 1 half of that, divided by (1 r_0) is 98.84. So therefore the present value of this thing has to be the same as the present value of that thing, and therefore there must be some trade in the derivatives market you can make, where you sell some of these interest rate derivatives and you buy some of these interest rate derivatives, which guarantees you 98.84 in both cases. So that means the present value of what you have to deliver in cash-- the value of what you'd have to deliver in cash-- is 98.84, still 21.7 dollars, in present value terms, less than what you've received. What have you done with this 120 dollars? You've invested that at the same interest rate and so now you've got a profit. You owe 98.84, jacked up by the interest rate, but the 120 you've invested. You've got that 120 the interest rate. You've always got more that you're carrying on than the present value of what you owe, and you keep going to the end of the tree. When it ends, you're still going to owe 98.84, increased by the interest rate a bunch of times, but then the value of the money you have is going to be 120 increased by the same interest rate, and so you're going to end up with money for sure. So then you can just reverse it all, and get the money 21.7 locked in for sure at the beginning and owe nothing later in the tree. So to say it all one more time, you have to think of yourself as marking to market. If you're marking to market correctly, you know what you owe is only worth 98 dollars and what you've sold it for is 120 dollars. That's a profit of 21.7. But you want to make sure you can maintain the same profit forever, or to put it another way, if you've bought this bond-- you want to make sure you can lock in your profit forever. So how would you do this? There are different ways of doing it. Let's say you want this 21.7 dollars for sure at the beginning and you don't want to ever have to make any payments. In the end you want everything to cancel out. What would you do? How would you do this? This number tells you, you owe in present value terms 98.84 dollars. So you've gotten 120 dollars. You could take the 120 dollars, put 21.7 in your pocket, and now, with this 98 dollars, you can buy these cash flows. What can you buy? You can invest money so that you--you can buy the right interest rate derivatives so you're able to make all the payments of the future bonds. So this bond, the actual payments the bond is going to make, you can buy all those payments for 98.84 dollars. I guess that's the simplest way of saying it. I'm going a little bit in circles. What is the mortgage security down here if you know how the mortgage is going to pay? All this is, is a bunch of payments at different parts in the tree. It pays 8 dollars here it pays 8 dollars here. Somewhere low in the tree, it's going to just prepay for sure and pay the whole remaining balance. Down here, it's just paid off for sure, so it's prepaid. Sorry, it's prepaid at the top--at the bottom, it's prepaid. The fact that all these payments together are worth 98.84 means that by taking 98.84 dollars and trading on the derivatives market, you can buy all those payments for exactly 98.84. So therefore as you go farther into the tree, you always will have the payments to make. You've sold the bond short. What does that mean? Any time this bond makes a dividend payment, you have to make the payment. But you can always buy those payments for 98.84. How do you know you can buy those payments for 98.84? Well, by backward induction. Here, the payments are 8 dollars here, 92 dollars of remaining dollars. So there's a way in the interest rate derivatives market of buying 8 92.6, that's 100.6 dollars here, and buying 107.11 dollars here. So by spending this 98.84, you can get, buy this many interest derivatives, so you can get 100 dollars of payments here, and 107 dollars of payments here. Half of 100 half of 107, discounted at 6 percent interest, gives you 98.84. So it's possible on the market to buy 100 dollars up here and 107 dollars down here with this 98.84. Now out of those 100 dollars up here you've bought, give 8 of them to the guy you sold the bond short to. That's the coupon payment. Down here, give 8 of these dollars to the same guy you sold the coupon short to. Now that leaves you with 92 dollars up there and 99 dollars there. But this 92 dollars is the present value of what's going to happen next, and what's going to happen next up here is that you're going to owe 8 dollars to the guy here and you're going to owe 8 dollars to the guy here, but what's left will be worth 83 dollars and 97 dollars. So therefore with this 92 dollars, you in fact are able to buy this 92 105 here, because the present value of 92, almost 92,105 here, is exactly 92. That's how we got this number. It's 1 half times this number the coupon, 1 half times this number the coupon, discounted at the interest rate corresponding to here. That is 92 dollars. So therefore, by investing here in the interest rate market, you can buy that cash flow here, the 84 8,92 dollars. Pay the guy the 8, you'll still have 83 dollars left and with the cash you have over here, remember you bought exactly this much cash. You've got this much cash left. You can buy all the payments you need to make here, the 8-dollar coupon, plus you'll still have 97 left. So all the way forward through the tree, you could always afford to buy all the cash payments of this bond. So you can pay off the guy you sold it short to all the coupon payments that this bond is making, by having invested 98.84 at the beginning. And similarly, you got 120 by selling the bond short, so you've made 21.7 dollars and there's never any more cash coming out of your pocket. You pocketed the 21.7 and you invested the 98.84 in the derivatives market over and over, changing your investment, and therefore reproducing all the cash flows that you have to make to the guy for having sold it short. I didn't say it very well. How followable was that? Not very followable. Sorry, I didn't do a good job. Let's try again. What is the essence of what's going on? The essence of what's going on is that gain-by-gain or month-by-month, you can find someone else who'll always trade at fair odds with you. Fair odds means--in the interest market. They don't know, these people trading the interest rate market, they don't understand prepayments. It's not like the bookie here. They don't understand prepayments. They're not willing to be with you on what prepayments are going to be. They're just going to bet with you on what interest rate is going to turn up. But you see, the cash flows from the bond depended on prepayments and depended on the interest rate. So you calculated it was worth 98.84 because you know what prepayments to put in the future. So if you're absolutely confident on your prepayments, you're going to know what this bond is going to do in the future. So remember the prepayments. What are these prepayments? It's this stuff. So down here, where the 1s are, the guy's prepaid for sure, so you'd have to deliver to the market the entire remaining balance at that point. But see, when you calculated this bond, you were anticipating what all the payments were going to be, whether they were going to be the whole remaining balance or just the coupon. Taking the present value, what calculations were you doing? In the present value, you're doing calculations that this guy can do. You're just taking 1 half times this 1 half times that discounted. The interest rate derivative guy is willing to do that. He doesn't know what the prepayments are going to be, but you're never betting on prepayments with him. With the interest rate derivatives guy, you're just saying, "Let me pay you some money now. You give me money if things go up here, or I'll pay you some money now and you give me money if things go down here, if interest rates go up here or interest rates go down here." So because the present value of the mortgage cash flows evaluated according to the interest rate probabilities and discounting is 98.84, that means that you can successively trade on the interest rate market and reproduce all the mortgage payments, assuming you're right about what they're going to be. And therefore with 98.84 dollars, you can replicate what the mortgage is going to pay. And therefore, you make 21. 7 for free, because you sold it for 120. You only need 98.84 of that to reproduce all the payments of the mortgage bond. And how do you know that you can do that? Because it's just one step repeated over and over again. At every step, there's going to be a payment of say 8 dollars and a present value of what's left. And there'll be a payment down here of 8 dollars and a present value of what's left. Or maybe this thing is just a prepayment, in which case it's a single payment of 99.5. That's the remaining balance after 1 period. But when you figure out this number, it's always taken by averaging this number discounted with this number discounted. So therefore, averaging at the odds the interest rate guy will give you. So therefore, using this money, we're now doing the opposite of the World Series, using this money, you can buy this total payment, and you can buy this total payment, because that's exactly what the interest rate guy will give you. This is equal to 1 half of all that divided by 1 r_0, plus 1 half of all this divided by 1 r_0. That is this number, so therefore in the interest rate market, by using this cash, you can buy that and you can buy that. And that's enough to make the payment A8 that the mortgage is paying, you keep your promise. And over here, if the mortgage prepaid, the remaining balance, that's that number, 99.5, you can pay that too. And then the mortgage is done. Here the mortgage is going to go on, but see, it's going on at present value you've calculated at 92.6. You bought 92.6 8. You use the 8 to pay off the coupon. You still have 92.6 dollars in your pocket here. You're going to use that to buy the future payments of the mortgage, some of which will be a coupon, and maybe this will be another coupon, plus the present value of what's left. If it goes down here again, the guy might prepay, but you're going to have enough money to make that prepayment. So with this 98.84 dollars, you're just doing fair odds over and over again. You're buying the future cash flows of the mortgage and therefore with 98.84 dollars, you can keep all your promises, and yet you've gotten 120 at the beginning, so you've locked it in. That's it. Any questions? I don't know if that was too clear, so somebody ask a question. You're great at asking questions. Is this followable? Student: > Prof: Okay, that's too good. Too great. Okay, let's see if I can do another example. Let's suppose that we've got this bond. Let's say you can't trade in the interest rate derivatives market directly, but you can trade in the bond market. So let's get more realistic now. Let's suppose that there's a bond market. Now here we had interest rates--so it was a 30-year bond, the starting interest rate was 6, and the volatility was 20. So we had that sheet that was bond market trading, so let's just go to that. File, where's open. So callable bond. Here we are in the bond market. Let's say there's a 9 percent coupon bond, doesn't matter what it is. We start at the interest rate of .06. Was that where we were starting? And the volatility was 20. So here we have the same exact--exactly the same interest rate process as before, so those are the interest rates, just as we had before. Now let's talk about a bond. So it's a non-callable bond. I forgot already what I said. How long was this bond? It was a 30-year bond. Didn't have to be 30 years, but anyway, it's a 30-year, 9 percent bond, and its value was 140.93. So the bond is worth 140.93. If the interest rates go up, same interest rate process, it can go to 121.4 or to 159.4. So now let's suppose you can't trade in the interest rate market any more. What should you do now? Student: Don't you need another bond? Prof: Well, you've got the interest rate. You've got the 1-month [correction: year] bond that you can trade at an interest rate of 6 percent and you've got this bond market. So anyone will buy and sell with you. Remember, this is the 30-year, 9 percent coupon bond. They're all willing to buy and sell this with you. And you've got this mortgage that everybody else thinks is the price is worth 120, but you're sure it's worth 98.84, because you know the prepayments. The homeowners are smart and they're going to prepay and nobody else realizes they're going to do it. So what should you do now? You can't trade interest rate derivatives any more. All you can do is trade in the bond market, so do you have any idea what you could do? What would you do? This is even slightly more realistic example. You've got a mortgage that you know is overvalued. You've got a bond that you can trade, and of course you can trade a very short bond, the 1-year bond, which is trading at 6 percent interest. You can trade a 1 year treasury, and here's the 30 year, 9 percent treasury, which happens to be worth 140, so what should you do? Well, you know that you could sell this mortgage short, get 120 dollars for it, and you think the value of the payments is only 98, so you'd love to do this. The trouble is, the future values depend on a lot of uncertainty. It may be that the payments you might have to make are more than 98, so what are you going to do? How would you lock in your profit for sure? Can anybody figure out what to do, just intuitively? It seems pretty complicated to figure out what to do. So you sell this bond for 120. You put the 21.7 dollars in your pocket. You have 98.4 dollars now that you have to spend to somehow acquire payments that are going to just allow you to make the bond payments you've sold short, the mortgage payments you've sold short at every node, so you never have to give up any more money. So what should you do? You want to acquire some assets with this 98.84 dollars that will put you in a position where you have 100.6 dollars up here and 107.1 dollars down there. So how can you do that? Well, you have a combination of the short--you have this 30-year bond you could invest in. If you spent 98 dollars on the 30 year bond, that's 70 percent of that, so that would give you 84 up here and 105 down there. So it wouldn't match what you really need. On the other hand, you could put your 98 dollars in the 1-year bond, which would give you 98.84 times 1.06 and 98.84 times 1.06. So you've got this choice, or you can put 100 dollars here and get 106 dollars there. The interest rate we said was 6 percent, so that means there's a 1-year bond that pays 106 in these two cases. There's the 30-year bond, where 140 dollars could be worth this in the two cases. So let's say you can't go trade on the derivatives market, it doesn't exist. Or at least you don't know how to trade on it. But what you do know how to trade is on the bond market, and--the long bond market and the short bond market. So let's call this the long bond market, and the short bond market. So what would you do? Any thoughts here? Let me repeat the problem. You find, like you typically do when you're a trader, you know something other guys don't do. That's what you're making your whole livelihood on. You understand that prepayments are going to be very fast. The people know how to prepay. The rest of the market, hasn't occurred to them yet that people can prepay. They're grossly overpaying for the mortgage, paying 120 dollars. So you go and sell the mortgage short. Now that means you have to deliver what the mortgage is paying. You have to deliver it to other people, so that's a lot to take on. But I say that you can sell this bond for 120, put 21.7 in your pocket, take the remaining 98.84 dollars and now buy the cash flows that you're going to have to deliver in the future. How do you know you can buy all the cash flows? There are 30 years of cash flows. There are coupon payments, there are prepayments. There are all kinds of complicated payments of the cash flows. How, with this 98.84 dollars, are you going to be able to buy them all exactly? All you can do is trade, buy the long bond and buy the short bond, or maybe sell the long bond short or sell the short bond short. So how, by trading these two securities over and over again, can you replicate the cash flows of the mortgage? That way you will have hedged out your risk, and you'll have the 21.7 locked in without ever having to worry about anything in the future, provided your prepayment calculations are correct. If you're wrong about prepayments, then you're going to be in big trouble, so you're betting on knowing what the prepayments are. So what should you do? Well, here this thing is going to--the cash flows at this point are going to be worth 100.6. The 8 that you have to deliver, 92.6 for the present value of the future cash flows. Here they're worth--let's just do the real thing. Never mind that stuff--here they're worth 107.11. Now you know that 1 half times 1 over (1 r_0) of 106 1 half over (1 .06) times 107 is 98.84. So the average of these discounted is that number. You know that the average of these numbers--so this is the non-callable bond, so it's not these numbers. It's this number 9 and this number 9. It's paid a coupon, so the average of these numbers, discounted by 6 percent, is that. So what does that tell you you should do? I claim by combining this bond and this bond, you can produce 100.6 and 107.11 here. So we know that this top bond is going to pay you 130.4 up there and 168.4 down here. If you bought X units of the long bond, that's what your payoffs would be. The short bond is going to pay you 106 in both cases. So if you bought X units of the short bond, that's what your payoff would be. You want the payoff to be 100.6 and 107.11. So there must be an X_L and an X_S that equals that. How do you know there has to be? Because it's 2 equations and 2 unknowns and these are independent equations. In fact, you can tell what X_L has to be. This gap between 100.6 and 107, that gap is about 7, and this gap is about 38. So 7 is like 1 fifth of 38, so X_L is going to have to be 1 fifth. I know in advance that this is going to turn out to be about 7 over 38. Just by general principles, you know there's a solution for X_L and X_S. So I know there's a solution to that because it's 2 linear equations and 2 unknowns and they're not degenerate, so I know there has to be a solution to that. And I also can tell you what X_L has to be, because the gap, that's the difference between the top number and the bottom number, is 7. That gap over there is 38. So obviously the middle gap, 106 and 106 is 0. So if I take X_L to be 7 thirty-eighths of that number, the gap is going to go down from 38 to 7. Then I'll just have to find the right X_S to make that equal. So that combination of X_L and X_S will produce this payoff here and this payoff there. So I know what combination of the long bond and the short bond to hold so I produce exactly these things. So I'm going to get a cash flow of 100.6 and 107.11 and I'll be able to use that to make the coupon payment of 8 in both cases and on top of that, have enough money to continue buying future cash flows. Now what will the cost of the X_L and X short be? It will be X_L--I'll have to pay 100 dollars for the short bond, if I have to do X_S, X_short, and I'll have to take 7 thirty-eighths of 140, that's how much it'll cost me to buy the long bond. So the right combination of short bond and long bond will give me the right payoffs. And it's clear that there is an X_S here and an X_L here, such that I get the payoffs I want of 100 and 107. But the last thing to notice is the cost of this X_L and this X_S, which is going to be 140 times X_L 100 times X_S. That cost will be exactly 98.84. How do I know that--therefore I'll just be able to do it. I'll ask you that question in a second. Here's what this hedging amounts to. The hedging amounts to again, you know because of your superior knowledge of prepayments that the mortgage cash flows, not the mortgage itself, the cash flows that are going to come from the mortgage are only worth 98.8. Someone's handing you 120 dollars in exchange for making those mortgage cash flows. Okay, so what do you do for that? You take the 98.84 dollars out of the 120. You take 21.7. That goes into your pocket. The 98.4 you have to use to buy the future cash flows. The first cash flows are going to be 8 dollars, but you're going to need more money to buy the cash flows that come after. How much more money do you need? 92.6 here, 99.1 there. So how can you put yourself in a position to have 100.6 dollars here and 107.11 dollars here? Can you use this amount of money to buy this value at the next step? We saw in the derivatives market, yes you can. But even if you can't trade in the derivatives market, you don't need to if you could trade a short bond and a long bond. You would just find how much of the long bond do I hold and how much of the short bond do I hold, so I can get these cash flows of 100.6 and 107.11? The answer is, you have to solve that equation up there. What X_L and what X_S gives you that number? You know that there's some X_L and some X_S that will solve that, because it's 2 equations and 2 unknowns. I'm repeating myself. You even know what X_L is without writing down the equations, because the gap has to be--one thing, there's no risk, and the other thing, there's a big risk. So the only risk in the payoff has to come from the long bond. So that gap of 38, if you take 7 thirty-eighths of that, you're going to get the gap to go down to 7. So the X_L's going to turn out to be 7 thirty-eighths. X_S you have to solve by algebra. So you know how much that X_L is and what the X_S is. That's what you hold, that combination of X_L and X_S, you hold here and you get exactly the payoffs. And then the final step is to notice that you can exactly afford it with 98.84 dollars. How do you know that you can afford it? Because what you want is 100.6 and 107.11 and that costs 98.84. You're buying two things together whose payoffs together are worth 98.84. So therefore the cost of the two things separately have to be worth 98.84. So it will turn out when you solve for X_L and X_S, you'll exactly be able to afford it with this amount of cash. So you can just do that going forward all the time, constantly re-hedging your portfolio. So that's the essence of dynamic hedging. It's a very beautiful idea which I probably haven't explained in the optimal way, but the point is that, to summarize the whole thing again, you know something about a bond, but you're subject to more risk besides what you know. You hedge out the extra risk, still relying on yourself to be right about what you know. You relied on your being right about the prepayments. You don't know anything about the future interest rates. But there's another guy like the trader in the World Series, the broker in the World Series, who's willing to make bets on the interest rate with you. Or to say the same thing, who's been calculating the values of the bonds, the short and the long bond, as if he was making bets on the interest rate. He's calculated at the same 50/50 odds, discounting by the interest rate. So because there are all these guys on the market who are willing to make these game by game bets, either directly--I'm almost done--they either make the game by game bets and the interest rate directly in the derivatives market, or what's equivalent to that, they've used that calculus to figure out the value of these long and short bonds. So by trading through the long and short bonds, you're effectively doing the same interest rate bet. So either way, by trading through the two bonds, or trading directly in the interest rate derivative market, you're able to buy, by going game at a time. Year by year, you're able to buy all the cash flows of your mortgage, the cash flows that you're predicting it's going to have. And therefore, you can make the profit for sure. It's predicting something, being confident in your prediction, then being able to buy what you've predicted the cash flows are for a smaller price than you can sell the security for. That's how you locked in your profit. Okay.
Quantitative_Finance_by_Yale_University	18_Modeling_Mortgage_Prepayments_and_Valuing_Mortgages.txt	Prof: So we're talking now about mortgages and how to value them, and if you remember now a mortgage-- so the first mortgages, by the way, that we know of, come from Babylonian times. It's not like some American invented the mortgage or something. This was 3,500-3,800 years old and we have on these cuneiform tablets these mortgages. And so the idea of a mortgage is you make a promise, you back your promise with collateral, so if you don't keep the promise they can take your house, and there's some way of getting out of the promise because everybody knows the collateral, you might want to leave the home, and then you have to have some way of dissolving the promise because the promise involves many payments over time. So it's making a promise, backing it with collateral, and finding a way to dissolve the promise at prearranged terms in case you want to end it by prepaying. And that prepaying is called the refinancing option. And because there's a refinancing option it makes the mortgage a much more complicated thing, and a much more interesting thing, and something that, for example, a hedge fund could imagine that it could make money trading. So I just want to give you a slight indication of how that could happen. So as we said if you have a typical mortgage, say the mortgage rate is 8 percent-- maybe this is a different answer than I did-- so here we have an 8 percent mortgage with a 6 percent interest rate to begin with. Now, if it's an 8 percent mortgage the guy's going to have to pay much more than 8 percent a year because a mortgage, remember, there are level payments. We're talking about fixed rate mortgages. You pay the same amount every single year for 30 years, now you're really paying monthly and I've ignored the monthly business because it's just too many months and there are 360 of them. So I'm thinking of it as an annual payment. You have to pay, of course, more than 8 dollars a year because if the mortgage rate were 8 percent and you had a balloon payment on the end, you'd pay 8,8, 8,108. That's the way they used to work, but they were changed. So you could imagine the old fashioned mortgage would pay 8,8, 8,8, 8,108; if you didn't pay your 8 somewhere along the line they'd confiscate your whole house and then take what was owed out of it and you could get out of it by paying 100. The new mortgages instead of paying 8 every year for 30 years you pay 8.88 every year for 30 years because if you discount payments of 8.8 for 30 years at 8 percent you get 100. So the present value is 100 at the agreed upon discounting rate or mortgage rate 8 percent. And so you see how important this discount rate is. And the remaining balance, however, goes down because every time you're paying you're paying more than the 8 percent interest. You're paying in the first year 8.8 instead of 8 and so that gap of .88 is used to reduce the balance from 100 to 99.117. And so you see the balance is going down over time and making the lender safer and safer because the same house is backing it. So it's called an amortizing mortgage. Now, why is it difficult to value? Because you have the option, any time you want, and there's a good reason for that option, any time you want you have the option of getting out of the mortgage and just saying, "Okay, I've paid 3 payments of 8.88, I don't want to do it anymore. I want to pay off 97.13 and then let's call it quits." And they say, "Okay," and there's nothing they can do about it. Now, when are you going to exercise that option? You're going to exercise that option either because you have to move, that's the intention of it, or you'll exercise it when it's most advantageous to you. Now, why could it become advantageous to exercise it? Well, you don't really want to exercise the option and this is the way most people think of it backwards. They think, "Oh, the interest rates are going down. That means I'll get a new mortgage with a lower interest rate." They're hoping for exactly the wrong thing. If the interest rates go up what they've got is a much better mortgage because they're continuing to buy at the same 8 percent interest and maybe interest rates in the economy have become 12 percent and they're actually making money. So people who borrow in times of high inflation do better. When there are times of deflation the borrowers get crushed. Irving Fisher said one of the main reasons for the Depression being so bad is all the entrepreneurial people in the country, as usual, were borrowing, and then there was a deflation and so they were getting crushed. And the very people who drive the economy were being hurt the most. And so that feedback, he said, was responsible for part of the severity of the Depression. So you see interest rates can go up or down and what happens? When they go up, if they go up high enough to 19 percent you think, "My, gosh, I've made a fortune holding this mortgage. I'm still borrowing at 8 percent and I can invest my money at 19 percent." So you've made a fortune and the poor lender's gotten crushed. On the other hand if the interest rates go way down here, so the present value of what you owe if you kept paying it becomes huge, you don't have to face that big loss because you just prepay at whatever the remaining balance is there and then you've protected your downside. So by paying attention and deciding when the optimal time to prepay is, you can save yourself a lot of money and thereby cost the bank a lot of money. So when exactly should you prepay? When should you exercise your options? Well, in this example if you never exercised it you'd be handing the bank, effectively, 120 dollars even though they lent you 20 [correction: lent you 100]. So the bank would have made a 20 percent profit on you. But if you exercise your option optimally you're going to make not 100-- the bank is not going to get 100 dollars out of you, they're going to even get less than 100 dollars. They're going to get 98 dollars out of you. So when exactly should you be exercising your option? Well, we went over this last time. I'll do it once again. So remember, the payment you owed was 8.88,8.88, blah, blah, blah, 8.88. The remaining balance started, of course, at 100 and then it went down to 99.11 and then it kept going down from there. So since I can't remember the numbers let's just call this B_1, the remaining balance which happened to be, you know, it was 99.11 the first time. Let's call this B_1, then I went to B_2, B_3 etcetera and then B_30 is equal to 0, no remaining balance after that. So we said, what should you do--I'm going to do the calculation now a little bit differently-- I said after every payment of 8.88 you could always say to yourself, "Do I want to continue or do I want to pay my option?" Now, you notice that if I had divided this by B_1, say, if you had a mortgage that was a little bit smaller, barely over a 1 dollar for example, that would divide everything by B_1. The payments would all be divided by B_1 and the remaining balances would all be divided by B_1. So I could always scale this thing up or down. There's nothing fancy about 100, nothing important about 100. If the original loan was for 200 you just double all your payments and double all your remaining balances. What could be more obvious than that? So I want to think in those terms of a mortgage that always has 1 dollar left. So suppose at any stage you had 1 dollar left in your mortgage. Your remaining balance was 1. So let's say at any node, let's ask the question, what is the value of 1 dollar of remaining balance? So if you start at 100 and you haven't prepaid, here you've got B_2 dollars. Of course, whatever the value of that is divided by B_2, that's the value of 1 dollar. So I'm just going to figure out the value of 1 dollar of remaining balance and I'm going to call that W, let's say. I'll call that W of some node S. So where am I? I'm in some node in this interest rate tree, right? Here's our interest rate tree, and I'm anywhere just here, and I'm doing backward induction so for all successor nodes I figured out what 1 dollar of remaining balance is. And let's say it's in period 1,2, 3,4, 5, so I'm in period 5, B_5. So what is the remaining balance at this node which I call S? So it's some node right there of--oh no, I've lost it. So W_S is going to be what? It's going to be the minimum of 1, you could just pay it if you wanted to, or you could wait. 1 over (1 r_S), and then what would you have to do, you would have to make your payment. Well, what's your payment? The payment is this 8.88 but divided by B_5 plus the remaining balance of 1 dollar. So (B_6 over B_5) times the remainder times W_Sup. Now, why is this right? I hope it is right by the way. I should have thought of this a little before. So this is the remainder of 1 dollar left. So if I divide by B_5 here I'm not going to have a remaining balance of B_6. I'm going to have a remaining balance of B_6 over B_5. So if I started with 1 dollar of remaining balance then I know that in the next period I'm going to have B_6 over B_5 dollars of remaining balance left. It doesn't sound too convincing, by the way. Well, it's right, and that happens with probability 1 half. And then with the other probability 1 half, plus I make the payment, but I go down instead of up and so I have B_6 over B_5 but I have W_Sdown, and that's also times 1 half. So either I pay off my remaining dollar or I end up with this many dollars. Assuming I had a 1 dollar of remaining balance I'm either going to pay it off, the remaining balance, or I'm going to have this much left next period and 1 dollar of remaining balance is going to be that. So that's it. So I know now by working this backwards I can tell what 1 dollar at the beginning is worth. And so it's exactly the same calculation I did before except I'm talking about 1 dollar. I'm always figuring out 1 dollar of remaining balance instead of the whole thing. Present value of callable, so here's present value of 1 dollar of principal. And so remember the present value of a callable mortgage was 98.8. Here the present value of 1 dollar, figuring it out that way, is .98, obviously it's divided by 100, but the key is that now you can see just by looking at it where the 1s are is where the guy decided to prepay. So it's the same thing as before, but you see before you couldn't tell very easily from the numbers when I did the 100. Sorry, that didn't quite make it. Before when I did the present value with the 100 all these numbers were 98s and 97s. I mean, where has he prepaid? It's hard to tell where the prepayment is. If I do it all in terms of 1 dollar of remaining balance then just by looking at the screen I can tell where the guy prepaid because there are 1s there. So I know where he's prepaid. Wherever the 1s are that means he's prepaid. So I can tell very easily what he did. All right, that's the only purpose of doing the same calculation in a somewhat trickier way. So if you think about it a second you see I've just divided by--I've always reduced things to if you had 1 dollar left. All right, so this tells us what to do, when the guy should prepay and when he shouldn't prepay. So if you're now in the world looking at what's happening you can find the historical record of how people have prepaid. So let's just look at the historical record, for example. Here, if you can see this, this is blown up as big as it goes. So this is what you might see as the historical record of percentage prepayments annualized from '86 to '99, say. So you notice that they're very low here, and then they get to be very high, and then they get low again, and then they get high again. So why do you think that happened? So what is this? This is prepayments for a particular mortgage, 8 percent. You take all the people in the country who started in 1986 with 8 percent mortgages. There's a huge crowd of those because that was about what the mortgage rate was that year. So a huge collection of people got these mortgages in '86 and you keep track of what percentage of them prepaid, really every month, but you write the annualized rate, and then this is the record. So why do you think it changed so dramatically like that? What's the explanation? Student: Stock market. Prof: What? Student: Stock market. Prof: It looks like the stock market, but I assure you the stock market had almost nothing to do with it. Why would prepayments be so low, and then be so high, then be low, then be high? What do you think was happening? Student: Interest rate change. Prof: Interest rate. We just did that. We just solved that. That was the whole point of what we were doing. So you tell me, what do you think happened in '93? This is September '93. I don't know if you can read that. What do you think was going on then? Student: Interest rates got low. Prof: Interest rates got low, exactly. So you may not remember this because you were barely born. In the early '90s there was a recession and then the government cut the interest rates. In the '90s, the early '90s there was a recession and the government kept cutting interest rates further, and further and further. There was this huge decline in interest rates through the early '90s, and so what happened? All these people who, in '86, who had these 8 percent mortgages--the new interest rates were lower and so they all prepaid. You got this shocking amount of prepayment. So this graph, which seems sort of surprising and looks like the stock market, turns out to have nothing to do with the stock market. It has to do with where the interest rates are. Well, do you think interest rates explain everything? No. What else could you notice about the--escape. What else have we learned here by doing these calculations? Well, what we've learned so far is that if the interest rates in the economy are at 6 percent, that's where they started, remember we said they started at 6 percent and there was 16 percent volatility. Here I had 20 percent volatility. It doesn't matter. I mean, that's a plausible amount of volatility, a little high, but that volatility. The mortgage rate of 8 percent is not going to give a value of 100. It's going to cheat the bank if the homeowners are acting rationally. The bank could get 120 if the people weren't acting rationally. They were just never exercising their option. It they're exercising their option optimally the thing was only worth 98. Now, I told you at that time the interest rates should have been around 7 and 1 half percent, not 8 percent given this 6 percent interest rate in the economy. The mortgage rate should be 7 and 1 half percent. So we deduced last time that obviously not everybody's acting optimally. Well, you can tell that looking at this diagram. How do you know that not everybody's acting optimally? Remember these are '86 mortgages, so everybody's taking them out at the same time within a few months of each other, the same 8 percent mortgage. How can you tell from this graph that they're not exercising their option optimally? It's completely obvious. Just looking at it for one second you can say, "Oh, these people can't be exercising their option optimally," why is that? Yes? Student: They should be exercising all at the same time if they were acting rationally. Prof: So as he says we've just done the calculation with those 1s and 0s. I told you when the right time to exercise the option is, so, everybody's got the same circumstance. Every single person if all they're trying to do is minimize the present value of their payments they should all be prepaying at the same time. Here you see that very few people are prepaying, but it's getting up to almost 10 percent so probably this is a stupid time to prepay, but the point is still 10 percent of them are prepaying. And over here when presumably you ought to prepay, in the entire year, right, they have 12 chances during the year. It takes them an entire year and only 60 percent of them have figured out that they should prepay. So you know they're not acting optimally. So just from that graph that would tell you, and you have further evidence of that. That's evidence that they aren't acting optimally. Furthermore you have evidence that the banks don't expect them to be acting optimally because the banks aren't charging them 8 or 9 percent interest, which is what they would need to pay to get the thing worth 100, they're charging them 7 and 1 half percent interest which for the optimal pre-payer is worth much less than 100 to the bank. So the banks wouldn't do that. They would just go out of business if they did something stupid like that. They wouldn't do that unless they thought that the homeowners weren't acting, at least not all of them acting, optimally. So suppose you had to predict how people are going to act in the future and you wanted to trade on that? What would you do? How would you think about predicting it? So this is the data that you have. What would you do? You have this data. These are 8 percent things. You also have 9 percent mortgages issued the year before, and then maybe a year before that there were 8 and 1 half percent interest and you have that history, and you've got all these different pools and all these different histories. How would you think about figuring out a prepayment--how would you predict prepayments? Well, the way economists, macro economists at least in the old days, used to make predictions, they would say, "Hum, the first quarter looks pretty good." What are they predicting now? Now, they're saying unemployment is probably going to keep rising for the next quarter or two well until the next year, but at that point things are going to turn around and we expect the economy to get stronger, come out of its recession and unemployment should gradually improve from its high which we expect will be 10 and 1 half percent to something back down to 6 percent by the end of 2011. That's more or less the economists' prediction. Now, can you make a prediction like that about prepayments? Would it make sense to make a prediction about that? Why is that an utterly stupid kind of prediction? What is the essence of good prediction? If you wanted to predict something and you were going to lose a lot of money if your prediction was wrong how would you refine your prediction compared to what I just gave as a sample prediction? Yep? Student: You have to have a number of scenarios and > to each one. Prof: Exactly. So what he said is if you're even the slightest bit sophisticated you're not going to make a bald non-contingent prediction. Things are going to get worse the next two quarters, then they're going to start getting better, then things are going to get as well as they're going to get after two years. You'll solve the problem after two years. What happens if another war breaks out in Iraq? What if Iran bombs Israel? What if there's another crash in commercial real estate? How could that prediction possibly turn out to be true? It's a sure thing it's going to be wrong. It's just impossible that's going to be right because the guy making the prediction has made no contingencies built in his prediction. You know that guy's making a prediction for free. Someone may be paying him to hear him, but he's not going to be penalized if his prediction is wrong. No one in their right mind would make such a prediction. So the first thing you should do in predicting prepayments is to realize that you've got a tree of possible futures, and given this tree of possible futures you're going to predict different prepayments depending on where you go on the tree. So you see, prediction is not a simple one event--it's not a one shot thing. Just as he so aptly put it, it's a many scenario thing. You have to predict on many, many scenarios what you think will happen and that makes your prediction much better because, of course, if there is a war in Iraq, and if there is a catastrophe in Afghanistan, and if Iran does bomb Israel, and if the commercial real estate market collapses things are going to be a lot worse than this original guy's prediction. So everybody knows that, so why not make the prediction more sensible? So, on Wall Street that's what everybody's done for 20 years. Now, they haven't done it for 30 years. It's just 20 years that they've been doing that. So when I got to Kidder Peabody in 1990 they were making these one scenario predictions. It's a long story which I'll tell maybe Sunday night. I ended up in charge of the Research Department and so we made, you know, other firms were doing this already, we made scenario predictions, okay? So now what kind of scenario predictions are you going to make? When you make contingent predictions there are an awful lot of them. You can't even write them all down, so what you have to do is you have to have a model. So what kind of model should you have? I'll tell you now what the standard guys were doing on Wall Street at the time. They were saying--here's interest rate, sorry. Here's the present value of a mortgage. Here's the present value of a callable mortgage, present value of 1 dollar of principal, so realistic prepayments. So if we go over here we'll see that people said, "Look, from this graph it's clear," they would say, "that when interest rates went down people prepay more so why don't we have a function that looks like this?" So, prepay, that's the percentage of remaining balance that is paid off. So what does that mean? Remember, after you've made your coupon payment you have a remaining balance, B_5. You could pay all of it, or none of it, or half of it. So the prepay is what percentage of the B_5--that's just after you've paid, right? So, B_2 lets do that one. B_2, just after you've paid 8.88 the remaining balance has now been reduced to B_2. You could, in addition to the 8.88, pay off all of that B_2. Typically some people who are alert and think it's a good time to prepay will pay all of B_2. Others will pay none of B_2. So if you aggregate over the whole collection of people the prepay percentages, out of the sums of all their B_2s what percentage of them are going to pay off. So we look at the aggregate prepayment. That's the old fashioned way. And we say, "What percentage of the remaining balance is paid off?" So you'd make a function like this. You'd say, "Well, prepaid might equal 10 percent." Why am I picking 10 percent? So if you go back to this picture you see that prepayments seem to be around 10 percent when nothing's happening. So you say 10 percent plus maybe you're going to get some more prepayments so you might write--well, I just wrote down a function plus the min. The min, say, of .60 because it never seems to get over 60 percent if you look at that you see it never gets over 60 percent really. So the min of 60 and 15 times the max of 0 and (M - r_S - sigma over 133). That would be a kind of prepayment function. So what does this say? What happens? You're normally going to pay--so this is this whole function here, so I should write this as .1 plus, can you see that over there, maybe not, so this plus .1. So there's a baseline of 10 percent and if the interest rate is high, so the interest rate is above the mortgage rate no one else is going to prepay because this is going to be a negative number and this will be 0. So you're just going to do .1,10 percent. On the other hand, as the interest rate gets low and falls far enough below the mortgage rate people are going to say to themselves, "Ah-ha! I have a big incentive to prepay now. Maybe interest rates have gone down so far I can no longer hope they're going to go back up above the mortgage rate. I should start prepaying more." So more people are going to prepay and this thing is going to go up. I just multiply it by some constant, but it'll never go up more than 60 percent. That's what this function says. And sigma, this is the volatility--all right, so let's just leave that aside. So there's a prepayment function that seems to sort of capture what's going on. It's usually around 10 percent when there's no incentive. It never gets above 60 percent, but as the incentive to prepay, as interest rates get lower and the incentive to prepay increases, more and more people prepay. That's kind of the idea. All right, and then you would fit fancier curves than that. You would look at M - r_T and you would fit a curve that looks like this. So if there's just a little bit of incentive to prepay, the rates are a little bit lower than the mortgage rate, nobody does it. Then quickly a lot of people do it and then they stop doing it. So this is like 60 percent and most of the time you're around 10 percent, and you try and fit this curve. You're going to have millions of parameters and since you have so much data you could fit parameters. That was the old fashioned way and that's how people would predict prepayments. Now, that's not going to turn out to be such a great way, but it certainly teaches you something. So let's look at what happens if you now--with those realistic prepayments you compute the value of a mortgage. So this is the prepayment that you'd get for the different rates and so you can see that as the rates go down the total prepayment is going up. And by the way, it's more than 60 percent because you've got this 10 percent added to the 60 percent, so the most it could be is 70 percent, which it hits over here. So you get 70 percent as the maximum prepayments, and as interest rates get higher no one prepays except the 10 percent of guys. Now, by the way, why are people prepaying over here even when the rates are so high? It's because some people are moving or they're getting divorced and they have to sell their house. So obviously you're going to get some prepayments no matter what. People have to prepay, and why is it that people never prepay more than 60 percent historically or 70 percent, because not everybody pays attention. Now, I called them the dumb guys last time, but as I said, I probably fit into that category. It's people who are distracted and doing other things. They're just not paying attention and so they don't realize. They don't know what's going on, so they don't realize they should be prepaying. So as interest rates go down more people prepay. As interest rates go up less people prepay. And if you did some historical thing and figured out the right parameters you'd get a prepayment function. So how did I figure out this was 15? How did I figure out this was .6? Why should I divide this by 133? What's sigma? Once you get those parameters historically you now have a well-determined behavior rule of what people are going to prepay, and from that you can figure out what the prices are of any mortgage by backward induction. So how would you do it again by backward induction? The same we always did it. Over here, what would you do over here? How would you change this rule? Well, you would just be feeding in the prepayment function. So what would the prepayment function be? Well, people wouldn't be doing a minimum here, right? They're not deciding whether or not to prepay, they're just prepaying. So let's get rid of that. They're prepaying. So this is the value of 1 dollars left of principal. So some of them are prepaying and that's the function, so prepay, and that depends on what node you're at. And here it says what percentage of the remaining balance is being prepaid. So that tells you, that rule, who's prepaying, and then with the rest of the money that's going on until next time 1 minus that same thing, 1 minus prepay times exactly what we had before. So this part of 1 dollar got prepaid immediately so that's the cash that went to the mortgage holder. The rest of the cash got saved until next time and here's what happens to it. You have to make your coupon, then you have a remaining balance, and then whatever is going to happen is going to happen. So you'll study this and you'll figure out I'm sure. It takes a little bit of effort to see that through, but with half an hour staring at it you'll understand how this works and you'll read it in a spreadsheet so you can figure out the value of a mortgage. You get a value of a mortgage, and now we can start doing experiments by changing the parameters and see how the mortgage works. Now, before I do that I want to say that there's a better way to do this. I mean, maybe these numbers are estimated--what's a better way of doing it? How did I do it at Ellington, how did we--I mean at Kidder Peabody? How did we predict prepayments? What's another way at looking at prepayments? Let me tell you something that's missing. I used to ask people who wanted to work at Kidder Peabody or Ellington the following little simple puzzle, and most of the genius mathematicians always got this answer wrong. Of course we hired them anyway, but they'd always get this wrong. So the question is, suppose you've got a group of people like this and you figure out what the value of the mortgage is, and interest rates have been constant all this time. Let's suppose for one month interest rates shoot down, interest rates collapse and half the pool, 60 percent of the pool disappears. So now you've only got 40 percent of the people left you had before, and then interest rates return to exactly where they were to begin with. Should the pool that's left be worth 40 percent of the pool that you had just here, or more than 40 percent, or less than 40 percent? So remember, you had 100 people here. You're the bank who's lent them the money. You're valuing the mortgage payments they're going to make to you, you're getting a certain amount of money from them, 60 percent of them suddenly disappeared in 1 month leaving 40 left, but now interest rates are back exactly where they were before. Is the value of the mortgage starting here with the 40 percent pool worth 40 percent of what it was originally, more than 40 percent or less than 40 percent? What do you think? Yes? Student: Is it worth more than 40 percent because those people don't understand interest rates and therefore they're not > option properly and > their mortgages? Prof: Exactly. So that's an incredibly important point. It's called the opposite of adverse selection. Every one of these events is selecting the people left not adversely, not perversely, what's the opposite of adversely, favorably to you, so the guys who are left are all losers, but that's who you want to deal with. You don't want to trade with the geniuses. You want to trade with the guy who's not paying any attention. So the guys left are the people who are never going to prepay or hardly ever going to prepay and so it's much better. Now, this function doesn't capture that at all, right? It doesn't say anything. It just says your prepayment's depending on where you are. So whether you were here or here you're going to get the same prepayment, but we know that that's not going to be the case. In fact, it's clear that over here there must have been a much bigger incentive than there was over there. So the prepayments are the same, but actually interest rates here were vastly lower than interest rates there. So this is not such a good function. So how would you improve? What would you do to take into account this adverse selection, or actually pro-verse selection? What is the opposite of adverse? Well, it doesn't matter. What would you think to do? Your whole livelihood depends on it, millions, trillions of dollars at stake here. You've got to model prepayments correctly, so how would you think of doing this? Just give me some sense of what a hedge fund does or what anyone in this market would have to do. Well, most of them did this. So what would you do? Yeah? Student: Buy up old mortgages, because the market is probably under estimating their value. Prof: Well you would buy it up when? Student: Right after... Prof: Right here you'd buy it up, right there, but what model would you use to predict prepayments? Not this one, so how would you imagine doing it. You would imagine making a model just like your intuition, so what does that mean doing? Someone's asking you to run a research department, make a model of forecasting prepayments. All the data you have is aggregate data like that. You can't observe individual homeowners in those days. They wouldn't give you the information. I'll explain all that Sunday night. So this is the kind of data you have, what the whole group of people is doing every year, but what would you do to build the model? Adverse selection is very important or pro-verse selection. It's embarrassing I don't remember the word, favorable selection, a very important thing. So how would you capture that in your model? Yep? Student: Would you split it into two groups and then model it separately? Prof: So maybe another thing you could do, what if you instead of having this function that says what the aggregate's going to do all the data's aggregate, so all you can do is test against aggregate data. But suppose you said, "The world, all we can see is the aggregate, but the people really acting are individuals acting, not the aggregate. It's the sum of individual activities, so what we should do now is have different kinds of people." Oh gosh, sorry. It was there already. So let's go back to where we were before, so realistic. What you ought to do is you ought to say, well, 8 percent--remember we had two kinds of people already. We've already got two kinds of people, sorry. We've got these guys, the guys who never call, so they're people. That's a kind of person. And suppose you go down here and you have the people who are optimally prepaying? Suppose you imagine that half the people were optimally prepaying and half the people never prepaid? Well, would that explain this favorable selection? Absolutely it would explain it because when you went through your little tree and you went here, and here, and here, and here, by the time you got down here all those people, all the optimal pre-payers they're all prepaying. So you start off with half-optimal guys and half-asleep guys. Once you get down here all the optimal guys have disappeared and the pool that's left is all asleep, so of course the pool is worth much more here given the interest rate than it was over here. In fact, if it goes back then again to here where it was before--sorry that's same line. If it goes back to here--have I done this right? No, I've got to go back twice here and then here. So once it goes back to here if it goes here, here, here and here then the pool is going to be much more valuable here than it started there. There are half as many people, but it's worth much more than half of what it was there. So the way to do this is to break--so then you're looking at the individuals. You're saying one class of people is very smart, or one class of people is very alert, it's a much better word, one class of people is very alert. One class of people is very un-alert and as you go through the tree the alert people are going to disappear faster than the non-alert people and that's why you're going to have a favorable selection of people who's left in the pool. Well, of course, there are no extremes of perfectly rational or perfectly asleep in the economy so what you can do is you can make people in between. How do you make them in between? Well, suppose that, for example, I only did one thing. Suppose it's costly to prepay? Some people just say to themselves, "I'm going to have to take a whole day off of work. I'm not going to write my paper. I might lose some business that I was going to do that day. A whole bunch of stuff I'm losing, so I'm going to subtract that. I'm not going to prepay. I'm not going to even think about doing it unless I can get at least a certain benefit from having done it." So you can add a cost of prepaying and people aren't going to prepay unless the gain that they have by prepaying exceeds the cost of doing the prepayments. So to take the simplest case let's suppose the very act of-- never mind the thinking and all that-- the very act of prepaying, going to the bank literally costs you money. So if you have a value, if the thing is 100 and you can prepay, you know, if you do your calculations and don't prepay today it's worth 98 and if you prepay today the remaining balance is 94 you're saving 4 dollars, but if the cost of prepayment is 5 you're still not going to do it. So you get a guy with a high cost of prepaying, an infinite cost of prepaying, he's going to look like he's totally un-alert. A guy with zero cost of paying is going to look like he's totally alert. So you can have gradations of rationality, and you can have different dimensions. So you can have cost of prepaying and you can have alertness. What's the percentage of time you're actually paying attention that month? What fraction of the months do you actually pay attention, and you can have a distribution of people, different costs and different alertnesses. So that's the model that I built. It's a simplified form of it. It gives you an idea. So here's this burnout effect that I showed that if you take the same coupons, but an older one rather than a--an older one that's burned out will always prepay slower, so the pink one is always less than the blue one because it went through an opportunity to prepay. So here you start with a pool of guys on the right, and then after a while, after time has gone down a lot of them have prepaid. So here's alertness and cost. So you describe a person by what his cost of prepaying is and how alert he is. The more alert he is and the lower the cost of prepaying the closer to rational he is. The less alert he is, the higher the cost of prepaying the closer to the totally dumb guy he is. And so you could have a whole normally distributed distribution of people and over time those groups are going to be reduced because a lot of them are prepaying, but they won't be reduce symmetrically. The low cost high alertness guys are going to disappear much faster and the pool's going to get more and more favorable to you. And so anyway, all you have to do is parameterize the cost, what the distribution of people in the population, what the standard deviation and expectation of cost is and of alertness is, and that tells you what this distribution looks like. So you're fitting four numbers and you've got thousands of pools and hundreds and hundreds of months, and fitting four parameters you can end up fitting all the data. So look at what happens here. So here's the same data. So I just tell you I know that in a population, given what I've calculated in the '90s there, I know what fraction of the people have this cost and that alertness, what fraction of the people are so close to dumb that their costs are astronomical and their alertness is tiny, what fraction of the people have almost no cost and a very high alertness, so I'm only estimating four parameters because I'm assuming it's normally distributed. Given that fixed pool of people I apply that to the beginning of every single mortgage and I just crank out what would those guys do. In the tree if they knew what the volatilities were when would they decide to prepay, and then I have to follow a scenario out in the future and I say, "Well, along this path which guy would prepay and which guy wouldn't prepay and what would the total prepayments look along that path?" And so this has generated the pink line from the model with no knowledge of the world except I fit those parameters and look how close it is to what actually happened. So it turns out that it was incredibly easy to predict, contingently predict what prepayments were going to be and therefore to be able to value mortgages. And this was a secret that not many people, you know, a bunch of people understood, but not that many understood, and so for years we were trading at our hedge fund, first at Kidder and then at Ellington with this ability to contingently forecast prepayments at a very high rate. And why was it so stable, the prediction, and so reliable? It's because the class of people stayed pretty much the same and every year there'd be the same kinds of people with the same kinds of behavior. Some were very alert. Some were very not alert, but the distribution of types was more or less the same and you could predict with pretty good accuracy what was going to happen from year to year. Of course, then after 2003 or so the class of people started to radically change and many more people who never got mortgages before got them and it became much harder to predict what they were going to do. But so in the old days it was pretty easy to predict. And why was it so easy to predict? Because it was an agent based model, agent based. So, by the way, I added this volatility here, so these guys who just ran regressions they had to have a volatility or something parameter. So you see as volatility goes up the prepayments are slower. Well, they just had to notice that and build it right into their function. I didn't even have to think of that or burnout. None of those things did I have to think about because if you're a guy optimizing here and volatility goes up, so you reset the tree so that the interest rates can change faster. The option is worth more so you're going to wait longer. You're not going to just exercise it right away because you've got a chance that prices will really go up so you can wait a little longer, afford to wait longer. So prepayments will slow down. So all I'm saying, all of this is just to say that if you have the right-- so it's agent based, it's contingent predictions, those two things together enable you to make quite reliable predictions about the future if you're in a stable environment. And so what seems like a bewildering amount of stuff turns out to be pretty easy to explain. So now what happens? So do you have any questions here or should I--yes? Student: You said you assume that those two parameters are normally distributed. Did you select among some sort of variance? Prof: Some sort of what? Student: Variance. Prof: I had to figure out what the mean and the variance is. There's mean and variance of cost and mean and variance of alertness to get that distribution, right? So how do I know what the population--so let me just put the picture up again. So who are the hyper rational guys? They are the people with the really high alertness up there and the really low cost, so they're the guys back there. They're the hyper--or maybe it was the guys, you know, one of these corners with very high alertness and very low cost. I forgot which way the scale works. It might be going down. So anyway, the guys with very high alertness and very low costs are the hyper rational people. At the other corner you've got the guys who have very low alertness and very high costs. They're the people who you're going to make a lot of money on if you're the bank. So how do I know how many people are of each type? Well, I don't. I have to fit this distribution. But you see I have so much data. I've got this kind of curve. This kind of curve I've got for every starting year for the whole history and there's so many different interest rates and so many different-- so I'm applying that same population at the beginning of every single curve and then seeing what happens to my prediction versus what really happened. So I've got thousands, and thousands, and thousands of data points and only four parameters to fit. So I pick the four parameters to fit the data as much as possible. If I assumed everybody was perfectly alert instead of that curve that I showed you, I put a huge crowd here of perfectly rational people then I would have found that I would have gotten prepayments at 100 percent up there and at 0 all the way over here and so it wouldn't have fit that curve. So that's how I knew that there couldn't be that many perfectly rational people. Yes? Student: How can you know for sure that there are only two patterns? Prof: You mean how do I know cost and alertness, maybe there's some other factors? Yes, well there probably are other factors. So what would you commonsensically think are the factors? What keeps people from prepaying? I think the most obvious one is it's a huge hassle and they're not paying attention. So those are the first two that I thought of. Could you think of another one? Student: Maybe their age. Prof: Their age, exactly. So maybe demography has an effect on it. So maybe, for example, you get more sophisticated the older you get. So that was another factor we put in. So I'm not telling you all the factors, but these were the two main factors. Another factor was growing sophistication. We called it the smart factor. That's another factor. So over time you get more sophisticated. So anyway, the point is with a few of these factors you got a pretty good fit, and it was pretty reliable, and you could predict what was going to happen contingently. So now if you want to trade mortgages what are some of the interesting things that happen? The first interesting thing to notice is that what do you think happens as the interest rate goes down? So the first thing to notice is--so I'll just ask you two questions. Let's go on the other side. I'm running out of room. Suppose that you have the mortgage value, what you get in the tree? So in this tree that we've built, here's the tree, it's going like that, and at every node we're predicting-- for each class of people we're predicting where his 1s are. So that class is prepaying. The other class is not as smart so they're not prepaying here, but maybe when things get really low they'll start prepaying here. So each class of people, each cost, alertness type has its own tree. They're the same tree, but it's own behavior on the tree, and then I add them all together. So what happens with the starting interest rate? So here we had .06 and this value was 98 or something, right? Now, suppose the interest rate went down to .05. I drew this picture of interest and mortgage value. What do you think happens? So the interest starts--this is '98,6 percent is there. As the interest rate goes down what do you think happens to the value of the mortgage? If you're a bank and you've fixed--the mortgage rate is 8 percent. That's a fixed mortgage rate, but now you've moved in the tree from here to here. Do you think your mortgage is going to go up in value or down in value? Student: It's going up. Prof: It's going to go up because the interest rates are lower and the present value of the payments is getting higher. So if the interest rate goes down the mortgage is going to go up like that, typically. But will it keep going up like this and this? If it were a bond it would go up like that, right? A bond, a 1 year bond which owed 1 over 1 r would keep going up and up the value before it got negative, say. It would go up. As r got negative it would go way up like that. So does the mortgage keep going up like that? As the interest rate goes down is the value of the mortgage going to get higher and higher and higher? Suppose the guy's optimal, what's going to happen? This is 100 here. What'll happen? Yep? Student: He's going to prepay. Prof: He's going to eventually figure out that he should prepay so it'll go like this. If he's perfectly optimal he'll never let it go above 100. So it's going to go something like this. As the interest rate gets higher you get crushed, and as the interest rate gets lower you don't get the full upside because he's prepaying at 100. He's never letting it go above 100, right? So if he's not so optimal maybe your value will go up, but not so astronomically high. So this idea that the mortgage curve, instead of being like this goes like that, this is what was called negative convexity. Now, the next thing to know is suppose that the guys are partly irrational so it's going above 100. So it's starting to go like this. Then what do you think? As the interest gets really low what's going to happen? All right, you just said it, so. If the guy was rational, perfectly rational it would go like that. He'd never let it go above 100, but now suppose guys are not totally rational? What's going to happen is they're going to, sort of--as rates get a little bit low they're going to overlook the fact that they should prepay. So now it's advantageous to you. Things are worth more than 100, but if rates get incredibly low even the dumbest guy, the highest cost guy is going to realize he has an advantage to prepay and so things are going to go back down like that. So the value's going to be quite complicated. So this is the mortgage value as a function of interest rates. Just common sense will tell you this. In a typical bond as the interest rate gets lower the present value gets higher. You should expect a curve like that, but because of the option if it were rationally exercised the curve would never get above 100. It would have to go like that. But now if people are irrational you can take advantage of them and get more than 100 out of them. But if the situation gets so favorable to you it becomes blindingly obvious, eventually to them, that they're getting screwed, and eventually they act and bring it all the way back to 100 again. So this value of the mortgage looks like that. So that's a very tricky thing. I'll even write, very tricky. So if you don't know what you're doing you could easily get yourself hurt holding mortgages. You could suddenly find yourself losing money holding mortgages. So that's my next subject here. I want to talk about hedging. So we know something now about valuing mortgages. Now I want to talk about hedging, and what hedge funds do, and what everyone on Wall Street should be doing which is hedging. So if you hold a mortgage you're going to hold it because maybe you can lend 100 to a bunch of people but actually get a value that's more than 100. So it looks like you're here, but if interest rates change a little bit suddenly this huge value you thought you had might collapse back down to 100, or the interest rates might go up and it might collapse to way below 100. So you look like you're well off, but there are scenarios where you could lose money and you want to protect yourself against that. So how do you go about doing it? What does hedging mean? And I want to put it in the context, the old context of the World Series which we started with before. So it's easier to understand there, and so many of you will have thought about this before so you'll be able to answer it, but if I put it in the mortgage context it would seem just too difficult. I don't know why I did that. So the World Series--I'm going to lower it in a second. So suppose that the Yankees have a 60 percent chance, I said beating the Dodgers, I thought the Dodgers would be in the World Series, a 60 percent chance of winning any game against the Phillies in the World Series. And you are a bookie and your fellow bookies all understand that it's 60 percent. So some naive Philly fan comes to you and says I want to bet 100 dollars that the Phillies win the World Series. Should you take the bet or not? Yes you should take the bet because 60 percent of the time you're going to win 100 dollars--no. Yes you should take the bet. If he bet on one game you would make, with 60 percent probability you'd win 100 and with 40 percent probability you'd lose 100. So that means on average your expectation is equal to 20. So if he's willing to bet 100 dollars on the Phillies winning the first game of the series with you, you know that your expected chance of winning is 20 dollars. You're expecting to win 20 dollars from the guy. Now, suppose he's willing to make the same bet, 100 dollars for the entire series? What's your chance of winning and what's your expected profit from him? Is it less than 20,20, or more than 20? Student: More than 20. Prof: More than 20. It's going to turn out to be, so a 7 game series, it's going to turn out to be 42 which we're going to figure out in a second. But what's your risk? What's your risk? In either case you might lose 100 dollars. The Phillies, they're probably going to lose, but there's a chance something goes crazy and some unknown guy hits five home runs in the first four games or something, and some other unknown guy hits another four home runs and you lose the World Series. You could lose 100 dollars, and maybe the guy's not betting 100 dollars but 100 thousand dollars or a hundred million dollars. You know you've got a favorable bet, but you don't want to run the risk of losing even though there's not that high a chance you're going to lose. What can you do about it? Well, you know that there are these other bookies out there who every game are willing to bet at odds 60/40 either direction on the Phillies or the Yankees because they just all know-- they're just like you. You all know that the odds are 60 percent for the Yankees winning every game. So suppose this naive guy, the Phillies fan, comes up to you and bets 100 dollars on the World Series that the Phillies will win. You don't want to run the risk of losing 100 dollars. You know there are these other bookies who are willing to take bets a game at a time 60/40 odds. What should you be doing? What would you do? Yes? Student: Bet on the Phillies winning because they give you better odds so you're guaranteed your profit. Prof: So what would you do? So this guy's come to you, and you're not going to be able to give the-- we're going to find out exactly what you should do in one second, but let's just see how far you can get by reason without calculation. So this guy's come to you and said, "I'm betting 100 dollars on the Phillies winning the World Series." This is the night before the first game. Every bookie is standing by ready to take bets at 30 to 20 odds. What would you do? Student: You'd bet with the bookie that the Phillies would win because... Prof: That what? Student: That the Phillies would win. Prof: Yeah, how much? Student: 100 dollars. Prof: You'd bet the whole 100 dollars? Student: Well, you get better odds, so. Prof: But would you bet the whole 100 dollars on the first game? The guy's only bet 100 dollars on the whole series. Student: You'd bet 80 > dollars. Prof: So it's not so obvious what to do, right, but he's got exactly the right idea. You can hedge your bet. So here we are. I shouldn't have put that down. Don't tell me I turned it off. That would just kill me. God, I meant to hit mute. I think I hit off. Oh, how dumb? So you would bet on the--while that warms up. I can see it. All right, so what happens is you'll have a tree which looks like this and like this, like this and like this, like this and like this and let's say we go out a few games like this. Now, this is a 1,2, 3 game series. All right, so I've done it. Here's the start of World Series. This is the World Series spreadsheet you had before. Now, here's the start. Here's game 1,2, 3,4, 5,6, 7. So if the Yankees win the series they get 100 dollars. You get 100 dollars, sorry. Oh, what an idiot. So every time you end up above the start, win more than you lose, you get 100 dollars. On the other hand, if you lose more than you win you lose 100 dollars, and so ctrl, copy. Here is losing 100 dollars. So now this tree, remember from doing it before, is just by backward induction. If you look at this thing up there it says you get, 60 percent I think was the number we figured out over here, so right? So 60 percent is the probability of the Yankees winning a game. So you take any node like this one you're always taking 60 percent of the value up here plus 40 percent of the value here. So if you do that you find out that the value to you is 42 dollars, just what we said. So let's put that in the middle of the screen. So the value is 42 dollars. Now, if the Yankees win the first game you're in much better shape. So winning the first game means you moved up to this node here. All of a sudden you went from 42 dollars to 64 dollars. And if the Yankees lost the first game you would have gone down to that value which is like 9 dollars. Your expected winnings when the Yankees are down a game, you know, they're still a better team so actually it's more likely even after losing the first game that the Yankees would still win the series. So you see the risk that you're running and you can calculate this. So what should you do in the very first game? This tells you that your expected winnings is 42. Of course .6 times 64 that's 38.4 .4 times 9 is 3.6. That is 42 dollars. So that's 42 because it's the average of this and this, and 64 is the average of .6 of this and .4 of that. So what should you do? Well, on average you're going to make 42 dollars. What's the essence of hedging? You want to guarantee that you make 42 dollars no matter what happens. No matter who wins the series you want to end up with 42 extra dollars assuming the interest rate is 0 from the beginning to the end of the series. So how can you arrange that? What can you do? Well, so that's the mystery. I'll give you one second to try and think it through. You should get this. What would you do here? Are there no baseball bookies in the--yep? Student: Didn't we just bring this up before like with our hedge funds? Can we put something else aside that you view at a percentage rate that you think you can trust and then you can trust the rest of it to whatever the real probabilities are? Prof: Well, you can bet with another bookie at 60 to 40 odds. If the Yankees win the first game you're just doing great. If the Yankees lose the first game you're looking to be in a little bit of trouble. So the point is you're not going to get the payoffs until the very end either plus 100 or minus 100, but already by the first game you're either doing better than you were before or worse than you were before. You're already, in effect, suffering some risk at the very beginning. So this is one of the great ideas of finance. You shouldn't hedge the final outcome. You should hedge next day's outcome. If you're marking to market that's what you'd have to do. Marking to market you'd have to say my position now--my bet is worth 64 dollars. The Yankees lost the first game, the bet would be worth 9 dollars. So what does it mean to protect yourself? Not just protect yourself against what's happening at the end, that's really what you want to do, but in order to do that you should protect yourself every day against what could happen. So every day you should end up with 42 here and 42 there because, after all, that's what you're trying to lock in. No matter who wins the first game you should still say I'm 42 dollars ahead because I got myself in this position. So how could you do that? Well, let's bet at 3 to 2 odds, right, 60/40 is 3 to 2 odds. Let's make a bet with another bookie at 22 and 33 here. So 22--I put it in the wrong place. This is the 33 and this is 22, but plus 33 and minus 22. So what are you doing here? Notice that this is 2 times 11, this is 3 times 11. This is 60/40 odds. I'm betting on the Phillies. If the Phillies win one game I collect 33 dollars. That's what I should do that he said. He said, "Go to the bookie across the street and bet on one game, not the whole series. Bet on one game with that bookie across the street, 33 dollars versus 22 dollars." Let's say you can only bet 1 game at a time with the other bookies, actually, maybe you were saying all along bet on the whole series, but let's say you can only bet one game at a time with the other bookies. You'd bet 33 dollars on the Phillies in the first game. That naive Philly fan has put up 100 dollars on the series. You're, in the first game, going to put 33 dollars. You've taken his bet so you're hoping the Yankees win, but that's bad to be in a position where you have to hope. You don't want to do that. So you take his bet on the Phillies because he's given you 100 to 100 odds. That's even odds even though you know the Yankees have a 60 percent change of winning. You go to the bookie across the street and you bet at 60/40 odds on the Phillies, but you don't bet the whole 100. You only bet 33 dollars of it. So if you win you get 33 dollars. If you lose you only have to pay the guy 22. So what's going to happen? After the first day this position is going to be worth 42 and this position is also going to be worth 42, exactly where you started. So because a win in the first game is going to put you so far ahead in your bet with the first naive Philly better, and a loss in the first game is going to put you so far behind, you hedge that possibility by going 33/22 in favor of the Phillies. You take a big bet on the Yankees and then you make a smaller bet on the Phillies that cancels out part of the big bet on the Yankees, but you've made the two at different odds and so on net you're still going to be 42 dollars ahead. Let's just pause for a second and see if you got that. So by doing this you can't possibly lose any money. And now you're going to repeat this bet down here and here. So in the next--you see where do things go next? Here you're down 8 dollars. If you lost again you'd be down 32 dollars. Now things would really be bad. After the Yankees lost two games in a row your original bet would look terrible, but things aren't so bad because you bet on the Phillies here. You already made 33 dollars. So how much money do you think you should be betting on the Phillies down here? Well, you want to lock in 42 dollars at every node no matter what happens. This 42 dollars, by making the right offsetting bet you can keep 42 everywhere, here until the very end, and so no matter what happened you can always end up with 42 dollars. That's the essence of hedging. So let's just say it again what the idea is. It's a great idea and we don't have time to go through all the details, but the great idea is this. You've made some gigantic bet with somebody. Why do you bet with anybody? Because you think you know more than they do. The whole essence of trading and finance is you think you understand the world better than somebody else. So understand it means you think something's going to turn out one way that the other guy doesn't really know is going to happen. So you're making a bet on whether you're right or wrong. So when you say you know you don't know for sure. You just have a better idea than he does, so you want to use your idea without running the risk. So how can you do it? If your idea is really correct there may be a way so that you can eliminate the luck. So here if you really know the odds are 60/40, your class of bookies knows the odds are 60/40, and some other guys who doesn't know thinks the odds are 50/50 and is willing to bet against you, you can lock in your 42 dollars for sure. You don't just take a bet and hope you win. You can take a bet and then hedge it to lock in your profit for sure, step by step, and that's what we have to explain how that dynamic hedging works. So I have to stop.
Quantitative_Finance_by_Yale_University	8_How_a_LongLived_Institution_Figures_an_Annual_Budget_Yield.txt	Prof: So we're spending a couple classes these days learning basic facts and vocabulary about finance, and along the way we're trying to apply the simple lessons that Irving Fisher taught about turning a financial problem into a general equilibrium problem and making use in particular of the budget set. That very simple budget set we wrote down at the very beginning turns out to be quite useful and people often can get quite confused. So the last issue we ended with, I'm going to take up again. Suppose that you've got a very long-lived institution like Yale. How should Yale think of how much to spend every year? What is Yale's budget set? Almost every big institution like Yale creates a fiction of an annual budget and they talk about the deficit and having to bring the deficit under control and making cuts to close the deficit gap, but really there is no such thing as a one-year budget set. I mean, why one year? Why not one month? Why not one day? Nobody expects Yale to balance its budget every day. Some expenditure comes in one day. They have to hire an electrician to fix something unexpected. They're going to spend more money than they take in student tuition that day. So the fact that they're supposed to budget the balance every year is just a fiction. Irving Fisher taught us that Yale really has-- if you can borrow and lend and you don't have to worry about risk there's one infinite-lived budget set. It's an infinite horizon budget set where you just take the present value of all the expenditures, that's the left hand side, and the present value of all the revenue, that's the right hand side, and make sure that the left hand side is smaller than the right hand side over the whole course of Yale's life. So that simple principle has a tremendous implication which was overlooked, to the chagrin of the last Yale president. So as I said, the issue was in 1997, I believe, it could have been '96 something like that, 1997, Benno Schmidt, who was then the Yale president, released a white paper, he called it, documenting the fact that Yale had deferred maintenance in the buildings, he called it, and a study that he commissioned, a very good study that he commissioned, argued that the deferred maintenance-- Yale could be brought up to snuff and then go on afterwards as a normal running institution provided it spent 100 million dollars a year for ten years, and that included fixing every college-- they're going to do more than one a year over a 10 year period. So Yale's total budget, as I told you, was about 1 billion dollars at the time, and then here all of a sudden was this 100 million dollar a year expense for 10 years. That's 10 percent of the Yale budget. And a lot of the costs you can't change. You have to have the lights on. You have to heat the buildings. You can't really reduce those costs. So Benno Schmidt came to the conclusion that he'd have to reduce the costs he could change by 15 percent in order to balance the budget, to cut about 100 million dollars a year out of the budget. So he announced one day that he was going to fire 15 percent of the faculty by attrition. If they were junior faculty he wouldn't promote them, and if they were senior faculty, wait until they retired and not replace them. So this, needless to say, caused a tremendous commotion among the faculty, and as I told you a committee was formed and I had to present the report. So actually the report went pretty carefully through all the calculations made in the white paper, but the heart of the report was simply to apply the lesson of Irving Fisher. So what is the lesson of Irving Fisher? Let's suppose that there's no inflation so that when they say 100 million dollars a year they mean 100 million real dollars a year. So Irving Fisher would say Yale's going to live forever. Let's suppose that Yale wants the same quality of education every year forever, so it should have the same real spending every year forever after it compensates for inflation. So at the moment we're assuming there's no inflation. So what does that mean? That means that you just look at the right hand side and you say, what's Yale's revenue? Well, whatever it was before we were told by this report of the president that as long as you did the deferred maintenance Yale would be back in balance. So what's the loss of revenue on the right hand side? It's 10 years of 100 million dollars a year as you can see. Now, you need an interest rate. What should the interest rate be? Well, should it be the nominal interest rate or the real interest rate? Well, we're supposing now there's no inflation so it should be the real interest rate because all the hundreds have no inflation in them. So what real interest rate shall we use? Well, the white paper used 5 percent because they thought that was the number that Yale could earn after inflation pretty reliably every year. They think that's the real rate of return Yale gets, and so they discounted it 5 percent. Now the real rate of interest typically in the economy is 3 percent, but let's suppose that we calculated this at 5 percent. The present value of 100 for 10 years is 772. Now, how could you do that in your head? Well, we know that 5 percent is going to double every 14 years, 5 into 72 is about 14. If it doubles every 14 years 10 years is going to be less than half the value of the bond. So if you got 100 forever at 5 percent interest that would be 2 billion, and we know for only 10 years it's less than half the value, so considerably less than half the value, so it's not one billion it's something less than that. It's 772. So I just did that in Excel and I calculated 772, but in your head you know that if it had gone on for 14 years then the present value, our formula, our famous formula is that you would take the coupon 100 divided by the interest rate .05 times (1 - 1 over (1 R) to the 10th). And so we know that if this were 14 instead of 10 you'd get a half here. So this is 20 times 100 which is 2 billion times 1 half would be 1 billion, but since it's only 10 years and not 14 years it's less than a billion, so 772. So in your head you could have probably figured that out approximately. So you could be sitting there in the audience hearing Benno Schmidt talk and be computing in your head that we're talking about something under 1 billion, like 3 quarters of 1 billion. So now, how much does that mean reduction in every year? Well, if Yale's going to spend the same amount every year that means it should be spending 5 percent of 772 less every year. That's 38.6 million dollars less every year. So that's a drastically smaller number than 100 million dollars a year. It's crazy just to think that because you've got these expenditures for 10 years and then no expenditures after that, that you should cut the budget by a 100 million and then let it go up after 10 years. So you'd only need to cut it by 38 million. Now, by the way, 5 percent is a pretty arbitrary number. Suppose you put 3 percent here? Well, 3 percent would give you a much higher present value, but then when you multiply it by 3 percent at the end for the annual reduction it will give you a much smaller number. Anyway, this number, which I computed in Excel, but again you can do it sort of in your head, is 853 million, but you multiply that by 3 percent and you get 26 million a year. So now the reduction is starting to sound like it's not such a frightening thing. So let's stick with the 5 percent which is what the white paper, take all the assumptions of the white paper and take it literally, and then notice that they never said anything about inflation. So actually, this calculation of present value loss--there's inflation, and say the inflation at that time is around 4 percent. In fact all the Yale contracts that are still in place assume a 4 percent inflation even though inflation's less than that now. But anyway, so that 100 million a year of dollars is actually less in present value terms because what should you discount by? If you look at the present value of 100 million dollars over 10 years and you take into account its dollars you should be discounting by the real interest rate times the inflation, so by 9 percent, a tiny bit over 9 percent. So if you discount that by 9 percent you get 641 million as the present value loss to Yale. Now, given that there's inflation how much should you be spending every year? You should be spending in real dollars, reducing your expenditure how much in real dollars? Well, by 5 percent of the 641 million. So if you have 641, that's today's present value. There hasn't been any inflation yet. So that's the real loss in dollars. So if you ask, what's the real expenditure reduction every year, it's 5 percent of 641 and that's 32 million. So 32 million is a far smaller number than 100 million and requires a far smaller drop in expenses, so our committee recommended that we cut the faculty by 6 percent instead of by 15 percent, and 6 percent--there are a lot of people leaving every year. You can do 6 percent pretty quickly. So the upshot of this is that it is a simple application of present value, a very elementary calculation. It came as somewhat of a revelation to our administrators, I'm afraid, and the day after the report the provost of the university resigned. Two weeks later the dean of the university resigned and two months later the president of the university resigned. And Rick Levin, the current president, took over and he cut the faculty by 6 percent, but by no more than that. And then, of course, the finances of Yale got much better and he's since added back that 6 percent plus a little bit more than that. So just to tell you, though, something good about the Yale administration, the provost who resigned that next day happens to be a friend of mine. I've had dinner with him every month for the last 12 years since this happened and he's never once criticized me or shown the slightest discomfort about the report that basically ended his administrative career. He cares so much about Yale and was so determined to do the right thing. He just thought he made a miscalculation and stepped aside. So I believe that he wanted to do the right thing for Yale and just made the wrong calculation, not that he had some political agenda or something to cut such a huge part of the faculty. So it's the most honest and most Yale-loving administrator that you could imagine. And I didn't know what the reaction would be of someone like him after giving the report. I was quite terrified, actually, that they'd be-- they were still the president, the provost and the dean, that they would be quite angry at our committee, but they responded with tremendous integrity. Yes? Student: Why did you multiply the present value by the interest rate to find the >? Prof: You tell me. Why did I do that? So someone else tell me. So that's a good question. Why is that? Yes? Student: It's like finding the coupon of the perpetuity with a 5 percent interest rate, because it's like you're rearranging C over r equals the present value, so it'd make it present value times the interest rate equals C. Prof: Right. So the question was why, after I figured out the present value loss like 772 million, why did I multiply that by 5 percent to figure out how much Yale should reduce its spending every year. And the answer that was given down here is that I'm assuming that Yale is going to go on forever. So Yale can reduce its expenditures every year forever and by doing that make up for the same present value loss, so forever means perpetually, so it's a perpetuity. So how much do you have to reduce-- what is the coupon reduction, the expenditure reduction every year at 5 percent interest that just makes a present value decline of 772 million? Well, it's 5 percent of the principal. If you have 772 million in the bank and every year 5 percent of that you throw away, you've thrown away the whole value, at 5 percent interest, of the 772 million. So by reducing your expenditures by 5 percent every year you defray the 772 million dollar loss. So the critical thing, the critical mistake that the administration made is they had a short run problem with a bunch of short run costs, but Yale's going to live forever and Yale should share the cost and the loss over all future generations, not just make the current faculty, and the current students, and the current city bear all the costs of this one shot loss, one shot problem that Yale faced. So they weren't thinking in Fisher's terms of taking the present value over the whole course of the lifetime of the institution. They were thinking, well, we've got to spend 100 million dollars this year we better cut costs by 100 million dollars. But that's obviously crazy. Like suppose you had to spend an extra 100,000 dollars in one day. Does that mean you should lay off your faculty for one day so you can find the money to pay that? And of course not, so you have to spread the loss over the lifetime of the university. Are there any other questions about this principle? Yes? Student: If you wanted to return to say spending 100 million dollars a year again after 10 years would you spend 77 million a year for those just 10 years if you wanted to incur the whole cost over a fixed period of time? Prof: If I wanted to incur the whole cost over 10 years? Student: Yes. Prof: Then I would have to reduce my expenditures by 100 million dollars a year. If at the end of 10 years I wanted to be back even then I would have to spend less. I would have to cut my expenditures by exactly the money I was pouring into the buildings. So if I wanted to reduce my expenditures by an equal amount every year it would have to be 100 million dollars for 10 years, right? If the maintenance costs go over a 10-year period and I want the expenditures to go over a 10-year period, right? So if I want the expenditures to be reduced evenly over a 10-year period I'd have to do 100 million dollars a year. If I wanted to eat away the costs all in 1 year--I guess I didn't understand you're question. You're saying if I wanted to reduce expenditures entirely in 1 year and then return next year to my usual pattern of expenditure then I'd have to cut the 1 billion dollar budget by 772 million. So that would involve basically firing the whole faculty and saying take a year off you're on furlough, sort of what they're doing in California. Yes? Student: Can you also spread the present value cost evenly over 10 years and not like 100 million dollars every year, but 100 million in present value terms. Prof: I could do that if I wanted. I could rearrange the 100 million any way I wanted to. So you would cut less than 100 million dollars this year out of the budget and a little bit more every year after that? Student: Assuming you wanted to get these costs over with in a 10-year timeframe. Prof: Well, one way to do the costs over with in a 10-year timeframe is reduce costs, reduce paying the faculty by 100 million dollars every year for 10 years, right? That would obviously do it, because that's the money I need to get. You could now rearrange that by reducing costs a little less at the beginning and a little more at the end of the 10 years, but I would say that doesn't sound-- why do that? That's kind of what bad politicians do. They say, "It's not our fault. We'll just make those guys in year 10 get totally crushed," and pretty soon they are in year 10 and then they've got 200 million they have to cut costs. Yes? Student: So say in 25 years Yale wants to do another round of rebuilding all of the buildings they'll still be paying for the buildings that they built 25 years prior? Prof: Right. So there's a good question. So actually some people, the administration, that was their best response, they said, "Well even though the white paper said this was a one shot thing, and after we do this 10 year plan Yale is back in good shape, and of course every year Yale has allowed maintenance expenses. That's part of the budget is maintenance. So after we get the buildings back in tip top shape we're going to keep them in tip top shape by doing these normal expenditures every year so we should never have another period where you have to do something drastic like that." That's what the white paper said, but after the report they responded just like you said. They said, "Well, we didn't really mean that. Maybe in 25 years we're going to have to do another remodeling effort." And so well, if you need to that then it wasn't just a one-time deferred maintenance. It means that you've drastically underestimated the cost of keeping up the buildings over Yale's whole future, so then you would have these reductions in expenditures for the first 10 years and then in year 35 you'd have to have more reductions, and then in year 70 you'd have more reductions like that. So you have to take the present value of all those things and then figure out how much to reduce expenditures on an even basis and so it would be much more than 32 million. It would be 60 or something million or 50 million. So you're exactly right, but that's not what they said in the white paper. So I took them literally what they meant. So what happened after that? Yale has done much more building expenditures than that, but that's because Yale's endowment went up to 23 billion. So from 3 billion which it was at the time it's now 23 billion so Yale's launched an incredible program of building construction. Basically they've done two things. They've built a huge number of construction jobs and they've hired a lot of administrators and stuff. So the faculty is still not that much bigger. It went down 6 percent. It's now back a little bigger than it was before. So the plan to expand the college and expand the faculty hasn't happened yet. So Yale faces another choice now. You know the endowment went to 23 billion and then this past year they managed to lose down to 17 billion, 30 percent got lost. So we're down to 17 billion now. So again we have the same question. We just lost 6 billion dollars. How much should we reduce expenditures every year? So what's your answer to that? Student: About 30 percent? Prof: Not 30 percent. So how much would you reduce expenditures? Why wouldn't it be 30 percent? Because Yale spends a lot of money it doesn't get from the endowment, right? It gets money from tuition, for example. So what should Yale do? What do you think Yale's going to have to take out of the budget now? Student: > calculation. Prof: Yeah, and let's say it's still 5 percent real interest then what would you do? Student: Present value's 6 billion dollars and we assume we're at 5 percent interest. Prof: Yeah, so what's that? Student: 6 over .05? Prof: 6 times .05, so what's that? Hard to do these things in your head, right, but what is it? Student: 300 million. Prof: 300 million, so Yale's got to somehow cut 300 million out of its budget so it's not going to do it in one year, but over the course of the next few years it's going to have to cut 300 million. Now the budget is well over 2 billion so that's 15 percent of the budget, though, Yale's going to have to cut. So this is a serious thing. How do you cut 15 percent of the Yale budget? Student: Firing faculty. Prof: Firing faculty, well, I hope they don't do that. I think they learned their lesson so I doubt if they'll do that. Things are already changing. They're charging for long distance telephone calls and all kinds of stuff like that. That doesn't get you quite 300 million, but there's going to be a bunch of stuff like that. So anyway, we have another budget problem, by the way. So these kinds of budget problems are happening all over the country. I gave a talk at Albany University and they're going to abolish their graduate economics program, SUNY Albany. These are serious problems losing that much money. But in any case 6 billion translates to, right, the difference here is 6 billion and you multiply that by .05 just as we said and that equals 300 million a year. So Yale won't do it right away, but over the course of a few years Yale's going to have to reduce its budget by 300 million, so they're going to obviously choose to do a lot less building and presumably some of the new people that got hired they're going to not keep. So any other questions? Yep? Student: Doesn't that presume that the endowment stays that way? Prof: Yes. Student: Could you also, once the stock market and the real estate goes back up, can you have some assumption that they don't need to cut as much? Prof: Right, very good question. So in the front he's saying this presumes that we know for sure that the endowment lost 6 billion. It'll never recover it. Maybe that's a temporary drop in the stock market and it'll go back up, and basically the principle he's applying is he's saying you can't make these drastic reductions in annual expenditures, firing people and then two years later realizing you've got a lot of money trying to hire them back because you won't be able to hire them back. So clearly Yale has to have a more complicated rule about how it gradually adjusts its spending when there's a change in the endowment. And so we're going to talk about that later because it involves uncertainty and how to think about uncertainty. But you're absolutely right. So Levin did not announce a 300 million dollar reduction immediately, but he announced a big reduction immediately, and you're going to expect next year if the stock market doesn't drastically improve for there to be another reduction. And, by the way, this number could go down as well as it goes up. So we're going to come back to Yale's investments and what they're like. A lot of Yale's investments are called private equity investments that are very hard to value. So for all we know this 17 is a lot worse than that, but we'll be finding out in the next year or two. It's not like a hedge fund where you have to value all your assets by what the market will be willing to pay. A lot of these assets there is no market so they just sort of make up what the number is. Anyway, we're going to come back and discuss this. It's a very interesting question. So one last thing about this present value calculation, one last obvious thing, it's hard to keep in your mind the difference between real and nominal. So let's just do a very simple thing. The mortgage, mortgages are traditionally nominal fixed payments. So for example, a 100,000 dollar 30 year mortgage at 2.3 percent is about 4,600 dollars per year. How did I do that so quickly in my head? Well, because I know if the interest rate is 2.3 percent and you're going to pay it forever you'd pay 2,300 a year. We know at 30 years at 2.3 percent, 2.3 percent doubles almost in 30 years. That's 69. That's getting pretty close to 72, so maybe it takes 31 years or something to double. So after 30 years the remainder is worth half the mortgage. So you've lost half of the value by only getting it for 30 years. So instead of paying 2,300 you have to pay 4,600. So the coupon over .023 times (1 - 1 over 1.023 to the thirtieth), that's 1 - 1 half about, so if this coupon equals 100,000 the payment is going to be-- since this is 1 half the payment isn't going to be 2,300. It has to be twice that, 4,600. So it's 4,600 per year. So if there's no inflation that means you're making the same real payment every year. Now what happens if there's inflation? What if inflation goes up? Now what's going to happen to what you have to pay? How would you figure that out? Well, if inflation is another 2.3 percent or something, then the nominal interest rate 1 i is going to equal the real interest rate times the rate of inflation. So let's say this is 1.023 and this is also 1.023, so that's 1.046, a little bit more than 4 6, almost a little bit more than 4 6. So you know that the interest rate the mortgage companies are now going to charge is going to be 1.046. So the 4.6 is going to be the mortgage interest rate and so you can figure out by the same calculation what the coupon's going to be. So what's the coupon going to be? Well, instead of doubling every 30 years at 4.6 percent it's going to double approximately every 15 years. So this is going to be doubling twice. This is 1 quarter, so this'll be 3 quarters here. And so if you multiply everything, 2,300 a year times 4 thirds--am I doing the right calculation here? I'm telling you it's so easy to compute in your head and meanwhile. Oh, I forgot to change this to 4 6, so the interest rate is 4 6. So this to the other side is 4,600 times 4 thirds and that's 6,000 about. So the annual payment is going to go up to 6,000 instead of 4,600. It was 4,600. The interest rate went up because there was inflation, so of course they're going to ask you for more money every year, because if you pay the same amount every year and this is the real payment-- if you make the same amount and this is time in terms of inflation corrected dollars you're paying less and less every year. So clearly if you started with no inflation and a number like this, so no inflation and now you've got inflation but the same real interest rate, and the present value of your expenditures, the real present value, right--the mortgage company's going to want, the lender's going to want to get the same amount back in real terms as it got before because the inflation hasn't changed the real world. So Irving Fisher would say the inflation is just a veil. Everybody's going to want the same real interest rate and so the mortgage is going to have to return the same real thing it did before. The present value in real terms, or the real payments is still going to be 100,000. So if the real payments go down over time and have the same present value they had before it's got to be that they're higher at the beginning and in real terms lower at the end. So sure enough 6,000 is a much higher number at the beginning than 4,600. So of course when inflation went up and everybody knows it's up the mortgage companies are going to ask for higher annual payments so it'd be 6,000 a year instead of 4,600 a year. But now if you inflation correct that, the 6,000 every year is going to be less, in terms of real goods, less and less every year, but the present discounted value of this thing has to be the same as where you started. So the effect is the young borrowers are going to be spending a lot more in real goods when they're young and a lot less when they're old. So inflation has an unfortunate impact on mortgages quoted in nominal dollars that it makes the repayments happen earlier. So the young who have less money are having to pay a huge amount, and when they get old the inflation's so high that that same 6,000 dollars is practically nothing. So when they're 50 and 60 they're paying practically--they're peanuts to them, but when they were young it was really a hardship. So there's a big problem with nominal mortgages, which is that in inflationary times it kills the housing market. Fortunately we're not in inflationary times. Any questions about that? All right, so that's the basic lesson of taking the present value. And again, you've always got to sort out the nominal from the real, and look though the veil, and don't get all mixed up by the fact that there's inflation. It's the real thing that you want to concentrate on as much as you can. So that's it for the obvious lesson of present value. Now I want to introduce another word which is very famous in finance. It's called the yield or yield to maturity. And I'm going to do it, unlike the way I've presented in the notes, I'm going to do it in terms of a hedge fund, so if you can see this? So yield, the next topic, or yield to maturity is a way of trying to compute one number that summarizes how good a bond is, or how good, how well a hedge fund has done. So I think the more interesting case, and the less obvious one, is to start with a hedge fund. How do you measure how well a hedge fund's doing or how well it's done in the past? Yeah, how well it's done in the past. We're going to spend a lot of the course talking about this in various ways, but the first way to do it involves yield to maturity. So let's see why the problem is a little complicated. So I imagine that there are three investors in this hedge fund. So every year some of the investors are going to decide what to do, and they're going to decide whether to withdraw money. Here's investor one. Maybe he's going to withdraw money. The hedge fund's just beginning. He's going to put in 100 dollars. The other two guys haven't done anything. So now the hedge fund before this guy put in his money had nothing. It's just beginning. He's put in his 100 dollars, so the hedge fund's got 100 dollars. So that's it. So I'm imagining these all happen, they usually happen quarterly or annually or something. They don't happen every day. There's a fixed moment at which everyone deposits their money. So let's say they happen annually. The guy puts in 100 dollars at the beginning of the year. For the rest of the year nobody can do anything. They can't take money out. They can't put money in. So the hedge fund, let's say, manages to put the 100 dollars to work and finds a 7 percent return. So it's now got, the hedge fund all together has got 107 dollars. So let's just go to the hedge fund all together. The hedge fund had 100 after these guys, because only one guy put in money and now the hedge fund's got 107 dollars. Well, that 107 dollars is all the first guy's money, because nobody else has put anything in. He still owns it. So, so far the hedge fund got a 7 percent return. Well, now the next year, we're now at the beginning of year 2, our first investor thinks to himself, "Well, they did fine, 7 percent, not great, but I'm okay. I'm not going to do anything, won't take any money out or put any in. A rich second investor puts in 1,000 and another guy puts in 200. So now what's happened to the NAV of the fund? Well, the first guy, at the moment they put in the money, the first guy still owns 107 of the dollars. The second guy's now got 1,000 in the fund and the third guy's got 200 in the fund and the hedge fund now has 1,200 plus the 107. That's 1,307. That's how much money is in the fund. So that's at the beginning of year 2 if you're still following this. If you're not following it interrupt me. Sorry. So what happens in the beginning of the next year, year 3, well let's say our guy--so the hedge fund makes money and this time it made 3 percent, a crappier, sorry, a less good return, only 3 percent. God, it's on film. I'm glad that's going to live for posterity. Only a 3 percent return, and so the hedge fund which ended the year at 1,307 now by the next of this next year it's made 3 percent on that so it's up to 1,346, so 39 dollars, 3 percent on 1,300 so 1,346. Now of that who's got the money? Well, our original guy he's now made--everyone made 3 percent so his 107 turned into 110. The second guy's got 1,030 in the fund, and the third guy's got 206 in the fund and the total fund is 1,346, Now let's suppose that our guy, this is the beginning of year 3, our first guy says, "3 percent, that's a terrible return. I'm taking my money out. I've had it. It's 110 dollars. That's what I have. I'm taking it out," and no one else does anything. So at the end of the year now he's down to zero and everybody else is where they were and the hedge fund thing has gone down a little bit. Well now next year the thing does even worse. It makes a 0 percent return. So everybody's money is just the same except that the second guy decides this is really getting lousy and he takes half his money out. So this is taking half his money out. What was his money? He was 1,112 and half of that is 556. So he takes half of it out leaving half behind, and the column on the right reduces what the hedge fund's total cash is. But now the hedge fund has a great year and it makes 50 percent. Having made 50 percent--sorry, so this guy takes half his money out. At the beginning of the year the fund does badly then the fund--I skipped the 8 percent. There was an 8 percent return, sorry. Oh, what an idiot. Anyway, so the next year the fund returned not 0 percent it returned 8 percent. So the first guy after the 3 percent return this guy took his money out. The other guys left it in and then the fund had an 8 percent return. So it's a little bit better, but this guy decides to take half his money out. Then the fund has a 0 percent return and after that this guy decides to take his money out, half his money out, but then finally the last year the fund gives a 50 percent return, which is fantastic, so everybody does well. And now let's say they all decide to take their money out. So now there's nothing left in the fund, and they withdrew the total 934. So what I've done here, just to summarize it, is every year people are putting in money or taking out money at the beginning of the year. You can never take out more than you have or you can put money in. The fund earns returns over the whole year and then people, again, decide to take money out or put money in and then the fund earns a different return the next year, and eventually the fund returns all the money or people withdraw the money. So the question is how has the fund done? How would you summarize in one number how the fund has done over its 1,2, 3,4, 5 years of earning returns? That's the question. So this is a standard--this is obviously what happens every day with hedge funds. So how do hedge funds report how they've done historically? So do you have any suggestions? What would you do to summarize how the hedge fund has done? If you had to pick one number what would it be? How good an investor is the fund? Yeah? Student: Just multiply the return. Take a geometric average. Prof: So one thing you could do is you could say--he said literally multiply all of these returns. What does that mean? That means if you put 1 dollar in the fund at the beginning you'd earn 7 percent. If you left it there and never took it out you get another 3 percent. Then you'd get 8 percent on top of that, then 0 percent, then 50 percent. Of course this is a multiplicative thing, so he says you'd get 1.07 times 1.03 times 1.08 times 1 times 1.5. Multiplying all that would give you the number of dollars you'd have at the end of 5 years given that you put 1 dollar in at the beginning and never took it out. And if you wanted to annualize that he said take the geometric average, the fifth root of that and that's the constant rate of return that would have given you the same amount of money at the end that you would get by having left 1 dollar from the beginning in the fund all the way to the end. Is that clear to everybody? That seems like a logical thing to do. That's what money hedge funds do do, in fact. That's the number they tell you. Now, why might not that be a great number? Did everyone follow what his suggestion was? So by the way, his number's going to come out to be--well, I don't know. Anyway it's going to be some number. We could do that. In fact it wouldn't be that hard to do. Let's just do it. Sum, oh this wasn't a very--ah! How about equals? Oh, dear, all right, circular reference. Equals sum. Oh, why did I get zero here? Oh, because I'm trying to multiply these. I'm adding instead, so equals. I'll just have to do it one by one. That times the next one, times the next one. There's obviously a much faster way of doing this. Times the next one, times that one and zero, that's what 1 dollar would have gotten you if you had put it in and kept it until the end, and now he's saying take this to the fifth power. So I'll take up this .2 enter. So 12.2 percent, now why isn't that the right number? Why might you think there should be another number? What's another number? What's the matter with that--way back there? Student: It's grossly inflated by that last year's 50 percent return. Prof: Well, is it grossly inflated, but why is it grossly inflated by that? Student: There are going to be lots of years where it doesn't do that. Prof: That's true, but you've taken that into account. So the years we didn't do that well like the 0 percent return that brought the average down, so why is that a problem exactly? Yeah, it's averaging the good years with the bad years, so. Yeah? Student: As far as a measure of past performance it doesn't take into account that after three mediocre years a lot of money was removed from the fund. Prof: That's the crucial thing. So I didn't do extreme enough numbers. The crucial thing to take into account is that suppose you have a fund that starts off, many funds like my fund started off with very little money, but we did it at the right time because we knew that was a good time. You're going to see when the leverage cycle, we talk about it. It was at the bottom of the leverage cycle just like this past year. We're up 30 percent this year. So at the bottom of the leverage cycle you're going to have a great year. Of course we hardly had any money because the fund was just starting, and so we made 50 percent the first year. But then everybody said, "Oh, these guys must be geniuses," and they poured a huge amount of money into our fund, and let's say the next year we did 10 percent. Actually we had another great year the second year, but let's say that we did 10 percent the second year. So the young man in the front is saying you made 50 percent on pennies and then you made 10 percent on a gigantic amount of money. It isn't right to take the average of 50 percent and 10 percent because almost all the money that you managed you made 10 percent on not 50 percent on. That's his point. So how would you deal with his point? How could you figure out a way of computing the right return to compensate for the fact that some years you have a lot more money at stake than you have other years? Yes? Student: Take a weighted average? Prof: Take a weighted average. Well, how would you take the weighted average? Sounds a little complicated. That's what I'm going to do, but it's not immediately obvious how to do it. So I wouldn't have expected you to be able to answer that. You're right on the right track. So does anyone have anything else to say? Yep? Student: I guess you multiply each > , and then you add it all up and divide it by the > Prof: All right, so I'm going to now give you the answer which is a little bit like that. She's saying do some dollar weighted thing, and so you somehow weight the numbers by how much money there was invested for that year. So because there was a lot more money invested in year 3 than there was in year 1 that number should somehow have a bigger weight. And it's not exactly clear how the weights are going to get in there, but it's obvious that that's something like that you ought to do. So here's the mathematical solution that the internal rate of return or yield gives. So it says every year let's look at what happened in the fund. We shouldn't care about which investor put in which dollar. We care about how the fund managed dollars. The names of the investors don't make any difference. It's how did the fund manage its money. So in the first year the fund got 100 dollars. So as for producing money it produced a negative 100. Money went into the fund. That was the one guy invested. We don't care who it was. The total that went into the fund was 100. The second year 1,200 went into the fund. Those are the second two guys. The third year 110 came out. That was the first guy. The fourth year 556 came out. That was the second guy. This is beginning of the fifth year. The third guy took out 155 dollars, and then the last year the second and third guys took out everything that was left. So from the point of view of money creation and use this is every year what went into the fund and what came out of the fund, the net inflow out. So there are a bunch of numbers. So the question is, so the one number summary is what rate of return, it's called the internal rate of return which if you discounted all these numbers what would Fisher say if you discounted all these numbers? If you had to use just one interest rate, Fisher would say, what's the present value of these cash flows? Well, if the interest rate was 0 you just add up all the numbers and you're going to get a big positive. If the interest rate is infinity then that means that after the first year you're discounting everything to 0 and you're going to get negative 100. So you could say, what interest rate could you discount all the cash flows at to produce 0? That would be like saying at that interest rate, all the fund has done is rearranged its money. It's taken money in and put money out, but at that same constant interest rate the present value is 0. So it's allowed you to trade money across periods at this internal rate of return, the interest rate which makes the present value zero. So 10 percent turns out to be the right number. So if you discounted things by 10 percent, you see what the formula is, you take the inflow and you discount it by 1.10 to the first power and this you discount by 1.10 to the second power, the inflow, the net outflow, I guess, which is 110 you discount by 1.10 to the third power etcetera. You keep discounting by that and you get all the discounted net flows. You add them all up and you get practically nothing. That's adding them up and this is taking the square, and I used Solver to figure out what the right discount rate was to make all this zero. So that's the simple way of averaging, dollar weighting everything. You don't care about who the people are. You don't care about whether one guy's putting money in, another guy's taking it out at the same time. You just care about the net, and if you've got a bunch of net numbers, that's the net outflow, and you're trying to say, what's the single rate of return? The idea is to say at what interest rate? If there were a bank paying an interest rate and all those things discounted gave you zero that would be like saying the fund is functioning just like a bank. No matter when people put the money in or take it out they're always getting this rate of return which is 10 percent. So they're getting a constant 10 percent rate of return no matter when the money goes in or out and that kind of gives you a measure of how well the fund's doing. So that's the internal rate of return, or the yield to maturity. It says take the net cash flows every year. Find the number which when you discount at that number you get present value equal to zero. So it's 10 percent which is a different number from 12 percent. Now before we got the geometric average of 12 percent. Now very typically this is the case that this internal rate of return is lower than the dollar return from putting the money in at the beginning, assuming the fund doesn't just collapse and go to zero at the end. So why is that? For funds that have survived typically that number, 12 percent, is higher than 10 percent. Why would that be? What does that tell you about the world? Someone who hasn't--well, go ahead. Student: That it's easier to make money with a smaller amount of money? Prof: It tells you that, and how is it that the hedge fund--it could tell you that. It tells you that the hedge funds are doing better when they have a smaller amount of money than when they have a larger amount of money, exactly. You've concluded that it's easier to make money when you have a small amount. What's another possible explanation? Student: People normally invest a lot after a big year > Prof: Right. I think that's the reason. The reason is that people pour money into hedge funds just after they've done incredibly well, and they keep pouring money in, then eventually there's a blow up. And so when the blow up comes the hedge funds have zillions of dollars and they're losing a lot of money. Then everybody pulls their money out and that's when the cycle is going up and then all of a sudden the hedge funds have these huge returns again, but they hardly have any money. So, any other questions about this? All right, so internal rate of return is a way-- we are going to see that it has many shortcomings, but it's a way at getting at the idea, as several of you have said, that you can't just take the geometric average, which is what every hedge fund like ours always produces. That's the number we tell everybody because it's a better number than the other one. So the geometric average of the returns are, if you're an investor who puts 1 dollar in at the beginning and leaves it there forever what's your geometric average of all your returns. That's not a good reflection of how the hedge fund's done necessarily because some years the fund had a lot of money to work with. And so the average dollar didn't do that well, and now there's a question about how should you measure the average dollar, and I've given the internal rate of return. There are actually other formulas you could give. This is the most famous one. Now let's see how this internal rate of return is used all the time on Wall Street. By the way, if you're not following what I'm saying you should please interrupt me. So what if you took a bond, a simple coupon bond? What is a simple coupon bond? The yield to maturity of a simple coupon bond, I'm now on this lecture called yield, what is a simple coupon bond? A simple coupon bond pays the same coupon every year and then pays the principal and the coupon at its maturity. So the yield to maturity is going to be the price, which is like a negative payment--suppose you knew the price of this bond. If you knew the price of the bond, and so the bond is promising all these payments, how good a deal is that? Well, how good a deal it is they would say is you simply take this first negative payment and all these positive payments and find the unique interest rate which when you discount it will give you present value of 0. And so if this is a coupon bond, say paying 7 percent, say the face is 100, it pays 7 dollars forever, and 107 at the end, and the price is 105, what do you think the yield to maturity is going to be? Can you say anything qualitative about it? Suppose it's a 7 percent coupon bond, face of 100,10-year bond, no one thinks that it'll default, but its price is 105. What is the yield to maturity in that case do you suppose? Just a vague guess, I just want a qualitative number. Student: 6.7? Prof: 6.7, that's qualitatively wrong. Well, I mean it's not qualitatively wrong. No, it's qualitatively right. It could have been better. So he's right. So what if the price were 100 what would the yield to maturity be? Student: 7 percent. Prof: 7 percent, that's obvious, right? If it's a 7 percent coupon bond on face of 100 and its price is 100, price = to the face, then obviously the thing that discounts you back to 100 is going to be 7 percent interest. So if the price were 100 the yield to maturity would just be 7 percent. But I told you the price was 105, which is a lot more expensive. So it's a bad deal. So it's not going to be as good as 107. So it's not going to be 7 percent and he said 6.7. So I think it would be a little worse than that, but that's qualitatively just what I asked for, something worse than 7 percent. So who said 6.7 percent? You did. Student: I just took the price of the bond over the coupon payment and that's 6.7, but it's not the only > Prof: So that's another number. So I'm going to come back to your question. It's a good question. So do you all see that if you measured the yield to maturity on this bond--so the bond, remember, pays 7,7, 7,107 and its price is 105. So the yield to maturity is going to be that number such that 105 = 7 over (1 the yield) 7 over (1 the yield) squared 7 over (1 the yield) cubed ... 107 over (1 yield) to the tenth, that's 105. So what we observed is that Y has to be less than 7 percent because if Y were exactly equal to 7 percent this would give us 100. But this bond is more expensive, so you're paying more to get the same payments you would--than the face. You're paying more than the face to get the same payment. If the price were equal to the face it would be a 7 percent yield. So since you're paying more you're getting a worse deal, so it's pretty obvious that if you want to discount this number to more than 100, namely 105, Y is going to have to be less than 7 percent. So that's the first thing we said. Now what did he do? He gave a number and he said 7 over 105 which he said was about 6.7 percent. So that number that he gave is called the current yield. It's another number people give, and he figured that was 6.7 percent. So let's believe him that's 6.7 percent. How does that number compare to the yield to maturity, to Y? Well, we could compute this out on Excel since I'm doing so brilliantly at it now. So we could go 7,7, 7,7, 7,7, 7,7, 7, and 107. Those are our payments and then we could try some yield to maturity, internal rate of return and let's guess 1.067. And now we'd say the cash flow is going to be this, is going to be the left. Oh dear, I have to number things. So again, there's probably some clever way of doing this. So this'll be--I forgot to write the year. Let's just add this. Equals up 1 enter. So I'm just going to copy this. All right, so now I've numbered all the years. Equals up 1 enter and now control copy. So I've numbered all the years here and here are the payments. And now at this yield to maturity I'm going to go equal the thing on the left divided by the yield to maturity that we're guessing raised to this power. Now I can just copy that and I've got all these cash flows. Oh, what did I do that time? Student: <<overlapping conversation>> Prof: What? Student: <<overlapping conversation>> Prof: Control copy, sorry. Student: <<overlapping conversation>> Prof: Control copy, right? So I just want to copy this? Student: <<overlapping conversation>> Prof: Oh, I see. Yeah, yeah, yeah, right, right, right, so here I've got the--you are right. So there's a trick here which I forgot which is the discount rate, the internal rate of return E I've got to put a dollar sign, dollar E, dollar 1 so that way it remembers the spot. So now when I copy it it's going to remember that. Student: B1. Prof: What's B1? Student: <<overlapping conversation>> Prof: Oh, B1. Thank you, so there are two mistakes, B1. Now, control copy. So I'm supposed to be showing you how easy it is to do this, but--all right, so anyway that's it. So if you see for each number here I've got the payments for every year and I've discounted them by taking this internal rate of return, and now I just have to sum all this. Equals sum parenthesis. Oh shit. Student: <<overlapping conversation>> Prof: I'm trying to sum it, you're right. So here equals, I want to sum all these. So what did I do wrong? Student: C1 colon C10. Prof: C1 colon C10, that's what I thought I did, but obviously I didn't. Good, and now we can do this and square it. So that's the thing I want to minimize, and so now I'm going to Tools, Solver, Min, C12 by concentrating on this number, and solve. Student: <<overlapping conversation>> Prof: All right, what did I do? Student: <<overlapping conversation>> Prof: Here's the sum, here's the... Student: The original price. Prof: Oh, the original price. Ah ha! Thank you very much. So we need the original price of 105. Very good, so I see that preparing this would have helped. So here's the sum. So we just summed all these things, and here we're going to--so we're summing those, right? So I summed all these and then I've got the original price 105 enter. Now we'll add equals this plus this. Student: <<overlapping conversation>> Prof: You're right, this minus that. And now we want to square this, equals up squared enter and now we'll do Solver. Hopefully there isn't another mistake. So Tools, Solver, so I want that times E1. Oh, that's very bad. Anyway, you can solve it using Solver and it's extremely simple to do, and a child could learn how to do it. So we get Solver and we solve all this, and you should be able to use Excel with no problem at all. So the question is what are the relationships between the current yield and the yield to maturity, and suppose there's some actual interest rate. So there's an actual market interest rate of, say, 6 percent or something. So those are the things that we want to sort out now in the next five minutes. So let me go back to the notes and we'll re-ask all the questions here. You can see that's Solver. I've broken Solver. Suppose that there were an actual interest rate in the economy and our bond, the bond that was 7,7, 7,107, if the actual interest rate was, say, 6 percent the price of the bond would be more than 100. So some price which will be the present value will be greater than 100, obviously, because it's paying--if the interest rate's only 6 percent this is giving you more than 100. Now, the current yield is 7 over the present value, exactly analogous to what he said. So if someone calls you on the phone, you haven't gotten these calls yet, but when you get older you'll get--they're screened now, so it's harder to get these, but it used to be a few years ago you'd get called on the phone quite often and somebody would say he's running a bond fund, and the bond fund is really doing great, and he wants to tell you that the bonds they have in the fund last year paid a current yield of 7 over the present value which is much bigger than the interest rate of 6 percent, and therefore you should buy his bonds. Now, what can you say about that? Suppose somebody tells you there's a market price for the bonds, which we know is the present value at the interest rate of 6 percent, and he tells you that, "Look, look at the market value I got last year, the yield I got; the current yield I got on these bonds. The present value was some number bigger than 100, but I take 7 over the present value and I get something bigger than 6 percent. At your bank you're only getting 6 percent, so therefore you should invest in my fund." Is that a good argument to invest in his fund? Why not? Now, this bond is called a premium bond because the price is bigger than the face, and a discount bond means the price is less than the face, and a par bond, the price equals the face. So just because a bond pays a coupon of 7-- it may be when the bond was issued everybody thought the interest rate was going to be 7 percent forever, so that's why they picked a coupon of 7 so that the price when they first issued it would be equal to its face value. But maybe the next day, so it's still a 10-year bond, practically no time has changed, but unexpectedly the interest rates fell to 6 percent. If you take the same coupon bond paying 7 all the time at 6 percent interest its price is obviously going to go up in the market because everybody is going to discount the 7s, not at 7 percent, but at 6 percent and get a number that's bigger than 100. So you're going to have to pay more for the bond because the present value's higher. However, people who now will try and market the bond they're going to tell you, "Well, look at the market price," whatever the market price is. So the current yield is the market price. They'll say, "Look at the market price. This is what we bought the bonds for. I'm a fund. I went out and bought these bonds. Look at the price I paid and I got 7 dollars for these bonds this year in income and 7 over the market price of the bond is bigger than 6 percent, so I was doing a great job. You should invest in my fund." So, that can't be a correct thing to say or a persuasive thing to say, because the market price reflected the fact that the interest rates were 6 percent. Everybody was properly computing the present value, and let's say the market price was equal to the present value, the present value would indeed be greater than 100 and in fact the current yield would be more than the interest rate of 6 percent. So why is that? So, theorem, if market price equals present value at a going interest rate then the current yield on a premium bond is always greater than the interest rate. So why is that? So in this case, if I hadn't screwed up the Excel we would have calculated the present value. So 7,7, 7,107 there's only a 6 percent interest. So everybody taught by Irving Fisher computes the new present value which of course is bigger than 100 and that's the market price. Some unscrupulous salesman starts a fund, buys the bond for whatever this present value, the market price is, then goes out to a bunch of clients, potential clients, investors, and says, "Look, my very first year in business I spent a little more than 100 dollars and I got 7 dollars as a coupon and 7 over this little more than 100 is giving me at current yield that's more than 6 percent. I beat the interest rate. You should invest in me, and by the way, I'll charge you a little fee to do that because I'm doing so great." Now, that's always going to be the case so it has to be that he really hasn't accomplished anything at all. So why is it easy to see that whenever I computed the present value it was going to have to be more than-- this current yield would always be more than 6 percent. How do I know that? Yep? Student: Because of the face value that's going to be at the end at maturity isn't going to reflect that increased interest or relatively higher interest. It's going to be the original face value. Prof: Exactly. So let's say, to keep this simpler, let's suppose these were 10s everywhere, and the interest rate went down to 5 percent. Now, what's going to be the present value of this bond? It's not going to be 200, right? If the bond paid 10,10, 210, suppose I have something paying 10-10-10 and 110, and the coupon is 5 percent. The present value is going to be less than 200. The coupon is always double the interest rate, so it looks like that's what you'd get if you had 200 dollars, but at the end, as he's saying, you're only going to get 110 and not 210. So this present value of this thing has to be less than 200. So if you double the coupon--if you halve the interest rate, the interest rate was originally 10 percent, if you cut the interest rate in half to 5 percent it looks like your annual coupon is double the interest rate, but at the end you don't get principal that's double the original principal. All you did was double--relative to the interest rate of 5 percent, the coupon's twice as big as you normally expect, but the face isn't. So therefore, this has to be worth less than 200. If it were 200 at 5 percent it would give you 10, 10,10, 10,10, 210, but this gives you 10, 10,10, 110, so obviously the present value is less than 200, but therefore 10 over something less than 200 is going to be more than 5 percent. So that's his intuitive proof, which is the essence of the thing, that if ever you have a coupon bond that's a premium bond then the current yield is always above the interest rate. So you can always advertise it as having a spectacular current yield when in fact it's just priced perfectly fairly. So I'm going to just continue this story of what's the right way to measure things and how you can get confused by measuring the wrong way next class.
Quantitative_Finance_by_Yale_University	12_Overlapping_Generations_Models_of_the_Economy.txt	Prof: All right, well, today I'm going to talk about Social Security again. There's going to be one more discussion of Social Security later. I'm going to defer most of my plan until later, but I want to finish the discussion so that we totally understand the subject. It'll also allow me talk about demography and introduce one of the most famous models in economics called the Overlapping Generation Model. So in the 1940s someone named Maurice Allais, a French economist, introduced the Overlapping Generations Model into economics. He wrote it in French and it was sort of rediscovered by Samuelson in the 1950s. I'm not sure whether Samuelson had read Allais. I think Samuelson may well have read Allais, but anyway Samuelson--so these were 1947, something like that, 1958 in which Samuelson rediscovered it. And you'll see it's a very basic thought and it seemed at first to challenge everything that we've learned so far. So the idea of the Overlapping Generations Model is that time doesn't have a beginning and an end like we've assumed so far, time might go on forever. Now, whether or not you believe time-- whether there's scientific proof that time goes on forever or scientific proof that the universe has to come to an end, let's face it, many of our institutions presume that time goes on forever. The chief most important among them is Social Security which we'll see is the easiest thing to, the model's design to understand. The idea of Social Security is the pay as you go Social Security. The idea of Frances Perkins was that every young generation was going to give money to the old, but they shouldn't worry so much about it because when they got old the next young generation would give them money. Obviously if you thought time was going to come to an end the last young generation, knowing that they were the last generation, would refuse to give money to the old because they weren't going to get anything back when they were old. But then the second to last generation knowing that when they got old that they'd get nothing from the last generation's young they wouldn't give anything either to the old, and working backwards like that if everybody's rational and it's common knowledge that the world is going to end nobody would ever participate in the Social Security scheme. So it's clear that there's some thought that the world might end, or at least there's a thought that it's not worth bothering about the world ending. So the Overlapping Generations Model is meant to take that idea extremely seriously and imagine life going on forever. So let's take the simplest example where there's a generation that begins--generations last when they're young and old. So let's say we're at time 1 here, and there's a generation that's young and a generation that's old. Maybe I'll write it a little bit lower. Sorry about that. So there's an old generation and a young generation and the endowment of the old generation is 1. The young generation has 3 when it's young, 1 when it's old, 3 when it's young, 1 when it's old, 3 when it's young, 1 when it's old. So when you're young you have 3 apples. When you're old you have 1 apple. The next generation when it's young has 3 apples. When it's old it has 1 apple and so on forever. So this'll be T = 1 here, 2 here, 3 here, 4 here, etcetera. So it goes on forever like that. Now, what did Allais and Samuelson both basically say? They both basically said, look, everybody when they're young is incredibly well off. They're working. They're productive. When they're old and retired and feeble they don't have very much, but what can you do? Where can you trade? According to Samuelson what does the old have to trade? It doesn't look like there's any trade that can take place. So it seems like it would be very helpful if the young would give the old something, and when they got old the next generations young could give them something. So the young could constantly be making gifts to the old. That was Allais and Samuelson's idea and it's very closely related to Social Security. So Samuelson got a little carried away with his idea and he said that Social Security was the greatest and only true beneficial Ponzi scheme ever invented because in a Ponzi scheme, this has gotten a lot of attention lately thanks to our famous Madoff. So a Ponzi scheme is basically an investment strategy where you take the money that people give you, and you buy yachts with it, and then when they ask for their money back you tell them that you've gotten great returns and you just hand them money that new people have given you. So they think you've gotten great returns. And when that second generation of people wants their money back you tell them, well, you've invested it brilliantly, you've gotten great returns, but all you're doing is giving them the money that the third generation is giving you, and you keep going like that until finally you owe so much money you can't find new people fast enough to pay the people off and then everybody discovers the Ponzi scheme and it all unravels. And the people at the beginning have made out very well and the people at end who, you know, the second to last generation they've lost all their money and then lawsuits accumulate. And it's quite interesting that in the Ponzi scheme the very first generations that benefited are not free because the whole thing was a scheme. The guy Madoff running it knew from the beginning what was going to happen. And so those first generation of people, there's no reason why they deserve to make their great returns. They benefited from the Ponzi scheme, so the last generations suing Madoff are effectively suing the first people as well, and so we'll see how the courts decide it. But often the people who get out of the Ponzi scheme early still are held liable and the money is taken back, so we'll see what happens in this case. But anyway, so obviously Ponzi schemes are terrible ideas in general. But Samuelson said well, when life is going on forever there might not have to be an end to the scheme. It just keeps going. This guy gives to this guy. This guy gives to this guy. There's no reason for the Ponzi scheme to end if you really think that the world's going to go on forever, and therefore Social Security is a great Ponzi scheme which is actually beneficial. So Samuelson even wrote this as a journalist for Newsweek and there's many-- I happened to be a little boy when he was writing this stuff and I remember some of the articles and I've gone and found them. And so he describes the benefits of Social Security as a Ponzi scheme. So this didn't turn out to be quite right, but it certainly sounds plausible. Another thing he said was he said that in the Social Security-- money, you could think of as a Ponzi scheme, money too, because you have worthless pieces of paper, but you're willing to hold them when you're young, you'll accept them for goods because when you get old you can find the next guy who's willing to give up goods for your money, and that guy is willing to take the money for it because when he gets old he can find the next generation's young who's willing to give up good for his money. So the money, which is a worthless piece of paper, never gets exposed as being worthless because there's always another generation around to take it who thinks they're going to be able to use it later. So these are fascinating topics that Samuelson discussed, but I don't want to discuss them in this class. I want to discuss Social Security, and so I'm going to do a variant of the model that Samuelson never thought about, which I think is a much more realistic model. So I'm going to do overlapping generations with land, and you'll see that in this model I'm going to add land to it. It's, I think, a more interesting model and I'm not going to discuss the paradoxes of infinity because once you put land, even though time goes on forever the paradoxes disappear. So rather than spending all the time on the paradoxes, and how they come about, and do they make sense, I'm just going to add land from the beginning and it will recapitulate in a nice way almost everything we've done this semester and there won't be any paradoxes. So what do I mean by land? I mean suppose that land produces 1, so this is land output, produces 1 every period. So there's another output called apples that just, you know, a tree that's going to live forever, let's call it land, produces 1 every single period. So here are the periods and this is what's happening in every period. Now, land seems to make the situation much more complicated, but in fact it will turn out that we can analyze this pretty easily. So let me summarize, again, the model. The model is that every generation has 1 agent or a million identical agents, let's say. Every generation has endowments, so every generation t has endowment. It's generation t so it's an endowment at time t and at time t 1 equals (3, 1) and let's say they all have utility and the utility of every generation t, which only depends on what they consume when they're young and old let's say is log x_t log x_t 1. So everybody cares about consumption when they're young, consumption when they're old, they don't care about consumption any other time. They begin with 3 apples when they're young. They know they're going to have 1 apple when they're old. Everybody's like that for generation t greater than or equal to 1, but generation 0 just has U^(0), so I can call that U^(t). Generation 0 only cares about consumption when old and that's that guy at the top. But I also have to talk about the land. Generation 0 owns the land. So that's the economy, very simple economy, but it looks much more complicated than anything we've done before, but it will turn out not to be, but it looks it at first glance. So every generation has 3 apples when young, 1 apple when old except the very first generation which has land in addition to his 1 apple when old, and that land produces 1 apple forever. So we have to figure out what equilibrium is and then we have to look at Social Security. And by doing this we're going to understand Social Security much better than we did before. So are there any questions about this, what's going on? Then I'm going to try and write down what equilibrium is and then solve it, and then we're going to talk about Social Security. Yep? Student: Is U not supposed to be >? Prof: Oh, well if you only can eat 1 good if I put log x_1 here it would be the same thing. Remember if I take a monotonic transformation, if I double the utility or take the utility, e to the utility like that, which is just equal to x_1 it describes the same utility. The guy's not trading anything off. There's only 1 good, so more of the good is better for him. It doesn't matter if we call it log x or x_1 is the same thing, but that's a good question. Let's call it log x_1, make him symmetric. All right, well, how would we define equilibrium? So there's financial equilibrium, and then we're going to see if we can solve this. So what's happening in financial equilibrium? Well, it's kind of interesting here. There's going to have to be a price of goods every period q_t. That's the contemporaneous price of apples. There's going to be the price of land every period, pi, let's call it pi_t. So this is apple price. So these are contemporaneous prices. With contemporaneous apple price, land price, what else do we need? Well, we have to decide what everybody's going to consume every period, so generation t what they're going to consume when young and when old. Then there's generation 0, what they're going to consume when old. What else do I need to describe equilibrium? That's probably it. And so what's the budget set everybody's going to face? A budget set for t greater than or equal to 1 is the set of all--let's call it young consumption and old consumption. So generation t because it's going to consume something when young and when old, such that, what? What's the budget constraint? Well, when they're young if they want to consume goods they have to spend q_t to consume goods. So this is young, call that Y. And when they're old they're going to have to consume, sorry, when they're young they're consuming--what else would they want to do? They might want to hold land so we could call that pi_t and I better add a theta here for their holding of land, pi_t theta, that's how much land they hold. Remember how we did this? And then what have they got? We'll they've got their endowment, time t. This is time t, let's say. This is generation t. So their endowment is going to be e^(t)_t, but that's 3, so I might as well write e^(t)_t just as 3. And what else have they got? Nothing? Everybody comes into the world with just apples when young and apples when old, so when they're young they've got 3 apples they can sell. They can consume something, so 3 - q. The stuff they don't consume they sell and they can buy land with it. Ah, god all this time this never happened. Sorry about that. And when they're old what can they do? Well, when they're old at q_t 1, times Z now, are they going to bother to hold the land when they're old? No, because they're going to be dead and they don't care about their children. All they care about is eating as much as they can. So they're going to sell all their land, so that's got to be less than or equal to, what? And so here's the--what are they going to get when they're old? Well, they have q_t 1 when they're old, and their endowment, of 1 what? They can sell their land pi_t 1 times theta. Whatever they bought the first time they can now sell when they're old. Plus what else do they have? So one last term, what else is it? So see what they do. Why would you buy land? Well, because when you're young you're so rich you don't want to consume everything when you're young, so instead of consuming your whole 3, you consume less. You buy the land because the land's going to be worth something next period. So what is it going to give for you next period? What do you get next period from the land? Well, if you own the land you get what? You get the dividend. So the dividend we have to multiply by the price, which on one of the early classes I forgot. And the dividend is 1, that's the dividend, but how many dividends do you get? How many apples? It depends on how much of the land you had. So if you had theta units of the land you get, you know, if you had 3 acres of land you get 3 apples which you can sell for a price q_t 1. You also still have the 3 acres of land which you can sell off when you're old. So that's the revenue you get by selling off the land and you also sell off some of your endowment, maybe, and that's how you can buy when you're old. So that's what the budget set is of the young, of every generation. And the budget set for generation t=0 is simply x_1, is simply Z, we'll call it Z such that what does this guy do? Well, q_1Z has to be less than or equal to, what does he have? q_1 times 1, plus he's got all the land. So he's got 1 acre of land. That's all the land there was, so he's got pi times--pi_1. He's got all the land, so I've normalized the land to be 1 acre. So pi 1 times all land. That's what that guy can do. So equilibrium is, x_t is best for generation t in budget set t and x_1, so this is this and theta, and x_1-- did I write theta? Oh, I forgot to write theta in the definition of equilibrium here, so I have to write a theta t there also having to keep track of how much land they're going to have. This is t = 1 to infinity. So the equilibrium is what are the prices every period of apples and land? What does every generation do in terms of their consumption and how much land they hold and how much does that very first generation consume. It's obvious they're going to sell all their land to consume as much as they can. So the budget set, so x_1 solves. So Z = x_1 and y Z theta equals that, best for generation t in this budget set, and Z = x_1 is best for generation 0 in this budget set. So to say it in words it's very simple in words, and then we have this mathematics and it looks complicated but we're just going to say it's going to be very short to solve it even though it looks very complicated. So the problem is this. We've got generations who are rich when young, poor when old, there's land that lasts forever. The only way people can save is by holding the land. That's like holding stock. That's holding something real. So when they're young they're going to take some of their extra endowment, because they're so rich when young, they've got 3 when young, and they're going to use it to buy land. And when they get old they're going to sell the land, and eat the endowment from the land, the dividend from the land, and sell the land and use that sale proceed to also increase their consumption when old. So they'll be taken care of when they're old because they're able to hold the land. And the question is how do we solve for this equilibrium? And so why is it--so just to go back to Samuelson and all that, why is it so interesting? Well, one of the reasons it's interesting is that people when they're young have to think about the price of land next period when they're old because they know they're buying the land today. They can see the price today, but when they get old they have to, you know, why are they buying the land today, partly for the dividend next period when they're old, but also for the resale value of the land. So everybody is thinking to himself, what's the value of land going to be next period? And of course the value of land next period depends on what the young in that period are willing to pay, but they're thinking about what they're willing to pay on the basis of what they expect to happen the period after. So everybody has to think about the guy after him, and what the guy after him is thinking about what the guy after him is thinking, and it looks very complicated. And we want to solve for an equilibrium which everybody can rationally anticipate what the guy in front of him is going to do which means rationally anticipate what that guy is rationally anticipating the guy in front of him is going to do, and you have to solve for the whole equilibrium and see how it turns out. Any questions about this? It looks very hard, but it's going to turn out to be very, very simple. Yes? Student: For generation 0 why haven't we added the dividend that he would get from holding the land in the second period? Prof: By the way, I haven't said what happens to the dividend in period 0. So actually I think that was a good point. So he gets 1. He also gets the dividend in period 0, so I'm glad you asked that question. So to answer your question, remember the convention that we've made which holds in the market and it's one of the reasons for the breakdown of the market. One of the reasons why the market seized up in the last year or two, or the last year, is because when you buy a stock like the land somebody has to give the money and the other guy has to give back the stock, and the people buying and selling are not actually meeting each other and simultaneously transferring money for the ownership of the land. One guy's in San Francisco and the other guy's in New York and they're doing it through some screen or something. So the physical asset isn't quite changing hands. So you have to make a convention about when do you say the deal has actually concluded. So the convention is, that we always use, is that if you buy the land at time 0 you don't get the dividends-- at time t, if you buy the land at time t you don't start getting the dividends until time t 1. So if the young generation buys the land at time 1 they don't get the dividend until starting at time 2. So the very first dividend at time 1 is going to go to the old guy at time 1, which I had left out here. So the old guy does get a dividend, it's the dividend at time 1 because he began owning the land. So he had it before, so he gets that piece of land. Even though he's selling the land at time 1 he still gets the dividend at time 1, and the generation that bought it at time 1 doesn't start getting dividends until time 2. So that was an excellent question, and it was an oversight of mine, so exactly right. And that's how it happens in real life. Of course, the length of time might be 3 days or it might be 1 month. It depends on the security, what the settlement rules are, but there's always got to be a break between when you buy the stuff and when you start getting the dividends because it just takes time for the whole physical process to happen. So they say t 3 is a very common kind of settlement, or t 1. That means that in 3 days or in 1 day, and so if you're desperate for cash and you have to give-- so anyway, I won't get into--we'll come back to this when we talk about the crisis and what happened. So people who are desperate to get stuff, it doesn't start coming for a little while, so. Any other questions? Yes? Student: Should we multiply the price of apples by q_1? Prof: Should I what? Student: Should we multiply what >? Prof: Absolutely. Very good. Any other comments? All right, now how do you solve this? Well, let's figure out how to solve this. So the first thing you could notice is that--so Fisher never thought of having infinite time and never thought about Social Security. Maybe he thought about Social Security. I'm not aware that he had any thoughts about Social Security. We didn't have Social Security so it's unlikely he had been thinking about it. So I don't think he thought about time going on forever, but that doesn't mean his methods aren't-- he died, by the way, in 1947, I think, something like that, so right around the time Allais wrote his paper. So what is it that he said? All his lessons are going to hold true. The first thing he said is that look, in every period there are qs on every side of things. Here are q_t, q_t, q_t 1, q_t 1, q_t 1. So if you just double--there's no loss in generality by taking all the q_ts to be 1. We have no theory of inflation yet, because there's no money or anything. So you might as well assume we're measuring everything in terms of apples and take q_t to be 1. So without loss of generality, as they say, q_t = 1, and of course that means we can divide every equation by q_t. So pi_t divided by q_t would go here and we'd have a 1 and a 1. We divide this one by q_t 1, still it's an equation. We have Z less than or equal to 1 pi_t 1 over q_t 1 1 times 1 times theta, so we just re-normalize all the prices. So, re-normalize all nominal prices in terms of apples. So one simplifying thing is we can get rid of--so think of pi_t as the price of land in terms of apples. So we just get rid of all the qs here. Just assume that they're 1, and so we have this equation. And now that means that pi_t = price of land at time t in terms of apples at time t. So that was a normalization we did many times before. We said that we might as well assume the contemporaneous price. We can't figure out what inflation is, so let's figure there's no inflation. The price of apples is always 1 and we're going to measure the price of land in terms of apples. So we get the same equation that now looks a lot simpler. So the qs, we don't have to really worry about. We're just worrying about the pis every period. So what did Fisher say to do? So we've got to worry about--what did Fisher say to do? What was his--whenever you have an economy, a stock market economy like this, what did he say to do? What was his advice? He said turn it into general equilibrium. How? By doing what? Yeah? Student: Adjust the endowments. Prof: So Fisher said, Fisher's lesson, forget about assets by putting their dividends into the endowments. That's his first lesson. So you see this is a good summary of what we've learned so far, and a second lesson was look at present value prices. So he says forget all these pis and things like that. Just look at the present value. So we're looking at p_1, p_2, p_3 ... where p_t, price at time 0, let's say or time 1, it doesn't matter, price at time 1 of an apple at time t. So once you knew the presence of the endowment then, I'm not going to write all this, the endowment of all generations 1 and above it stays the same, (3,1), (3,1), (3,1), but the endowment of generation 0 is now 1, 1,1, 1,1, 1,1 forever. And the budget set, everybody's going to have a budget set determined by the ps. So now we're just one step from solving this. So there's one more thing to notice before we can solve it, so by symmetry, so observe that by symmetry we can hope to find an equilibrium with p_t 1 over p_t = p, a constant. So every generation is the same. The only relevant price for a generation is the tradeoff between the price of goods when they're young and the price of goods when they're old. That's what Fisher said. The veil of the stock market is just a means of transferring wealth between when you're young and when you're old, and really you should calculate--all these guys have to calculate. If I buy the stock now when I'm young it's going to cost me a certain amount of money and I'm going to be able to get a return. So the real rate of return, right, that they're all going to calculate is going to equal-- we'll, by putting in pi_t dollars today they get out pi_t 1 the dividend, 1, tomorrow, right? So tomorrow they're going to get pi_t 1 1. So if they buy 1 share of stock it costs them pi_t and tomorrow they get pi_t apples, we're measuring in terms of apples, and in the future they get pi_t 1 1 apple in the future. So that's the real rate of return. That's like 1 r, 1 r_t, but we're going to assume that that's a constant. 1 r we're going to guess it's a constant and that's just 1 over this p that I told you about before, the ratio p_t 1, the present value. So this ratio is just the interest rate between time t and time t 1. So Fisher says you don't have to think about all the stock market and what the return on the stock market and all that's going to be. Really you're just trading off. By doing all that calculation you're figuring out what's the tradeoff between time t goods and time t 1 goods. In the Fisher economy you don't look at the stock market. You assume that everybody knows the present value prices and therefore the tradeoff between time t and time t 1 goods, and we're going to assume that's a constant because the thing's so symmetric how else could it turn out except a constant. So now we're ready to solve it. We've done all the tricks, almost, to solve it. So what is equilibrium going to be? So here's equilibrium. It's going to be a very simple equation. At every generation you're going to have an old and a young. So what is the total supply of goods in every generation? How much goods are there? There's 1 for the old apple. All right, if you look at any generation like this one at time 2 there's that one, no not that one, a little less. The one in the middle that's the 1 for the old guy, then there's the young guy who has 3, right, and then there's the apple that the land produces. So this is young apples and this is the dividend of apples. So that's how many apples there are in the economy. So who's going to be eating them? Well, there's going to be an old guy eating apples and there's going to be a young guy eating apples. So how much is the old guy going to eat? Well, the old guy's going to spend half his money, and how much money does he have? Well, from his point of view he's just trading off when he's young against when he's old. So from his point of view he's got 3 apples when he's young plus 1 apple when he's old, but that's worth, to him, the tradeoff between apples when he's young and when he's old is just given by p, divided by p. All right, so this is the whole trick. So we have to spend a minute until this dawns on you why this is true. And now what's the young going to do? The young generation, what's their income? Well, they only care about the tradeoff between prices when they're young and when they're old. So when they're young and when they're old they don't care about land according to Fisher. They don't have to think about that. They just have to know the price, which we're assuming is p for everybody, the tradeoff between young apples which are worth more than old apples. So to them they have the same income 3 1 p. Now, these ps refer to different time periods, but we're assuming the same. Here's the young. This is the young, so this is divided by 1. So this is the young and this is the old. And once I solve this equation we'll have the whole equilibrium, but we need to understand this equation [note: the equation is: (1 half times (3 1 p) over p 1 half times (3 1 p) over 1) = 1 3 1 = 5]. So where did I get this equation? So let's take any time period 2 like T = 2 for example. We know the total apples around that can be eaten are 5. That's on the right hand side. The old guy's apple, the young guy's 3 apples and the land producing 1 apple, 5 apples in all. Now who's going to be eating the apples? There are going to be old guys and there are going to be young guys, eating apples. So the old will be the generation 1 guys. They're going to be eating apples, and then the generation 2 guys are going to be eating apples. Now, the generation 2 people they've got 3 apples at time 2, so they're looking at 3, but they've got expectations in their head. They're going to think ahead. What's the price of stock market today versus tomorrow? Fisher says they do all that thinking, they realize the tradeoff between consumption at time t when they're young and consumption at time t 1 when they're old. That's given by the price p. We've assumed there's a price p. So they're going to say to themselves, "Okay, I've got 3 apples when I'm young, 1 apple when I'm old is not worth the same in present value terms-- it's just 3 1 P because the old apple's not worth as much at time t as it as time t 1, it's 3 1p. I'm going to spend half of my income and the price when I'm young I've assumed that's one." So that's what the young are doing. The old guys, now the old guys what they're doing at time t depended on what they did when they were young. But when they were young at time 1, they knew there was a tradeoff between time 1 and time 2 apples, but we've assumed it's the same price tradeoff, so we've assumed it's the same p, and so they did the same calculation. When they were young they were going to spend half their money, this time 1 generation is going to spend half its money when it's young, half its present value when young, divided by-- so when they were young they were going to do that, but when they're old now they're looking forward to spending half their present value when they're old, and the price of apples when they're old is given by p relative to when they're young. So they're going to spend 1 half times the present value of their income, divided by the present value of the price of the old apple which is the apple we're talking about because they're consuming when they're old now. So their consumption plus this consumption equals 5. Now, at least half of you must be baffled, so ask me a question to see if we can get to the bottom of this. That's it. That's the whole equation. As soon as we solve this we'll figure out all the prices and everything in the whole economy. And so we're at the end, but this requires a little bit of thought, so go ahead. Student: Shouldn't it be 4 1 p because there's the dividend, or maybe like 3 2 p? Prof: No. Student: I mean, where does the dividend fit in? Prof: That's a good question. The dividend fit in here because, yes, there's a dividend. Here's the dividend that got produced, so there's an apple to be eaten from the dividend, right? Now, you're saying--so it's a very important question you're asking. So it's correct what I wrote, but it doesn't sound correct. So what he's saying, the question is, what happened to the dividend. This generation, say, this young generation, either one, say the old generation. The old generation, when they were young at time 1 they bought land looking forward to their old age. They sold the land, and they got the dividend. How come that's not factoring in to their demand? That's his question, right? The answer is because that's precisely the point of what Fisher did. Fisher said, yes, in the real world everybody is thinking to themselves, like generation 1, "I'm young now. I'm buying the land because when I get old I'll be able to resell it and I'll also get the dividend." But Fisher has thought ahead. Fisher's saying if the guy's going to think about pi_t 1, that's what he'll be able to sell the land for, and he's going to think about the dividend he's going to get, and his rate of return is therefore divided by how much he had to pay for the land today. That's his rate of return. But see, the bottom thing is how many apples he had to give up, pi_t there, is how many apples he had to give up to get the land. The numerator is how many apples he gets next period after selling the land and taking the dividend. So that ratio is the tradeoff between apples today and apples in the future for him. So if he says to himself, what Fisher says, the only thing the guy cares about is that ratio, that tradeoff, which we're calling p, 1 over p. That's the tradeoff he's going to have in his mind. And so what is his income? This guy began with no land. Only 0 began with the land. Everybody else buys the land only as a means of getting to more consumption when they're old. So the whole point of Fisher's insight is you don't have to keep track of how the guy's managing to get the payoff when he's old. All he's doing is he's recognizing a tradeoff of 1 r or 1 over p, that tradeoff between consumption when young and consumption when old and all he can do is turn his endowment when he is young into more endowment when he's old at that ratio, and it doesn't matter how he does it as long as we have the right ratio. So Fisher says forget about the assets. Just keep track of the present value prices and these will tell you the ratio of transformation of goods when young to when old and that's all you need to know to make a decision. That's the whole point of Fisher. You don't need to think about the assets. Now, after we get the ps we'll go back and figure out what the price of land is. Any other questions? Yes? Student: Can you explain again why the price of the second part is just 1? Why can you use 1 >? Prof: Yes, because I'm taking p as the ratio. So p, this p is here, so it says if I had 1 apple at time t how many apples could I get at time t 1, [correction: 1 over] p of them, right, because this ratio--so for every apple I have down here I can get [correction: 1 over] p apples at time t 1. If the ratio of two prices is p it doesn't matter what their levels are--so I might as well as think of one of them as 1 and the other one as p. I could think of the first one as 2 and the second one as 2 p. That would be the same thing, right? So if I thought of the first price as 2 and this price as 2 p I'd put a 2 here, a 2 here, and a 2 here and it wouldn't change anything. Remember, we learned this the very-- this is why the lessons of general equilibrium they seem so obvious and then you put them in a slightly different context and you realize how clever Fisher was. If you double all the prices you're not going to change anything. It's the price ratios that matter. So it's the tradeoff between apples when young and apples when old that matter. If you assume that tradeoff is given by p you might as well assume that the first guy, for all we care, he might as well assume that he's measuring the prices when he's young in terms of 1, and the prices when he's old in terms of p. Those were very good questions. This is a little confusing but when we go back to the original equilibrium it'll be clearer, I think. But so that's the only equation that we have to satisfy. So we can solve that equation now. Any other questions? Let's solve that equation. That equation is I'm going to multiply by 2 p, so I'm going to get 10 p on the right-hand side, right? Because if I multiply by 2 p I get 5 times 2 p is 10 p. On the left-hand side I'm just going to get 3 1 p 3 p p squared. So if I rearrange I just get p squared--uh-oh, my usual problems here. p squared - 6 p 3 = 0. p squared - 6 p 3 = 0, so p = 6 (and I'm using the quadratic formula which I assume you know) - b squared - 4--. So 6 squared - 4 times 1 times 3, minus 12, over 2 = 6 - the square root of 24 over 2. So the square root of 24 is a little bit less than 5, so this is going to be a little bit more than 1, sorry a little bit less than 5, so this will be a little bit more than 1, so the whole thing will be a little bit more than a half. So let's say it's .55. So here's a crucial step. How did I know when I said 6 plus or minus, why did I take the minus? Because if I had taken 6 plus this I would have gotten a gigantic--well, let's come back to that. So how did I know to take 6 minus that instead of 6 plus this? So if this is the p then what are the prices? What are Fisher's prices? We've just solved for equilibrium and these prices are going to be--we call this 1,1, maybe .55, .55 squared, .55 cubed etcetera. That's what Fisher says the prices are. And we can now figure out everybody's consumption. Y and Z, what's Y going to equal? Y is this thing on the right, 1 half 3 1 p, so it's .355 divided by 2. So that's 1.775. And what's Z? You should check. I'm going a little fast here for myself. 3.55 divided by 2 is 1.775, so what is Z? It's going to be 1 and a half plus--no, it's 3.5 divided by 1.1. Student: > are those numbers > Prof: p is .5--I'm going too fast for you, ah ha! p is .55, right? I just got p. So if I want a C now, go back to consumption, what's the consumption going to be when you're young? It's going to be, Y is going to be 3 .55 divided by 2 which equals that, right, 3 .55 that's the guy's income and he consumes a half when he's young, so that's 1.775. And when he's old he's going to have the same income, so 1.775 divided by p, so it's going to be 1.775 divided by .55, and that you can see--no, that doesn't look right. Yeah, that divided by p and that's going to be a little bit more than 3 and so, in fact, if you solve it out it turns out to be 3.225. Did I go too fast there? I'm plugging in .55 there. So it's 3.55 divided by a half. That was that number, 1.775 divided by p which was .55, so you can see it's a little bit more than 3, because .55 into 1.7 is a little bit more than 3. In fact, if you solve it out to some decimal places it's that. So we've solved what everybody does. Now we know what everyone's going to do. The young are going to spend 1.775, are going to consume 1.775, they're going to consume 1.775 here. They have an endowment of 3 apples. They're not going to eat them all. They're going to consume 1.775 of them. And then the old, at the same time, what are they doing? They're consuming 3.225, but you notice that those things add up to 5, so the consumption when they're young plus the consumption when they're old-- so the consumption of this old guy there is 3.225 and you add the consumption of that, yeah, I went too high there, the consumption of the young guy just under him is 1.775, the two of them add up to 5. That exactly clears the market. So at time 2 you repeat the same thing, at time 3, etcetera. So you see we've already cleared all the markets except the one at time 1 which looks more complicated, but we've cleared all the markets. Now, what's the price of land going to be? What's the price of land? Nowhere to write that. Let's write it here. What's the price of land which is going to be a constant? How do we figure that out? How would Fisher say you figure out the price of land? So the price of land at time 1, say, what would Fisher say? Yep? Student: Whatever the young guy would pay for it? Prof: That's one way of getting it. So what's he paying for it? Student: Whatever he doesn't spend on his consumption. Prof: Right, so from this equation he spent 1.775. His income was 3, so what's left over? What did he spend on land therefore? Student: 1.225. Prof: So the price of land has to be 1.225. Now, that's not the way Fisher suggested finding out the price of land. What did he say you should do? What's the fundamental theorem? Student: Present value of all the payments. Prof: And what is that? So the land pays 1 apple every period. Student: > Student: So it's paying 1. Prof: So it's paying 1 p 1 times p squared 1 times p cubed 1 times p to the fourth, right, because looked at from the point of view of time 1 you get an apple next period relative to the apples today. That's worth p. An apple in 2 periods is worth p squared at time 1 because an apple at time 2 is worth p apples at time 1 and worth p squared apples at time 0. So you just keep doing this, but this is a perpetuity and so therefore it's equal to? Student: 1 over r. Student: We're going to >. Prof: Yeah, 1 over r. So it's equal to 1 over r, and so what's r? So what's r? How do we figure out what r is? Student: If we know p then we can find r. Prof: 1 over 1 r = p, right, = .55, so therefore 1 r = 1 over .55 and r = (1 over .55) - 1. And so this is a little less than 2 - 1 is going to be like .81 or something, and you take 1 over .81 and you get the same number. So Fisher solved everything. I mean, the Fisher method solves it all. Let's worry about time 1. We haven't done that. So what happens every period? Every period like from 2 onwards, the young guys says, "Ah ha! I've got 3 apples. What am I going to do with them?" He says to himself, "Well, the price of the land is 1.225 so I could eat some of the apples or I could buy some land." And what does he decide to do? He says, "Let me eat 1.775 apples and spend the rest of my money buying 1 acre of land. Now, why am I doing that? Because next period I know the price of land's going to be the same 1.225 and I'm going to get a dividend of 1, so I'm going to be getting a rate of return (we just calculated) of 81 percent." So this ratio up here, this is another thing, this also this number is equal to 1.225 1 divided by 1.225. That's also equal to 1.81. Remember r we just calculated over here. Where did I do r? r was 81 percent. That's the same number here, 81 percent. So everybody says to himself, "Given that there's an 81 percent rate of interest I'm happy to hold the whole unit of land because at that rate of interest I'm just trading off consumption today for consumption when I'm old at the rate that I want to." And at time 0 the market clears also. So we cleared the market for every time 2 through infinity, and that was by this equation. That was up here. By picking the right p we know every market from T = 2 onwards was clearing. And Fisher would say by Walras' Law we don't have to worry about time 1, that's going to clear as well and sure enough it does. It's a little bit different now. It's just the old guy, but the old guy with his land which is 1.225 plus his dividend of 1-- his land which is worth 1.225 and his dividend of-- hope I wrote down the right price of land all this time. Oh, that would be bad. So the old guy, what does he do? He has his 1 apple plus he has the land so he's going to consume--the old guy has his--oh, I see. So what happens at time 1? The old guy has his dividend that he had before, so he's got the dividend of the land because he's owned the land forever. So he gets the dividend of 1, so that's 1, plus he has an endowment of one, so he's consuming 2 now. Plus he sells the land for 1.225. So that all adds up to 3.225, and then if you add the young generation's 1.775 that indeed clears the market at time 1. So the market's going to clear in every single period, but we only had to solve it for periods 2 and onwards which were all symmetric because by Walras Law, according to Fisher, once it clears from time 2 onwards without even bothering to check we know it would have had to work at time 1 and sure enough it did. So as I said, let's summarize now what we've done and then we can start drawing the lesson. So what we did is we started with a complicated model with land and people having to look forward and expect what the price of land was going to be depending on what the next generation wanted to hold, which depended on what they were going to think the generation of that were going to hold etcetera. Very complicated stuff. And we saw that to solve it was very simple. You just do the Fisher thing. If everybody's rational you can forget about the assets and the land and turn everything into present value prices and put the endowments-- so you forget about all the assets and just put the dividends into people's endowments and look at all the present value prices, and the present values prices by symmetry, we're assuming, just grow exponentially, decline exponentially. And then we can solve the one equation and figure out what that price was, the exponential number p that's to the nth power gives the nth price, the present value price, so solving for that p we then cleared the markets. We found out what everyone's going to do when young and when old, and by plugging in now Fisher's formula, the price of every asset is the present value of its dividends, we figured out what the price of land was every period, so we've solved for the whole equilibrium and sure enough it clears. And in equilibrium everybody's doing this calculation. If I buy land today I'm going to get that rate of return on the land which corresponds to the p. It's going to be 81 percent, and so everything works out. So what's this got to do with Social Security? Are there any questions about this? I sense a little bit of puzzlement still. You shouldn't be that far away from understanding it, so let's hear a question. What don't you don't understand? Just point to an equation you don't understand. Yes. Good, brave of you. Student: How do we show that theta should equal 1? Prof: So Fisher says that--the way I solved it is I ignored the assets. So I didn't pay attention to what the assets were. I just put the dividends in the endowment. I didn't pay any attention to what people were holding of the assets because Fisher says forget the assets all together. Just do the present value prices and augment the endowments. And I found the present value prices by getting this factor p, and then it was just p to the n and I found what everyone was going to consume. That was it as far as Fisher's concerned, but then Fisher says once we've found general equilibrium we can go back to financial equilibrium and figure out what the price of land is, which is the present value of the dividend, so it's price is 1.225, and the step I left out, which you're asking about, you can also figure out what assets everybody's holding. So Fisher's saying--what assets are they holding? Well, the guy, he's consuming 1.775 here. We figured out the price there of 1.225 so it must be that he's holding exactly 1 unit of the asset, and so the asset market is clearing too. But that's no accident. Fisher's saying if you clear all the markets doing the present value general equilibrium stuff and you go back to the financial equilibrium you're automatically going to be clearing all those markets too. So I left out the step because somebody anticipated all that and got me to calculate the price of 1 in a cheating way, he said assume theta's 1 then figure out how much money you're spending on the asset, so we did that. What I should have done is done Fisher's trick of figuring out the price of the asset, which is 1.225 and then, of course, we know the guy must have bought 1 asset in order to use up his budget set, but that clears the market for assets. But Fisher knew that was going to happen. It always has to happen. That's the beauty of what he did. Yes? Student: So in that equation over there we have to assume p is less than 1? Prof: Yes, so the point is, thank you, I'm coming back to exactly that point. So the point is when you look at the present value of land it's going to be p p squared p cubed p to the fourth .... The present value of land had better be finite, so in other words p has to be less than 1 otherwise the value of land would be infinite and it wouldn't make any sense because in the very first old guy with an infinite value of land would buy more apples than there possibly were in the world. So you know that the real interest rate has to be positive. If the real interest rate were less than 0, and you had some asset that paid a constant dividend forever, that asset would have an infinite value. So the presence of land, which pays a constant asset forever, forces the real rate of interest to be positive. So Samuelson and all his talk of negative real interest rates, it can't really happen. Land's going to pay some dividend probably forever, so there's going to be a positive real rate of interest. And so it means in Social Security, if the young give up 1 to get 1 back when they're old they're always going to be losing because there's a positive real rate of interest, and so every generation has to lose. So it's precisely the point. Because of the presence of land you know that the real rate of interest is going to have to be positive. Fisher never made this argument. He said it's impatience and maybe if people are incredibly patient it could even turn out to be negative, or if output was bigger [correction: smaller] next period than it is this period you could even have a negative rate of interest, but not so when you have land with a constant dividend forever. Then if the interest rate is constant it'd better be positive, otherwise the land would have infinite value. So it's a new argument for a positive rate of interest. The land has to have a finite value. Any other questions? So when you solve for a couple of these you're going to do it very easily, I mean, after you've done it a couple times this will seem very easy to you. I know it seems a little confusing now, but let's just do a couple more thought experiments. Suppose we do Social Security? What will happen with Social Security? How does that work? What does Social Security mean? Well, Social Security means the young give the old something and until now we talked about it as if the young could give the old part of their endowment. The young pay taxes and the taxes get handed over to the old guy. That's pay as you go and we talked as if it wouldn't change the equilibrium, but we said at the same time that Social Security was the most gigantic program any government anywhere in the world has ever adopted and the giveaway was bigger than GNP for a year, 17 trillion compared to 12 or 14 trillion. So clearly it's going to have an effect on the interest rate. So we ought to take that into account if we're doing a more careful analysis of Social Security. So what would Social Security do? How would I take into account Social Security? Suppose every young person gave 1 apple to the old guy at the same time? How would I figure out what happened in the new equilibrium? How would the economy change? What would I change and solve differently? Well, all I would do is I would change this to a 2. Every young guy now only has 2 apples when he's young because he's given 1 of them to the old and the old would have 2. So all the way through here I would just change all this to 2,2, 2,2, 2,2, 2. That's what I would do. That's the change. Then I have to re-solve the equilibrium. So how would that change? What would I change in my one equation? Well, the apples in the economy, the young apples, the guy's only got 2, but the old's got 2 and there's still 1 apple coming from the land, so that's still 5. But now every generation's going to be behaving a little bit differently. They're going to have 2 when they're young and 2 when they're old. This guy will have 2 when he's young and 2 when he's old and otherwise it's the same thing. So I just re-solve for the equilibrium. So if I re-solve for the equilibrium multiplying by 2 p I'll have 2 2 p 4 p multiplying by 2 p. Sorry, I just confused myself. I multiplied by 2 p. I've got 2 2 p multiplying by 2 p. I have 2 p here, plus multiplying by 2 p I have 2 p squared here. Hope I'm doing this right. And I've got 10 p on the right like I had before. So now I've got 2 p squared - 10 p and that's 4 p, so it's still 6 p (it looks like) 2 = 0. And so p = 6 or - 36 - 8 over 4. And so that, I hope I did that right, I hope you're checking it. So that turns out to be p is 2.8, no. Social Security, p is .38 now. So now it equals .38. So 6 - square root of 28 so it's working out pretty much, so .38 is the new price, so therefore the interest rate 1 over 1 r = .38. So what do you think happens to the interest rate? So r now equals--before I write it you can figure out what it is yourself in a second. Do you think the interest rate went up or down in the new economy? What would Fisher have said? Student: Up. Prof: Up, it went way up, and so it's actually 347 percent. So the interest rate went from 81 percent to--no that can't be right. It went to 161 percent. So the interest rate went up. So the loss is even worse than it seemed before. Remember, in present value terms, when you're young you give up 1 and when you're old you get 1 and so you lose the present value. So the present value of that trade is this plus that over 1 r. Well, now that r has gone up you're losing even more. So Social Security at the current interest rates looks bad for every generation. After you do the Social Security and everybody understands it's happening it's going to be even worse in terms of present value. So Social Security, again, everybody is giving something when they're young to the old. So the guy at the very beginning, at the very top, gains a lot. Everybody else, every other generation loses and you can compute the utility after Social Security compared to before Social Security and it goes from something like 2.7 to 2.3. So there's a substantial loss for everyone's utility except for the first generation. On the other hand we rescued the first generation. Now, there are two more experiments. I'm not going to be able to finish today, but I'm going to mention them. Experiment one is suppose we had more and more children every generation? How would we take that into account? Well, it's very simple to take into account. The same thing with the trivial change you can figure out what happens with more and more children. So I'm going to go back to (3,1). This will only take me one minute. Sorry about this. I know time's running out, but let me just finish this story. So if we had more and more children in every generation, so every 30 years let's say the population doubled, that's not such a high growth rate per year, you'd have 6 and 2 here and then it'd go up to 12 and 4. But, again, it's all exponentially growing and the dividends would also be growing. So this would be 2 and 4 and 8 and 16 etcetera. But as you will see in a second--I won't do it this time. Next time you'll see that it's very easy to solve for the new equilibrium. You put a double here thing because the young, there are twice as many young. You just solve it and you do the whole thing. And what happens is Social Security isn't solved. Samuelson was in a way wrong again. Even though there are two young people for every old person--so every young person only has to give up half an apple. You only have to give up half an apple when you're young and when you're old you still get a whole apple back. It sounds like now surely you should gain, but the point is you don't because the rate of interest gets higher. And then we're going to have generations that alternate in size, but all these are very easy to solve once you figure this out. So on Thursday you have to solve a problem just like that so you get the hang of it, just one problem to do for Thursday.
Quantitative_Finance_by_Yale_University	26_The_Leverage_Cycle_and_Crashes.txt	Prof: What I'm planning to do today is to spend a half an hour or less just telling you a little bit about what a new theory might be, what I call the Leverage Cycle, and then spend the rest of the time maybe answering questions about the course that you might have. I could, if you wanted to, devote the whole time to what the new theory is, but why don't I at least pause after a half an hour and see if you have questions? So what is the thing that's been missing from the entire course and has been missing from economic theory, I think, almost entirely for all these years, and certainly missing from all the textbooks that you might have looked at during the course of the semester, and you remember there was a list of 20 books or something you could have read, and that's the idea of collateral. It's the idea that in order to guarantee that you're going to keep your promise you have to put up collateral, and people just don't trust in everyone else keeping their promise, they want collateral. So if you put that into the model what sorts of things might be different? So I want to just work out an example so you can see how they might change. I want to talk about an example that's going to illustrate what happened in our crisis. And I guess that it's a little interesting that I wrote this and I presented this in 2000 at the World Congress, and it got published in 2003, so this was long before the crisis. Now, as I said, there had been other smaller crises before in 1998, maybe '94, maybe '87, certainly '98, and of course I was thinking about these previous crises when I built this model, but not many other people thought much of those other crises. And as it happens, this last one that we're still at the bottom of, or a little past the bottom of, I think is very similar to the ones we had before, but just much bigger. So here's my simple version of it. I'm going to give two models, a very simple one with two periods and a slightly more complicated one with three periods, and of course all the interesting things happen in the three-period case, but just to make it simple to understand I'm starting with the simpler one. So suppose that there's a security which I'm going to call Y that everybody holds. Why is there no chalk? Gosh, I taught the class in here, I just finished lecturing in here with a whole box, oh here it is, a whole box of chalk. So suppose that there's a security Y that I'm going to think of as a mortgage security, or you could think of it as a house, or you could think of it as an oil well that has uncertain output in the next period. And then there's going to be something like gold that I'll call X. So this might be like gold, and this might be like a mortgage security, or like an oil well, or you might think of it as a house, but I'll think of a mortgage security, an oil well. It's something that pays an uncertain outcome in the future, and this is something that's very stable and you know exactly you've got gold this period, if you just save it you'll have the same gold next period. So now people are going to differ according to how optimistic or pessimistic they are. That's my idea of, not everybody's the same. So I imagine that there are two possibilities next period. Either the Y, the oil well, could produce--it's a gold-well really. It could produce 2 pieces of gold, I mean, 1 piece of gold, or it could produce .2,20 percent of a piece of gold. So everybody begins with 1 oil well, 1 mortgage security and 1 piece of gold, so they can consume the gold or they can make it a filling for their teeth, or they can wait next period and then they'd have it in either state next period because it's perfectly durable, or they could use the gold to buy more oil wells, each of which might pay off 1 or .2. So that's it. Now people care about the consumption of gold. The only reason to get the oil well, as Fisher, as we've assumed all through the class, the only reason to get the oil well is that it might produce gold for you next period, gushing oil, money, gold. It might gush some gold for you next period. So people care about consumption, how much gold they eat here, times the probability that they're going to be up here, times how much they eat here, plus the probability that they're going to come down here, times how much they eat here. In other words they are risk neutral with no discounting and they just multiply consumption here and here by the probabilities and add the consumptions, and then add it to the consumption here. Everybody's got the same utility, but with one difference. H is the probability agent H attaches to going up. So I think of these people as a continuum of buyers now. Instead of 2 buyers like we've always had, or 3 buyers, or even 1 buyer , I've got a continuum and they're different because some are more optimistic than others. Now, this is stuff that we haven't really paid much attention to before. So these optimists are the people who have H very close to 1, and lots of other people have Hs in the middle, and there are some people who think H is 0. That's the way they differ. So of course the very most optimistic person thinks the oil well is worth 1 piece of gold. He doesn't discount, and he thinks he's going to get 1 for sure, so he'd be willing to pay 1 for it here. The most pessimistic person thinks the oil well is only worth .2. And let's say she'd only be willing to pay .2 for it here. So what's the price of oil wells going to be? Well, if we just had our usual model, a one period model, we would see that the people with the high H would sell their gold to buy more oil wells because they thought it would be valuable, and the people with the low Hs, thinking the oil wells weren't worth much, would sell them to the high H people to get more gold in the present. That's basically what would happen. And you'd get some dividing line where the people above A would be buying oil wells, spending all their money. And the people below A would be selling oil wells and getting more money. So, for example, if A was .69, which is what it's going to turn out to be, Mr. A, what does he think the value of an oil well is? He thinks it's .69 times 1 .31 times .2 which is .06, so .69 .06 is .75. So Mr. 69 thinks the oil well's worth about 75. Everyone above him thinks it's worth more than 75, so if the price were .75 everyone above would want to buy and everyone below would say it's not worth .75 so I'll sell it, and since they're risk neutral their valuation is independent of how much of it they have. So these people below would want to sell everything, and these people above would want to buy everything. So that's nothing different from what we've done from the very beginning except that maybe the one difference is people would go to the extreme. These guys would spend all their money buying oil wells because every time they bought an oil well at a price of .75 this guy, for example, was sure it's worth 1. The more he buys the better he is. So he'd spend all his money in oil wells and these guys would sell all their oil wells, but other than that it's very similar to what we've done. So what's the difference going to be? The difference is just one thing. Where do I divide this dividing line A? Well, can these guys up here afford to buy all these oil wells? Well, the answer is, so far, it doesn't look like that's possible, because if the dividing line is way up here these guys up here don't have enough money to buy all the oil wells down here. After all, they only have 1 piece of gold apiece and if the oil well costs 75 they can each buy 1 and 1 third. If you multiply that by 1 and 1 third you're never going to buy all these oil wells down here. So this seems like it's too high for A to be. So the new twist is, maybe the guys up here who want the oil wells, who are so sure they're going to do well, maybe they can borrow money to buy the oil wells. So they can make a promise to pay money in the future, maybe .5 and .5 in the future, say, and then sell those promises, borrow money in other words, promising in the future, and then use that money to buy more oil wells. So that's what people do in the market. Any hedge fund, the three definitions of a hedge fund, the three defining characteristics of a hedge fund, I think I might have said once, are, a) that they hedge, so unlike other money managers they're always trying to hedge. And we talked about what hedging is. And many, many more managers are doing that than ever before. It's different from 50 percent of the people, but not from, you know, the hedge funds are 5 percent and the other 45 percent are also hedging, so that's not so different. The second thing they do is they borrow money to make their investments. A lot of these other managers aren't allowed to borrow. They may not be allowed to hedge either. Those are called long only managers. They can't hedge. Some of them can't borrow. Hedge funds hedge and borrow, and then hedge funds charge high fees. That's the third defining characteristic. But anyway, so they borrow. And in the economy, I told you last time, a huge number of people borrowed a huge amount of money. So borrowing is obviously very important. So how much are they going to be able to borrow? I mean, this guy, number one, he'd like to borrow as much as he could. Every time he borrows money he's sure that he's going to be up here, so every time he borrows 1 dollar he gets to make an investment that he's sure is going to be a great investment, and he's planning on paying everything back because he's sure he's going to go here, so he's going to be incredibly rich. So he's going to pay back what he borrows, but he's going to get such a profit he's going to make a fortune. So if people could borrow however much they wanted to, and promise to payback, this guy would borrow everything, Mr. 1, I mean, would borrow everything and imagine he was going to get up here for sure, and imagine he was going to keep his promise for sure, and he bid the price up almost to 1. But now, who's going to lend to him and how much will they actually lend to him? Well, in our old world we didn't worry about who was going to lend. Everybody assumed they were going to get paid back, but in reality people don't assume they're going to get paid back. The lenders are going to say to themselves, "Wait a minute, if this guy promises us to pay us, say, .5 and .5 maybe he'll be very rich over here and he'll be able to pay us back, but I'm not sure he's going to be so rich here. I don't even know what he has. How do I know what the borrower is going to actually have in these states?" I don't want to look into his personal bank account and find out everything about him. That's the way, banks who lend sometimes do that and they go to a lot of effort to check how reliable a borrower you are, but people in general, most of the lenders, you don't want to do that. That was the idea of securitization. We don't have to have so much careful looking into the personal finances of everybody. Much simpler is to use the asset Y as collateral. So if Y is collateral, what does that mean? When you lend 1 dollar to a borrower the borrower just doesn't borrow the dollar promising to pay something back in the future. The borrower says, "if I don't pay you back you can take the asset." So the question is, for each unit of the asset Y, how much can you borrow when you have the asset as collateral? That's the question of leverage. So if you take the value of Y divided by the cash down--so let's do two numbers. So the borrowed, dollars borrowed using Y as collateral, that divided by the value of Y, that's what we call the loan to value, LTV, loan to value. Another way of saying that is the borrowed, if you take Y, dollar Y minus dollars borrowed, that--let's write it in the denominator. Dollar Y minus dollars borrowed, and here you put value of Y, so just dollar Y, in other words. The dollar of Y minus the dollar borrowed, that's the cash you had to put down. So that's the dollar of Y divided by the cash down. That's what's called leverage. So, and it's obviously the same thing as loan to value because you just sort of invert the number and do a subtraction, you get leverage. So if you knew the loan to value you'd know the leverage and vice versa. They're the same thing. So what should the loan to value be? And so as I said, historically what's happened over the last ten years for housing is you had to put 14 percent down. The leverage was 7 for buying houses, non-agency houses, non-prime houses, starting in 2000, and then it went to 33 or 35 to 1 because you put down less than 3 percent in 2006. So this leverage shot up and then it suddenly collapsed. You had to put 25 percent down, so leverage fell to 4. So that, I'm going to explain, has a big effect on the price of housing and the price of mortgage securities. So what should leverage be? How can supply and demand determine what leverage is? So it seems like you've got to clear all these markets. You've got to figure out how does the Y market clear, how does the gold market clear, and then on top of that you have to figure out leverage. It seems like it's a lot of complicated things to figure out. And I think economists just thought, "Oh, there's so much going on, and people are really generally keeping their promises anyway, let's ignore the fact that you have to have all this collateral." Well, I think that collateral is the heart of the problem in finance. So how would it work in this model? So are you with me about where we're going? So you have to conceptually figure out how to think about the problem. In other words, conceptually, the question is, how can supply equals demand, which sounds like one equation, how can that determine the interest rate, supply equals demand for loan, how can that determine the interest rate and the leverage? It seems like you have one equation and how can you determine two things with one equation? Well, the answer is that you can do it, but first we need a conceptual framework to think about it. So it seems like a contradiction almost, a mathematical contradiction, so it must be that the problem is ill posed, and so I claim it is. So what you really should be thinking is that there's not just one interest rate, and one leverage, you should be thinking that there's the promise and then there's the collateral and those things taken together define the contract. So let's say the promise is .2, .2, and the collateral is 1 unit of Y, .2 of X, .2 of X. So you're promising 2 units [correction: 0.2 units] of gold in the future and you've got 1 unit of Y as your collateral. So that implies a delivery of .2 and .2. Why is that? Because in the good state at the top the collateral is worth 1, so if you've made the promise and the lender can seize your collateral if you don't pay, you're going to either pay .2 or he's going to seize the collateral, and so you're going to pay .2. Maybe you'll sell some of the collateral to pay .2. And if the promise is .2 down here, the same thing, either he's going to seize the collateral, the lender will seize the collateral or you'll sell it and keep your promise. In either case it'll deliver .2 and .2, and it's going to sell for some price. And the price is actually going to be 1, so the interest rate effectively is 0. Now, why is that? Well, because at time 0 over here no one discounts the future. Gold at the beginning is worth exact-- to everybody--a unit of gold at the beginning is the same as a unit of gold at the end in both states because everyone's probabilities add up to 1. H (1 - H) is 1. So you might as well consume at the beginning or for sure at the end. So since there's a lot of gold sloshing around here there are always lenders willing to lend at a 0 percent interest and they're getting their money back for sure. So it'll turn out that the interest rate on this kind of loan, which is riskless, is going to be 0, because no one's discounting and they're getting their money for sure. But what if you promised .3 and .3 with 1 unit of Y as collateral? Then what would the delivery be in that case? Well, the delivery wouldn't be (.3, .3) because the only thing protecting the promise is the collateral. The delivery would be .3 and .2, right? Because in the up state your collateral is worth 1, and so you would be forced to pay the .3, in the down state you would do what a lot of homeowners are doing now and say, "Okay, I owe you so much money. My loan to value is 150 percent. The value of my house has gone down to 2 thirds. The loan is 150 percent of the value of my house. I'd be crazy to pay you 150 percent. Effectively I don't own my house. I owe so much more on my house than the house is worth. I can't give it to my children. I can't do anything with the house anyway. Why should I just pay such a huge amount of money? I might as well just give up the house." They walk away from the house and the lender gets .2. So (.3, .2) would be the delivery, and of course if it was .4 and .4 it would also be .4 and .2. Now, if you made this promise of .3 and .3 you'd be delivering something more than .2 at the top. So the price, of course, would be more than .3 [correction: more than 0.2]. So the price might be--price of the .3 promise will turn out to be something like .261, say. It might be .261. Let's just say .261. So effectively you're borrowing .261, you're delivering .3. This is the .3. This is up here, pi_.3 = .261, the sub .3. So effectively your interest rate is, in the state when you can pay back at the top, your interest rate is .3 over .261. It's like 14 percent or 15 percent actually. It's 15 percent, so .3 over .261 is 1.15, so this over here means 15 percent interest. So you've effectively, because they know you're going to default in one of the states you have to pay much more than you borrowed in the good state. So effectively you're promising a 15 percent interest. You're promising it in all the states. You're only delivering a portion of what you promise in the bad state. All right, so what's my point? My point is that the apparent contradiction, supply equals demand determining both interest and leverage, is no contradiction at all because actually we've got many supply equals demand equations. There are many different loans depending on the ratio of the collateral to the promise. There are many different loans and each of them sells for a different price. So we've got many different things we're determining, many interest rates, but one supply equals demand equation for each one. So every supply equals demand equation produces one price. There's no contradiction. However, that still leaves us with the question, which of these many contracts are going to be traded? Can we say that the economy as a whole has a single leverage? And there the surprise is, and this is the end of the first part of the model, the surprise is, yes we can. Only this one is going to get traded. So everybody in the economy, no matter how optimistic you are or how pessimistic you are, even though you have the available chance to make a bigger promise, and of course having to promise a bigger interest rate, sorry, there's the interest rate. Even though everyone has available that opportunity, they won't avail themselves of that. Everybody will trade on this promise. So how could that be? And by the way, before we answer that question let's just see that if everyone used this promise that in fact the price we talked about before would prevail. So why is this .69--that A should be a little lower, it doesn't look like .69. It looks a little too high, but anyway it's supposed to be 69 percent of the way up. Why is that the right price? Well, how much could these guys buy? Well, the top 31 percent, what can they do? They've got .31 cigarettes. So I'll write it over here. They've got .31 cigarettes between them. The top 31 percent are the buyers, right? So we've got 31 percent here and 69 percent of the people down here, and here's A = .69. So these guys have .31 cigarettes between them. Now, if they promise, every time they buy an oil well they promise .2 units, every one of them, they're going to buy all the oil wells in the whole economy. So however many people there are here, let's call it mass of 1, maybe it's a million people, mass of 1, they're going to borrow .2. So this is their own gold and this is borrowed gold. Student: When you say cigarettes you're talking about gold? Prof: Did I say cigarettes? Yes, I meant, yeah. It's another example of gold. I meant gold. So you could think of gold, consume it now or consume it later. Cigarettes you can consume now or consume later. I have all these things in my head of what I could have interpreted, so yeah, I mean gold. So you can consume the gold, thank you, the gold now or the gold later, so each of these guys owns 1 unit of gold. So 31 percent of the population has 1 unit of gold. So you've got .31 total units of gold. They end up buying all the oil wells, and so how much can they borrow on all the oil wells using as collateral? So the oil wells they started with, they borrow using those as collateral, and the oil wells that they buy they also use as collateral. So they've got all the oil wells. They're making the (.2, .2) promise but it has a price of 1. There's no interest. The interest rate is 0, so they're borrowing .2. So the total amount of gold that they have at their disposal is .31 .2, and how many oil wells do they have to buy, 69 percent of the oil wells, .69. And if you take 31 and 20 that's 51 over 69, which is about .75, which is exactly what I said the price is that's going to make this guy, Mr. 69, exactly indifferent to buying or selling. So all the people up here are going to say, "At the price of .75 it really is a good deal, I want to buy and borrow as much as I can." People down here are all going to want to sell. The people up here with the money they started with plus what they can borrow are going to be able to indeed buy all these oil wells at a price of .75. That's what we just found and that's why that's the equilibrium. Did that go too fast, or almost too fast? Yeah, question? Student: I was just wondering, for the price of the .2 pounds, why is that 1? Prof: Because you're going to get the money for sure. So how much money is being lent, basically .2. So there are a huge number of guys down here. Their total amount of gold is .69, right? There's one unit of gold in the whole economy. They own 69 percent of the gold and they're only lending in total .2. So there's lots of extra gold that they have that they're not lending. They don't care whether they get gold now or gold later because there's no discounting and they're getting the money back for sure. So competition between these lenders is going to drive the interest rate all the way to 0. If the interest rate were positive they'd all want to rush in and lend because then they're going to get more gold out at the end than they had at the beginning and there's not discounting. So the competition among lenders will drive the interest rate down to 0, and they're guaranteed to get paid back because the collateral's big enough. You had a question? Student: I'm still confused. For the first state if you only promise to pay .2 in the future, so shouldn't the price be .2 right now? Prof: Oh, and I said the price is 1. Yes. The price per unit is .2. Yeah, that's horrible. Thank you. The price is .2, exactly. The price is .2 for the promise of (.2, .2). It's price of 1 per unit promise. The price is .2, exactly. Gosh, what a terrible mistake. Thank you very much. It's .2, exactly, and that's why these guys they're able to-- they're promising .2 and the price per unit promise, so this price was, yeah, its price is .2. So per unit promise their price is 1, in other words. So they're promising .2 and per unit promise the price is 1, so the price of the whole promise is .2, exactly, so it's just that, so that was-- so the price is .2. Using the whole of the economy's worth of oil wells as collateral you can promise 20 percent of all the gold and then you're going to get-- you'll be able to borrow doing that the same amount, 20 percent of all the gold, because the interest rate's 0. Yes? So that's why this total amount of gold that they can get their hands on, some people call it liquidity, all the stuff they can get their hands on, capital, they take all that and they buy all the oil wells they can. This is how many are being sold, and that's therefore what the price is. The ratio of 51 to 69 is almost exactly .75, so I'm rounding off a little bit. And that's why Mr. A of .69 is indifferent at this price to buying or selling. The guys above him all want to buy. This is how much money they can get their hands on and therefore what they can spend. All these guys want to sell. That's what they're selling. That's why this justifies the price, and these guys are the ones lending to these guys. The pessimists have nothing to do but lend because they don't want to buy the asset. Does this make sense? I'm just going to repeat the same thing with a three period model where it gets more exciting, but the logic of this is critical. So is everyone with me? Now, there's one thing I left out in this one period model, two period model, which is what about the (.3, .3) promise? The optimist, H equals 1. Take that guy. He says to himself, "I can't lose. Why should I be satisfied with only promising (.2, .2)? Why don't I make a bigger promise like (.3, .3). With my bigger promise I get more money today, and with that extra money today I can use it and buy an oil well, and I'm going to make a profit of 33 percent. My .75 is going to turn into 1 for sure, so why isn't that just a brilliant thing for me to do? Why should I be satisfied? The more oil wells I get my hands on the better I seem to do." So why is he not making the (.3, .3) promise? So it sounds like he ought to, but if you think about it one more minute you'll realize that he shouldn't. And why is that, because he could promise (.2, .2). So if he makes the (.3, .3) promise of course he has to give up the (.2, .2) promise because the oil well he used as collateral for the (.3, .3) promise he no longer has available for the (.2, .2) promise. So the question isn't, should he do a (.3, .3) promise. Well, if that was the only thing he could do of course he would do that, so of course it looks profitable, but he's already got a great profit opportunity. The question is, is it a better profit opportunity and the answer is no. Why is that? Because he is still delivering .2 down here when he makes the (.3, .3) promise, but when he makes the (.3, .3) promise he delivers more at the top, namely .3, but that's the state he's sure is going to happen. So compared to the (.2, .2) promise he's giving away more money just in the state that he thinks is going to occur. That's very expensive for him. That's a horrible thing for him to have to do. And who's lending him the money? It's the guy down here, and the guy down here, that's the pessimist. He doesn't think that top state's going to occur so he's only willing to pay extra money at the beginning-- he's not willing to pay very much extra money at the beginning because he's going to get stuff in a state he doesn't think is going to happen. So anyway, I don't have time work it all out, but if you think it through you'll realize that nobody wants to do this trade, because the guys at the top who seem to have the greatest advantage in borrowing more, when they borrow more in this way where they're defaulting, they're actually paying more only in the state that they think is going to occur and the people doing the lending are getting money only in the state they think won't occur. So both of them think it's a worse arrangement than the original (.2, .2) arrangement, and so even though there's a price and it's available to be traded nobody will want to trade it. So the market does indeed pick out a single leverage, and what is the leverage? The leverage as we calculated from this number is the price of the asset, which is .75 divided by the cash down which is .55, because you can borrow .2, and that's 1.4 or something. I don't know exactly, but let's say 1.38 leverage, 1.35 is the leverage. So it's not that high, the leverage. And the principle is, that we just discovered when you have this kind of heterogeneity, different kinds of heterogeneity produce different amount of leverage, and I'm not going to be able to talk about that, but with this kind of leverage the promise will always be the maximum for which there is no default. That's how much borrowing is going to happen, and the market's going to allow. So in what market do we always see that happening? In the Repo market, it's a one day market overnight. You put up a security as collateral, and you can borrow money on it, and there's almost never any default on those markets. Even in the tremendous crisis we just had almost zero defaults in the Repo markets. Mortgage markets there were defaults, but there the heterogeneity isn't just how optimistic you are, it's whether you like to live in the house or not, so it's a different case which I won't have time to cover. So this is part one. We're just going to say the same thing in part two. I'm going slower than I thought, but anyway, the last model is going to be part two. So are there any questions about that? Did this first part... Yeah? Student: Maybe this is sort of a silly question, but... Prof: I'm sure it's not. Student: Are there some lenders sort of in the middle like more optimistic pessimists who think the upstate is more likely to occur so maybe they're willing to lend more money? Prof: There are. There are a whole continuum of people between 0 and 1, so the guys in the middle they really don't have any choice here. You see in the next model there's going to be a difference, but now you really don't have any choice. If you're above A you should buy to the maximum. If you're below A you should sell everything, and you don't care if you lend or not because you're definitely going to get paid back. So they're all willing to lend. So let's now go to the next model. So that was a great question. So far we only get two categories of people, buyers-borrowers, sellers-lenders, so we're going to move beyond that in the next example. Any questions about this one? So we get equilibrium leverage and leverage has a tremendous effect on the price. Why does it affect the price, because the fact that these guys were able to borrow so much money is what made the price so high. If they couldn't borrow that would wipe out this .2. They couldn't have borrowed that, so they would have only had this much to spend, so the price would have had to be much lower. And of course these guys wouldn't have been able to afford all of this. So as the price gets much lower more people would want to buy and you would have the marginal buyer down here, and there'd be a much lower price. So this borrowing is what jacked up the price. Leverage means high prices. It seems like the most obvious thing in the world and commonsensical thing in the world, but remember it never got mentioned in this course, right? It never gets mentioned in any textbook. The price is supposed to be the fundamental value, the present value of all the dividends, or the expected present value of all the dividends, meaning minus the covariance or something. Where was leverage in that formula? It didn't happen because we didn't have the idea. We assumed that everyone could borrow as much as they wanted to, but here we see that they can't borrow as much as they want to. They're limited in how much they can borrow, and because they're limited it's going to turn out, if you make the limit less severe they're going to borrow more and the price is going to be higher. So you ignore leverage by saying people can always borrow whatever they want to, then it never gets mentioned, but it's the heart of the matter, I think, at least in a crisis. So let's just do one more version of the model, which is this same thing, but now with 1 extra period. So what's the extra period going to do? The extra period is, we've got instead of two periods we have three periods. So what's going to happen is the .2 only happens with two pieces of bad news. You have to go down twice to get .2. Otherwise Y pays off 1. And everyone's going to begin at the beginning there with 1 unit of Y and 1 unit of gold just as before, and they could consume in the middle, or they could consume in the end, but they have no more endowments. All their endowments are right at the beginning, 1 unit of Y and 1 unit of gold. There's no discounting. They just care about the expected consumption. The difference is now it takes two periods to see the realization, so two pieces of bad news. Now, why is that interesting, two pieces of bad news? Well, when I was in the crisis both in '98 when I thought about this model, created this model, but also recently, is people start to realize things are going wrong. So if something goes wrong and now everyone says, "Well, things are still okay now, but I realize we're closer." It takes a lot of things to go wrong for things to collapse, but each time one of them goes wrong you're a little closer to the collapse. So I make the assumption that agents are all identical except agent H-- high H means you think you're going to get up moves, but there are two moves, at the beginning and also in the second period. So if you're an optimist about the first up move you're also going to be an optimist about the second up move. Now, let's suppose your H equals .87, say, just to pick a number, which it's going to turn out to be a pivotal guy. Mr. 87 at the beginning, the chances of going down are 13 percent for him, then 13 percent more, so the chance of getting a disaster, he thinks, is 13 percent squared, 1.69 percent, under 2 percent. So he thinks the value of the asset is over 98, under 2 percent here the rest of the 98 must be over there somewhere, so obviously his valuation is over 98. Now, once he gets down to here he realizes the chances have gone from 1.69 percent to 13 percent. So his valuation is going to be a little bit more than 87, because it's going to be 87 percent of that and 13 percent of that, so it's 87 plus a little bit. So he's going to go down from 98 something, to 87 something. So of course when the first down state happens everybody gets more pessimistic including Mr. 87. He now thinks that the asset value maybe went from 98 to 87, which is an 11 point drop, and everybody's going to have a drop. He went from 98 plus to 87 plus a little bit. So it's an 11 point drop is what he thinks happened. So you can see this is bad news. When it takes two things to go wrong the first piece of bad news people are going to take it as bad news, but the interesting thing that happens is that actually they get more uncertain. Things go up you get 1 for sure. Now you've learned something. There's no uncertainty. Here the move down created more uncertainty than you had before, and not only that, more disagreement. I mean, Mr. .9 and Mr. .8, neither of them thought there was much chance of getting down to here. .9 thought 1 percent squared, that's negligible. .8 thought 2 percent squared; that's .004. The difference between negligible an .004 is still negligible, practically, so they hardly disagree here, but once you get down to here they're both starting to get more worried and they're actually differing a little bit more than they did before. So that's what I think happens in these crises. You go from everyone knowing if 25 things in a row go wrong we're in trouble, but nobody's really thinking, except the guys at the very bottom, that all of this stuff can go wrong. But once each thing goes wrong now everyone gets more and more worried and there's more separation between what people think. So that's just description of the model. So what's going to happen is the question. So we're almost at the end here because we don't have to do much more calculations. So what will the prices be at the beginning and down here, and what will the leverage be at the beginning and down here? Well, remember our principle that the leverage will always be worked out in this case of heterogeneous beliefs so that people can promise-- so there will be no default. The maximum promise is the most you can make without any chance of default. So you can see that--I'll tell you what the prices are. They're going to be that. So if you made a two period loan, a long loan, a lot can go wrong over a long loan. You can get all the way down to .2, so you're not going to be able to borrow very much if you make a two period loan. If you make a one period loan, in a day not much can go wrong. That's why these Repo markets are so short. In one day practically nothing can go wrong, well here something does go wrong, but you can fall to .69. It's a lot better than .2. So you could borrow at the beginning .69. That'll be the equilibrium promise at the beginning, will be .69 with no interest. The equilibrium promise here will be .2 with no interest. The equilibrium promise there will be 1 with no interest. So this turns out to be the equilibrium. Why? Notice how shocking it is. Nobody thinks the price drop from 95 to 69 is justified. That's a huge 26 percent drop. Mr. 87, he thought the price should go from 98 to 87. That's an 11 point drop. Mr. 1 thought it was worth 1 at the beginning. He still thinks it's worth 1. That's no drop. Mr. H equals 0 thought it was worth .2 at the beginning and still thinks it's worth .2. That's no drop. No matter who you pick, I think the worst one is .5, .5 thought it was worth--we have to figure it out, 25 percent chance of going down here, 75 up there. So .75 .5 is .8, right? 25 percent of .2 is .05. So Mr. H equals .5, thinks the expected payoff is .8,75 percent of one of those 1s, and 25 percent of .2 is another .05. So .75 and .05 is .8. So he thinks down here where he's a .5 it's now worth .5 and .5 of this. It's .6. So he thought the drop would be from 80 to 60, a 20 point drop. That's the biggest drop anybody could imagine, 20 points. Most people are at 11 points or 0 points or something like that. Nobody's at a 26 point drop. That's way bigger than anybody could imagine is justified by the bad news in the economy, yet that's what the equilibrium becomes, from 95 percent to 69 percent. So why is that? And that's the end of the story. What happened in the drop? Well, three things went wrong. The first thing is that 87 is the marginal buyer, so everyone above him bought. All these optimists were buying. Everyone else sold and lent money. Student: You just assume that, right. Prof: What? Student: You just said let's assume 87 is the marginal buyer? Prof: I'm assuming that and it's going to turn out to be the correct answer. Now, how did I know 87? Well, you'll see at the end. Yeah, question? No. Just fixing your hair, that's okay. So Mr. 87 is the marginal buyer. So those guys at the top bought. Now, how could they afford to buy so much? Well, they're borrowing so much. They're borrowing .69 plus they already had their .31 [correction: their .13], so together they can spend .69 .13. That's .82 that they're spending and they're only buying 87, and so 82 over 87 is about 95. So there's a little rounding going on. So that's why the price is .95. Now, why did it crash to .69? It crashed because look what happened. These total optimists at the beginning, the top 13 percent, they spent all the money that they had, their 13 percent gold, they spent the 13 percent. They borrowed everything they could to the hilt so they owed .69 in both states. So what happens to them here? They spent all their gold and they owe the total value of their collateral. They're wiped out here. They've got nothing left. So the most optimistic people in the economy, they're just out of the economy. They've all gone bankrupt. So now we've got a smaller population with less optimistic people, and so these new optimists are going to do the buying now. Well, first of all they don't think the asset's worth as much for a bunch of reasons. One is they got bad news, so the people who are left don't think it's worth as much as they did from the beginning. Plus the most optimistic people at the beginning aren't there either, and then lastly and most importantly the people who are left can't borrow very much money because the leverage at the beginning was .95 over .26, you could borrow 69, so you had to pay down .26. That's 3.6 leverage. Here the price is .69. You can only borrow .2, so you have to put .49 down. The leverage is 1.4. So you went from 3 and 1 half leverage to 1 and 1 half leverage. The leverage collapsed, and so these guys who are left they are not as optimistic themselves because they've got bad news, the most optimistic people are gone, and the people who want to do the buying can't borrow as much. So there are three reasons that drives the price down. The marginal buyer becomes a much lower guy than before, and so that's why the price is lower. It's not just the bad news because Mr. 87 would never have justified that drop. It's because the thing has fallen into more pessimistic hands. So all those bankers and hedge funds who bought all those mortgage securities at the beginning, they've been wiped out by now. They're way up here. They can't buy. They're much more sober people who are left who also know we've had bad news. They're willing to pay less to begin with, and they are more pessimistic, and they can't borrow very much, so the price drops for all those reasons. I think that's the essence of the crash. Three reasons, the people going bankrupt who are the most optimistic buyers, the second reason because the news was bad. That's the first reason. The news was bad, optimistic buyers going out and the leverage collapsing, so the price drops a long way. So I'll end with one more slide and then sum up. The last slide is his question about the classes of people. It's a little different now than it was before. There are different classes of people. So let's just think about this. Why was the marginal buyer Mr. 87? I mean, after all we just computed, Mr. 87 thinks the value of the asset's 98, not 95. Mr. 86 also thinks the value of the asset is 98 about, so why didn't 86 buy? He was getting a good deal at the beginning. Why wasn't 86 buying when he thinks it's worth 98 here? Mr. .86, remember, is not supposed to buy. He's going to buy the next time. See Mr. 86 there, he's the cautious optimist. Mr. 86 there, just below 87, he's going to buy after the crash, but he's not buying now. So why is it that he's not buying at the beginning? Well, so this is the only subtlety, but it's the answer to your question. Mr. 86 says to himself, "I can make a profit. I think it's worth 98 and I only have to pay 95. That's like a 3 percent expected return and I'm risk neutral so that's great. If I'm right it goes from 95 to 100. I can get 5 percent. On the other hand, maybe I should wait for the crash. If the crash comes I only have to pay 69. I can get 40 percent return, 31 over 69, whatever that is. I can get a 40 percent return if there's a crash. That's much better than my 5 percent if I'm right." So that guy is waiting to make money in the cash. So of course by waiting and buying in the crash he's helping to reduce the terrible calamity, because he's a buyer. If we just had more people like that--I think of that as Warren Buffett, I called him the cautious optimist, all the way down to Mr. .74. Mr. .75, for example, also thinks the asset is worth more than .95 at the beginning, but he doesn't buy either, so all these people, the cautious optimists, they're holding out for the crash and the crash would be much worse without them, but they don't eliminate the crash because there are not enough of them. So here are the three classes of people you were thinking about. They're not quite as optimistic. They still think it's a good buy, but they decide not to buy waiting for the crash. Now, how did I know that it would stop at 87 and 74? How did I get all those numbers? Well, I don't have time to derive them, those are the equations, but I can explain it very simply. You see, thinking you're going to take advantage of the crash means you must have a high H. You think if things go here they're still going to end up okay. That's why you think there's a big profit opportunity. But if your H is too high you don't think you're ever going to get to the crash. So you've only got this small intermediate group of people, the Warren Buffett like people, who are optimistic enough to think that we're going to pull out of our depression, pull out of the crash and still there's a profit opportunity, and yet think that the crash is likely enough so that they'll wait for it. People who think they'll make a bigger profit, higher H once the crash starts, well, they don't even think the crash is going to happen. So I've made a big assumption that the people with high Hs always have high Hs, but I think that's life. I think that's not a bad assumption. Every hedge fund guy I've ever talked to who thought that this was a low probability event also thought we were going to come out of it and things wouldn't be that bad. So I'm not saying that these people don't learn. Everybody learns. When they see the first piece of bad news they're more pessimistic. You go from 1.69 percent to 13 percent. So it's not like people aren't learning. They are learning, but relative to the rest of the population if you started optimistic you stay optimistic, and that's why there's only a small group of Warren Buffetts who can save the situation. So that's my model of the leverage cycle, of what happens. Three bad things happen, bad news, can't do anything about that, the leveraged buyers get crushed, go out of business and leverage collapses. And when the prices are really low the whole economy is suffering tremendously and innocent people who had nothing to do with all these markets, the price of everything, every asset is low so they can't borrow. They can't get loans. Margins are so tough. They're small businesses. They can't borrow. They're totally crushed down here, so how would we save the economy? We'd undo the three things that happened. We can't undo the bad news, but the three things that happened were uncertainty went up. It wasn't just bad news, it was scary bad news. So this gap between 1 and .2 is much bigger than that gap. That's why the leverage went down. Volatility went up. So you have to contain the bad news. That would help. You have to contain the bad news, that's A. So you can't eliminate the bad news, but you can contain the volatility of the bad news. Secondly you have to increase the leverage, and thirdly you have to make up for the people who've gotten destroyed. The buying power is gone. Somehow the government has to replace that temporarily. So those are the three things we should be doing now, and in the long run we should never have let leverage get so high up here. That's what made the price so high up here, and that's why everyone got wiped out down here because they were borrowing so much. We should never have let that happen. So if we regulate the economy not to let leverage get so high we won't have such a crash, but if we do have a crash the way to deal with it is to undo the three things that went wrong. That's the sort of story that I've been telling. Yes? Student: Do you have a theory for what the right amount of leverage is? Prof: That's a wonderful question, and of course I've been asked that before. So let me put it in several different ways. Let's take the most hypercritical way. I presented this theory, remember, starting in 2000, so way before the crash. And so people would say then, "Oh, very nice, very cute, but first all there's not going to be a crash and secondly how could we ever know what the right amount of leverage is. It's an impossible pie in the sky goal to regulate leverage. Well, you see, that's why--I say it's difficult, I agree, but we've already faced this problem. We regulate the interest rate. How does the Fed know that the interest rate's too low or too high? What the Fed does is it monitors a bunch of stuff and realizes the economy is overheated. Things are changing. Suddenly output is going way up and inflation is starting to go up. Then the Fed raises the interest rate, or maybe people are being thrown out of work then the Fed lowers the interest rate. So something changes in the economy. They don't know so precisely what to do, but something's changed that gives them a clue about which way to move interest rates, and over the course of 80 years, I guess since the Depression, since it was created, over 70 or 80 years since then they've gotten better and better at regulating the interest. So I put this picture up for a reason last class. You remember the picture, which I'm going to get to now, of the history of leverage. So here's the history of leverage, the purple, in the housing market. And then the blue is the history of leverage, it's the loan to value, basically. I put money down starting from the top and going down. So from the bottom it's loan to value. So I've got the history of loan to value in the securities market and in the mortgage market. Now, I think that the Fed should be monitoring this, and not only should be monitoring it, should be making it as public as the interest rates are. So how come I had to present Ellington's data on observations it made in the market, because Ellington seems to have been the only company in the county that kept this data. Nobody else seemed to recognize how important it was, and we kept it. So the Fed doesn't have these numbers going back. If it did it would have seen that leverage had suddenly jumped up here and that leverage was much higher than it was before, and it would see if it monitored leverage in the housing market that leverage was skyrocketing. Of course everybody knew this, they just didn't think it was an important thing to pay attention to, but if they were paying attention to it and keeping these numbers, we had to do this at Ellington by going house by house through every house looking at what the leverage was and taking the average, if they had done that, I mean they could have done that easily, and if they did do that, and if they were publishing it, and every economist was aware of it I think things would have been very different. They would have said we ought to tighten leverage. Exactly how much should we tighten it? Well, they would have said, "I don't know exactly, but we would have forced banks not to allow loans with 3 percent down." Should it be 10 percent, or 15 percent, or 8 percent? It's a little hard to say what exactly the right number is, but we would have picked a number higher than 3 percent and we would have avoided a huge problem, and in later years we'll get better and better at picking that number. So I'm trying to answer your question. So in the securities market another thing you could do, another trick you could do is you could say we'll pass a rule that says you can't-- here leverage is going down, right? They're asking for more and more margins. You could pass a rule that says you can't double your margins from 10 percent to 20 percent or 20 to 40. You can't double them in under four months, say, on average across some security class. You can't double them in less than four months or less than six months. So that would have kept leverage from collapsing so fast, and then lenders knowing that when the crisis was starting, you know, they're making one day loans. See, they always think. "Well, it's a one day loan and things start to look dicey I'll just demand a huge amount of leverage the next day. I'll get my money back tomorrow and then the day after tomorrow I'm not going to make the same loan. I'll ask for a lot more margin." So I'm saying, suppose you tell them in advance you have to keep making the same loan and you can't double the margin? You can increase it but you have to take at least six months to double it. Well, they'll know in advance that they're not going to be able to react very quickly to problems, and so in advance they'll ask for more margin down so they won't have to double to get to a safe level when something starts happening because they'll already be safer. So that's a way of not having to actually know what the right number is by just slowing down their response and relying on them to anticipate how bad things might be and they're already starting to respond at the beginning. So I'm not saying I've got exactly the right formula, but you see I think if you think about it and start to work on this, and most importantly you make these numbers public, you're going to change the way everybody, you know, rules will develop. Yeah? Student: To sort of connect to that, so are they going to set like one leverage rate or is it going to be like for each class? Prof: Yes, each class of security will have a different leverage. Student: When you say class of security like do you mean like different... Prof: Well, the government already makes a lot of loans through Fannie Mae and Freddie Mac, but Fannie Mae and Freddie Mac will have to ask for at least 20 percent down. Prime securities, prime mortgages will have to have at least this much amount of money down. So, on the housing market you'll have to have a certain amount of money down. On Treasuries you can have a very high leverage. On mortgages, plain simple mortgages, you can have not quite as high a leverage, but a pretty high leverage. On mortgage derivatives, which are much more complicated, the leverage has to be much less. So you might say there'll be some rule that says-- so anyway those are the kinds of classes that I have in mind, and we have to work out exactly how they're going to be regulated. So it's a little bit complicated. So let me answer your question in two parts. Yes, it has to depend on the kind of security, and b) even trying to answer your question I'm revealing that it's not so obvious exactly what the formula is and how to do it, but this has to be worked out. Yep? Student: Is this some kind of like Phillips curve relationship here that you could make between the amount of leverage and unemployment that kind of it's all the same like Phillips curve like other occasions that end up being awful also or is it... Prof: Yes, yes. I think that's the whole point of the crisis that the things feedback on each other. The feedback is the most important thing. So in the crisis let's take any one of these. When leverage starts to go down that makes the prices start to go down, but when the prices start to go down people get more worried that things are going to go down further, I mean, they have good reason to worry, and so the leverage goes down more which makes the prices go down more, and so they feed back on each other. So definitely it's a spiral of one thing affecting the other. And of course, the more the prices are going down the more the optimists are losing money and your best buyers are getting wiped out, and that's a third thing. Those three things are always feeding back on each other. Student: Is there a Lucas like critique, though, of saying that people should be able to expect this coming forward and they should account for that? Prof: No, because the model was totally rational. Every person did expect all this. Everyone anticipated perfectly what would happen. So Lucas critique is people should realize the environment they're in, but here in this environment everybody up here understood from the very beginning that the prices were going to go down to .69. They realized that there was going to be this acceleration of problems, and so they all anticipated it, but still they wanted to buy because they didn't think they were going to get down there. They thought they were going to go up here. So remember, I don't know if I have it in this slide, but one of my most amazing pictures was this one of what happened to the market. Open. So what happened to the market here, which I think I showed you last time, I mean, I know I did, but I'll just show it to you again. Now with this new perspective you can look at it. Presents, so this is Jerusalem, I gave this talk in Jerusalem. Second talk, so you remember this picture? I hope it was in this slide. Yes, it was here. Here. Remember what happened in the world? It was shocking how bad and how fast it was. So in 2007, beginning of 2007, right, we're not far from the beginning of 2007. That's three years ago people were expecting 40 percent losses for these lower tranches. So how could you get such an astronomical loss? What was happening? They were already anticipating this spiral. If you looked at just what housing prices were there, and you say 30 percent guys being thrown out, and housing prices are down 4 percent, that's hardly any loss at all, because if you get 96 percent back on the house and you have a few expenses and only 30 percent are defaulting, there was hardly anybody defaulting. Remember that curve we showed where there weren't almost any losses and no one going delinquent yet? They already anticipated that there were going to be lots of people thrown out of their houses and when they got thrown out of their houses the housing prices were going to collapse. So this market was collapsing already because people were anticipating a lot of the feedbacks and stuff that were going to happen later. They didn't just extrapolate the number of defaults, they also had to extrapolate the housing prices and stuff going down. And so in this model everybody is doing that complicated extrapolation and they're figuring it all out, but even so they still want to put themselves in the cycle because they still think they have a profit opportunity. They can't stop themselves from investing. That's why you need regulation. It's like a prisoner's dilemma. Everybody knows what the danger is, they still want to do it and the only way to stop them from doing it, you can't lecture them about irrational exuberance, they know what's going to happen and they still want to do it. They don't think that's going to happen. They know what could happen and they still want to do it. Now, I think in reality Shiller is partly right. I think that people didn't really realize how bad it could have gotten. My own hedge fund lost money. We didn't anticipate how bad it was because so many things went wrong. We just underestimated all the feedbacks. So there is the spiral and there were just more things going wrong than we anticipated. So I wouldn't stick 100 percent to my story. I think there's something to what Shiller says, but I wouldn't definitely stick to 100 percent of his story of it being all irrational exuberance. Any other questions? Now that we have five minutes left for--so I'm willing to keep going. So let's just pause. Any more questions on this story of the crisis or anything else about the crisis you want to ask, or...? Yeah? Student: How receptive are the regulators to this idea? Prof: Well, that's a good question. I talk to them now all the time whereas I never did before. So I'm meeting Dudley tomorrow. He's the head of the New York Fed. So I go there quite frequently like once a month now. I'm on some panels. There are other academics going too. So I didn't do that before, so clearly they are paying attention to it. I think there are other people saying that leverage is important, Soros, being a famous hedge fund person who says it. There are other people saying that you should reduce principal. Remember, I said that the way to solve the housing foreclosure problem is reducing principal. They're now holding hearings in Congress. I could have gone Tuesday to testify, but I have already testified, but they're having other hearings now. I didn't go because I was teaching, but there were a lot of people who went, and a lot of people said we should reduce principal. And a year ago when I was saying that hardly anyone else was saying it, although there were others, but very few. The people at my hedge fund, we all pretty much see eye to eye on this and some other hedge funds were saying that. But now, I think, there's a growing consensus that we have to reduce principal. What does that do? It makes the loan smaller relative to the value of the house. In other words, it reduces the leverage of homeowners. So we have to get back to a credible level of leverage. So the bad news is that although they're very receptive and although they're listening carefully and they keep inviting me to speak I don't see much signs that they're doing anything. And the one thing that they should have done by now is collected all this data. So they should have gone to all the big lenders and said, the Fed should have, and said, "This is the margins we're charging on all our different securities, here they are," and then the Fed would be able to monitor how much they were going up and down. Now, a bunch of these lenders themselves have also become excited about what I'm doing, and they're starting to publish reports about it. So one, Credit Suisse, for example, their research department now thinks that a better measure of money is not just M1 and M2 and all that stuff, but how many leveraged loans are made in the Repo market, and they add that to the money supply, and they think that gives them a much better picture of the economy. So it's all sort of based on these ideas and I think I got them interested in it, or was one of the people that got them interested in it. But they aren't going to publish their leverage numbers unless everybody else does because why should they give away private information? Why should they say, "We're lending to Ellington on slightly less generous or more generous terms than we're lending to some other guy." One of the two of us is going to feel bad about it, and so they're not going to do that. And so the government is the only one that can get the information out of them. And the government shouldn't say who are they lending to person by person, they should give the average number. This is the average margin they're charging people, the average number the banks in general are charging people then you won't be revealing any private information, giving away any secrets. So that's the worst news that they're not collecting the data yet, and it's shocking to me. So I'm going to yell at Dudley about that again Friday, but I've done it before, so hopefully they're going to do that. They say they're going to do that, so I believe they'll do that. And I believe that once they have all these numbers they're going to start to think differently. So there are all these initiatives in Congress, and in the Fed, and in the Treasury to try and monitor leverage and try to regulate it, but every time they get down to actually doing something they ask questions like you did, what exactly should the rule be, and they seem paralyzed by not being able to figure out the exact rule. But I think that's an unnecessary paralysis because we don't have to have to the final rule to start doing stuff. Yes? Student: I've got one more question. How and who do you think should be doing this? Prof: The Fed. The Fed has the power to do it. The Fed already regulates margins on stocks, right? They set the margin at 50 percent or something, and so they could change that and they have changed that in the past. So the Fed has the authority to do that. The Fed did that after 9/11. They called everybody up and said, right after 9/11, and said, "You cannot change your margins," and nobody changed their margins. I mean if ever there was a day when people were nervous and wanted to have a higher margin it was on 9/12. Nobody changed their margins. So they've done it before, but that's a pretty extreme day.
Quantitative_Finance_by_Yale_University	25_The_Leverage_Cycle_and_the_Subprime_Mortgage_Crisis.txt	Prof: So I'm going to talk about what led up to the crisis and how the crisis makes us realize that the things about the theory that we've been learning all semester that ought to be slightly different, and I've been working on a new version of the theory for the last ten years, what I call the Leverage Cycle, which I have to say didn't get very much attention ten years ago, but which now seems to be, I don't know, it seems to be getting more attention. It's almost like life imitated art, really. It couldn't have turned out more like the theory than I would have expected. So I'm going to tell you the facts and then try to fit a theory to it, and probably will spill over until Thursday, and I think Thursday I won't spend that much time finishing. I'll have a review class if anyone's interested for the whole material. And I think when you see the critique of the theory it might help put the theory in a little bit more perspective. But anyway, nothing of what I say these last two days you should feel is going to be on the exam. It's just more information that you might find interesting. So we talked last time, remember, at one of those special classes about the sub-prime mortgage market, and the idea was that you would pool together a bunch of loans. These are the--I can do this, I guess. You'd pool together a bunch of individual mortgages like this, and then you'd put them in a giant pool, and then cut the pool up into a triple-A bond, a double-A bond, a single-A bond, a triple-B bond, and this is the over collateralization and the residual. And I'm not going to go through the whole structure, but suffice it to say that the idea of this is you take individual loans which are very risky, after all these are sub-prime borrowers so everyone knew that they were risky, and you create what's supposed to be an incredibly safe bond. The definition of triple-A bond is that it has a 1 in 100 chance of going bankrupt in 10 years, of losing any principal in 10 years. That was the definition they claimed. I heard a talk about power failures last night, by the way, the power grid which went out all across from Cleveland to Manhattan in 2003, and they said that was an event that should happen once every 10 years. And then when you hear what happened in the event, someone didn't trim a tree, and the line sagged into the tree, and so then it shut itself off, and then the city next door they had the same problem with someone not trimming a tree, and that line shut off, and once you have two or three lines shut off the system automatically goes down. It seems like it could happen much more often than once every 10 years. But anyway, it's the same thing here. This is supposed to be once every 10 years, 1 in 100 chance, and it happened in a giant way. So the idea of the triple-A, so they're supposed to very safe because if the first house defaults, the first homeowner defaults, instead of paying back the 100 he owes, let's say he just stops paying, and then you throw the guy out of the house, but then you get to sell the house. The house is there as collateral for the loan. Now, the loan should have been 100. The house should have been worth much more than the 100. That's why it should have been collateral. So you should have had 120 dollars of the house to sell so even if the house went down by 33 percent to 80 that's still only a 20 dollar loss, or let's say 20 cent loss on the dollar loan, and that 20 cents comes out of the triple-B piece. So you notice how many losses do you have to have if you're losing 20 cents on a house? To have 5 dollars worth of losses you've got to have 25 of the 100 houses go down, and another 25 of the houses have to go down to lose this one, and then another whole bunch of them, 35 more to go down. So you've got to have like 85 houses going down before you touch the triple-A, because the losses always come from the bottom and work their way up. So when they made these deals they thought it was inconceivable that you'd have 85 percent of the houses defaulting, or that you'd lose so much more than 20 percent on each house because things like that just hadn't happened before. And so it seemed like they were incredibly safe. So that was the structure. And the idea, again, was to take risky securities and by securitizing them create a whole bunch of apparently perfectly safe securities. Because, as we said, the goal of most investors is to invest in something that's completely safe, they don't have to worry about getting more in one state or more in another state. And this seemed like an ingenious way of turning 1 trillion dollars of very risky sub-prime loans into, this is 81 percent, into 800 billion of very safe bonds and maybe riskier bonds down below that. So you could never find 1 trillion dollars worth of people willing to lend to sub-prime borrowers, but you didn't have to after the securitization, because 800 billion of the loans to them were by people who thought they were perfectly safe. You only had the guys buying these bonds down here who thought that they were running a very big risk. So the whole idea of securitization, the whole idea of the American financial system was to-- well, let's see what the whole idea was, was to create as many safe loans as possible. So you could put it a little bit more generally. I should have had this picture before. You could say if the states of the world-- if you're here today and you might have many of these different states of the world tomorrow, some people know that they're going to be rich in some states and poor in other states. What they'd like to do is get the same amount in every state. They can do that by directly buying safe bonds. That's what everybody's trying to do. They're trying to hedge themselves to get completely safe bonds. Most people don't know how to hedge so the financial system creates safe bonds for them. Other people, they do know how to hedge, but their cash flows are different in the different states because, for example, they run a business and if interest rates go up that might be bad for their business. If interest rates go down it might be good for their business, so they've got different amounts of money in the different states. And then to create hedging instruments for these people you'd like to create securities that pay a lot in states where they want the money so that way they can buy hedging instruments. So the purpose of the financial system is to create cash flows in states that people want them. For the majority of people that's the same thing in every state. For other people it's something like the Arrow securities. So they can buy money in the states when they're running short. And why is this connected to mortgages, because how do you know that anyone's going to keep their promise to deliver money in those different states, or money in every state, how do you know the people making the promise will keep their promise? Well, you don't. That's why you need collateral, and the best collateral in the country is the houses. So the purpose of the financial system, as we said all through the course, is to create securities that pay off in different states of nature, of the type people want, and that are guaranteed, so that people keep their promises, guaranteed by collateral. Houses as the best collateral made it inevitable that the most sophisticated part of the market was going to turn into the mortgage market. So at first glance you would think the most complicated part of the market is the stock market, but no. It turns out that collateral is the key, because without guaranteeing a promise the promise isn't really very good, and so houses are the best collateral. So we'll see now that the change in the theory that I want to describe is what happens when you suppose people might break their promises and you have to take into account collateral. All right, but let's get back to the facts. So there were 1 trillion dollars of these sub-prime mortgages around. So then what happened? I want to skip through this pretty quickly. People thought that it might be dangerous and they wrote insurance on the sub-prime mortgages. So an insurance on a sub-prime mortgage, CDS, Credit Default Swap, would say if 1 dollar of the principal of the triple-B bond disappears, and we saw how that could happen, you take one homeowner who loses 20 cents, I mean, that will come out of this first, but after all this stuff is wiped out, 20 cents of the losses because the homeowner instead of paying his dollar doesn't pay it all. The house is sold. You only get 80 cents back, that 20 cents comes out of the triple-B, so the insurance would then say--the buyer of insurance would get to collect the 20 cents. So this seemed like another way for people even in the BBB range to guarantee their payments. Well, it turned out that the writers of insurance didn't just write 20 cents in case there was a 20 cent loss, they might write 10 dollars of insurance on the 20 cent loss. So these Credit Default Swaps are getting very close to Arrow securities. So the theoretically inclined economists who didn't think very far ahead in the Clinton Administration, namely Larry Summers and people like that, Bob Rubin, they were ecstatic about these Credit Default Swaps because to them it reminded them of Arrow securities. And they thought, my gosh, the market is coming close to creating Arrow securities and isn't it great that people will now be able to hedge much better because they've got these Arrow securities that they can trade. Now, problem was that who's writing the insurance? The people writing the insurance are big banks and people like AIG. So they're saying if you lose 20 cents we'll pay the insurance. Now, of course, that's a promise just like the promise to repay is and that should have been collateralized. The trouble is that when AIG as a triple-A rated company wrote its promises many of the people who bought the insurance just figured that's such a great company it's obviously going to have the money, probably isn't going to happen anyway, so I'm not going to worry about the collateral, and they managed to make all of these promises without putting up collateral to guarantee that they are going to keep their promises. This mistake that people make, "Well, it's probably not going to happen anyway that we're going to even collect the insurance," you shouldn't have bought the insurance if you didn't think you were going to collect it. So obviously, even though it's a low probability event, you have to think what will happen when it comes time to collect the insurance. Are they going to have the money? Now, many banks in Europe bought these things and they are accused of having realized that they wouldn't be paid off. They only bought it so they could convince their regulators that they actually had a very sound bank and therefore didn't have to set aside capital, and they knew very well that they probably wouldn't be paid off. They just didn't think that it mattered because things wouldn't go that bad. So in any case, to circle back, we've got these sub-prime mortgages where you've written a bunch of apparently safe bonds. A lot of people, but not many, 20 percent holding dangerous bonds, realizing that they're dangerous, and you've got a bunch of insurance written on the dangerous bonds, but of a much bigger, five times as big as the amount of dangerous bonds. If something goes wrong with that pool these bonds are going to lose and then the writers of insurance are also going to lose a huge amount of money. So what happened? Well, on top of that there was a CDO market where you took the triple-B pieces and broke those up like you did before into bonds, more triple-A's and so on. So if something happened to this original pool and a lot of homes started defaulting that would wipe out all the triple-B's forcing all these people to pay insurance. And on top of that the CDO market which is just the same thing done again, but using the triple-B's as collateral, all these things would get wiped out including the triple-A's here. And then that wasn't enough. Wall Street then wrote CDO-squareds on the triple-B and A pieces of the CDOs. All right, so we talked all about this last time. So now I want to get into what happened. Any questions? Yes? Student: So when these were being securitized like the triple-A is there any way to distinguish on paper the normal triple-A's and the triple-A's derived from like triple-B's, for example, or are all triple-A's just the same and there is no way to distinguish them? Prof: No, a buyer knows very well where his triple-A is coming from. A buyer has access to all--so if you were a buyer-- the hedge fund I work with, Ellington, was a big buyer of these kinds of things, and also you'll see what our strategy was, but we knew very well that--so let's go back to this. We were a big buyer of things here, like these triple-B's we bought a lot of. So we could get for every single home in this pool we knew the history, we know the loan to value, the income of the borrower, what zip code the borrower lives in. We know a tremendous amount of information about each one of these individual houses, how they've paid before, what kind of credit rating they have. All that information we have, and so we build the model of how reliable we think these borrowers are and what they're going to do. And so on the basis of that information we can predict what we think the value of the BBB is going to be, and whether it makes sense to buy insurance on it or not. So what was our strategy, by the way, in our hedge fund? Our strategy was, take a pool where we think that the pool is really a good pool, buy the riskiest piece which is down here, the residual that I described last time, for which there is no insurance. Now, it may be that the whole world goes to hell and we lose money on our residual, but so how do we hedge that? What we do is then we take what we think is a bad pool of loans, they're from a county that we think people aren't as reliable, say, and we don't buy the residual. In fact, we do the opposite. We buy the insurance on the triple-B. There is no insurance on the residual. So for the bad pool we've bought the insurance. For the good pool we've bought the residual, and so if we're right the residual is going to pay a lot of money because these people aren't going to default. And if the bad pool is as bad as we think they're going to default and we're going to collect the insurance. So we're going to win on both, and if the whole market collapses, well, our residual will go to zero, but so will the BBB in the bad pool and we'll collect insurance and so we'll be protected. So that was our strategy. So, yes, the answer is you have a lot of information about what you're buying. Student: It's not actually a triple-A, it's a triple-A of a bad pool. Prof: Yeah, this appears the triple-A of a bad pool, but the people buying the triple-A know exactly what's in the pool. Now, they may be dumb and not bother to think about it and just trust the triple-A rating without thinking about it, but probably a lot of them did think about it. And if we take this pool, the CDO, these triple-A's were held mostly by big banks, and you would have thought they were the most sophisticated of all the buyers because they're the ones creating the pools. So they certainly know what's in the pools. They're the ones who created this original pool here. They're the ones who underwrote those loans and so they're the ones, they know everything about it, and they're the ones holding all these triple-A's. So we're not talking about people who have no idea what they're doing. We're talking about people who supposedly do know what they're doing. All right, so that was the basis of the market. Now, what happened? So I can describe our hedging strategy and our models, but I'm not going to do that. So this was our strategy. You go long the residuals short the bad pool. Now, what happened? Here's what happened. There was an index that was created in the beginning of 2006. You just put together a huge number of triple-B bonds and triple-A bonds of different pools and average their prices. That's the index, and so they're all 100, you see? And then in January of 2007 all of a sudden the market starts to go crazy, and by March and April it's collapsed. These bonds, a lot of them, the triple-B's, have collapsed from 100, where everything was, all the way down to 60, just like that. In a few months it went from 100 to 60,100 here, three or four months later it's 60. This is March of 2007. Now, what was the stock market doing then? You might remember the stock market, S&P, so here's the stock market, too far in historical time, but anyway, here's the stock market. It had this NASDAQ collapse, but this point right here is October 31st, 2007. So ten months or nine months later the stock market reaches its peak. So all this time from here up the stock market is climbing and climbing and climbing. So the sub-prime mortgage market has collapsed, but clearly the rest of the population doesn't think that things are that bad. So just to put everything in perspective, where else are we? What other big--housing, let's look at housing prices here. We're going to come back to this graph if you can see it. So this is 2000 here. This is 2009 here. Green is the housing. This is Shiller's housing index. So if you set it at 100 in 2000, up here at the very top, that's the middle of 2006, it hit its peak and then started to come. So housing hit its peak in the middle of 2006, the third quarter of 2006, and then sort of didn't come down very fast, but started to come down. Sub-prime mortgages collapsed in January of 2007 and the stock market started its very quick collapse in October-November of 2007. So it was first housing prices turned, then sub-prime mortgages collapsed, then the stock market ten months later collapsed, so we have to explain all of these things and what was going on. So in the--sorry, where was I? So this is the sub-prime market collapsing. Why did this market collapse? What happened to make them collapse? This is actually an example of the wonderful nature of the American financial system. The fact the market collapsed is a great thing because why did it collapse, what was the information that made people think that things were going to go down? Well, it was this information, cumulative loss by reporting month. Let's look at some. These are Countrywide, they're one of the bad guys, that is they're one of the ones whose loans went bad and the company went out of business, basically, and got bought by Bank of America. So look at delinquencies historically. So for 2003, these are Countrywide loans given in 2003. It's the brown thing. So here are their delinquencies, right? They start at 0, naturally and then they go up to 2 percent and they stay there as a function of the pool. Some of those guys are defaulting and being thrown out of the pool. That's how delinquencies can go down. Also people can start paying after being delinquent. Delinquent just means you're missing some payments. Look at 2004. They're still hardly doing anything. And then look at 2005. Well, all of a sudden delinquencies start going up. In 2005--they're 5 percent by the end of 2007, but delinquencies, 5 percent delinquencies. We're just talking about people who missed a few payments, 5 percent delinquencies. They haven't actually been thrown out of their house. It takes 18 months. Nobody's lost anything. They've just been delinquent for a little while. So what was the catastrophe that made the market collapse? Well, this is it. So WALA means Weighted Average Age. So look at the months. So you take things that were issued in--this is the securitization. They're bundled together in the beginning of 2006. This is the second half of 2006, but the loans actually started in 2005 they just didn't get--the homeowners got their mortgages in 2005. They got securitized in 2006. So you look at the delinquencies and you see that nothing happens the first 12 months, these are losses, and then eventually it goes it 1 percent. The losses go to 1 percent. We're not talking about giant numbers. Well, everybody saw that. Then they looked at the losses for things issued second half of 2006, and the losses, that's this blue line, they are going to, we're talking about 20 months later, they're going to 1 percent or 1.2 percent. You look at the things issued in 2007, which means that the loans you're really measuring from somewhere in the middle of 2006. At 1 year you're at half a percent. And in the second half of 2007 you're at .2 percent losses, so no losses at all. So nothing horrible has happened except for the fact there's an obvious pattern here. It seems like every newer vintage is getting worse, and worse, and worse, and worse. And so it was on that basis, just seeing things getting worse before there were any losses. Remember, these are very sophisticated people betting hundreds of millions of dollars. They're thinking hard about this. Even though nothing had happened yet the market collapsed. So this collapse that happens here is before anybody has lost any money. Hardly anyone's been thrown out of their house. Nothing's happened in the economy, but the traders have already figured out things are on a bad course, things are going to look really bad and the market collapsed. So we had warning. This is the beginning of 2007. We're almost at the end of 2009, so it was almost three years ago. Nearly three years ago everybody should have known that the market had figured out that there was going to be a catastrophe in the sub-prime world, a real catastrophe because the losses were going to be 40 percent. That's what they were expecting. You can't have losses like that unless you throw out, you know, it's a huge number of people that have to get thrown out of their houses, and you have to lose a huge amount of money on each house in order to get losses of 40 percent. Like I said, if you lose 50 percent on every loan you have to throw 80 percent of the people out of their houses to get 40 percent losses. So this meant that people were expecting gigantic catastrophe. By the way, that was an exaggeration because this is the triple-B piece. I meant the triple-B piece was going to lose 40 percent. So the triple-B piece is only protected by 6 or 8 percent so it means the total losses would be 10 percent, 10 or 15 percent, which means if you're losing 50 percent on a house 30 percent of the people are going to be thrown out of their houses. So it's like 30 percent losses and 30 percent of the people thrown out of their houses. That was the expectation then, but that's still terrible. There were five million sub-prime people, so the market at this point is expecting 30 percent of them to be thrown out of their houses with 30 percent losses even though the losses are 1 percent or less. So you can see how far sighted the market is. So our government, everybody should have been warned right at this point that something was going to happen. Now, did the stock market realize this was such a catastrophe, absolutely not because the stock market waited until the end of 2007, which we're talking about here, and now look at where the losses are in sub-prime bonds. Here the stock market started to go down. So it had all this warning that something horrible was happening in the mortgage market, but the stock market owners thought nothing of it. They thought, "Well, how could this possibly affect us?" And only here do they start to catch on. So to give you an example of the losses, this is only up to December 2007, people kept announcing losses. Merrill announced 9 billion. Citi Corp announced 10 billion and then the next week another 10 billion. UBS announced 3.7 billion and then another 10 billion. Goldman announced 5 billion, Morgan Stanley 4 billion. Every other day someone was coming out saying that they had lost all these billions. And that was only in December 2007. The losses accelerated like crazy through 2008, so there were hundreds of billions of dollars lost. Now, the whole sub-prime market is only 1 trillion, but remember there was all that insurance written on it. And who was writing the insurance? These very same people were the ones writing the insurance. So you not only lost the hundreds of billions in the sub-prime market, but also multiply that by 5, the hundreds of billions all these guys wrote in insurance and in CDO triple-A's that they held. So, all right, now let's say one other fact that's quite interesting. These are prepayments. So I told you that in sub-prime loans for the first two years, the sub-prime loan, you'd be locked into the loan. A huge penalty if you prepaid, but between year two and year three you could prepay, get a new loan, refinance it and then in year three the interest rate would jump. So what would people do? Well, people who made all their payments the first two years would be regarded as reliable payers and so of course they would refinance. They'd no longer be such sub-prime people. They'd refinance into loans with lower interest because they'd be regarded as better credit risks. So if you go back to 2003 you see that after the second year prepayments go up to 70 percent. So 70 percent of the people would refinance their loan between year two and three. In 2004, that's the pink one, the same thing happened, 60 or 70 percent of all those people over the course of a year refinanced their loans. So that means that the original lenders got 70 percent of the money back. It's like a prepayment like we have in mortgages. Well, in sub-prime these guys had a huge incentive to do it once they proved that they were good people. And as I told you, most of the sub-prime borrowers are young people who had screwed up with their credit cards and things like that, and after they paid for a while people would realize that they'd settled down and give them a new loan, but look what's happened to these numbers, so if you jump to 2007 all these things just collapsed, no more prepayments, and once there are no more prepayments that means the lenders don't get their 70 percent back. So if you're a hedge fund figuring, "How much can I lose if I buy one of these sub-prime things," you know that between year two and year three you're going to get 70 percent of your money back so you can't lose more than 30 percent. All of a sudden you're getting 10 percent of your money back which means you could lose 90 percent. So, why would that have happened? Well, we're going to come to that. So those are the basic facts. I don't have time to say more than that, so any questions about those basic facts? Now we need something to explain how they happened. Yes? Student: So ultimately the slope of the line is getting steeper, is that what you're saying, so the projected loss percentage, right? Prof: Exactly. So people were realizing--yeah, that was all that it was. People just said to themselves every-- that's exactly what I'm saying that people said, "Look, we know that losses are going to increase, but they're probably not going to get very far. Historically they get to 3 percent or 4 percent or something like that. That's it. That's all we have to worry about. And it's early on, so it's not like we've seen any losses, but they just seem to be happening so much faster than they did before. Let's extrapolate that curve." Now, how do you extrapolate a curve like that? There are so many ways you could extrapolate it. So the market extrapolated and thought, "Gosh, things are getting just much worse," and the market started to collapse. So you see, in real trading markets people respond very quickly to very little information. I mean, their whole livelihood depends on it. It's all they're thinking about and so they're coming up with quick conclusions, which in this case like in many others, they're not so crazy. They're realizing something bad is happening and they're acting very quickly, and so huge--billions of dollars are being lost just on the basis of this amount of evidence. I think this brings home how fast the market acts and how expectations about the future are driving prices, and therefore how much information-- you remember, we said that if you just pay attention to the market you can learn a lot. Well, we didn't learn that much, the whole stock market. They weren't paying attention to what was happen. The mortgage market was collapsing. That should have meant something, but they weren't paying attention to it. Nothing in the world seemed to change because there were no people on the streets yet. Now there are people unemployed, there are people on the streets, there are going to be millions of guys on the streets pretty soon, homeowners on the streets. And of course so now the stock market has caught on that things are really bad. All right, so any more questions about this? So now I want to talk about a way of understanding what happened, and then I'm going to end. So I'm going to go from more general to more specific. So I'm going to talk about a way of understanding what happened and then we're going to talk concretely about how you would change the mathematics we've been doing all semester. So my view of all this is that it's the leverage cycle, which is--the leverage cycle, as I'll define it in a second, has to do with putting up collateral to make sure you're going to pay, and so far in the course we've paid no attention to that, and in all of economic theory they never paid attention to that. You can read anyone of those textbooks that were on the reading list by all of the great Nobel Prize winners, and all the great financial economists, and you'll never see the word, hardly ever see the word collateral, and you'll never see, what's the equilibrium amount of collateral? And so that's been entirely missing. So, in fact, if you think about macroeconomics and the Fed they always tell you that if things go bad in the economy reduce the interest rate. That's the way we can stimulate investment. We can raise the price of assets by lowering the interest rate. If we raise the interest rate we'll lower the price of assets. We can always get the economy to boom or slow down by adjusting the interest rate. The most important thing ever done in macroeconomics in theory and practice is to establish the Federal Reserve and give it the responsibility of managing interest rates. Now, in my view it should be managing collateral rates and not interest rates. And in fact it has the power to manage, it's been given the authority to manage collateral rates when it was created, but it just never exercises that authority. Now, as I said in class, Shakespeare already had this idea. In The Merchant of Venice, as we said, they were haggling over the interest rate and not just over collateral and Shakespeare anticipated the impatience theory of interest and Shylock, who you know, the modern reading of The Merchant of Venice is that it's about anti-Semitism and Shylock is supposed to be a bad guy. I don't think Shakespeare intended that at all. In fact, Shylock is much more sophisticated, by far, and much better understanding of what's going on in the world than either Antonio-- well, certainly than Antonio who is the merchant of Venice and Bassanio's actually, I think, quite clever, although Harold Bloom makes Bassanio out to be an idiot and a dupe, and can't imagine how Portia could possibly marry such a guy. But anyway, I think that Bassanio is a very attractive guy and I think that Shylock, he's the only one who really understands what's going on. So he explains the entire modern theory of impatience to Bassanio and Antonio and says that's why the interest rate should be high. And then they haggle over the collateral. And of course, Shakespeare, in my view, thought the collateral was much more important than the interest because nobody can remember the rate of interest they agreed on, but everybody remembers the pound of flesh collateral. And remember that the play ends with the ships all sinking, apparently, and so should Shylock take his collateral or not, and the court rules not that you should reduce the collateral or you shouldn't take the collateral but you should have a different collateral. It should have been a pound of flesh, but not a drop of blood. So it's the responsibility of the judicial system and the regulatory body to monitor not the interest rate, not the amount of the borrowing, but the collateral that's put up for it. And that's exactly what my message is going to be. We have to manage the collateral. And so I wrote about this starting in 1997, and 2003, and then again in 2008, and I've written with a bunch of people, and I have students who wrote on it. And Araujo and Pascoa were two Brazilians who wrote about it. I gave a talk there in 1997. I got them going on it. And then Bernanke himself wrote about collateral in the '90s at the same time, even earlier than I was, but he didn't have the idea of leverage and collateral rate. He knew that you needed collateral. He talked about collateral, but he didn't talk about the ratio and the rate. So what do I mean by that? If you have a house that's worth 100 dollars, say, it's collateral for a loan because if you don't pay the loan they can take your house. So that's called no recourse collateral if they take your house, but they can't go after you for anything more. Now that, in fact, is not by law what happens, but in practice what happens. If you default on your mortgage they'll take your house, but they aren't going to come after you to try and get your income or something like that. So it's as if all they can do is take your house. In some states explicitly by law they can only take your house. In other states you still owe the money, but they always just say, "Forget about it. We're just taking your house." So I'm going to assume that they take your house and no more. If the house is worth 100 dollars and you borrow 80 then the collateral rate is 125 percent, because a 100 dollar house is protecting an 80 dollar loan, so it's 125 percent. The loan to value, it's an 80 dollar loan on a 100 dollar house, is 80 percent. The margin is the margin of safety, it's a 100 dollar house so the lender thinks that he's protected because he's holding a 100 dollar house and he only gave you 20 dollars. So it's 20 percent and the leverage is 5 because with 20 dollars of cash you've managed to buy a house worth 5 times as much, 100. So these numbers are all the same thing. It's just different ways of saying the same thing. So I prefer leverage, but collateral rate, they're all the same thing. Student: Could you explain what the 5 is? Prof: 5 is a 100 dollar house and you only paid 20 dollars. You borrowed the other 80. So with 20 dollars of cash you can manage to own a 100 dollar asset, so the leverage is 5. So people who borrow a lot can own huge quantities of things even though they had hardly any money. So, as I say, when you're negotiating the loan you have to negotiate the interest rate, but you also have to negotiate the leverage. How much cash do you have to put down in order to get the house? How much can you borrow using the house as collateral? Now, in the standard theory that Fisher taught that we've described in this class, you've got supply and demand determining the interest rate. Leverage never appeared. We just always assumed everyone was going to repay their loan. So in my theory supply and demand are going to determine both the interest rate and the leverage. Now that seems a little shocking because how can one equation determine two variables? So I think it's for this reason that economists, basically all these years, ignored leverage because they just didn't see any way to fit two variables with one equation and solve for two variables. So they just said, "Well, for simplicity we'll assume everyone always repays." Now, what is it that's going to determine leverage? Well, this is common sense as Fisher and Shakespeare before him said that interest rates are determined by impatience. In my view leverage, there are many determinants, but the most important determinant is volatility, the volatility of the asset price. Why is that? Because you've got a house of 100 protecting the 80 dollar loan, if you think the housing price is going up and down and it might fall below 80 then you're not going to feel very safe. If you think the housing price is rock solid at 100 you're going to feel very safe and you'll even loan more than 80. So the volatility of the housing price, obviously, is what controls how safe the lender feels, and so volatility has got to be the most important determinant of leverage, but it's hard to see how to fit that into a supply and demand equation. So the theory, my theory, is going to be that the higher the leverage is, which supply and demand is going to determine, the higher the asset prices are, and the lower leverage is the lower the asset prices are. Now, why should this be the case? Well, in my view there are many different potential buyers, let's say a continuum of potential buyers and each of them has a different view of what the asset is worth, and so you have this continuum. Now, let's, for simplicity even, suppose that everyone has a number in his head about what the asset's worth. That's what we did on the very first day. Everyone had a reservation price of the asset. And let's say, though, that they're willing to buy more than one football ticket. They're willing to buy as many football tickets as they can get as long as the price is less than the reservation price. So what happens, the people who have the highest valuation naturally are going to buy the assets, and the people with low valuations are going to sell them, and somewhere there will be a marginal guy. So people above here are going to be the buyers, and people below here are going to be the sellers. And what's the price going to be? It's going to be the valuation of this marginal guy. He's marginal precisely because he's indifferent between being a buyer or a seller which means the price for him is just right. These guys up here think the price is too low. That's why they're buyers. These guys down here think the price is too high. That's why they're sellers. So this is all consistent with what we saw in the football ticket example. Now, one little twist is where does this have to be? Well, it depends on how much money these guys up here have. So Fisher actually said this. If you make people who really like to consume now richer you're going to get a different interest rate, or if you make the patient people richer you'll have a lower interest rate. Well, the same logic here. If you make the natural buyers richer you're not going to need as many of them to buy the assets and the marginal guy will go up here and the price will rise, not because the payoffs of the asset have changed, but because the marginal buyer has gone up. So to put it another way, a more important way, if it's easier to borrow because leverage is higher, so you can buy that 100 dollar house with only 10 dollars down instead of 20 dollars down, then each of these natural buyers instead of being able to afford to buy one house can buy two houses or two mortgage securities, or buy a house that's twice as big. So the natural buyers, with a lot of leverage, a few of them will be able to buy all the assets, and the marginal buyer will be very high and the price will be very high. If there's no leverage and no borrowing it's going to take a lot of them to buy all the assets, and the marginal buyer will be down here and the price will be very low. So leverage is clearly going to affect the price. And notice how shocking this is. What would Fisher say about this? So this sounds like such common sense, how could this be wrong? It sounds like it's so obvious. But now, why didn't anybody say this before? Why didn't Fisher say this? Because remember what Fisher said. He said the price of every asset is the fundamental value of the cash flows. You take the future cash flows and you discount them by the interest rate, say, and that's what the price is. I'm saying, even if the interest rate doesn't change, you just change the amount of leverage so these natural buyers at the top, fewer of them are going to be able to buy all the assets, then that's going to make the price higher. So the price is not going to be equal to the fundamental value. In fact, there isn't a fundamental value. It all depends on the different opinions of the different people. So what are the reasons they differ? Why should there be people who disagree about what the value is? I think that there are basically four reasons, or five reasons. Four of them, anyway, are one, these people, let's say, are more risk tolerant than the people down here. So the people down here are so scared to hold these assets because they might pay low numbers, low payoffs in some states and high payoffs in other states. So that assumes that they can't insure themselves against everything. So that's another crucial ingredient to my theory which I'm not going, you know, in the background here is the idea there's not insurance for everything. So the asset here is going to be regarded as risky if it pays less in some states than other. So because some people are less risk averse, they're more risk tolerant, they're going to be willing to pay more for the asset. That's one reason. Another reason is these people might just be more optimistic than these people. So far we've assumed that everybody believed in the same probabilities. What if these guys' probability of the up state is always higher than these guys' probability of the up state? Then they're going to be willing to pay more than these guys are. Another reason might be these people simply like the asset. They like living in the house. These people are the New York bankers. They're just lending money. They couldn't care less about living in the house. The house to them is just a source of income. For these people, they really want to live in the house. So another thing could be some people just have more expertise. They know how to read all these statements of loans. They can analyze the loan level data, and these people don't have the time, or it gives them a headache, or they don't know how to find the loan level data to go through, house by house, who the homeowners are and how reliable they are, so naturally they're going to be scared of buying because they're going to figure these guys know more than they do. So these are all different reasons why some people would be willing to pay more than other people. And so therefore, and as I say, in the standard theory the asset price is supposed to be the fundamental value. We don't talk very much about the heterogeneity of the people and how that makes the definition of fundamental value hard to maintain. So in my theory, in short, in equilibrium in normal times or good times there's going to be too much leverage and therefore too high asset prices, and in bad times there's going to be too little leverage and therefore too low asset prices, and this recurs over and over again, and it's what I call the Leverage Cycle, what I called the Leverage Cycle. Now, let me give you an example of what people really had to pay for these things. So for a bank buying a triple-A security there's regulation which forces them to put a certain amount of cash down. So they have their depositors' money, so they can buy things with depositors' money, but they have to put some of their own capital down. So how much do they have to put down? 1.6 percent, so they could leverage 60 to 1, a 100 dollar asset, they only paid 1.6 dollars in cash. If you look at all the so called toxic mortgage securities of which there were 2 and 1 half trillion, these are the things that crushed all the banks that they held, I went through security by security and made a guess as to how much cash was put down by the buyer of each of those securities and on average I got-- so this is not absolutely accurate, there are a lot of guesses, but I got 16 to 1 as the leverage. So that meant that, if that number's right, it means 150 billion dollars of cash was paid, and 2.35 trillion was borrowed. That's 16 to 1 leverage. So that means that, you know, think about it, Bill Gates and Warren Buffett, two people by themselves, in 2006 had almost 150 billion dollars. So that means two guys in the whole economy could have bought every single toxic mortgage security because they could have borrowed the rest of the money they needed to buy. So when you think of where this line is what I'm saying is that for all the mortgage securities, all the toxic mortgage securities, sub-prime, all those supposedly dangerous securities you could have had the marginal buyer way up here. That's all that was required. Those are the only number of people, this top little echelon of people bought all those securities, could have bought all those securities because they had enough money to do it, and they hardly had to put anything down. All right, the same was true with housing. Now, let's look at this theory a little bit. So I should have--sorry, I could have put this in a better thing. So I give all these talks with Shiller for alumni during the crisis. We haven't given one in a while, but there was, you know, lots of them. Like every month or two months we'd be giving one of these talks and they'd bring in all these donors to say, "Yale needs your money now," and they'd say, "We don't have any money. So anyhow, I'm just joking. So we'd have a lot of these talks and Shiller would always put up the green graph. So on the right hand side, I showed you this before, it's his famous diagram. He did a brilliant thing. He decided to collect data on every transaction. Every time someone purchased a house he'd keep track of it, because it's all public information, and then he'd compare it to the same house that was sold before, and do a few other tricks that I don't have time to explain, to make an index of the housing prices in the whole country. And so he'd done this going back many years, but starting in 2000 the thing that he called attention to before anybody, he said, "Look at this. Look at this line. The housing price index from 2000 to 2006 it's gone up by almost 100 percent." The housing index was 100 in 2000 when it started, that's 110, sorry. This is 100. It was 100 when it started here in 2000 and it goes up to 190 in 2006. That's 90 percent in 6 years. To almost double in six years that means it's gone up 12 percent a year or something. So a staggering increase in the price of housing, and then it started to go down. So he called attention to this already as it was coming up. So in 2004 and 2005 he was saying, "My gosh, there's a bubble. It's going crazy," and he'd say, "Everybody is nuts. Americans, there's irrational exuberance and people are so crazy that they just think things are always going to go up and the price is going up higher and higher and higher." And then when it got so high the narrative changed. People started getting worried and they started telling everyone the world was coming to an end and the prices went down, and down, and down because we have irrational exuberance. And things are picking up a little bit, but we don't know whether people are irrationally exuberant, or pessimistic, or they're blipping, but anyway, they're irrational. So that's a story that has a certain compelling nature to it and he deserves a lot of credit for calling attention to it. But in my story I say these prices are related to leverage. So I went through every loan, loan by loan, that wasn't a government loan. So these are private loans. You can't get the data on government loans. So on private loans you know every time someone took out a mortgage they were selling the loan, so therefore they published the data. You know what the appraised value of the house was or the sale price if they were buying it for the first time, and you know what all the loans are. So I added up the value of all the loans and I divided it by the price of the house, and I subtracted it off to get what the down payment was, the cash down payment, so this is 2 percent down, 4 percent down, 6 percent down, or if you take 100 percent minus this, this is the loan to value, so this is 100 percent. You've borrowed everything. Here you borrowed 98 percent of the value, 96 percent of the house, 94 percent of the house, etcetera. So in 2000 these are slightly riskier people. Amazingly they're putting down 14 percent, not amazingly. They're putting down 14 percent so it's 7 to 1 leverage. But then look what happened. The leverage went up, and up, and up, and up, and up, and up, and then it was, in 2006, less than 3 percent down. These people were 30 to 1 leveraged. I said the securities market was 16 to 1 leveraged, the triple-A part 60 to 1 leveraged. Here they're 30 to 1 leveraged and so the prices went up. But yes the prices went up because the leverage went up. You hardly had to put any money down. That's why people were willing to buy such expensive houses because they weren't actually putting that much money down. And then leverage collapsed like this and you had to put more and more money down, and then the whole market, you know, you can't get a loan basically anymore unless you're getting a government loan. And so leverage collapsed and the housing prices went down. Leverage was collapsing faster and in front of housing prices. So I think it's the leverage which is a crucial determinant of the price, and not irrational exuberance, although I think there is irrational exuberance, but I think leverage is what's underneath it and more basic. Now, let's do the same thing with prices. So we did the sub-prime index before. This red line is the prime index. So we're talking about not sub-prime homeowners, but prime, people with brilliant credit ratings and stuff. So even now years, three years after the crisis has started, the losses on these pools are still in the single digits, 5 percent, 6 percent, things like that and most of these, 8 percent maybe, and most of these, these are the trip--the top piece of a pool of prime borrowers. So most of these loans are, they're protected by 8 percent of the bottom piece. So you have to go through 8 percent losses before you touch them at all. So it's just inconceivable that you'd see 40 percent losses, but so what happened? These bonds were at 100. This is 100 over here. The price is 100. They're at 100. Now, the interest rate is changing and the prices are going up and down because they're supposed to be floaters which always pay more or less depending on the interest rate. So they should be locked in at 100, but they're not floating exactly on the same time, you know, they don't change their float so fast. So the price is going up and down because of that, but it's clear that nobody thinks there are going to be any losses. And then all of a sudden in 2007, but later, this is much later than the sub-prime market collapse, these prices collapse, and they collapse all the way to 60, shocking. It's just inconceivable, I think, that people could have thought there are going to be 40 percent losses, or that everybody could have thought there are going to be 40 percent losses, and then they've shot back up to 80. So there's been a huge gain. So if you look at a typical hedge fund like Ellington you'll see that we lost a lot of money, and now we've made a huge amount of money. So that was not such brilliant hedging, but anyway. So, but now why did these prices collapse and go back up? Is it that people just got totally irrationally pessimistic and then they said, "Oh, things can't really be that bad," and things got better? Well, let's look at the leverage, what is the down payment, the same thing as before on triple-A securities. Now amazingly the Fed has never kept these numbers, and they're still not keeping these numbers. So I testified in front of Ben Bernanke and the Board of Governors on October 2008. There were several of us, but it was for four and a half hours. And I showed them this graph. So this graph is at my hedge fund, Ellington--it's just a bunch of securities that we're used to trading. It's how much they were offering to lend us, what the down payment was they were insisting if we wanted to leverage as much as we could. So we didn't leverage anything like that, but this is what they were offering us on the kinds of securities that we're interested in. So this is not the greatest data because we're only looking at what we're interested in, and we're only looking at the offers made to us. So, but looked what happened. In '98 when there was a leverage crisis, that was the last one, I must have skipped a slide where I said the last leverage cycle ended in '98. It was 10 percent down. That means 10 to 1 leverage, and then suddenly it went to 40 percent down. So leverage drastically dropped. The down payment, the margin, radically increased for a few months during the crisis then it went back to 10 percent. Then we had 10 percent down for a long time. That's 10 to 1 leverage. And then for a couple of years it became 5 to 1 leverage, so 20 to 1,5 to 1, sorry, 5 percent down means 20 to 1 leverage. So the leverage had drastically increased, and then leverage suddenly started collapsing and lenders asked for more and more down payments, more and more down payments. And leverage was just collapsing, and it happened ahead of the prices, and then leverage actually picked up here and went down again. Then--this graph is quite old now, May. I should have updated it. Leverage has gone way up again and the prices have gone way up. So you see, leverage goes down the prices go down. Leverage goes up the prices go up, and leverage is still heading up and the prices are much higher. So that's my view. It's leverage that's determining a lot of these things. All right, and so as I said, there's recurring leverage cycles. In 1998 there was a leverage cycle. That's when Long-Term Capital--so there was a book on the collapse of Long-Term Capital that Lowenstein wrote that's on the reading list. Before that was Orange County. You remember my firm Kidder Peabody went out of business in 1994, the end of '94. The beginning of '94, Orange County got bankrupted partly thanks to buying securities from Kidder Peabody. Some of you may live in Orange County. In any case that was the derivatives crisis, and in 1987 there was a stock market crash, so anyway, it's hard to document all the historical leverage cycles because the Fed has never kept this data, and most other firms don't keep their historical data. We at Ellington realized after '98 that this was a huge problem, leverage, and so we kept all the historical data. That's when I wrote my first paper on leverage and collateral and that being a crucial ingredient of the-- so we have this data and practically nobody else has. So for me the most important thing, the first step the Fed should do is keep track of the leverage that is being allowed for, the margins that are being demanded on every security, housing and securities. And I heard this talk, I told you, last night on the collapse of the electric grid in 2003, and so I said, "What have you done?" Obviously the obvious question everyone wanted to know. So, "What have you done to make it safer?" And they said the one thing they did is now they've spent tens and tens of millions of dollars getting more data. So they now monitor every single power line in real time. They had farmed that out to other people before and they weren't very careful about it. Now they're incredibly careful about monitoring every single line. So as soon as one line goes down they switch the electricity and they move it evenly across a bunch of other lines. In the old days when a power line went down the grid automatically-- sort of, electricity went, the power went to the next closest place and that would overload the next closest one and maybe make that one go down. Now if they know it's gone down they choose how to re-divide it. But the point is, you can't do all that without information, and they're spending tens of millions of dollars monitoring everything and we still are not monitoring what leverage is. I think it's a shocking thing. We should be monitoring leverage and then we should be regulating it, and instead we haven't even begun to monitor it, much less to figure out how to regulate it. Now, why was the leverage cycle--I said, this recurs over and over again. So why was the leverage cycle so bad this time than it was before? So this is my short version. I have a long version of this. The short version is because leverage got higher than it ever did before, and there are lots of reasons why leverage got higher than it ever did before. We had this period of low volatility for a long time, so it made it higher. We then had securitization which we didn't have before. So a sub-prime borrower would have had to put down a huge down payment in the old days, because people would have regarded it as such a risky thing, but once we packaged all the sub-prime loans together in a big security and the triple-A guy got the best of the houses, not each house, not a share of every house, but only a share of the very best houses, it all of a sudden became a much safer loan and so you could borrow a lot more money against it, against that triple-A loan. So the triple-A piece, using that as collateral, you could borrow a lot of money, a big percentage of the price of the triple-A thing you could borrow, whereas if you had a single sub-prime loan people would never lend more than 50 percent of the value of the house or something. The second reason why things were so bad was because we had a double leverage cycle. We had leverage shooting through the roof not just in securities as it had before. As I showed you in '98 where it was at 10 percent down, and then there was a collapse to 40 percent down, and then back to 10 percent down, that was a big change, in the crisis stage, leverage collapse, but here we had it in housing as well where there was a feedback between the two. So why is it that all these people stopped being able to refinance their loans in 2007, which contributed so much to the losses? It's not because the interest rates were suddenly too high for them. Those didn't change at all. It's that the lenders suddenly demanded a much bigger down payment. Instead of 3 percent down they had to put 25 percent down and they couldn't afford to do it, so they couldn't refinance their loan. They didn't have the cash, so they were stuck with the old loan, and so the original lender was in much more jeopardy. And then the last thing is the CDS market. So I have to explain this. That's why it's going to spill over into next time. So these insurance things, there are many ways of interpreting what they did and why they were so dangerous, but one of them is that they allowed people to write insurance to lose huge amounts of money. So that's an obvious thing. That's why the losses were so big, but more interesting than that, they allowed the pessimists to leverage themselves, because in our old story from way back here, in this old story--where was the old story with that? In this story, remember, I said that the natural buyers, you'd have fewer of them if they could leverage a lot. So what were these guys down here doing? Well, they couldn't do anything except sell the assets and maybe make the loans. As the price got higher and higher these guys down here, presumably, were getting more and more disgusted and thinking, "Well, this market's ridiculous, and the price is way too high. We don't want to buy here." And I've talked to a lot of insurance companies like Northwestern Mutual Life, the guy who runs that. He said, "We used to be a big buyer of mortgage securities and sub-prime mortgages and stuff in 2004, and the price got so high in 2006 to us it became ridiculous so we just dropped out of the market." But dropping out of the market is one thing. What if they could bet against the market? Well, they had no opportunity to do that before. They couldn't express their negative view, but starting in 2005 where this CDS market really took off, they could suddenly express their negative view. So in my view and in my opinion what happened was that at end of 2005 the pessimists for the first time were able to bet on the market going down. And so that's what started to make prices go down, because of the CDS market. When prices started to go down the mortgage securities that had been sold with all that leverage for high prices started to go down in price. That meant that new securitizations weren't worth it. You couldn't make the profit that we were talking about before, putting all of these things together and selling off the bonds. The bonds are being sold for a lower price. You couldn't lend all that money to these people. You were getting the money to lend to the people by selling the bonds. If you sell the bonds at a lower price you don't have the money to lend to the people. So in order to make the bonds sell for a higher price they demanded that the homeowners put up more collateral, and then that meant the homeowners couldn't refinance, and then that started to make the world more dangerous, and that's why, then, on securities, the lenders on securities reduced the leverage and then the whole thing started to spiral. That's my story of how the things started. So let's say that. In the bottom of the leverage cycle the same bad three things always happen. Number one there's scary bad news that creates more uncertainty and more disagreement. So it wasn't just that people thought that losses were going to go from 40 percent to 20 percent on sub-prime mortgages. It's that they went from 4 percent expected, with a range of 1 to 5 percent, to 30 percent, but maybe they'd be 80 percent, the losses. There was a huge volatility--nobody really knew what the hell was going to happen. They had to extrapolate those curves. How do you know how to extrapolate? For a decade the curves had been flat. Suddenly they're starting to accelerate. How do you know how to extrapolate them? There's huge uncertainty, huge volatility, and so naturally the lenders are going to be much more nervous and lend only with much more collateral. Once the lenders lend with much more collateral those people at the top can't afford to buy things anymore. They're going to have to sell. So there's de-leveraging. Sorry, and the people at the top are going to have to sell, but the price is going to go down, and because they borrowed money and using an asset as collateral, their leverage--we talked about that-- their losses are going to be gigantic because they're betting, essentially, on things going up, and things are going down so they lost a huge amount of money. So this is always the same thing. There is scary bad news. Margins get tougher, and the most optimistic leveraged buyers are the ones who got crushed because they were betting on things going up and they go bankrupt. So now, what's so bad about this? I'm running out of time here, and I haven't gotten to how the math is going to change. So what's so bad? So I'm going to talk for four more minutes and hand back the exams, or should I just hand back the exams right now? What do you--are you? I'll talk four more minutes. Some of you aren't going to come next time, maybe most of you, so I'll do how the math changes next time. So what's so bad about the leverage cycle? So let's just think about all the bad things that happened. Number one, you can have a tiny group of people at the top controlling the price, because they can borrow so much money. Now we've always assumed that everybody was rational. What if these buyers are kind of crazy? A few guys can make the price skyrocket because they can borrow so much money. Now, once they do that and they're making the price of assets skyrocket, people are going to build more of those assets. So they're going to use real resources to build projects that are probably crazy and are going to be very costly to reverse. But let's leave aside now people being crazy. What else happens in the leverage cycle? Well, in the leverage cycle when you're leveraged a lot, as we said, that's going on the Tobin diagram to the right. It's like borrowing money to bet in the stocks. That means if the stocks go up you multiply your winnings. If the stocks go down you multiply your losses. So in the leverage cycle people who are lucky, if things keep going up, they get incredibly rich. It's a tremendous mystery in economics. Why is it that inequality increased so much? Well, one of the reasons, I think, is the leverage cycle, that people were betting and making more and more money and so that's why inequality was-- is helping to spread inequality. Now, another thing is the worst, probably the biggest problem is that once the asset prices fall everything gets hard to do. So if you want to get a new credit card, what does it mean to get a credit card? It means that you sell your promise, right, to a buyer. Now, why should a buyer buy your promise for 100, you're promising to pay back in the future, so he's paying 100 for you when the very same promise that someone made six months ago is selling for 65 because the prices have all collapsed. They're not going to buy the new promises when they can buy the old promises at such a low price. Who's going to buy a new mortgage when the old mortgages are selling at 65? Who's going to buy a new auto loan when the old auto loans are selling so low? So nobody can get a new loan. Nobody can sell a new promise, and no business can sell its promise. There are old businesses that everybody understands whose bonds are out there being traded at very low prices. The investors are going to all buy the old assets not the new assets. That's why activity collapses. Then another terrible thing is, what if the optimists are indispensable to the economy like the big banks? They go out of business and then everything topples. Well, why didn't the big banks take that into account? Shouldn't they have realized that the losses would be so big and try to protect themselves? Well, they're not taking into account that when they go under and the managers lose a lot of money that there are other people they don't care about like all their workers and the rest of the economy that's losing even more that they're not paying attention to. So they're not internalizing all the losses when they go out of business. Another incredibly bad thing is, what we're suffering from now is, debt overhang. There are a tremendous number of people, homeowners to name one, who are under water. That means they owe more money than their house is worth, or banks that have more debts than the value of the assets they hold, or firms that have more debt than the value of the assets they hold. Now, many of these people don't just go bankrupt. They keep going because maybe they'll get lucky. Maybe some miracle will happen and the stuff they own is going to go up in value. So they don't stop. They still exist, but they're what people have called zombies. They're not doing anything productive because what's the point in fixing up your house if more than likely you're going to end up losing it anyway. So all these homeowners are not doing anything to take care of their houses, the banks aren't making loans, these firms aren't making productive investments because they know they're so far under water. So another horrible thing happens is that if you try to collect the collateral when people default, it's a costly operation. So in sub-prime loans it takes 18 months to throw somebody out of their house. So during those 18 months the guy's not paying his mortgage. He's not paying his taxes, all of which you have to make up for. He's trashing the house, or if he doesn't trash it he leaves the house and some neighbor trashes it and rips out everything in the house. The average sub-prime loan, when you force someone out of their house and sell it, you get back 1 quarter of the value of the house now. At the beginning people assumed it could never be less than 80 percent. Now it's 1 quarter. Then there are other more complicated things that can go wrong which I'm going to skip over. So let's just see what happens now with housing. So what is it that's happening with housing? If you look at people underwater, why are people defaulting on their houses? It's because they're underwater. So here is for every different kind of mortgage, starting at sub-prime and going down to prime. These are except government loans. This is the fraction of people who default every month, not every year, and here's their loan to value. So how did I figure out the loan to value? I had to look at all the original loans. I did this house by house, or Ellington, my hedge fund, actually the guys there who were former students here, they actually figured all this out. They went house by house. They got what the loan sizes were on all the houses, and then using the Shiller index they know what the house was bought for, and assuming the zip code index dropped by 20 percent they figured every house in the index went down by 20 percent, so they could get the current value of the house. So this is the ratio of the loan to the current value of the house. Current combined loan to value ratio. So 140 means the loans all together, first and second loans are 140 percent of what they estimate the value of the house is. So look at what happens. If you're sub-prime and you've got that--I can't see my--this is--140's over here somewhere, right? You're defaulting more than 6 percent a month. If you're 160 you're defaulting at 8 percent. Every month 8 percent of those people are becoming serious delinquent and probably will never repay; 8 percent a month. In one year they're all going to be gone. So you can see this is shockingly sensitive to loan to value. It's not that people are defaulting because they lost their jobs. They're defaulting because it's not worth it for them to pay. They're not stupid. Why should they pay 160,000 when the house is only worth 100,000? It's just how can they, you know, times are tough. What are they going to do, tell their children, well, we can't feed you? You can't go to school, because daddy and mommy have to pay this thing where we don't really have to pay it? They're not going to do it. So somehow, I couldn't convince Larry Summers of this, I tried hard. I wrote an Op-Ed in The New York Times in October of 2008. I wrote another one in 7, October. No, a year ago. What are we talking about, October of 2008 then March of 2009, saying that the only way to save the housing market was to write down principal. Now, writing down principal means saying, if the loan is 160,000, maybe the house used to be 200,000, the house is only 100,000 now. You just say, "We're writing off 80,000 of the loan. It's now only 80,000 that the homeowner owes." Now, who's going to pay for the lost 80,000? I say, nobody has to pay for it. The government doesn't have to pay a penny. The bond holder, the lender would be better off writing down the loan to 80,000 than throwing the guy out of the house and getting 40,000 in the end, because once the loan is written down to 80,000 the homeowner now has 20,000 of equity in the house. He'll either work hard to fix it up and spruce it up and sell it for 100,000, or he'll actually pay the 80,000. Either way the lender is going to get 80,000, not 40,000. So this is a win-win as I called it in the editorial with Susan Koniak, a coauthor, a law professor at BU. It's a win-win situation and it's not happening. And it's not happening because the loans are all in the hands of the servicers. So remember I said there was this big pool with all the loans in them and then there were the bonds. And so the bond holders, these are the people who'd like to see the principal written down, but the bond holders don't know who the homeowners are and aren't legally allowed to talk to them. There's a servicer in the middle who's a big bank who's writing the letter saying pay up, and if they pay up they distribute the money to the bond holders. If they don't pay up the servicer throws them out of the house. The servicer, the big bank doesn't own the loans. They're getting paid a percentage, like .5 percent of the principal, so they have no incentive to write down these loans. If they write down the loan in half they lose half their fee. If they write down the loan to 80,000 and then the guy sells the house they don't service the house anymore. They lose all their fees. Instead, Obama, thanks to my classmate Larry Summers and all his other advisors, they've given these servicers license not to write down any loans, but to pretend that they're writing down the interest on the loans. Now, that would be great, and that's actually what's happening. The servicers are basically not even kicking the people out of their houses. So these people are not paying anything now. There are millions of them not paying anything still living in their houses. In a year or two they're going to get thrown out, but of course they're not going to pay. This is the ideal situation for the servicer because he's still collecting his fee, the homeowners can't sell, they don't want to leave because they're not paying anything, and the bondholders are getting screwed. So it's a catastrophe. And finally, after a year, if you read the Op-Ed's in The New York Times and the The Wall Street Journal, in the last week or two they have been deluged with people saying, "Why aren't they writing down principal?" So this is something that a year or two ago I already advocated. Anyone with any common sense would have seen that was what was inevitably going to happen and we didn't do anything about it. So I've got one more minute to finish. So what should we do about the leverage cycle? Well, the thing to do about the leverage cycle is to reverse the three bad things that happen in a leverage cycle. The first one was that there was too little--the most important one is leverage collapse. So the Fed has to go and increase leverage. So it used to be 30 to 1 or 20 to 1 now it's close to 1 to 1 on many assets, although it's gone up a little bit. So the Fed has actually done something about this. What does it have to do? Not lend at lower interest. The Fed cut the interest rate to 0 and said, "Look how great we are." Well, that did nothing practically. The reason the Fed has cut the interest rate to zero is to give money to the big banks because the banks have to pay depositors like you and me. Now, on your checking account or savings account you're getting zero practically because the Fed lowered the interest rate to 0. That means the banks make money because they don't have to waste any money giving it to their depositors. That's the reason why the interest rate went down to 0, and they try to dupe the public into thinking it's because it's a Keynesian stimulus. It's not stimulating anything basically. What you have to do is lend with less collateral and the banks aren't willing to do it. The Fed has go around the banks and lend with less collateral, which I'm running out of time so I can't explain how it's actually done that and that's one of the big reasons leverage is starting to go up. Secondly, you have to replace some of the natural buyers who have gone out of business, the ones at the top who are doing all the buying. Without them the price is going to be worth much less. The government is going to have to do some buying. So through the PPIP program and other things it is doing some of that. And then finally the first thing, the most important thing, the crisis began with housing. Housing is the first thing you have to do to lessen the instability and the uncertainty in the economy. It's now started with housing and it spread to other people who are under water. That's where all the uncertainty comes from. So we have to straighten out who's going to go out of business and who's not going to go out of business. We have to write down principal of the homes. That's the way to reduce that uncertainty. And in the long run we have to prevent the next leverage cycle by never letting leverage get so high. So we have to keep the data and we have to prevent people from asking for so little margins.
Quantitative_Finance_by_Yale_University	16_Backward_Induction_and_Optimal_Stopping_Times.txt	Prof: We're now at the stage where we're considering the implications of uncertainty, so I hope that the subtlety, and surprise element of the class, will gradually pick up without increasing the difficulty. The complexity will pick up a little bit, but not the difficulty. It's just you'll have to keep a few more things in your head, but the mathematics isn't any harder. So we ended last time talking about default and inferring default probabilities, and so I just want to finish off that discussion. So suppose that at any stage of the tree, you know, lots of things can happen in the world. We're always going to model the uncertainty in the future by a tree with different things happening, and at each of these nodes people are going to have a discount rate. So maybe it'll be r equals 20 percent, and here r could equal 15 percent, something like that, and we want to add to this the possibility that there's default. So if we add the possibility of default, and these things keep going and maybe there are payoffs at the end or payoffs along the way. If at any point in the tree like this one we add a new possibility, which is the default possibility, so this happens-- by the way, when do people default? They never default before they have to make a payment. So when do they default, exactly when they're supposed to make a payment. So suppose that this guy is going to default here when he's going to make a payment. At every possible scenario he would default there. So we've got a very simple model of default, so not a very realistic one where the guy defaults in all of these following scenarios. So something's just bad. Once he's gotten here you know that he's not going to make the payment the next period. We further assume that not only does he default there, but he defaults on everything thereafter. So the payoff is just going to be 0 here. So this is going to be--originally we had probabilities p_1, p_2, p_3, let's say for the probabilities, now we're going to have probabilities d for default and then 1 - d times all of these, right? So essentially what have we done? We've simply replaced in our calculation of payoffs and present values, we've simply replaced these possibilities with probability p_1, p_2, p_3. We added another possibility, but the payoffs are 0 here. Nothing's going to happen from then on except 0, and we said that happened with probability d, which means presumably, all of these have to be scaled down by that so they still add up to 1. So essentially the point I'm trying to make is that default that leads to 0 payoffs thereafter is just like discounting more. Why is that? Because whatever calculation you did for the value here of what the bond could possibly be worth there is-- it's all the same numbers as there were before except we've multiplied it by 1 - d, so it's the same thing. So instead of going 1 over 1 r times future payoffs, that's no default value, so that times future payoffs. Now we've got default value under this special kind of default is going to be 1 - d times 1 over 1 r times the same future payoffs. I could rewrite 1 - d as 1 over 1 s or something, and so then I really have just 1 over 1 r times 1 over 1 s. So that's just 1 over (1 r s r s). So that's going to equal 1 over (1 r s r s) times future values. So the effect of this special kind of default--we just get 0 thereafter. The guy decides after this payment, "I'm not going to make any more payments. I'm defaulting from then on." That's the same thing when valuing the future payoffs, it's the same thing as instead of discounting by r, discounting by r s with a little bit r times s. If r and s are small numbers this [r times s] is probably quite a small number. So default probabilities get mapped into spreads they're called. They way to evaluate it is just you just multiply it by 1 - d, which is the same thing as discounting by a higher number, and that higher number is almost the same. It's very close to r d, as a matter of fact, because 1 - d is 1 over 1 s. If d is very small s is going to be very close to d as well. So what's the implication of this? The implication of this in a special case again where we just have no uncertainty, except we have default. So here there could be d_1, 1 - d_1 and here there could be probability of default 2 and 1 - d_2, probability of default 3,1 - d_3, and we've got interest rates r_0-- so this will be i_0, i^(F)_1, i^(F)_2. So if you knew what the interest rate was going to be today, you knew what the interest rate was going to be tomorrow, you knew what the interest rate was going to be the day after tomorrow, there's no uncertainty about interest rates, they're perfectly anticipatable, but you know that there's a probability of default each time. So in stage 1 this guy might default before making his payment here, which case you're just going to get 0. In stage 2 he might default instead of making his payment, won't pay the coupon, he'll just default, or in year 3 he might default. So what's the implication of what we just said? You can evaluate this bond, the payoffs of the bond, so let's say it pays a coupon, C, C 100 C. All right, the way you would evaluate that without default is you would just take the value of the coupon, the present value would have been--you would have done it recursively. You would have gotten P_3 = 100 C. Then you would have said P_2, you would have gone in your computer-- you would have said P_2 is 1 over (1 i^(F)_2) times 100 C. So the value here is the 100 C discounted by that forward rate, then P_1 would have been (C P_2) divided by (1 i^(F)_1). So you take the value here times that, so this is case there's no default, and P_0 would have been (C P_1) over (1 i^(F)_0). So that's how you would have done it by backward induction. But now that you know there's a chance that there's default you have to not multiply by 1 i^(F)_2. You have to multiply all these things by the probability of default. So you'd have to multiply this by, if we change colors, by 1 - d. You have to multiply this by 1 - d_2, and you'd have to multiply this by (1 - d_1) times (1 - d_2), and this by 1 -, sorry this would be 1 - d_3. This is (1 - d_3) times d_2, and this is (1 - d_1) times (1 - d_2) times (1 - d_3). So this value would be the old value you got here multiplied by 1 - d_3, multiplied by this one minus d_3. This value is what you would have gotten here, but you've already scaled it down, so multiplied by 1 - d_2 and this is 1 - d_1. So what's the upshot? So that gives you the price with default. Student: Professor? Prof: Yep? Student: When you're doing the backwards induction should you be tacking on like that or should we just take one at a time. So P_0 should be multiplied by all 3, or isn't it that you're taking whatever you get as P_1 as given and just multiply by... Prof: Well, I could have done it two ways. I could have written--so what you're suggesting is a better way would have been to say P_2, the default bond P_2 is going to be (1 - d_3) times P_3, which is also equal to P_3 because there's no default after here. The world just ends. Then P_1 is equal to (1 - d_2) times P_2, but that P_2, remember, is already (1 - d_3) times P_3. And then P_0 is going to be (1 - d_1) times (1 - d_2) times P_1, but that's equal to (1 - d_1) times (1 - d_2( times P_1, which is (1 - d_3) times P_3, right? So all right, if you go from here to here the value here's 100 C, so if P_3 is just 100 C let's leave it as 100 C. That's if the guy actually pays. So the present value would just be--oh, then you have to divide all this by 1 i_2. Sorry, this is 1 i^(F)_2. Oh, I'm making a mess of this. So usually you'll go back from here to here by discounting by the interest rate, but now we're going to have to also multiply by the probability that you default to go back here. So we get a lower number. P_2 is not just (100 C) divided by (1 i^(F)), that's the discounting, you also have to multiply by the probability of default. Then when you go back one period further you have to discount again. So I should have divided this by 1 i^(F)_1, you have to discount it, and also you have to multiply by the probability of default. But the thing you're bringing backwards is P_2, which has already taken into account the probability of default the next time. Then when you go back one step further you have to do the whole thing again divided by 1 i^(F)_0. Student: You shouldn't have a 1 - d_2 in there as well, shouldn't you just be discounting by 1 - d_1 and 0? Prof: This is P_1 not P_2. Student: You've already discounted by 1 - d_2. Prof: No, but I'm switching the Ps on you. When we go from here the value here we just calculated was going to be P_2, so here the value of P_1 taking into account default is (1 - d_2) times P_2, which already takes into account the default next time, times P_2 discounted by the interest rate here. So I've got the 1 - d_2 here. Now, when I discount back to here you're saying, "How come the d_2's showing up any more because I'm just at d_1, that's your question, right? So it doesn't show up. It's just P_0 is 1 - d_1-- oh, you're asking this, you're right, (1 - d_1)--you were right-- times P_1 divided by (1 i^(F)_0). That's right, but if I plug in for P_1, P_1 already had--that's where the d_2 came from, so P_1's got the d_2 in it. So it's (1 - d_1) times (1 - d_2) times P_2, and then P_2 had a P_3 in it. So I've got all the defaults in it. Are you with me now? So, sorry about that, so you were right, I said it wrong. So, but this isn't the point. This was supposed to be obvious. I didn't even think about it. The next step is the thing that's not obvious. Here are the potential cash flows. You're discounting them by the interest rate. You also have to discount it again by the fact that the guy might not actually pay you. So that gives you a lower present value. Yellow P_2 is less than the no default white P_2. When you discount again you're discounting the yellow P_2 by the interest rate here and also the fact that the guy might not pay. So you have to multiply by 1 - d_2 and also the fact that he might not pay, the forward rate, and you keep moving that backwards. So that was supposed to be obvious even though I made it sound complicated. What's slightly subtler is just saying the same thing backwards which is, suppose I knew all these forward rates. Suppose I had a bunch of bonds, suppose I had American bonds, coupon bonds. So the American coupon bonds are going to pay, you know, the 1-year pays a coupon C_1 and has a face of 100 and has a price Pi_1. The 2-year American bond has a coupon C_2, a face of 100, and a price of Pi_2. And let's say the 5-year has something, C_5, a face of 100 and a price Pi_5. Now from that we know that we can deduce what all the forwards are. We did that in the first class. So now suppose at the same time we have Argentina. Many Argentine sovereign bonds promise payments in dollars, by the way, they're trying to trade them internationally. So let's say we also have the Argentina bonds C-hat_1, 100, Pi-hat_1, that's the 1-year, down to the 5-year which is the Argentina C-hat_5, 100 and Pi-hat_5, its price. Now, let's suppose that Argentina could default whereas America can't. So it's quite likely that Pi-hat_1 will be less than the American Pi_1 and Pi-hat_5 is going to be less than the American Pi_5, because all these bonds might default. So if the coupons were the same, if C-hat_1 was the same as C_1 and C-hat_5 was the same as C_5 the fact that Argentina could default obviously would mean its bonds would trade less for the American ones. So the question is can you figure out the default probabilities very quickly in Argentina without having to do a lot of complicated calculations, and the answer is yes. And why is that? Because you could take this data and you could say--so we could just erase this here. We could say, assuming no default, we could explain these prices by finding, just like we did the America, the Argentine forwards, 1 i-hat_0, 1 i-hat^(F)_1 and 1 i-hat^(F)_4. So these are the Argentine forwards. Now, these forwards would be much bigger than the American forwards. Why is that? Because the prices in Argentina are so much lower. If you're assuming there is no default, assuming no default, contrary to fact, how could you explain all these very low prices? Well, you must think that in Argentina they've got very high interest rates and very high forwards, so they're discounting more and that's why they've got lower prices. And we know how to get those forwards assuming there was no default. So the trick, I'm merely pointing out now, is that if we now go back and say, ah ha, Argentina doesn't have different forwards because anyone in Argentina-- the bonds are denominated in dollars precisely so that people can be crossover investors. An American can put his money in Argentina. An Argentine can put his money in America, so you can move your money to either place. So it must be that the forward rates can't be different. If you knew for sure you were going to get paid in Argentina you'd have to have the same forward rates in America. So the reason these forward rates are higher is because there's a chance of default. So what is the chance of default? So I claim the chance of default is, and I was supposedly--you're supposed to realize this now. If I'd been clearer before you would see where I'm going. The chance of default is incredibly simple to find out. So it's 1 - d_t = what? Student: > Prof: But in terms of forwards is what? It's not Pi--this Pi, this isn't the 0 price. This is the big price of the bonds. So it's not Pi-hat_t over Pi_t. What is it though? Student: The ratio of forwards? Student: Pi_t - > Prof: This is going to be a bigger number than that, and in fact that ratio is the default probability. So this is assuming, remember, that if the Argentine bond defaults at this period, say, it's never going to pay anything after that. You're going to get 0 pay off and all the other Argentine bonds will also default. I claim that this [note: meaning, (1 - d_t = (1 i^(F)_t-1) over (1 i-hat^(F)_t-1)) ] is going to be the easy way of getting the default probability. And so the differences in the forwards is just explained by the default probabilities and so the extra Argentine interest, if this [the denominator] is a higher number than that [the numerator], 1 - d is approximately 1 over (1 d), and so it's basically if all the numbers i and d are small then i-hat^(F)_t - 1 is approximately i^(F)_t - 1, the American one, plus this default rate in Argentina. So I should probably have a hat because I'm referring to Argentina with the hat. So why is that true. I just argued it. How could that possibly be true? So you see what I'm claiming that you have now a very simple algorithm for finding out, inferring what Argentina default rates are. Again, I'm making a special assumption that when Argentina defaults you get nothing. That really isn't the case. There's some huge convention that happens and all the countries get together they defaulted on. They've got some big meeting, and someone like Brady invents some idea where they'll owe less and they will be a writing down of principal, by the way. So whenever this happens there is recovery after a writing down of principal. So what all the countries do is they say, "Okay, we know that you can't pay all that you owe us. We'll settle for half of it. We'll write down the principal and we'll hold you to that half, or to a third of it. So this is one of the things we curiously haven't done in America where all these homeowners can't pay and we don't write down their principal. We just throw them out of their houses. But anyway, let's say you wrote the principal down to 0 in that special case. You could easily infer from the price of the Argentine bonds what the default probabilities were, and by this formula. And so the question is, why is that true? We know how to calculate the forwards in America given the American data. That's was one of the first things we did in class. We said that every American company in the whole country, financial company, is doing that. Everybody has those forwards calculated. Now, if you're given the Argentine data, which is, after all, just coupons and the prices of the bonds, you could find Argentine forwards assuming there's no default. But there is default, so it must be that they have access to the American interest rates in forwards, but the Argentine bond might default. Do you see what we did when we did this calculation? The difference between the backward induction in America from here to here was just discounting by the American forward-- to go to Argentina we had to discount by the American forward and multiply by 1 - d, so discounting it again. So all I'm saying is that in the U.S. when we went backwards we just discounted by this thing. In Argentina when you go backwards you have to discount by this thing, so those things have to be the same. So the Argentinian discount is like taking the-- I hope I haven't got the thing--so the American forwards are going to be less than the Argentine forwards. It's going to be like that. So that's it. There's nothing else to show except that whenever you're going backwards here you're discounting-- remember, you're discounting by the interest rate times the probability that you're actually going to pay off, so that's what it is in Argentina. Hang on. I hope I haven't inverted one of these, yeah, exactly. So if you write 1 - d times the American thing in the denominator, so as I said, to do the discounting in Argentina at every step from going back from here to here what did we do in Argentina? We simply took 1 - d-hat, that was the default rate--hat--in Argentina, and discounted it at the American forward. So that's what I did here. So if I take 1 - d-hat, this is multiplied by 1, so I take 1 - d-hat^( )multiplied by 1 over this. I just get one over the Argentine discount, and that's how we calculated--that's how we went backwards with our recursion just taking the interest rate, the discount 1 over (1 i) times (1 - d) and that's how we discounted going backwards. And so therefore in Argentina if you're forgetting that there's default and you're just thinking you have to discount at the right rate and you're getting this discount you're getting this number, but in reality you should have been taking this divided by that. So therefore figuring out this and knowing that tells you what this has to be. So it's extremely simple to deduce what the market thinks Argentinian default probabilities are year by year if you make the added assumption that once they default they default completely. And if you think you're only going to get a little bit back, well then the calculation won't change that much. Yeah? Student: Can we also do it by using the price of 0s? Prof: Yeah, so you could also do it by using the price of 0s, but to me the best thing is, the easiest thing is using the forwards, but you can also do it by 0s. So that's all I wanted to say. As I said, the one last thing to say is that if these numbers are all small then 1 over 1 - d--or, 1 - d is approximately equal to 1 over (1 d). If d is very small those are practically the same things. Then if you multiply 1 over (1 d) by 1 over (1 i) it's almost 1 over (1 d i), so it's almost this thing. It's not quite true, literally true, but it's very close to say that the gap between Argentinian forwards and American forwards is just the default probability in Argentina, and that reason is why it's called a default spread. You just add some spread to the interest rate. You can guess by the spread what the probability of default is. If it's 8 percent interest there and 3 percent interest here somebody must think the probability of default is 5 percent there. That's it. So let's now move to a tree where you have to make decisions. So I'm going to now describe the method of backward induction which occurs over and over and over again, and we've used it a couple of times, but not in its subtlest form, so backward induction. Now, who first invested the idea of backward induction? Well, the first person who spelled it out formally was Zermelo in 1910, I think, that's within a couple of years, a famous mathematician, Fraenkel-Zermelo Axioms. And he proved that chess--that there's an optimal strategy in chess by backward induction. So, for example, let's take a game. We always are on a tree, but now we're going to use a slightly extended definition of a tree. A tree is going to look like this. So it's a root, a finite number of branches from every--I don't want to formally define a tree. You know what it sort of looks like, and there's no reason why the number of branches has to be two or even has to be the same from every point. But the reason we're going to extend it is, the node is going to be described by who moves. So let's say white is moving here and black is moving here. Now, let's say the outcomes are a win for white, a win for black, a draw, or a draw. So the question is, so it's a two-move chess game, white moves first up or down, and then after white moves black moves up or down and then the game ends. And depending on where, position you reach either it's a win for white, a win for black, or a draw. So what should white do? Assuming that black is a smart player what should she do? So what did Zermelo do? He said not only there is an optimal strategy, but you know what the outcome should be with rational players. So Zermelo said if white goes up then black is clearly going to go down and win the game. So white ought to be thinking here, if I go up, the game, although it won't end for another period, it's already lost. So the value of the game is already 0. So this method of backward induction attaches the value. Here we have values at the end, and so to figure out what the right thing to do is by backward induction you can propagate the values backwards. If black makes the right choice here the payoff is black gets the negative of white, so the right choices here are black could get negative 1 or could get 0, so black clearly wants to get 0. So black could win the game by moving down, so black surely will move down. So I should think of the game as already lost here and pretend that I had a shorter tree with the final valuation of zero at this node. Similarly, if white goes down it doesn't matter what black does the game is going to be drawn. So white should think to himself the game is already a draw if I go down. And now white has an easy choice, do I want to move to a loss or do I want to move a draw. So I could just pick a move for black here. Clearly white is going to go down and therefore with correct play the game is a draw. So by backward induction you figure out the correct play. Now, why is this surprising? Because chess has an incredibly big tree, not an infinite tree, there are all these rules that keep it finite. If you reach to the same position three times it's considered a draw. If you make something like 50 moves in a row without a pawn moving it's a draw. Whatever those rules are--I used to play chess quite a bit. I've even forgotten. But whatever those rules are they're designed to make the game finite, so the tree is finite. And so it's impossible to see the whole tree, and how should you know what to do at the beginning? Well, you don't know what to do at the beginning until you know what black's going to do afterwards, and so what could happen later in the tree. But if you were fast enough to put the whole thing on a computer you could figure out what to do at the beginning, because your best move at the beginning depends on what you think black is going to do next, which depends on what he thinks you're going to do after that, which depends on what you think he'll do after that. But if the tree ends you can always go backward from the end to the beginning and figure out what to do at the very beginning. So this is a familiar argument to all of you, I think. It was a beautiful argument in chess in 1910 and then it was anticipated--I mean, in mathematics in 1910. The chess players, of course, all knew about it, so Steinitz who was a world champion from when to when, something like 1870 or so to, or 1880 let's say to let's see, 19,21, to 1894. I think he was world champion from then to there. Lasker became the champion then. So he wrote a bunch of books and stuff in which he said there's a backward induction value to chess, but since we can't figure that out on general principles you can tell by looking at the configuration of pieces what the right possible move is, and so you can have positional values, so I'll do that, and then you can have the backward induction values. So for instance a positional value might tell you that having doubled pawns is a bad thing, having control of the center's a good thing and you add up all those pluses and minuses and you get these positional values. And so he said if you've got the right positional algorithm, right positional understanding, your positional sense of what to do, you only need to analyze one move deep. You can figure out what the best position's going to be and move that way, and if you really understand the game properly that positional thinking, that strategic thinking, so it's called strategic thinking, is going to give you the same decision as the exhaustive analysis of all the possibilities which was tactical thinking, so the two should amount to the same thing. Now, in fact, people can't do the full tactical thing and also they don't have the full strategic understanding either, so they kind of mix strategy and tactics and that's what makes the game interesting. So no one has ever written this, but I'm sure there's an interesting study to be made about what games are interesting and they must be the kinds of games where there's always a mixture of strategy and tactics. In game theory, as we describe it in economics, there's no such thing as strategy. All this is out. It's all just backward induction, which is what I'm teaching you. So the way computers play chess, incidentally, is--and the guy who invented this is Shannon, so he's a famous professor of information systems, so an engineering professor. So he said, well, you can't look at the whole tree which is too long in chess, so what you should do--so all this extends way further. Maybe you can only look two moves deep. So what Shannon recommended is look as far as you can put in your computer, apply some positional thinking to evaluate these positions at the pseudo end of the tree. So it's really not a win for white. Let's just pretend White's so far ahead that we'll call it a win, and a loss, and a draw, and a draw. That's just by looking at positional values. And then having assigned those terminal nodes values, now by backward induction you can figure out what the value is here and exactly what the right first move to make is. And after white's move black will come here, black can now look two moves deep, so black's going to look from here all the way down here. He's going to do his positional evaluator to these nodes and try and figure out what they're worth and then do backward induction to figure out what his right move is. Anyway, that's basically the idea of all chess algorithms, and then they've gotten refined by saying--wait a minute, there are lots of refinements. So I used to very interested in this. I don't think I'll talk more about it unless anyone wants to ask me something. So there's the origin of backward induction, Zermelo's proof and it's obviously a big deal in chess and the chess players all knew about it before Zermelo, but they didn't write anything down as formal as Zermelo. So how does this apply to everything we do in economics? Well, I want to give a series of examples culminating in market examples, but starting off a little far from life. So the first one I want to give is the red and the black. So these are just two games. This is the first one I invented ten years ago, but I don't think they're--anyway, I think they aren't that original. I thought they were when I invented them. But anyway, so the red and the black works like this. There's a deck of cards, 52 cards, a deck of 52 cards, so half of them are--26 red, right, and 26 black, which is all I care about the cards. And someone offers you a game and they say, okay, the deck is upside down, they've been shuffled, you can turn over a card and if it's black I'll pay you 1 dollar. If it's red you have to pay me 1 dollar. So I'm offering you this chance to play this game and of course you can quit whenever you want to. I can't keep forcing you to play, so anytime you want to you can quit. So that's the game, can stop whenever you want. And once you draw the card you throw it away. And so all these examples are going to be examples of stopping games and you'll see in economics that when you prepay on a mortgage or when you call a bond you're stopping the thing, the contract's ending. Life is going on, but that contract is ending, so want to know, when's the right time to take an action like that? So red and black is a simple game like that where you turn over a card. If it's black, you're in the black you win 1 dollar. If it's red you lose 1 dollar and you can stop whenever you want. So you have an option, so call this an option, and most people totally underestimate the value of options. So let's just figure out how to figure out the optimal thing to do. What would you do in this game? Would you play if I gave you the chance to play? I think I did this on the very first day. Yes, you're about to say something? Your hand twitched. Student: I was going to say we have deceasing marginal utility as well, so assuming we have > you wouldn't play the game because you would derive less utility from winning 1 dollar than you would > in magnitude that the loss > Prof: So I'm going to now disagree with what you said, but it's very interesting what he said. He said, look, if you draw a card at the beginning it's 50/50 whether you're going to win or not. If you win you get 1 dollar. If you lose you lose 1 dollar, 50/50 chance. If you're a little bit afraid, if a 1 dollar loss is more important to you than a 1 dollar gain right away it's not very good odds, I mean, it's barely even, and if you're a little bit risk averse and it's barely even you shouldn't play. But now, is it really barely even, this game? Yep. Student: Well, I mean, I think you should play because even if you get the first 26 red at that point just go to the end and you haven't lost anything except the time you've spent playing the game. You might as well play on the off chance that you'll get some blacks ones first. Prof: Right, so you can't possibly lose if you play this right. You can always go to the very end of the deck. We're ignoring a good point. We're ignoring your utility of time, so you can always go to the end of the deck and assure yourself of 0. So this is actually a pretty valuable option to be able to stop like he says. If the first one's black you could stop and then you've won 1 dollar. If a whole bunch of them are red and you lose, well, you can always go to the end of the deck and get zero. So you're never going to lose and you have a chance of winning. So obviously you should play. Even if you are risk averse you should play, but now the question is can we tell exactly. Suppose you're risk neutral? How many dollars do you expect to win would you guess? Yep? Student: 0. Prof: You'd expect to get 0. Now he just made an argument that you should expect more than 0, because for instance he said take this strategy. Pick a card. If it's black you win 1 dollar, quit. You're 1 dollar ahead. So at 50 percent of the time you're plus 1 dollar. If it's red the first time just close your eyes and play to the end of the game and you're going to get 0 because you're going to win 26 times and lose 26 times. So that's equal to .5. So there's one strategy that gets you 50 cents on average. You can't lose and half the time you'll get 1 dollar, but that may not be the best strategy. Student: You can play a bunch of times and at worst you'll break even and at best you could get all 26 black. Prof: Right. So he's saying this isn't ambitious enough. This surely gets a half a dollar, but you could do much better. Like, let's just wait. The first time suppose you get 1 dollar. Suppose you get black the first time, so that gives you 1 dollar. Now, the trouble is the deck is starting to turn against you. Now it's 25 blacks and 26 reds. So what would you do then? Student: I'd stop. Prof: You'd stop or keep going? Well, the deck is against you, so now your very next draw is unfavorable. And, by the way, playing to the end of the deck is going to lose you 1 dollar because there are 25 black and 26 red, so this argument that if you just play to the end of the deck you'll break even it's not true after you've already taken a black one out, so you could lose it. From then on you're starting to run a little bit of a risk. So we're ignoring risk aversion. We're just caring about expected dollars. The fact is the deck is against you, so should you play or not? And so first reaction is hell no, the deck's against me. Why should I draw another card? But you still have the option of going to the end of the deck, so the most you could lose is 1 dollar if you went all the way to the end of the deck, and who knows, maybe you'll get a run of more black cards in the beginning and make a lot more than 1 dollar. So you should choose another card. In which case if you get black again-- if you got red on the next card you'd be breaking even, but now it's 25/25 and by the previous argument it's obvious you should pick another one because the worst you can do is break even from then. But what if you got two blacks in a row? Well, now the deck is way against you. It's 26 red and 24 black, so now you've only got a 48 percent chance of drawing a black one the next time. The deck is going further against you. Should you really draw another card? It's more likely to be red. Well, the answer is yes. And suppose you got a black one again, meaning you're three up, and now the deck is 26/23. Sorry, I went the other way, 26 red, 23 black. It's getting further and further against you. Should you draw another card? Well, what you've got is you've got a bad deck working against you, but you've got this option working in favor of you. So the question is just how valuable is the option. And like I said, people always underestimate the value of options. And so--okay, go ahead. Student: Don't you want to play until your lose-condition is either balanced out or worse than your win condition? Prof: Yes, but what is that condition? Student: Thirteen blacks > Prof: If you got ten blacks in a row you would keep drawing blacks, is that what you were saying? Student: Well, I mean, at that point if you assume that that's all > , assuming that you pick another red and then play out the end of the game you could lose, it would be... Prof: Thirteen more. So you're saying you want to keep drawing blacks until if you play to the end of the deck you would lose as much as you'd won up until that point. So you want to never run the risk of losing more. But you see, that strategy would get you to quit after the first one. After the first black if you ran to the end of the--your strategy doesn't make sense. By going to the end of the deck you're always going to undo everything you've won until that point, because you'll be zero no matter what if you go to the end of the deck. Yep? Student: Shouldn't you quit whenever you have 1 dollar, because say if you have more black cards than red cards then the number of black cards left in the... Prof: Deck is less... Student: Is lower than the number of red cards left in the deck, so you should quit whenever you have 1 dollar. Prof: No. So he's saying just the commonsensical thing. After you draw one black card he would quit because now the deck is against you. It's 25 red [correction: 26 red] and only 25 black. The deck's against you. Why go on and play against an unfavorable deck? You've got your dollar, be satisfied and quit. That's his recommendation, but that's wrong and it's because you're doing what everybody does. You underestimate the option. The option is incredibly valuable here and now I just want to show how to compute what your optimal strategy is, and I think you'll be surprised. You should keep drawing, not three times--if you got a fourth black card, so you've already made 4 dollars. It's a sunk cost. You've got this horrible deck. It's 26,22. Should you keep playing? Yes you should. Yes you can. If you get a fifth black card in a row you're up 5 dollars. The deck is horribly against you. Should you keep playing? Yes you should. So anyway, it's really shocking, I think. So now let's just see how to compute this out so that we don't have to argue about it. It's just a little bit of mathematics and you just see how surprising this calculation is. So how would you do it? Well, the key is to figure out how to put it into a tree. So I'm not going to draw the picture because it gets too complicated, but basically what you want to know is how valuable-- remember the tree in backward induction? It was, take the thing at the end and then figure out by propagating the values backwards. So if I have black and red here, and I've got 1 black card and no red cards, the value to me of that is what? I'm going to win 1 dollar for sure. If there's only 1 black card left in the deck and no red cards I know I'm going to play to the end and get 1 dollar, and obviously the value of 2 black cards and no red cards is 2 dollars etcetera. And I also know, what's the value to me of no black cards? You know at every stage what's left in the deck because you've seen what came up before. So if you're at the very end of the deck with no black cards and 1 red card what's the value of that position to you? Student: 0. Prof: 0, not minus 1,0, why is that? Because you're going to quit, you're not going to play and that's the critical step, seeing that this is 0. Someone said minus 1. That difference between 0 and minus 1, that's the whole heart of the thing. So 0 and 2, the value of that is also 0. You're just going to quit. So what in general is the value? What is the value of V if there are B black cards and R red cards what's the value to you? Well, a crucial step is that you can choose to quit by not playing. So this is the value from then on to you. So B black cards left, R red cards left. You could get 0 by quitting, or you could draw a card. Now, what happens to you if you draw a card? What happens to you if you draw a card? Well, with probability B over (B R) you win 1 dollar, right, but then you move on to the new deck. So what do I write V here, V of B - 1 and R, but with probability R over (B R), you drew a red card, so that's minus 1, but then you move onto a deck that has 1 less red card, and that's it. You either decide to stop or if you've decided to draw a card you know what the chances of getting a black card are. You look at the black cards, 26. I'm down there. It's 21 out of 47. It sounds horrible, 21 out of 47, I win 1 dollar. 26 out of 47 I lose 1 dollar. So the immediate draw is terrible, but if I get a black card I move to this situation, and if I get a red card I move to this situation. So do you agree with me that that's what the value's going to be? Are there any questions? This is a critical formula, a critical spot. Does everyone--Sophia you're now in trouble. Somebody came and said hello to me after class and now I know a name, so does this formula make sense? Student: Yes. Prof: Kathleen, yes? Is it Katherine or Kathleen? Student: Katherine. Prof: Katherine, okay. Katherine, so you agree with this formula, right? But this formula's the key. It's just like our tree. Once you know what the values are down here you can always go backwards and figure out the value here. So what is the tree? The tree is going to have--well, I'm going I'm going to do it on a computer. So now we can just do this on a computer. I hope I don't have to do that. So you have this, by the way, it's on the web. Oh no! Why are all these, oh okay, there aren't question marks. So here it is. So you can see that on this, I can do it with this, on this thing it's--by the way, I did my own spreadsheet and an undergraduate last year thought it was so messy that she just redid it for me. So this is her doing. It looks much better than I did. So anyway, here are the number of cards. This is what the number of black cards left. This is the number of red cards left, and then when you go to the corresponding coordinate like this one, this is the value of the game when you have 1 black card and 1 red card. Even though there's an even deck it's a favorable game to you. Why is that? Because you draw the first card, if it's black, which happens with probability 50 percent, you win 1 dollar. So you've got half a dollar. If it's red, which happens with 50 percent probability, you draw the next one and so you end up with 0. And by the way, if you got a black the first time, obviously you stop. So you get 50 percent chance of 1 dollar and stopping or 50 percent chance of going to the end and getting nothing, so it's value of 50 percent, but that's a bad way of calculating that number. She's got a much better way of calculating it. So what she said is if you had no red cards and only black cards the value is to go to the end of the deck and just win them all. So if you've got only red cards in the deck and the top line is no black cards obviously you should quit right away. So we've got this first thing trivially done. Now, how do you figure out this thing? Well, if you look at the formula up there it's just the formula you wrote, we wrote, which is you could quit if you wanted to. So you have to take the max of 0, but if you go on and draw, I can't read what's written there, if you go on and draw there's going to be the probability of red, this is the probability of getting a red over the total number of cards times losing 1 dollar, plus what happens is you then move. If you drew red then you go to--what did she do? Student: > the value. Prof: C 4, oh C 4 is here, right. So sorry, I was getting confused with the cards. So C 4 is this squared. That's the value in here. So C 4 says if you draw a red card the first time, it happens with this probability, the number of reds over the total number of cards, you lose 1 dollar and then you move to the position C 4, which is 1 back here, the one where you've got 1 less red card and just a black card left. On the other hand, you could have drawn the first time, not the red one but the black one divided by the total number of cards, and you would have won 1 dollar, but then you would have moved to the position where you had 1 less black card, which is D 3, which is up here. So instead of doing the whole game, she says, half the time you win, but then you move over to here and get that value. Half the time you lose, and then you lose 1 dollar, and then you move over to here. So she's done that. That same formula appears in every box, so all you had to do was just copy it. It's max of 0, and then the chance that you're going to lose 1 dollar, which is the number here of reds over the totals times minus 1 dollar and then moving over to here. Or you could get the probability of winning 1 dollar with the black cards. So you win 1 dollar, but then you move up to here. So it's very simple. So she's done it. And notice that although the deck is even at 1 card each, so it sounds like a fair game, it's not. It's a favorable game because you have an option, so you all understood that, but the thing is the option is much more valuable than you think. So let's see what the value of the game is. It's when you had 26 black cards and 26 red cards, so we have to go way over to here. Sorry. Where am I going? That's not the right answer. Here it is, 26,26, the value of the game is 2.6 dollars, not just half a dollar. You wanted to quit, wherever you are, at half a dollar. He's not looking up anymore. So he wanted to quit after the first draw, but it's much better than that. So now what the shocking thing, though, is, so this means with 26,26 you have a favorable game and you should draw. If you didn't draw it'd be worth 0. So obviously you're supposed to draw here. If you get a black card you're going to go here. So here you're down. You've gotten a card and you've got one more, you know, it wasn't that likely you were going to get black, but if you did--50 percent chance you go here. So you win 1 dollar and now you're at this position. Now, if you're supposed to stop at that point, what would you have done? If you were supposed to stop at that point you would have had value 0. So the fact that that number is positive is telling you even when the deck is against you, 25, you can't see it, it's 25 blacks and still 26 reds it's still a favorable game. You should draw a card and if by some miracle you won 1 dollar you would have moved to here. So now you're 26 red and 24 black, but the game is still favorable. You should draw another card, and if you win again you're here. Now you've gone one, two, three times you've drawn blacks. You should still draw another one. Four times getting blacks you should still draw another one. Five consecutive black draws the deck is now 26 against you and 21 in your favor. You should draw again. The game is still slightly favorable, and it just seems shocking that could be the case, but this is the proof that it's the case. So anyway, that illustrates the power of the option of being able to continue. And if you work, you're going to work out low numbers 2 and 3 in the homework, and then you'll see very clearly why it is that this option is just so powerful. It's uncannily strong. So are there any questions about this? Yes? Student: I'm still a little bit confused. I know that the option value is positive, but the probability actually is a little bit against you. So especially after five wins why do you want another draw, because yes, the option value is a little bit positive, but the probability is still against you? Prof: This isn't the option value. This is the value of playing. So it says the option value is more important than the fact that the cards are against you. So he's asking, my TA is asking, how could it possibly be that the deck is now 26 red and 21 black totally against you and according to this calculation you should still draw? He can't see the advantage in drawing because the odds are pretty high you're going to get a red card next time. Well, that's true. You're going to get a red card next time, but the thing is your downside is limited. Here's a way of thinking about it. You're up 5 cards. You can never lose more than 5 dollars from that point on because you can always play to the end of the deck, right, which means you lose the five back that you already won. So there's a downside--the downside of losing is limited here. On the other hand there's a big upside to you. You might by some miracle draw 10 consecutive black ones at that point and then you could quit. So your upside is much bigger than your downside. Now, the upside is less probable than the downside so it's not so obvious which is going to be bigger. Is the option value more important or is the fact that the deck is against you more important? It would be impossible to intuit the answer, but we don't have to intuit it. We just proved it. We solved for the optimal strategy. Are there any other questions? It's quite amazing, right, this--I'm going to pause for a second. Yes? Student: How do you calculate the profit at a given position? Prof: That's what we just did. So let's try it again. Student: It may not be a total profit. Prof: So what we did, this number V is the expected profit you're going to make if you start with B black cards and R red cards. And now the intuitive mind figures that if B is less than R you've got an unfavorable deck and you should just quit, but that's not the case. You can figure out what the profit is, how, by doing backward induction. You couldn't tell what the value of this bond is here with all these defaults and stuff until you started computing backwards until you got to here, so the same way here. We know at the edges it's very obvious when all the cards are black or all the cards are red, that's up here, it's obvious what the value is. But if you have a position here you can figure out what the value is of being in that position of 1 and 1. You could quit and be 0, or you could say, what are my chances of getting a black card and winning 1 dollar? If I get a black card then I move to this position, but I already figured out this position's value because I'm doing backward induction, right? That's got one less--sorry, if I draw a black card I go this way. It's got 1 less black card and we already know that value of that position is 0. So to figure out the value of this position I know the chance of getting a black card, then I'm going to end up in that position which is value 0. I won't draw any more. Or I'm going to get a red card and then I'm going to move to this position over here whose value I've already computed. So that gives me the value here. How do I figure out the value here? Well, it's now 2 reds and 1 black. So this looks really bad. Actually this position, the value of this I happen to know is 0. How could it be, with 2 red cards and only 1 black card actually the value of the position is 0? Well, what do I do? The chances of getting a black card the first time are 1 third. So V of (1,2) is going to be 1 third of getting a black card plus then I go to here which is no black cards left and just red cards, which obviously is 0, plus 2 thirds. 2 thirds of the time I get a red card and lose 1 dollar, but then I'm going to move to here with 1 red card where I have V of (1 and 1), which I've already figured out the answer to, right? This was V of (1 and 1) has value a half. So therefore V of (1 and 2) is going to be 2 thirds times minus 1 V of (1,2), right? I just drew a black card so it's no longer--no, I drew a red card, so it's (1 and 1). So I started with 1 black and 2 reds, 1 third of the time I get a black card, 2 thirds of the times I get a red card, but after getting the red card the position is now 1 black and 1 red. The red card disappeared. That's over here. So I get a black card, I move to here. If I get a red card I move to there, but V of (1,1) is worth a half, so that's equal to 1 third times (1 0) 2 thirds times (minus 1 1 half), which equals 1 third - 1 third which equals 0. So starting at this point you've got 1 red card and 2 black cards. It looks horrible to pick a card, 2 thirds of the time you're going to get the wrong card, but you still have a position that's actually equal in value, because if you get that black card which wins you stop. If you get a red card you're now in a position that's equal deck and that's favorable for you, because if you get another black card you stop, and if you get a red card you keep playing until the end. So that's it. So how can you do this by backward induction? You have the stuff on the edges and then you solve for all these things along the side here, and having done that now I can solve for this one because I've got up and to the left. Now I do that row and then I can do this whole row, and then I can just by backward induction do the whole thing, and the computer does that instantly. So it figures out the value of every single node and it's shocking what the answer is. So are there any other questions about this? Ben, do you-- so... Student: Yeah, I figured it out. I tell you initially I'm thinking about it. Well, maybe this value is actually an option value. For example if you choose to play this game and after you win or you lose then you'll get an option to continue the game, and so I separated that option value to this. Prof: Well, that is your option. The option is always to keep playing or to stop, but the value I wrote down is the value of the game to you, of being able to play the whole game however you want. So now let's do another example. Yes? Student: Would you call somebody rational who doesn't play the game up to that point that you showed me, the point .05 > Prof: Right, so if you got... Student: My question is, is it preference to risk or is it actually the rationality of... Prof: Right, so this is going to become very important very shortly. So his question is I just proved if you can call that a proof by computer, the computer proved that even if you got 5 blacks in a row you should still draw another card. Of course things are quite risky now because there's a very good chance you're going to lose on that very next card. So he's saying if you're risk averse maybe you would stop there, and how can you distinguish somebody who's risk averse from somebody who's just dumb and can't make the calculation. So that's going to be a question we're going to take up in the very next class. But I would say that it's usually because people are dumb and can't make the calculation. So they just don't realize how favorable the situation is they're in by having this option to be able to play to the end, to stop when they want to stop. So let's just do one more example. Suppose that you are undergraduates and you want to get married. You've been told that's a good idea, and you--it's going to be a very sexist thing, but anyway this is also a game I invented which turned out not to be as original as I thought. So I call this the optimal marriage problem. So let's say you knew you were going to meet 1,000 women. You're telling it from the guy's point of view. You're going to meet 1,000 women and each woman you meet her suitability you can't tell until you meet her and talk to her, and after you meet her each woman's suitability is uniformly distributed on (0,1). So what do I mean by that? I mean you meet her, you talk to her, you get to know her, and before you met her, you have no idea how suitable she's going to be. After you've talked to her you understand how suitable. The best, it's 1. The worst, it's 0, and it could be a draw anywhere between 0 and 1. Before you meet her you have no idea. After you meet her you know exactly how suitable she is, and there are going to be 1,000 of them that you could meet. The problem is that after you've talked to a woman you can marry her then, or you can move on, but once you've moved on you can never go back to her. So you understand the problem. The problem is that let's say the first woman is .95 or .90. You think, gosh how suitable. This is a great match, but I've got 999 more women to go. Maybe I'll do better, and then you get 0s from then on, and so you've missed your .90, and so you're going to end up marrying the last one who's maybe a 0 for you. That doesn't mean she's a 0, just for you a 0. I'm trying. Anyway, so what should your optimal strategy be and are you playing the optimal strategy. So what do you think, just intuitively, what's the optimal strategy? Of course we're going to do it by backward induction, but what do you think it's going to look like, the optimal strategy? Yes? Student: The further you get into the game the less selective you should be. Prof: Right, that's what's going to happen. We're going to prove this, but he's exactly picked--he said, you set a threshold here at the beginning. You'll marry her if she's above some number. You keep to that threshold for a while. Then you haven't married anyone and you'd say, oh my god, I'm running out of women and then your standards just collapse. Desperation sets in. So that's absolutely right, but the only interesting thing is to figure out how high the standard should be. So how high do you think it is at the beginning? What would you say the number is at the beginning? Now, let me give you a hint. If you divide up--here's 1 and there's 1,000 women, so here's 0. So they're randomly picked. So if you could look at all the women, and pick out the most suitable one, what would her suitability be? Well, her suitability would be--so top, the top on average will be something like 1,000 over 1,001. This is a famous problem. If you take N people randomly, you take N numbers you pick randomly uniformly on (0, 1) the top one on average is going to be, if there's 1,000 women it's 1,000 over 1,001. Second top is going to be 999 over 1,001. So this very standard statistical result actually was derived by a former Yale professor in World War II. The Americans captured German tanks which had all their serial numbers on them. The first tank was number 1, the second tank was number 2, the third tank they made was number 3, so we captured a bunch of them and then we had to guess, how many tanks did they make? Anyhow, so it's related to this idea that if they're uniformly distributed on (0, 1) the top one's going to be on average 1,000 over 1,001, 999 over 1,001 etcetera. So what standard would you set for the first one? Right? You have to set some threshold here. Here's one and here's 0. By the end you'll take the last woman you've got--you're going to take her no matter what. So what should the threshold be? Well, it's hard to tell. We can't do it except by backward induction. So what would you guess? Student: 1 > Prof: 1, well then you'll never take her if it's 1 because the odds of getting exactly 1 are 0, so what would you guess? Student: > Prof: So you'd set the threshold this high, 1,000 over 1,001. So that means you're expecting to get as good a woman as if you could go to the very end and look at all of them, you never make a mistake. I told you, there's a chance you'll make a mistake. The first one's the best. It doesn't quite come to your threshold and all the rest are worse then you end up with a disaster here. So you have a chance of not doing that well, so you're setting too high a standard here, because you have a very good chance of saying no to all these women and then ending up with what's-- right? However, you're on the right track. So amazingly, this is the answer, this is the threshold. So you should set the threshold at where you expect the second highest woman to be, the second highest match to be, and that is why there's so many novels about the other woman because if you're playing optimally you should be ending up with the second best woman and there should be one other woman that at the end of your life you regret that you didn't wait for, but only one other woman. So anyway, I just want to prove this to you in the same way we proved it before just by solving for backward induction for the optimal-- so we can just do this by backward induction. We know exactly what to do. It's one thing to say what you should do. It's another thing to prove that's what you should do and I'm going to prove it now. So you can just see by backward induction how easy it is to do these things. I'm going to have to take four minutes. If you can hang out for four minutes we'll get this. So what happens with 2 women left? What's V of 2? What should you do? What should your threshold be for 2 women? So here's the threshold. Threshold for 1 woman is 0. If it's the last woman there whatever she is that's it. You might as well marry her. It can't be negative. And then the value--unlike Herodotus-- the value of 1 is going to be a half, right, because if there's 1 woman left you're going to take her no matter what and on average you'll get a half. So the question is now, what's the threshold when there are 2 women left and what's your expected payoff? So what's the threshold if there are 2 women left? You see the second to last woman, you talk to her, you find out how good the match is. You should take her if the match is above what? Student: 1 over 1,001? Prof: No, there's only 1 woman left after her, so. So a half, right, because if you don't take her you're going to go to the last woman and on an average you're going to get a half, so there's no point in taking someone whose match is less than a half when the very next step you're, on average, you're going to get a half. So your threshold is a half. So what's your expected quality of the match? Well, with probability a half she's going to be above a half, and if she's above a half she's going to be half way between 1 and a half, so it's 3 quarters. And with probability, sorry, and with probability a half she's going to be below a half and you're going to pass on her and go to the last one and it'll be on average a half. So this is 3 eighths plus, no. Probability a half, she's going to be 3 quarters and probability a half, she'll be a half so it's 3 eighths 1 quarter, is 5 eights. Now, what if there are 3 women, what should the threshold be for 3 women and what's the value of 3? Student: 5 eighths. Prof: So the threshold should be V of 2, which is 5 eighths, and what's the value? The value's going to be, what's the chance that you take the one you just meet? Well, the odds that she's above a half [correction: above V(2)] is 3 eighths, so it's 3 eighths times the average of 1, you know, half way between, so he's above 5 eights, so she's somewhere between 1 and 5 eighths. So that's going to be (1 5 eighths) over 2, plus 5 eighths of the time you pass on her and then you get 5 eighths. So that equals, if we just do that a little bit more generally, it's 1 - V (2)--So that's (1 - V (2)) times (1 V (2)) divided by 2 V (2) times V (2). So that's the formula. So in general V (t), you set the threshold at V -(t-1). So with probability V (t-1) you're going to get (1 V (t-1)) divided by 2, and with probability 1 minus, no. This is 1 - V (t-1), with probability of V (t-1) you're going to get--you're going to pass on her and go to the next thing so you get just V (t-1). So that's just a formula. V(t) equals some function of V(t-1). So you can program that into a computer. So I'm ending now with this one picture. That's the end of it. Sorry. I know I've gone over, but this is the last picture. It'll only take a second. So 0, yield curve optimal marriage, so here it is, with one woman your value--oh shit, sorry. With 1 woman the value is a half, 1 match to go. So the number on the left is with 1 match to go the value's a half, with 2 it's 5 eighths, with 3 we computed that too. So you can tell for however many women you want. Now, what I've done on the right number, is this N - 1 over N 1. So that's the second best woman how good she'd be on average for you, and as you go down further and further you see these numbers are getting to be the same. So this number and this number's practically the same and if you go down to the very bottom you'll see they're identical. Up to an incredible number of decimal places these two numbers are the same. So if there are enough women you're going to get exactly the second best, and it's going to be the problem of the other woman. But anyway, the point of all this was to just illustrate how powerful the option is. It's as if you could go to the very end and pick out the second best one even though you have to do them sequentially, so.
Quantitative_Finance_by_Yale_University	15_Uncertainty_and_the_Rational_Expectations_Hypothesis.txt	Prof: Okay, I think I'll start. So we considered for a long time a world of certainty. Hope something's okay. Considered a world of certainty where we assumed we could foresee the future perfectly, and we still managed to figure out fairly interesting things. But the world is much more complicated than that. It's a world of uncertainty, and in a world of uncertainty, economics comes into its own, I think, as a fascinating subject. So I spent a little time reviewing some mathematics for you last time that many of you already knew, so I'm going to take that for granted going forward and just start over, this time from an economic perspective instead of a mathematical perspective. So suppose today that we assume that you could buy a stock today whose price tomorrow could be 104 or 98 with 50:50 probabilities and we assume that everybody knew the probabilities. Know probabilities and maximize expected payoff next period, okay? Well, payoff this period. If we assumed--and we're going to drop this assumption, but I'm going to keep it for a little while-- if we assumed that all people cared about was their expected payoff next period and of course they care about their payoff this period, what would the value of the stock have to be? Well, under the simple rule for how people act, you'd take 1 half times 104 1 half times 98, and that would give you--what would that give you? It'd give you 101, okay, because this is 4 times 1 half is 2; - 2 times 1 half which is - 1, so it's 1, so that'd give you 101. So you would say that the price of the stock today would have to be 101. Now we could slightly refine this utility function and say people maximize the discounted expected payoff next period the payoff this period. And if the discount is 100 over 101, then we're going to have to multiply this by 100 over 101 and we'll get a price of 100. Okay, so that's the basic first step. We can incorporate uncertainty by assuming people replace the uncertain outcomes with certain outcomes in their head, and then discount, just like we've seen before. Of course, before we had utility functions but I'm not going to do that quite yet. I'm just going to say, suppose that we just did that, right? That would give us a theory of how people manage uncertainty and react to uncertainty and how they set the prices. So it's the expected--expectation theory of pricing. Now before we complicate the theory, I want to just take this literally as true and make some inferences from it. Well, the first inference you can make is that today's price would then be the discounted expectation of tomorrow's price. That's just repeating the same thing, but what's an implication of that? The implication of that is, if you didn't know tomorrow's price, know the expectation of tomorrow's price, you could guess today's price. I'm writing out this trivial thought because it's such an important idea. Once you have a theory of how prices formed, you can always go backwards, and as the naive, uninformed member of a society, you can learn, instead of learning about the stocks, you can learn all you need to learn, perhaps, by looking at the price. You may be interested in what the expected value of the stock is next period. To do that in a serious way, you'd have to study the firm, study the product, study the new inventions, the new technologies it was trying to adopt, get some idea of the quality of the manager. You'd have to do a million things to figure that out. But if you just look at the price today, maybe that's going to give you a good idea of what the expected value of the firm is next period. And that's another way--that also implies you can test the theory. Is it true that typically today's price is a good forecast of the price tomorrow, the expected price tomorrow? Obviously you can't just look at one instance, because you would just be looking--if things went up, you'd be just looking at the 104, and 100 wouldn't be a good guess of 104. But if you did this the next day, and things were independent, on the second day, of the first day, you'd have a new price, 104 the next day, and you could see whether the price went up or down or not. And by doing this 1,000 times or 100,000 times, you'd get a good idea if, on average, today's price was a pretty good predictor of tomorrow's price. So here's the--I did that experiment and here it is. Why is this so small? Okay, so from 1980--I didn't do this. I got someone this morning to do this at my hedge fund. So what did he do? He said, suppose you had 1 dollar to put in each day starting in 1980, you could keep track of how many dollars-- say you had 100 dollars, so it's 100 dollars. You have 100 dollars to invest each day, starting January 1^(st), 1980. You put it into the S&P 500, so you put it equally into all stocks, the 500 biggest stocks, and you see what the total price of those 500 stocks is the next day, and you subtract the original price, and that gives you your percent return on the first day. For example, if it was 101, it seems like it went up a little bit, you'd have a 1 percent--you'd have made 1 dollar in the first day. Then I told the guy, or he decided himself, put 100 dollars in the second day, in the S&P 500 and see what happened to that the next day. Maybe it went up 3 dollars the second day. So your total after 2 days would be 4 dollars. Not your total return, although that's how he's written it. It's just the first day, the stock when up by 1 dollar, the 100 dollars went up by 1 dollar. The second day it went up by 3 dollars, so altogether, it went up by 4 dollars. So the hypothesis is that today's price is a good forecast of tomorrow's price. So if you're averaging the 's and -'s over many days, so there are 250 days for 30 years here, that' a lot of days you're averaging. And this is the cumulative total of what would have happened to you, okay? Well, that 100 dollars, if you did that experiment 7,000 times, you know, 30 times 250. 30 times 250 is 7,500 times, you would have ended up with 350 or 400 dollars by the end. So does that contradict or confirm the hypothesis that we've just made, that today's price is a good forecast of the expectation of tomorrow's price? What would you say? Student: > Prof: Okay, well, so that's a subtle answer. So there are two things that I expected you to say, that one being the second and a very important one. It looks like 100 dollars became 400 dollars, but that was over 30 years, so what was the gain per year? 7,500 days, and you got a return of 250 percent, so you have to divide 250 by 7,500 and you get some incredibly low number. I forgot what it was, but it was something like .0047 percent, something like that. So you're making--so this is percent. I've already divided by 100 to turn it into percentages. So you make a tiny return. On 100 dollars, you might go up on average the next day to 100 and 1 half dollars, but that's making it--but this .0047 percent, so 1 dollar would be 1 percent, there would be a 1 here, but we've got a lot of decimal places there. So you're dividing 250 by 7,500. Maybe I've got one decimal too many there. So this is a tiny number. So in fact today's price is a pretty good estimate of tomorrow's price. You have 100 dollars and maybe it will turn in on average to 100.0047 dollars tomorrow. So compared to knowing nothing, if you asked yourself what's the average value of this stock tomorrow? No one's telling you it's normalized at 100. It could be 500, it could be 23, it could be 75. Who knows what the average of these stocks are? The S&P 500 are mixing stocks that are worth 3 with stocks that are worth 500 per share with stocks that are worth 75 per share. And it turns out that it's such an accurate predictor that you only are off by a fraction of 1 percent, on average, each day. So compared to knowing nothing, you have a huge insight into what's going on in the world and how valuable the stocks are going to be tomorrow. Tomorrow hasn't happened yet. Already by looking at the prices today, you have a tremendous idea of what the prices are tomorrow. So that's the first thing to notice, the theory's kind of confirmed. The second thing to notice as well, it doesn't seem perfectly confirmed, because this seems like a pretty positive thing. You know, it seems to be going up most of the time, and as he said, "Well, we haven't done the discounting yet." We should have done discounting, because tomorrow is not quite as important to you as today, so I shouldn't have just been looking at return. I should have looked at return per day. So I should have discounted each day by whatever the interest rate is. Let's say you think it's 4 percent in a year, divided by 250, since there are 250 days in the year. So approximately, I should have gotten 250, I should have discounted by that. So when you do that, the number gets even much closer to 0, but it doesn't come exactly equal to 0 and so we're going to see that we need something else to make up the difference. But it's such a tiny difference that needs explaining. So to summarize, we have this view that uncertainty is going to change everything that we think about the world and it will change a lot of things dramatically, but it's not going to change the idea that today, the price today of things is a pretty good indicator of what their value is going to be tomorrow, if you replace value tomorrow, which is uncertain, by the expected value tomorrow. So you can still learn a tremendous amount about the world, just by looking at the market. That's a very important lesson, so let's go a little further though. Suppose that you thought, well, maybe people--maybe I want to ask a more complicated question. I want to say, suppose I only look at stocks that went up yesterday. I only look at stocks that went up yesterday. Now maybe there's something about the market that, you know, momentum will keep carrying those stocks up tomorrow. So once the market gets rolling, maybe the market's not such a good forecast. Maybe, as Shiller says, there are all these psychological forces at work, and once things get rolling and prices have gone up yesterday, the price will keep going up tomorrow. So today's price won't be such a good indicator of tomorrow's price, because tomorrow's price is probably going to be higher. So I'm going to repeat now exactly the same experiment, except instead of putting 100 dollars in all the S&P 500, I'll only put the 100 dollars into the stocks that went up yesterday. Or I might even refine it by selling short the stocks that went down yesterday. Okay, so what does that do? Does that change the numbers? So if I blow this up, maybe it is blown up. Can't do any better than that. Does that change the numbers? Well, no. In fact, it makes it worse. It's closer to 0 now. So again, over all this time, it kind of went up to the same peak, but fell down even further, so this thing-- so again, the stock prices today, even if I try to refine it and get more clever. I try to fool the market. I say, okay, the market does a good job on average. Today's price is pretty good on average of predicting tomorrow's prices. What about today's prices of those stocks that went up yesterday, you know, the momentum thing? Maybe that's not such a good--maybe on that subset the market's not so good. Well, the market is pretty good on those too. So again, you have to do the discounting and you have to realize that there are a huge number of days here, so this tiny return is really nothing, averaged over all those numbers of days. Well, let's see if we can come up with another strategy. I forgot what other strategy I tried out here. Oh, suppose you could say, "I want to choose only those stocks that went up 20 days ago, or 25 days ago or 14 days ago." This number here, these bars here, represent for everything for the S&P 500, you try to say, "What's the correlation?" That's like the covariance but normalized so it's between 0 and 1. What's the correlation of a move yesterday and a move today? Does the fact that a stock went up yesterday mean that it's going to go up today? Or does the fact that a stock went up three days ago mean that it's going to go up today, between today and tomorrow? So if it went up two days ago--if it went up yesterday, from yesterday to today, does that suggest that it's likely to go up from today to tomorrow? So what this says--of course, if you only did the experiment once, you'd always find that it did something. Okay, so you have to do many experiments, and then figure out, it's a statistical thing, to sort of guess what the correlation is, estimate the correlation. Then you have to see whether it's significant. So anything in this blue band means the numbers are insignificant. So these bars represent what the correlation is. So no matter how far back you go, you basically, knowing which way the stock went 27 days ago tells you almost nothing about which way the stock is going to go today. There's almost no correlation. If it went up 27 days ago, it's statistically, over the last 7,500 days, slightly more than half the time, it went up again today. But such a small fraction of the time did it go up again, the more times up than down, that it's statistically insignificant. If you only do it five times, it's going to have to be one way or the other, so if you do it an odd number of times, it can't be exactly even so you just figure out what the statistical significance is. So none of them hardly, almost none of them, are statistically significant. So once again, it's not only the case that today's prices are good forecasts of tomorrow's prices, but today's prices, even if you add some information to it, seem to be--even if you try to refine your set and look at only buying stocks that 27 days ago went up, the prices of those stocks are still going to be a reasonably accurate forecast of tomorrow's prices. So I did one more experiment, or Rashid did one more experiment for me, in case he hears this in a year. He did the same thing on a portfolio of stocks. So he looked at a 12 month rolling average. He looked at the stocks that had done particularly well in the past 12 months and he bought those, and then he looked at the stocks that had done particularly badly in the last 12 months and he shorted those, and here's what his returns would have been, just taking the daily thing and just adding it. And you see, you get almost exactly back to 0. So this was the original compelling evidence, things like this in the 1970s and 1980s, led people--economists--to say that the prices of very many things seem to be very accurate guides to future prices, and they called it rational expectations. So the high water mark of this theory was in 1983, I think, the most amusing example, was Richard Roll, who taught at UCLA, and oranges. So Richard Roll did the following experiment. He said, it turns out that for concentrated orange juice, 97 percent of the oranges that are used for concentrated orange juice are grown on trees that are very close to Orlando, Florida, where the weather is pretty much the same. I mean, it's a small area, so whatever the weather is, it's that weather over the whole area. It's amazing that so many of the oranges are grown in the same place. I'm talking about concentrated orange juice. California's no competition for Florida. In fact, no competition for Orlando, Florida when it comes to concentrated orange juice, not oranges in general. So he said to himself, "How good is the market at predicting the price of orange juice, at predicting next period's price of orange juice?" And he found, just like we did here, it's quite good. But then he said, "Maybe there's other information that the market doesn't know about." So he said, "What about the weather?" So the weather has a tremendous effect on orange juice prices, because if it's--four hours of freezing temperatures starts to kill the trees, then you get less supply of oranges for the concentrated orange juice, and then the price goes up. So he said, since 1970 or so, the US Weather Bureau has spent 250 million dollars building all these weather forecasting units that make daily-- in fact, they make 36 hour, 24 hour and 12 hour forecasts of what the weather's going to be next period. So he said, "Really, if the market is so good and the market price today is really telling an uninformed investor what the price ought to be tomorrow, let me see now, by getting a record of the weather reports, could I improve on the market price? By putting together today's market price and the weather report today, the weather prediction today, could I make a better forecast of the market price tomorrow?" And he found out, no. Statistically, the weather prices does not improve price forecast. So how could you interpret that? How could that possibly be that knowing the weather reports doesn't help you predict the price better the next day than today's price? How could that be? What's the obvious reason for that? Yeah? Student: > Prof: Right, so the people buying and selling, they're also looking at the weather report, and so naturally, they've taken that into account. So what it illustrates though is that all this kind of information that you might think would go into affecting the value of the orange juice tomorrow, the market is already processing that because the people buying and selling, they're already looking at the weather report, and they're figuring out what the right price should be. So that was a pretty stunning conclusion, but he didn't want to stop there. So what did he do next? What if you were--you know how in comp. lit. they always says things backwards, the reader is detective or the detective is reader, you know--anyway, when I took comp. lit., that was the gist of every course, was to do everything backwards. That's how you knew you were clever in comp. lit. What would a comp. lit. person have done? Yes? Student: Used the price to predict the weather. Prof: He said, "Let's use the price to predict the weather." So he'd said, suppose the price today turned out to be higher than the price--okay, so--the price from yesterday to today went unexpectedly up. It went unexpectedly up. Then he said, "Okay, that means these market guys were surprised today to see the price go up." There's a weather forecast back here as well, and there's a weather forecast here, and he said, maybe you can now say if the price went up-- can you use that to now forecast the weather? So he said, suppose that whatever the forecast is here, you now say since the price went up, we're now going to forecast that the weather guys-- the price going up means they've learned something here about the weather probably being bad. So the question is, did the weatherman learn the same thing? So he says, "Let's test the hypothesis that when the price went up, these guys learned more about the weather than the weather predictors did, so that in fact the actual weather from this prediction is likely to go down." And that's just what he found. You can't use weather to improve the price prediction of prices, but you can use prices to improve the weather prediction of the weather people. That was one of those stunning confirmations of the rational expectations hypothesis, so what could explain that, by the way? Is that just crazy or an accident, or is there some logical explanation for that? Yeah? Student: People buying and selling oranges know more about the weather > Prof: Than the government does. So the people buying and selling oranges, this is billions of dollars of money changing hands. The government spent 250 million dollars in this area forecasting the weather. These guys have billions at stake. They in fact have better weather forecasting technology than the government does, and they're making better forecasts than the government is of the weather. So if you ask them, they would know better than the government what the weather's going to be the next day, and the price reflects that. Okay, so that's the efficient markets hypothesis, which seduced many in the economics profession, and there's still a tremendous amount of truth to it, at least at the level--if you don't know anything and you want to know something about the future, look at the prices today. That's going to tell you a tremendous amount about the future. Now the question is whether it's as precise as Roll seems to suggest, and we're going to see that it's not going to be. But anyway, for a while, these people, the rational expectations school, which is mostly in Chicago, they had the view, and Fama was one of the leaders, they had the view that this rational expectations pricing was the best-documented truth in all of the social sciences. That was what Fama said. So we'll have to come back to see that that's not always the case, but certainly looks good in these graphs. Okay, that's the first idea. Now the next idea that we looked at was, what is the most important thing to be uncertain? Well, there's output that you're uncertain about, but the next most important thing is the discount, the interest rate. After all, that's the most important variable in the whole economy according to Fisher. Who's to say the discount is always exactly the same thing, so, uncertain discounts. So now we said--and you've done in the problem set-- if the interest rate is 100 percent, it might go up to 200 percent, say, or it might go down to 50 percent, and now you want to ask, what's the value of 1 dollar here? It's a little subtler, because here, the expectation was all that mattered, the expectation of the payoffs. If I change this to 106, and I change this to 96, I haven't changed the expectation, so the price is going to stay the same. So the variance has nothing to do with what the price is. But things can get subtler. Let's suppose that what's changing is the discount rate. Now the variance is going to have a big effect on what the values of things are. So if we think this is happening with 50:50 probability, the guy--so what do I mean by this model? Today you know that the value of something tomorrow is going to be 1 half of what it pays tomorrow, up 1 half what it pays tomorrow down, discounted by 100 percent. Tomorrow, you're not sure whether you're going to be discounting it 200 percent or discounting it 50 percent. So then the value today is going to be 1 over (1 100 percent), times (1 half times 1 over (1 200 percent) of 1 1 half times 1 over (1 50 percent) times 1). Because over here, you know that this dollar's only going to be worth 1 third to you. Over here, you know this dollar's going to be worth 2 thirds. So that's the 2 thirds here and the 1 third here, and there's a 50:50 chance of each of these, and you're going to discount it by 1 over 100 percent, so that's what the value is to you today. So now you did a problem set where you had to do a bunch of these things. We're going to call that D(2), because that's what you would pay today to get 1 dollar for sure at time 2 in the future, and D(1) is going to be just 1 over (1 100 percent), which is 1 half, which is what you would pay today to get 1 dollar for sure at time 1. And I could compute D(3), and any other D that I wanted to. Okay, so we're going to see that interest rate uncertainty is the most important uncertainty in the economy. The value of everything is going to change. If the interest rates go up, all the bonds are going to go down in value. All the mortgages are going to change in value, although sometimes they go in surprising directions. But everything's going to change in value when the interest rate moves. That's going to subject everybody to tremendous amounts of risk and we have to figure out, how are they going to cope with all that risk? Before we answer that question, we want to answer the simpler question, how are they going to value things? And here we just have the same tree that we had before. So that's what we did last class, and I just wanted to finish that thought, which I didn't get a chance to do. So for period 3, we could have done a 3 period thing and assumed that this went up to 400 percent and would have gone to 100 percent or down to 25 percent, and then still paid 1,1, 1. Okay, so that's payoff for 1 dollar for sure, but now we've got still more uncertainty in the interest rates. So you figured out in the problem set what the value of that's going to be and you got D(3). So I could have done this for D(4) and any other T that I wanted to and in fact, that's also what you did in the problem set, you did it for all the way up to D(30). Okay, so I want now to just say one thing about the environment, before--we're going to come back and analyze this over and over again to see the risk the whole economy's exposed to and how people cope with that risk with interest rates changing, but I want to make one observation. These numbers, D(1), D(2), D(3), D(4), they reflect people's attitudes towards the future. What would you pay today to get 1 dollar at time 1? What would pay today to get 1 dollar at time 2? What would you pay today to get 1 dollar at time 3? So what is the shape of that function? Well, in the case of certainty, with a constant discount rate, that function would have to decline exponentially. So it would be an exponential decline. Why? Because this would be equal to 1 over (1 r), and this would be equal to 1 over (1 r) squared, and this would be equal to 1 over (1 r) to the fourth, etc. So after 100 years or 500 years, you wouldn't care, as long as r is .03 or something percent, .03, r is 3 percent. As long as it's a number like 2 percent or 3 percent, after 500 years, you just don't care at all about what's going to happen. If the whole economy, the society, is discounting the future and trading it off like this, you don't care at all about the future. So environmental improvements today, which don't have an effect for 200 years, would be regarded as stupid ideas. And environmentalists have been trying desperately to make an argument that 200 years from now really matters. So of course, they argue about the interest rate, but really, all they're doing is they're arguing that the interest rate, instead of being 3 percent should be 1 percent or something like that, and that's not really helping, because even 1 percent, if you keep doing that for 500 years, you're going to get a pretty trivial number by the end. So let me ask you the following question. Suppose you could have 15 dollars today, or--so this is an experiment Thaler ran, who was a behavioral economist. So, next month, 1 year and 10 years. How much money would you want next month instead of the 15 dollars today? Somebody give a number, shout out a number. What seems equivalent to you? 20. It happens to be exactly what the average--do you know the Thaler experiment? That's precisely the average. Thaler did a class like this, averaged all the numbers, he got 20, amazingly. What about for 1 year, what would you say? 50 to 100. And what about 10 years? 200. Okay, so I'll tell you the Thaler numbers. I stupidly forgot them all. What a turkey. Okay, so the numbers of Thaler--let's just go with those numbers, but what do you think about those numbers? So Thaler got--it's amazing--Thaler got 20,50 and 100 were Thaler's numbers, so very close to what you're telling me. 50 and 100. So what's the matter with those numbers. Let's go with Thaler's. They weren't that different from yours. What's the problem with Thaler's numbers? Student: > Prof: Rapidly, rapidly. This is just one month. You have to have a huge discount to care--this is--you're discounting by 33 percent or something a month. It's a tremendous discount to go from here to here. If you did that 12 times--so if you look at the monthly discount rate from here to here, you get 33 percent. From here to here, it's to the 12^(th) power, so you're discounting by 5 percent. From here to here, you've got the 120^(th) power, so what number to the 120^(th) gives you 6 and 2 thirds, not a very big number. In fact, the reciprocal of that number is the discount, is .75 to the 1. So this is .75 obviously, and then (15 over 50) to the 1 tenth--1 twelfth--is .9, and then (15 over 100) to the 1 twentieth is .98. So you're discounting by 33 percent, something like that, by 10 percent and then by 2 percent. So your discount rate is falling rapidly. You do experiments with animals, you get the same conclusion. You ask the animals--you can make an animal work and then they'll have to wait a certain time to get the food. Or if they work harder, they can get more food, but they have to wait a longer amount of time. So you try and do the experiment. I'm not sure these actually are believable, but anyway, they do these experiments and they figure out how much the animal is -- you know, these are birds and mice and all kinds of things-- trading off waiting for getting a bigger reward, and they get the similar kinds of numbers to what Thaler got by talking to psychological experiments with real people. How can you explain it? In the world of constant discounting, you couldn't possibly explain it. Now of course, you could explain it by saying, "Everybody's discount rate is going to get smaller and smaller over time." Their annual discount rate is getting smaller and smaller over time. But that's totally unbelievable, you know. It's just, you know that 1 year from now, if you were asked the same kinds of questions, you'd give the same kind of answers. So your discount between today and next month is going to be the same next year as it is now. So it's not the case that the 1 month discount happens to be high now because you're in college, and then the day you get out of college, you're going to be more mature and so you're going to have a smaller discount rate. When you get to my age, you're going to be even more mature and have a smaller discount rate. That doesn't happen. The discount rate doesn't go down like that. In fact, if anything, if you're rational, it ought to go up. I'm closer to death than you are. If I don't get the stuff now, who knows when I'll ever get it? So the discount rate should be going up, not going down, and yet it seems like there's so much evidence that it goes down. So this is a big puzzle in economics. So I just offer, again, I'm going to make a habit of offering theories. I'm not saying this is the right theory. I'm just simply pointing out that if you had this random discount, put uncertainty into the discount, put uncertainty into the interest rates. Uncertainty in the interest rates is the heart of finance. Every single person, every single serious finance person, thinks about--what do you call it?--uncertain variability in interest rates. So I take the simplest possible process, where the interest rates can go up or down by the same percentage. So for example, you could start at 4 percent, and then the variation or the standard deviation could be 16 percent, which means that 4 percent basically goes to 4 percent times 1.16 or to 4 percent divided by 1.16. That process actually, times e to the .16 or times e to the -.16, which is very close to times 1.16, that geometric random walk is the basic model of finance. And what you found in your homework is, you were supposed to find, that as you go out further and further, the effective discount rate does go down. And what I forgot to say, the punch line, Thaler's numbers here confirm what all the behavioral economists suggest, which is that there's hyperbolic discounting. So what they confirmed in these experiments is that if this is D(t), this should go down like t to some power, you know, t to the - some power, t to the -2 or t to the -1 half, or something like that. They don't pin down what this number is, but t to the -a, so it goes down much slower than the exponent, which is some exponent like .9 to the t. That goes down much faster than that does. This is a polynomial in t. This is an exponential in t. So it's going down much faster. So this is a classic--Thaler's numbers are a classic polynomial. In fact, with exponent 1 half. Thaler's numbers fit t to the -1 half, if you do the right starting point. So what did I show? I showed that any geometric random walk, no matter where you start, no matter what r(0) is, no matter what you start, no matter what standard deviation you go, if you figure out the sequence of numbers, D(1), D(2), D(3), D(4), not up to 30 years, which is where everybody else stopped, because bonds end at 30 years, but you do it for 100 or 200 or 500, D(t) is always eventually going to be equal to some constant times t to the -1 half, exactly consistent with Thaler's numbers. So I don't know if that's the explanation for hyperbolic discounting, but I thought it was pretty interesting, and anyone could have done it if they just didn't stop at 30 years, just kept going. And then there's some mathematics, you could compute examples, but there's some mathematics to prove that asymptotically, that's the right formula. Okay, so in fact this paper, I wrote this with a co-author, Doyne Farmer, whose daughter is a sophomore here and whose son just graduated by the way. He's in Santa Fe. So if you look at the picture here, you can see that these are the D(t)s when you exponentially discount. I've got it on a logarithmic scale, so if you exponentially discount, things go--the Ds drop off really fast. That's the dotted line, really fast. But if you do this random thing, you get the thing that goes much slower, and it goes with a slope of -1 half. Since I plotted things on a log scale, that's just what this means. Taking the log of this, you get a straight line with slope -1 half, and that's just what we found, and we managed to prove that that always has to happen. So if you look 500 years in the future, you start with 4 percent and you assume a constant discount rate. After 500 years in the exponential, nobody could possibly care about 500 years from now, But 500 years from now is 1 percent as important as now [in the uncertain case] if you discount-- if everyone knows the interest rate is 4 percent now, and it's going to go up or down and keep going forever, so it's quite shocking. Okay, so that's it. We're going to come back over and over again to this, and this is the yield curve that you get, the 0 yield curve like in the problem set, goes up and then starts coming back down. All right, does anyone want to say anything about discounting or how to compute this stuff? You know how I did this. Yes? Student: > Prof: Yeah, okay, you mean the intuition of why that happened. You computed it and you found it happened. What's the intuition? The intuition is that--so why should this thing go up and then go down, just like you computed in the problem set? The reason is because if the interest rate is moving in a geometric random walk, so it's doubling or getting multiplied by 1 half, the geometric average is, it stays where it was before, but that means since the arithmetic average is always bigger than the geometric average, the arithmetic average of 200 percent and 50 percent is actually bigger than 100 percent. So at the beginning, you're sort of going to be doing this arithmetic average and things are going to be getting bigger for a while. But when you go out farther and farther, why doesn't that matter? So what is the intuition? And by the way, this is a common thing in finance with-- someone named Weitzman, who was at Yale and now is at Harvard, did suggest this idea in economics. He said, for the environment, you should always use the lowest possible interest rate, and why is that? Let's do an example. Suppose the interest rate was going to go to 100 percent, so you're going to multiply by 1 over 2 and then keep multiplying by 1 over 2 forever, the interest rate stayed the same. Or let's say the interest rate was going to be less discounting, 2 over 3 and was going to stay there forever. Okay, and you get 1 here and 1 here. So I'm doing a very simple case where 50 percent of the time, it stays at 100 percent forever and 50 percent of the time, it goes to 50 percent. This is 100 percent and this is 50 percent as the interest rate. Stays at 100 percent forever or 50 percent forever. So you multiply by 2 thirds forever or by 1 half forever. So this could happen with probability 1 half and this could happen with probability 1 half. If you average this, multiply by all the 1 halves, and this multiplied by all the thirds, by all the 2 thirds, the 1 half is irrelevant, because this is such a tiny number compared to this one, right? Because every time, you're multiplying by such a small number up here compared to this, this thing is just negligible compared to this. So really, the total here is entirely given by what happened down here. Okay, so it's 2 thirds to the Nth power times 1, plus a totally negligible thing. Okay? So you're going to have half of this value is going to be the value here. So the high interest rate, the 100 percent interest rate, didn't matter. It's only the low interest rates that matter. So why is that? Because in the random walk, when you follow a random walk, it goes like that, so if you end up with a really low interest rate at the end-- so here we start with 4 percent. By the end, because it's a random walk, you don't know where the final interest rate's going to be. It's going to be some normally distributed thing like that. You don't know what the final interest rate's going to be, but the low interest rate's here at the end. Here's where the interest rate was the same as where you started, back to 4 percent. So I'm not saying that people typically go down here. That would be a ridiculous assumption. I'm saying on average, they're at the same level they were today. But the paths where the interest rate ends up high probably were high the whole way along, so they kept getting discounted, so they don't make any difference. The paths where the interest went low, the path was probably low the whole way along, and that's why those are much more relevant paths than these. So when you take your average, to get it, it's going to be, in this particular example, as if it was 2 thirds, 50 percent discounting forever, but of course, you're only averaging over these low paths, so I have to put 1 half in front of it. That's why it's not t to the -1 half, it's an a times t to the -1 half. Okay? So that's a vague intuition, but it maybe helps a little bit figuring out why that happens. Okay, so I don't know, this may have some significance for the environment. So I personally think that we should do something about the environment, even if it's only going to be 500 years away. I don't think we should just discount it to 0 because the interest rates are 4 percent and 4 percent to the 500^(th) power is some tiny number. That is, 1 over 1.04 to some 500^(th) power is a tiny number. Okay, so I'm going to march on now if there are no questions. What's the next most important kind of uncertainty that you see in the market all the time? It's the chance of default. Now we're going to see very shortly that default and the possibility of default changes a lot of things. But you could still be a rational expectations guy and believe that default is just no big deal. It's just that the payoff, which over here was 104 and 98, the default just makes the payoff lower. So what's the typical thing that defaults? It's a bond. So a typical thing that defaults is a bond. So suppose I had a 1-year bond from Argentina that could pay 100 or it could pay 0. This is an Argentine bond. So you'll have to forgive me if you're from Argentina. And then we have the American bond that can pay 100 or it can pay 100. Okay, so what do you see? These both promise 100. The American bond, if you look at the market today, is going to sell for a higher price than the Argentine bond. Why is that? Because people assume that the American bond is not going to default. So even if you put a 0 here, they assume that the probability for the American bond is 1 here and the probability of the Argentine bond is some number, .8 or .2 or something. The question is, what's the number that they put here? So there's uncertainty about defaulting, and if defaulting means paying 0--we're going to think a second about what it really means-- if it means paying 0, that's no big deal. We just calculate--in the expected payoff we have to take into account, not the usual dividends and all that stuff 100. We also have to take into account the possibility things default. So let's look at some of those curves. Oh no. Oh no, say it ain't so. Did I forget the curves? Hang on. So I've got another one on my...oh dear. I got another one of my--I think I'm on the internet in here by the way? No. Oh, I didn't realize this would happen. When I lost the internet--I had opened the file, but it doesn't--yes. Okay, this will only take a second. Yeah, wireless, connect. Connection successful, okay. So I can close this and this and now I can--sorry, it will only take me one more second. I beg your pardon for this. I had it. It disappeared when I walked over here. It's going to take a second for me to get on the internet. So what could we do here? We could figure out what the price of the Argentine bond was. So suppose the price of the Argentine bond is 80, and the price of the American bond is 95. What do you think--what does the market think the chance of Argentina defaulting is? How would you figure that out? So let's write d here and 1 - d here. You don't know anything about Argentina. You know it's a great country, they have wonderful everything, music, beautiful people, everything, you know. Okay, but their bonds happen to sell for a lower price than American bonds do. So assuming the American bonds can't default, because we're just going to print the money, and Argentina might default, because maybe they've tied their payments to the dollar, so they can't just print the money, what do you think D is? How can you figure out what D is? > Prof: Oh, that's bad. Oh dear. Well, so you know, in my Yale mail, this all goes to junk, but this is really bad. You'll have to cut that out. Oh no. Oh no! You can't infer anything from that. Okay, so here is the--let's do JP Morgan. Oh what a disaster. Okay, so where did I get this graph? Let's just do this problem. So this is JP Morgan, and this is the chance of defaulting. So you see that--oh no, this is JP Morgan. What are the chances that after 1 year, JP Morgan's going to go out of business? The market thinks it's surprisingly high, 1 percent and 1 half. I should have asked you what you thought. After 10 years, they think that JP Morgan, the leader, the great investment bank which is now a regular bank and the most successful thing, they think 10 percent, the market thinks it will be out of business within 10 years. So how did we know how to get that number? We can do another one. We can do Citibank. Citibank is a totally lousy American bank that ought to have gone out of business already but it's being propped up by the government. So of course, people think the government's going to keep it propped up, so over a year, it's actually got a smaller probability or about the same probability as JP Morgan, because everybody knows, the government's going to keep propping it up. But then, you know, eventually maybe the government's going to stop worrying about Citibank and so after 10 years, Citibank, what used to be the biggest bank in the world, has got a 25 percent chance of going out of business, 25 percent it won't even be here. Okay, so how did I know what those numbers were? How did the Ellington trader figure that out? Every morning they figure out the interest rates and they figure out the implied default probabilities. So what is the implied default probability of this Argentine bond? How would you figure that out? Well, according to our theory, what is the price of the Argentine bond? It's 80. What should I write that equal to? What? Student: > Prof: Okay, (1 - d) times what? Student: > Prof: Okay, well that's very good. So let me just see how she--where are you? Excellent, but you went too fast. You got the right answer, but it was just very fast. So the payoff of the Argentine bond is (1 - d) times 100 d times 0. So that's the expected payoff. That's what you expect to happen here. But she went--so she not only did that, but she went one step further and she said, "How would you--you have to discount it." So how does she know how much to discount it? Well, you could buy an American bond, just as well as an Argentine bond, so basically we know that the discount rate, the world discount, everybody has--the Argentines can buy the American bonds and so 100 dollars for sure is worth 95. So according to our hypothesis, you take the expected payoff and then multiply by the discount, 95 over 100. So that's = just as she said, to (1 - d), times 95. That's what she said and she was exactly right. So therefore you can figure out that 1 - d is 80 over 95 okay, and so d is 1 - (80 over 95), which is something like 15 percent, a little bit more. Maybe it's 16 percent, something like that. So it looks like there's a chance of 16 percent that Argentina is going to default. So that's how they figured out what all these default probabilities are. Any questions about that? Let's see if we could do a 2 period version, okay? So they've done 1 year. Now I'm not going to show you what Argentina is. Last year I got to show everybody what Argentina was. Unfortunately, my hedge fund's emerging market trader went out of business last year in the crisis, lost a lot of money, so we closed it down. So I can't show you what--it's too complicated. I didn't bother to get all the countries' prices and the default curves. We don't bother to compute them anymore, because we're not trading them. But we still are trading all these potential corporate bonds. All right, suppose it was 2 years. Suppose we had a 2-year thing, so this is the US. Now I'm going to do a simplified version first and then we're going to have to complicate it. Okay, so I guess I'm assuming that we're doing--okay, so let's do the case where we're doing 0s. So here's America and here's Argentina and we're just going to be trading 0s, okay? So it's going to get a little more complicated with their dividends, but not so much complicated. So there's a 2-year...those curves should be parallel, so here's Argentina. Now let's say that the American--so here we've got the 1 year bond, pays off in yellow. So 1,1 here. And let's assume--it doesn't really matter, but let's assume that that price is .9 and then the 0, the 2 year 0 in America, which pays off 1, 1,1 here. So I'll just write that in pink, 1,1, 1, is worth 70--what did I do? .72. Okay, now let's do the same thing in Argentina. Let's say the 1-year bond, which pays off 1 here and 0 there, this is default, so it's probability d. Let's say the probability of d is always the same. The 1 year Argentine bond let's say is worth .54 and the 2 year is .216, let's say. So now what does the 2-year--? So now we have to look at these paths. What is the 2-year Argentine bond going to be worth? It'll be worth 1 here, 0 here. But now if the 1 year Argentine bond defaults, it's the same country, so if they've gone out of business and aren't going to pay their 1 year, they're not going to pay their 2 year either, so it's going to be 0 here and here. So let's assume that's the payoff. So here we know the 1-year American bond is 90 cents, the 1-year 0. The 2 year American 0,72 cents and the 1 year Argentine 0 is 50--what did I say?-- 54, and the 2 year is 21.6 cents. So how are we going to figure out what these--and why assume the same default probability? I think I'll make it more interesting and assume d_1 and d_2. After all, most curves it changes, d_1 and d_2. Okay, so d_2 is actually quite irrelevant there. So this doesn't matter. So we've just got d_2. So solving for d_1 is going to give me--all right, so what do I do now? How would I solve this? What do you think I should do? How do I get d_1 and d_2? Which would I solve for first? d_1, this is...this is probably 1 here, 1 here, or it doesn't matter, you can call them all 1s. So in fact, let's put it in the same tree and call this 1 - d_1 and this is 1 - d_2. This is Argentina defaulting or not defaulting, and the US bond is still going to pay what it's promised, no matter whether Argentina--so this is the Argentina tree and this is the American. It's the same with the American payoffs over on the right, on the bottom tree, but it's the same tree on top of that one. So which would I get first, d_1 or d_2? Student: d_1. Prof: d_1, okay. So I know that 1 - d_1 times 1 (okay, that's there) d_1 times 0 (that's the expected payoff of the 1 year Argentine bond) times what = .54? Is that how I should solve for d_1 or am I missing something? Student: .9 Prof: .9, you have to discount it by .9. So then we could solve very easily. We would get 1 - d_1. 1 - d_1 = .54 over .9, right? Because this is just 0, so I just wrote 1 - d_1 over here and I divided the .9 there. That happens to work out very nicely to 60 percent. So we know that the chance of default is 40 percent in the first year. Now what's the chance of default in the second year, assuming you haven't defaulted already in the first year? If you default in the first year, you've wiped out everything anyway, including the 2-year 0. So what should I write now to get d_2? Well, with probability--the only way to get paid is to go up here. So I'd have to go (1 - d_1) times (1 - d_2), times 1--that's the only way to get any money, the rest isn't paying me anything--times what? Times what? I'm sorry, times what? Didn't hear it. Student: > Prof: .72, yes. It sounded like 1 seventeenth. Yes, .72. It didn't make any sense, 1 seventeenth. All right, so .72, exactly, is going to equal .216. so now all I have to do is I have to realize that 1 - d_2 = .216 over .72, times 1 over (1 - d_1). Okay, so that happens to be .3, I guess. .3 times 1 over (1 - d_1)--we just got that, it was .6--over .6 which = .5. (1 - d_1) we saw was .6, so I've got a .6 down here and this over this is .3, it's .3 over .6, which is just .5, so we now know that this probability is .5. d_2 is .5, so 50 percent I could write. So actually, it's quite interesting. We know that the probability--I wonder whether this was cumulative default. Must be cumulative default. So we know that things are getting worse in Argentina. The first year, there's a 40 percent chance of default, but even if you get through the first year, the next year there's going to be a 50 percent chance of default. Okay, so things are getting worse and worse and worse in Argentina in this example. I'm not saying in real life, but in this example. But by doing this, for any bond of any corporation or any country, you can learn a lot about what the market thinks about that country. So the market doesn't think very much of Citibank. It thinks Citibank in 10 years could have a 25 percent chance of going out of business. And for JP Morgan, it thinks a lot better of JP Morgan, but surprisingly not as much better as you would have expected. They could go out of business with 10 percent probability. There's very little chance they're going to go out of business in the next year or two, mainly because the government is there protecting them all. But in 10 years, you know, it could be very different. And so that's shocking to most people, I think, a shockingly high probability of those things going out of business. You wouldn't know yourself what those things were, except if you looked at the market. Now, I actually could have computed the prices this way, which is the way we used to compute them at Ellington, but there's a more direct way of computing them. There's something called a credit default swap. A credit default swap pays 1 dollar in case a bond defaults within some time period. It actually pays 1 dollar for every dollar of principal, 1 dollar in case a bond defaults within some time period. So I assume here that when you default, you get 0. You don't always get 0. Sometimes the guy is willing to work out something and pay you part of what he owed you, because after all, Argentina, if they default, and the US is angry about it, it can put a lot of pressure on Argentina, refusing to trade with it, doing all sorts of other things. Not that much pressure, but some pressure, and so maybe Argentina, if it can't pay, it'll agree to pay less and say, "Let's forget about the whole thing. You understand why we can't pay. We're just--bad things happen. It wasn't our fault. It was unlucky, so don't hold us to it. Take a little bit less and let us get on with our lives." So instead of putting 0s down here, maybe you would put a recovery down there. So we'll have to come back to that. So in case that there's a recovery, the credit default swap pays only the gap between what it was promised and what it actually paid. So it pays 1 dollar--pays 100 percent of the loss for any bond that defaults. So it pays 100 percent of loss, in case a bond defaults within some time period. Now that's if you buy 1 credit default swap. You could buy 50 credit default swaps on the same bond, so then you'd get 50 times the loss. So we're going to come back--this is going to be one of the causes of the crisis, that these credit default swaps got written that were so big. So you wouldn't have to actually do the computation I actually showed you. You could just look at what the price of the credit default swap is. Because here if the payoff is 0, that means the credit default swap is going to pay the whole 100, so its price is 16. That's telling you that everybody thinks--it wouldn't be 16--so what would the price of the credit default swap be over here, by the way? It wouldn't be 16 as I just said. That was wrong. What would the credit default swap price be over here? Student: > Prof: Right, so the credit default swap over here would have a price equal to 16. The default rate is .16, so it's going to pay 100 here. That's how much it defaulted by. So it's going to be .16 times 100--that's what it pays--so it pays 100 with probability .16, but then it's discounted, so it's times 95 over 100. That's what the price of the credit default swap is. So if you knew the price of the credit default swap, you could equally get the default. This is d. Over here is just d. So knowing d of course, that tells you the credit default swap. Knowing the price of the credit default swap, you could get d. So you could deduce d in two different ways, either from the American bond price or from the credit default swap. In either case, you have to know the American bond price in order to figure out what the discount rate is. So the credit default swap is sort of overkill. It's another way, it used all the information plus more to get the same answer more quickly. Now what would the credit default swap be worth over here? It's a little subtler. What's the credit default swap worth here? So credit default swap on Argentine 2 year bond = what? What would it be worth? How much would you pay for the credit default swap in this case? Well, 2 year bond over 2-year horizon, okay, so it's only a tiny bit subtler than before. The 2-year bond could default in any one of two cases. So it could default here or it could default here, so you're going to get the American .9, that's the discount. I don't know if you can see it over there, so let's write it over here. You could get the American--so over here, what's the value of going down here? It's 1 - d_1, discounted by .9, times 100--times 1. I guess the payoff is 1 here in this case, times 1. Or you could get paid over here. So when the 1-year defaults, the 2-year's defaulting too, so you could get paid here, or you could wait and get paid over here. So here it's--no, this was wrong. It's .9 times d_1 times 1, because to get paid over here, you have to default, or you can get paid over here, which means you didn't default the first period, but then you did default the second period and you get paid 1. But we've got to discount that. How much do we have to discount that by? Well, we have to--the payment's coming in the second period, which in America is discounted at the rate of .72. So that sum is going to give you the value of the credit default swap. So d_1 we know is .4 and this is .6, so it's going to be .36 .438. So it's = to .36 .432--no, .432 times d_2, which is 50 percent, so .216 okay, so that = .576. So that's how much you would pay for the credit default swap. Over a 2 year horizon on a 2 year Argentine bond you'd pay today .576. I think I managed to compute that correctly. All right, so I want to end this discussion of default with one observation, one theorem, which is that you can get all these numbers incredibly fast. How can you get these numbers incredibly fast? What's a trick? If recovery is 0--I'm only going to talk 2 more minutes here. I realize I've come to the end of time-- if recovery is 0, the chance of default-- the defaults, you know, if you default the first period, you default on all the bonds. If you default the second period, you default on all the bonds. Then the trick that the young lady who asked the first question pointed out right away is that-- I don't know where I wrote it--is that the chance of default from the very first equation is going to be very simple to compute, because you've got the--oh, I lost her equation. Anyhow, okay, because from the first equation where we had the chance of default here, we just got 1 - d is this 80--okay, how did we get this? We had the price of the Argentine bond is 80, compared to the--okay, so the American bond price is 95, so we just took 80 over 95. That ratio was the chance of not defaulting in the first year. Okay, so she did this incredibly quickly. This was a faster way of doing it. The Argentine bond is worth 80 ninety-fifths of the American bond. They're only paying in one state. That means the chance of Argentina paying divided by the chance of America paying, that's the only state where you get any money, must be 80 over 95. So that's a very fast way of figuring out what 1 - d_1 is. And for the 2 period thing, it's equally fast, okay? So you just do 1 - d_2--all right. I'm going to have to start with this next time, but anyway, 1 - d_2 is equally fast. So if you look at it the right way, you can compute all these defaults extremely quickly.
Quantitative_Finance_by_Yale_University	17_Callable_Bonds_and_the_Mortgage_Prepayment_Option.txt	So last time we found out how to evaluate options, especially stopping options where you don't have so many options. You either do something or you don't do it. That's the simplest kind of option. And we discovered through two examples, at least, that the option is worth more than people realize. So this time we're going to apply that-- and that the way to figure out exactly what it's worth and exactly what to do is to work by backward induction. So this time we're going to apply that reasoning to the two most important options in the economy, one is callable bonds and a much more important one is the mortgage option. And all of you at some time in your lives will probably own houses and have a mortgage option and have to think about what kind of mortgage to get and what the option is. So I want to teach you how to think about that problem. So let's start with the callable bond problem. Uh-oh, I forgot to turn this on. So let's start here with the callable bond problem. So callable bonds are issued by corporations and they pay, usually, an interest rate, say 9 percent. So the bond pays 9 percent, 9 percent and then some years later it pays 109, but at any point in time you have the option, the company has the option of calling the bond, and calling it for--so it's going to pay 9 100 at the end, so here it's 9. So at any time the company has the option of calling the bond. So what does that mean? It means after it's paid the 9--the company's issued a bond promising to pay 9 for say 10 years and then the principal in the 10th year, this is year 10, the total of 109. So that's the simplest possible bond. And the company occasionally has the option, we'll see in a minute why it would want this option, has the option of saying, "Okay, we don't want to make the rest of those payments. We want to get out of our promise. We've just paid you 9. We'll pay off the extra 100 that we're eventually going have to owe and we'll call it a day." So this is the payment and this is the remaining balance. So for a callable bond the remaining balance is always 100. So it's pretty obvious that if you've made an arrangement, so I owe you--like for example the prototypical mortgage was exactly of this kind. Somebody borrows money from you and they say, "I promise to pay you 9 dollars a year until the last year when I'm going to pay you 109. This is called, for those old mortgages it was called the balloon payment, but in typical bonds it's just the principal payment, the 100 face value of the bond. So the person who borrowed the money and has agreed to pay off over the years, he might have a reason why the house he put up as collateral is no longer going to be his house. He might want to move in which case the lender doesn't have a house anymore backing the loan and they have to have some way of resolving the loan and ending it. So the question is, after you've made a payment, how can you resolve the rest of the loan which is supposed to go on for 6 more years? Well, you just agree to pay 100 and then you call it quits. So that's a typical kind of bond. A non-callable bond is, you've committed to paying the 9 dollars and the 109 at the end and you have no option to get out of the thing. So we want to study what the difference is in value between the non-callable bond where you're obliged to pay the whole thing until the end, and the callable bond where you can get out of it by paying 100. And it's easy to see why a callable bond might have been invented, especially for a mortgage when you've got this balloon payment because you might want to dissolve the debt. But by putting in this option to dissolve the debt you drastically change the value of the promise, and that's what we want to calculate, how much that changes. So why might it change? Well, the interest rates might change. They might go up or down. Soon we're going to have them going up or down in a more complicated way, but suppose that the interest rate starts somewhere like at 8 percent, maybe, and it could go up to some number. Now, I'm always going to do a geometric random walk. This has become very fashionable in finance and you should be asking the question, is it special that we only have two possibilities? Life has many more than two possibilities. Suppose we had hundreds of possibilities, would that make a difference? The answer is it's not going to make a difference, but we're going to have to see why. So in a geometric random walk literally the thing can go up or down each period. So what does it go to if this is r_0? The next period we say it goes to r_0 times e to the volatility, which I usually call sigma, plus maybe a drift, plus d. And here it's going to go to r_0e-- let's write it with a little more room-- r_0 e to the minus sigma plus d, so what's happened here? The interest rate started at 8 percent. It gets multiplied by e to the d, which is just a number, so it's maybe tending to go up over time if d is positive or if d is 0-- think of d = 0--r_0 on average is going to stay at r_0, but there's some uncertainty. Maybe the interest rate goes up. We multiply it by some number, e to the sigma, and then we multiply it by the reciprocal of the same number or we divide it by e to the sigma. So using the exponential notation just makes the computations in the computer easier because the computer's adding numbers. This thing over here is going to be r_0 e to the 2 sigma 2d, right? And this will just be r_0 e to the 2 d, and this will be r_0 e to the minus 2 sigma 2 d. So the computer in calculating the interest rate at every step is adding exponents and it makes the calculation when you're doing gazillions of nodes much faster. So that's why it's traditional to use this notation, but really all I'm saying is you multiply or divide by the same number to see what the next interest rate is, and on top of that you might be sort of increasing all the things over time just because you think the interest rates are going up over time. So that's how we're modeling uncertainty, and everybody is supposed to understand what the probabilities are of these moves. So for now that's going to be our model of uncertainty and in a few minutes I'm going to try and indicate why complicating it won't have much effect. So are there any questions? This notation I hope isn't too complicated. Are there any questions about the interest rate process I'm assuming, the uncertainty that people are facing? Yeah? Student: Why is that middle probability on the far right, r_0 is always equal to >? Prof: Because I'm assuming that if there weren't uncertainty the interest rate was going to keep steadily rising by multiplying by the constant e to the d. So here I've multiplied it by e to the d. Here I'm multiplying it again by e to the d, and I'm going to multiply it again by e to the d. So if d is 1 tenth of a percent it means that the interest rate is rising at 1 tenth of a percent every period. You might just think interest rates are going to get higher in the future. You might have a more complicated function than steadily rising or steadily falling. It's just that this is the simplest to add a little complication without making it too complicated. Steadily rising or steadily falling and binomial uncertainty were the easiest simple things I could do. Of course a more realistic thing would do more complicated things. Any other questions about what this means? I know this can be confusing, this notation, so let's just figure out the notation. Make sure you understand it before I move on because it's really nothing but notation. I'm just saying the interest rate is 8 percent today. It can go up a little or down a little and then after that it can go up or down and the percentage rise and fall is always going to be the same relative to a drift and the drift might be 0, the drift might be positive. So to take an example, let's take an example here. Did I plug everything in? Yes. This is a spreadsheet that you have called callable bond. I did a little work on it, but not much. It's basically your spreadsheet. Everything is plugged in here. You're seeing that, right? So what I've done is I've said let's take over here the year, so here are the years, 0,1, 2,3, blah up to 31 or something. Then the bond coupon rate is 9 percent, so the bond is going to pay 9 dollars, 9 percent. The face is always 100. It'll pay 9 dollars until the end. So if I take the bond maturity of 30 down here I've got the 9 dollar payments and I've got the remaining principal, the remaining balance, what you could pay to dissolve the contract. You could after the first year, after paying 9, immediately afterwards you could pay 100 and say forget about the whole thing. So that's that, and so it goes all the way to year 30, and year 30 you see you're paying 109, and then the bond is over, 109 and by then the bond is over, there's nothing to talk about. So now I start off the interest rate somewhere at 8 percent, and I take the volatility, it's always said in hundreds, I take the volatility of 16. That means sigma = 16 over 100, because that's the way people talk about volatility of 16 percent. So that is a sort of standard volatility, 12 or 16 percent is about the annual volatility of these things traditionally, so I've taken the volatility at 16 percent. So I take the drift of 0 to make that simple. The d's disappearing, so what does that mean? It means that whatever the thing was last period when it moves to here I take the old number-- at the top there if you read this, this is the up multiplier. I just take e to the sigma d and that's what this says over here, exponent of--it just says that. So that's the up multiplier and that's the down multiplier. Let's just see how that looks. So if I look at the interest rates I start at 8 percent and they can go up by that multiplier, 16 percent up or 16 percent down. And see if you take 8 percent you add 16 percent to it, slightly more than 16 percent, because e to the .16 is a little bit more than 16 percent. You take 8,16 percent up is about 9.3 percent interest and 16 percent down you go from 8 percent to 6.8 percent. And things just go up or down so that's the uncertainty. So that's what interest rates are going to do. So everybody knows that you start at 8 percent and interest rates can go up or down by 16 percent for the next 30 years. The question is, what's the value of the bond? Well, if you couldn't call it--please interrupt me if you're not following. If you couldn't call it, non-callable bond, why would you expect it to have such a high price? Well, because the interest rate is, sorry, the interest rate, remember, is only 8 percent and on average it's going to stay at 8 percent. It could go up or down, but it's always coming back--the middle thing there is always 8 percent. So if you look in the middle it's 8 percent, 8 percent, 8 percent, 8 percent, so sort of the geometric average is 8 percent. On average it's going to be 8 percent. That's less than the payment, 9, so the poor bondholder is overpaying, paying 9 every year when the interest rate is only 8 percent and on average is going to be 8 percent. So obviously the bond issuer is giving a very good deal to the buyer by paying 9 when the interest rate's only 8 percent. And you know how you calculate this. At every step you'd have to do it by backward induction. So you'd write down, and we've done this before, the value at every node V_S, so if I take a node here what's the value of it? I don't know if I need to do a concrete example. How do I do this by backward induction? So I keep going like that, right? And then life is going to end. This is the last payment somewhere. Let's say the last payment is here so you're going to get 109 no matter what because that's the last period 109,109, 109,109. So we know what the value is here at the end because it's 0 beyond this point, and we know what the value is here. You're going to pay 109 no matter what so you just take the interest rate back here. So we know what the value is here. So the question is if you figured out the value at the end of the tree, which is trivial because at the very end you're just going to get 109 for sure, can you figure out what the value is at the beginning of the tree. And the way you do that is for every node you say to yourself, it doesn't matter which node you are like this one or that one, let's call is node S. So the value of node S, this is the value just after paying the coupon. So you've paid the coupon, you've paid the 9, now what's the value. Well, the non-call price, so let's do non-call, non-call bond, what is the value going to be? Well, just after paying the 9 here what's the value of what's left? So you're going to have to go up here. First of all you're going to discount by the interest rate here, so it's 1 over (1 r_S), so you're discounting by the interest rate there. Then half the time you'll go up. So what will you have to do if you go up? You'll have to pay 9 because that's the required payment, and then you'll be left in the same situation except that you'll be at the up state, whatever the value is there--plus V_Sup. If this node is S this node we call S_up and this node we call S_down. So I'm doing this by backward induction, remember. I'm saying, suppose towards the end of the tree I figured out what is the value of the bond just after making the coupon payment. Since there are no coupon payments at the end I know the value is 0, so having done it at the end, and working my way backwards now by induction, I can figure out the value at any previous node. So suppose I'm here and I've already figured out the value of all future nodes. The value here is simply going to be, value here is, just after the coupon payment, is going to be--I'm going to discount at the interest rate here, 1 r_S. Half the time I'm going to have to go up here, in which case I'm going to pay 9 and then what am I going to do? I'm going to be at a situation where I've just made the coupon payment and I see what the value left is. Well, that's the number we already calculated. So V_Sup 1 half--if I go down I'm down to here. It's 9 again V_Sdown. So that's pretty simple, and now I just have to solve it by backward induction. So that's what I did in this tree. Here are the interest rates, and now back here here's the present value of a non-callable bond. So at any node, let's pick one like this one, what's the value? It says it's 1 over (1 the interest rate) times the probability .5, that's 1 half, times the payment, that's 9 dollars, plus what the value would be if I went up because J 149 is this node. That's J 149 here, so it's just exactly what I wrote, 50 percent probability J 4 is the 9 dollars at the top plus the value of what I would get here, plus 1 half times the same 9 dollars I'd have to pay if I went down, plus the value that I'd get down here. So that's an extremely simple calculation to do, and because Excel is a brilliant--as I said created by Kapor whose sister was my classmate and was two years ahead of me at Yale-- Excel immediately understands--he called it Lotus-- immediately understands that if you give all these directions you can't figure out the value here unless you know what the value is forward. So Excel understands that you should keep going forward and starting at the end, and at the end it knows what the value is because it's just 0. So having got the value 0 at the end it then works backwards all the way through the tree and gets the value at the beginning and gets 113. So it's exactly what we want to do, and he's just written this brilliant program that understands if there's a dependency you can't calculate this without knowing this. He says, "Okay, I don't know this. I'll go forward into the program to here. I can't do these either. I'll go all the way to the end. Now everything is 0, so I know all these numbers. Now step-by-step I can go backwards and get all of them." That's what Excel is doing and it does it instantly. So there's no doubt about that, right? You all are way ahead of me on that. So the value's 113, that's a huge number, so obviously it's a very generous company. The company may not want to be so generous, so the company says, look, we want to be able to call the bond at 100. So that simple option, what's it going to be? What's the value going to be? Well, obviously the company could call it right away at 100. So it's going to make the value go all the way down to 100 because the company now has the option, whenever it wants to, like at the very beginning before making the first payment, it could pay 100 here, or it could pay the 9 dollars and then pay 100 here. So the question is, should the company do it, and when do you think the company will exercise the option? Why wouldn't the company exercise the option right away? So here it is. The bond's worth 113. Every period the company's promising to pay 9 dollars. That's like a 9 percent interest. The interest rate's in the economy only 8 percent at the beginning here. So it's losing money right from the start. Why shouldn't the company just say, "Okay, we gave ourselves the option, we're taking it right away. We're going to just pay you 100 and cancel the whole thing at the beginning." Why wouldn't they do that? Okay, hang on for one second. Someone else, why wouldn't they do that? You see, the puzzle is, the company has promised to pay 9 dollars forever. That's like 9 percent on a 100-dollar coupon. The interest rate is only 8 percent now, so the company's paying more money, 9 dollars. It could have borrowed and only had to pay 8 dollars. So the guy buying it is getting this huge bonus. He's getting 9-dollar coupons instead of 8-dollar coupons. He's probably telling his friends who aren't marking to market, look at my return. I've got 9 dollars the first year. Look at that great 9 percent return I got on my investment of 100. Why won't the company call it right at the beginning? What's the company waiting for? Yep? Student: It's hoping that the interest rate will go back up. Prof: Back up, exactly, because if the interest rates go way up-- after a very short amount of time if the company gets lucky the interest rates are going to go up. So here are the interest rates, right? So after a very short amount of time, 2 years, you get the up thing, the interest rates are 11 percent. So all of a sudden the company is looking great. It's borrowed at 9 percent and the interest rates are actually 11 percent. Effectively it's borrowing from the guy, 9 percent, and it's able to invest the money at 11 percent. To put it another way, the present value of the payment's left from then are much less than 100. So it's glad it made the deal. And on the other hand, if the interest rate goes down far enough then the company will be able to call the thing. Present value of the payments if it couldn't call would be way higher. Because it can call it can never suffer worse than having to pay 100. So you see that if the interest rates are going up or down and you couldn't call it then when interest rates go up that's really good news for the company because now the interest rates are over 9 percent on average going forward, so actually the present value of payments is 98. That's less than 100. On the other hand if interest rates go down then the company's really screwed, now the present value of what it owes is 127. At the beginning it's 113, so as interest rates go further and further down the company's made a worse and worse bond issue, but it doesn't suffer very much because of that because it can always get out of its deal by calling it. So in fact, astonishingly, it doesn't even call the first time. So here's the value. When the company behaves optimally it won't call the first time. When interest rates go up it says, "Ah-ha! We're going to make money, that's great, but when interest rates go down now the interest rate's 6 percent and it's still paying 9. The company is still not going to call the bond. It won't call the bond until the interest rates go down all the way to 5 percent. So anyway, by backward induction you get the value of the callable bond is 95, which is 95.529, which is a lot--let's write those down, in fact. So the callable bond, 95.529, and non-call was 113 point something, which I forgot already. So I hope you're following because this is going to get a lot more surprising when we do mortgages, but it's the same logic, 113.236. So the call option is worth 18 percent to the bond. It's a huge thing. It sounds so simple. Of course you should dissolve the thing for a value of 100. That's the only natural thing to do. So it's perfectly reasonable, you would think, for the company to give itself that option. "Look guys we're borrowing money, but there may be some reason why things get too complicated. Our company might close down. We want to keep our promise, so we just want to pay off the loan at 100, so give us that option even if our company doesn't close down." Well, the company has just taken an incredibly valuable option. Instead of making a promise worth 113, it's made a promise worth 95. So any questions about that? You could all get that and you all see why that's happening, and it's a bigger number than you'd expect. Yep? Student: When should they call it? Prof: When should they call it? You can tell when they should call it because--you'll know when they call it because if they do call it what's the value? So I didn't work out the--what's the backward induction? Sorry. So let's write down the formula when you do call it. How could I have forgotten to do that? What do you do when you do call it? So value, how do you figure this out? I just skipped this, sorry. Value of callable bond, so V_S, what is that going to equal? Now you've got an option. So V_S, remember this is value just after coupon payment. So what is the value just after the coupon payment? That's when you have to call. So in a second you'll see why that's the way the rule works. So just after the coupon payment what's the value of the bond? Well now that you have the option you can pay the minimum of the remaining balance. It's 100 all the time. This is just going to be 100. You could pay 100 or you could keep going. So if you keep going it's going to be 1 r_S times the same thing, 1 half, and then you're going to have to make the coupon payment the next up-- so just a second, where should we go? So here this is the interest rate, so at any node, you can pick any one like here in the tree, this one. That's the interest rate, so at that node you could, if you wanted to after making the coupon payment there you could pay the 100 and say, "Okay, we've made the payment. I'm making 100 more. Let's just call the whole thing quits," but if you don't you're going to move on, and when you move on you're going to go either up to here, so that's with probability 1 half. You have to make the coupon payment and then again you'll have the option of paying your way out of it, dissolving the contract or continuing. So you just have V_SU because that's exactly the value just after making the coupon payment at node S_U. That's V_SU, and so it's going to take into account that you're minimizing something. So you see, V_S, the value at any node, takes into account you could minimize by possibly paying the balance and dissolving it or you could continue. And so if you continue and things go up you have to make the coupon and then you're going to face a choice, but we assume by backward induction you've already figured out the value of that thing. Maybe it's paying the 100. Maybe it's not paying the hundred whatever that is, plus 1 half times 9 V_SD. So the only difference between this callable-- non-call case and the call case is you notice that the second term is exactly the same in the two cases, but here we've added the minimum of 100 in that because you either could continue or you could pay 100. Of course the values, V_SU up here and V_S, are not the same as the V_S's here because they've all been concatenated by taking the minimum with 100. So the computer now is going to solve this by backward induction, and now how can you tell what the computer has decided to do? If the computer said it's a good time to call that means the value at that point is going to be 100 because it's called by paying the remaining balance which is 100. So if you go to the present value of non-call you get all these present values. As the interest rate goes down you get crushed, of course, because you have the same payments and lower interest rates, you're discounting by less. But the callable bond, see, you shouldn't call here. It's 99.9 so that means when the computer took the minimum 100 in this thing it took this which was 99. It didn't use the option to call at 100, but if things go down again then it's going to call at 100. So it's got a threshold here where the interest rate has to go pretty far down before it calls at 100. It has to go down twice, but you notice this threshold. As time goes on the threshold is going to get tighter. So even if you're at the same interest rate four years, you know, this is 1,2, 3,4, this is 5 years later, and the interest rate's gone down once below the minimum bar here-- five years later you will call when the interest rate is, instead of 8 percent, is 6.8 percent, but 1 year later you won't call if it's 6.8 percent, and why is that? Well, why is that? How come if in the first year the interest rate went from-- remember it started at 8 percent and it goes down to 6.8 percent here you don't call, on the other hand if things had stayed the same for a few years and then in year 5, or year whatever this--how many years have we got here, 1,2, 3, no, year 0,1, 2,3, 4, so if in year 4 the interest rate goes down to-- oh, year 5 the interest rate goes down to 6.8 percent. In year 1 if the interest rate went down from 8 percent to 6.8 percent you wouldn't call, but if the interest rate sort of bounces around and then in year 5 it's back down at 6.8 percent you will call. Why would you call here even though in exactly the same situation you didn't call here? Why call here and not here? You can tell where you call because those are 100s and the computer's picked the minimum equal to 100. So why is it that it's going to call here, but not here even though the interest rates are exactly the same, 6.8 percent in both cases? Yes? Student: Because you can't get to the kind of really high interest rates from that point five years later. There's not enough time left. Prof: Exactly. So the point is the only reason not to call here--you're paying through the nose, it's horrible. The interest rate is 6 percent, you're paying 9. It's terrible, but you're hoping maybe things are going to turn around. The interest rate's going to soar then it's going to be a great deal for me. So I'm willing to have some short run losses in case I get a gigantic gain on the upside, and I know that I'm protected on the downside because if things go down again I can cut my losses and just call it 100. But if you run out of time, here the interest rate's 6.8, it's still way below 9 percent which is the coupon you're paying and you don't have much time for the interest rates to go back up, you better call then and cut your losses, exactly. So that's the whole logic of the thing. So any questions about that? And as I said, the option is worth much more than it seems. Could you all do a problem like this? You'll find out. So now let me just do one more example. I want to do an aside here. Suppose that we had a trinomial tree instead of binomial tree. So I have the same picture, but instead of two things happening I say three things could happen or five things could happen. So I would take the same tree and put this here. I'd always allow for something happening in the middle. And then, of course, it gets more complicated and I'm not going to be able to draw it because now this thing, three things could happen from here, and from here three things could happen. From here I have three things, so I have trinomial tree like that, right, where always three things could happen. So from here I could go here, stay the same or go up. Now, if I had a trinomial tree, and of course you could think of an N-nomial tree, would I keep the same numbers here? Well, I can't keep the same numbers because if I have 1 half and 1 half that doesn't allow any probability for going in the middle. So I'll put 1 quarter here, and 1 quarter. Now, what do I have to do to these numbers? Well, the drift I'm going to leave the same because on average it's still going to go up by d. So this was, remember, r_0 e to the minus sigma d. So this is the probability 1 half. I just made up three numbers, 1 quarter, 1 quarter and 1 half for the trinomial tree. Suppose those are my numbers? If I want to make this tree comparable to the binomial tree--what does it mean to be comparable? It means that the standard deviation and the expectation of the interest rate ought to be the same. So I'm using the fact that if they're normally distributed random variables all I need to know-- so if there were millions of successor interest rates and I took them with this-- if there are millions of these successor interest rates then as long as the standard deviation and the expectation were the same, no matter how I put the probabilities I'd get almost the same variable because it would be normally distributed with that standard deviation and that expectation, and normally distributed, as I said, means it's determined by standard deviation and expectation. So I've just picked 1 quarter, 1 half and 1 quarter. It's as if I had two moves where you could get two ups to go here, an up or a down, or a down or an up to go here, and two downs to go here. That's why a picked 1 quarter, 1 half and 1 quarter. It's like I added 2 six-month moves here and called it a 1-year move. So if I keep dividing the process and having it happen quicker and quicker, by the central limit theorem I'm going to get something normally distributed with a corresponding standard deviation and mean. So what is going to end up as the standard deviation here and here? Well, I know to get the same variance before, I had 1 half sigma squared 1 half sigma squared that equaled sigma squared, but now my variance is going to be 1 quarter sigma-- this is the new sigma hat squared, 1 quarter sigma hat squared because I'll go down whatever this sigma, so now I should put a sigma hat here. So 1 quarter sigma hat squared. So if I look at the variance of the exponent it's going to be a 1 quarter sigma hat squared 1 quarter sigma hat squared 1 half times 0 because half the time you just get the average. So therefore it means 1 half sigma hat squared has to equal sigma squared. So therefore sigma hat squared has to equal 2 sigma squared, and therefore sigma hat has to equal the square root of 2 times sigma. So I should put the square root of 2 here and the square root of 2 here. So now if I do a trinomial, for the trinomial to be similar to the binomial the binomial would be sort of here and here, and the trinomial there's a lot probability, you're stuck in the middle. So to get the same kind of average spread I'm going to have to have this thing sticking further out and this thing sticking further out, but if I choose my numbers by multiplying by the square root of 2 here, and the square root of 2 here, the standard deviation of this trinomial is the same as the standard deviation of the binomial and the expectation of the two are the same. And I could do the same thing with an N-nomial or an any-number thing I wanted to and I could always pick the standard deviation properly, pick these nodes properly so that I had the same standard deviation and expectation as I did with the original binomial tree. So just because I've got three nodes or five nodes on average they can turn out to be the same, and the average spread, the average spread squared can also be the same as the binomial. And if I do that I'm going to get a shockingly similar answer. So let's just see what we get. So what do I have to do now? I have to go to trinomial. So what did we do here? We did--9 percent was the coupon, and the interest rates start at 8 percent, and the volatility was 16. So if I go to trinomial, I put 9 percent to start, 30 years, 8 percent the starting rate and volatility is 16, and now I have to do the up multiplier, and by doing that you see I've multiplied up there in that formula there's a square root of 2 there, 2 square root of 2. So I've got just a slightly more complicated thing. I've just multiplied by the square root of 2 and that's how I've got all my nodes, so otherwise it's the same thing and I do the same backward induction except instead of being 1 half, 1 half I put 1 quarter here, and 1 quarter here, so it'll be 1 quarter V_SU 1 quarter V_SD 1 half, you stay the same, which will be 9 V_Ssame, whatever that is--so I probably lost you. So let me just say I want to convince you that this binomial assumption is not such a special case. So you should be thinking to yourself, two things happening next year, that's ridiculous. I could imagine a million things happening next year. So I say, okay I believe it. A million things could happen next year, so I'm going to write down a million things, not any million things, I'm going to say let's suppose that instead of two things happening in a year I say I divide what can happen over the year into a million different up and down moves. Now, in order to replicate sort of the original binomial, those million up and down moves, let's say 250 of them, 1 every day, those daily moves, of course, are going to be much smaller than the 1-year move. But if I make the drift be the old drift divided by 250, and the new standard deviation of the tiny things be the right ratio of the standard deviation, then when I compute the standard deviation of all the nodes here I'll get the same standard deviation as the binomial and the same drift in the binomial. So if I ended up with 3 nodes here I would just be multiplying by the square root of 2. And so by having a trinomial thing with a slightly adjusted move up and down, slightly spreading it and putting some probability in the middle, I can have the same variance and the same expectation. If I had thousands of nodes here I'd also have the same variance and the same expectation, and so I did it just for the trinomial. So let's see what happens to the value. If we look now at the interest rates, it was an uglier thing. I couldn't do it quite as--I was too lazy to do it as neatly, so the interest rates started at 8 percent and now they can go up to 10 or down to 6.3, and then the next period they can go up to 12 and 1 half. So you see there are different moves here. Remember the other one was 6.8 and 9, so if you don't get the same interest rate right away you move more violently up or down. So these three things, these two are spread out further than this. So what happens to the price? The present value of the non-call bond is 113.230 and what was it before, 113.236. It's not so different. And if I look now at the value of the callable bond it's 95.142 and what was it before, 95.529, a little bit different. So you can see that the trinomial thing gives you almost the same answer as the binomial. So I don't want to say anything more than that. So no matter how many nodes you have in the tree the binomial's going to give a good approximation provided that we shrink the periods. Instead of looking at a year, looking at daily moves or minute by minute moves, as long as those are binomial over a year a million things can happen. And so you can restrict yourself to binomial without any loss of generality just taking the time period short enough, because if it's a daily binomial over a year there's 250 outcomes or something and so for a minute there are thousands of outcomes over a year even though each move is binomial and you'll get the same answer. So that's that. All right, so we've done the callable bond idea, and the call option is worth a lot. Now, let's take a more concrete example, the one that you've all heard your parents talking about, if you don't own a house yourself, which is a mortgage. And I just want to do the same thing and help you start to think about how to value mortgages. So what's a mortgage? A mortgage is, you don't have the balloon payment at the end. You pay the same amount each period. Let's take a mortgage. So which example have I done here? So I've got a mortgage rate of 7 percent, a 7 percent coupon, you can see, and it's a 30 year fixed rate mortgage. Now, how much does that mean you have to pay every year? So, every year, what are you going to pay? You're not going to pay 7. What this means is, whatever X you pay-- every year that's your annual payment-- the 30th year you're still going to pay X, but if I took this all over 1.07 X over 1.07 squared this over 1.07 cubed this over 1.07 to the 30th I would get 100, equals 100. So that's how X is chosen, so that the mortgage is an annuity of constant X whose present value at the coupon is equal to 100. That's how you define the payment on a mortgage, but a mortgage has to be defined more completely than that. You also have to say what do you get by dissolving the mortgage, how much do you have to pay? So right away you have to pay 100. What would you have to pay here if you dissolved the mortgage right after the-- so remaining balance equals payment just after coupon necessary to dissolve the mortgage. So at the very beginning the guy gave you 100. If you want to dissolve it and undo it you should be able to do it for 100, but what about after the very first year you've paid X? By the way, X in this case is going to work out to 8.05. If you solve for X you get 8.05. That 8.05 discounted at 7 percent gives you 100. So obviously X has to be bigger than 7 because if it were 7 everywhere you'd need 107 at the very end to make it 100. Of course at the very end that's 30 years later, so that extra 100 can be compensated by an extra 1,1.05 all the way along. 1.05 all the way along is just the same as an extra 100 at the end. So the payment is 8.05. So if you're paying a 7 percent mortgage your annual payment is going to be more than 7 percent. It's going to be 8.05. So that's the 7 percent coupon of the mortgage, coupon of mortgage. Now, if you want to get out of the mortgage it's called prepaying. What would you have to pay here to get out of the mortgage do you suppose? What's the only logical thing to have written in the contract? Student: Penalty. Prof: Well, you could pay a penalty, but what if you don't want to have a penalty? Then what should the guy pay to get out of the mortgage? Yeah? Student: The remaining balance. Prof: The remaining balance, yes, but what is the remaining balance? That's the question, what is the remaining balance. Well, maybe you know what the answer is. Student: It's the present value at the time. Prof: Of what's left. So the guy here, the remaining balance, B_1, ought to be this number without this. You've only got 29 payments, only you're going to put a 1 here now, right? So it's B_1 squared and B to the 29th because you've made the first coupon payment. You've got 29 years left assuming the same terms as before it still is a 7 percent coupon, so you should discount the remaining 29 years at 7 percent to get B_1. So that's what B_1 is. So as you can see in the thing B_1 is 98.94. Now, 98.94 is an interesting number. You notice that the 8.05 minus 7 happens to equal--that plus B_1 has to equal 100, which is B_0. So why is that? So you started owing the guy 100. You've borrowed 100, you own him 100, and he's sort of charging you 7 percent interest. That's the way the deal works. So you would have expected to only pay 7 dollars next period. That's to keep up with the 7 percent interest. Remember, why did the old mortgages go from the balloon payment to this? Because in the Depression in 1933 every single farmer, practically, who owed the 109 because his mortgage was coming up defaulted. So the lenders decided they didn't want to be facing that situation where a guy owed 109. They'd rather have the guy pay X every period where there's never this gigantic payment that he's going to default. In fact, by paying X every period that lender's in a safer and safer situation. Why is that? Because he's asking for X which is 8 dollars even though the interest is 7 dollars, so the homeowner is paying 8.05. The interest was only 7. So he's making an extra payment of 1.05 dollars. So what do you do with the extra 1.05 dollars? You write down the balance. You say you've overpaid me by 1.05. I'm no longer going to say you owe 100. You're going to owe, now, 100 - 1.05. 1.05 had a few decimal places after it, and so it's going to be 98.94136. So that's this gap, so B_0 - B_1. The balance went down by exactly what the overpayment was beyond the interest. And so the next time the balance is going to go down even further because the next time the balance is only B_1. The next time what the guy owes--if he was just paying the interest he ought to owe only .07 times B_1, and yet he's still going to be paying 8.05, so B_1 - B_2. So the balance B_2 is going to go down even more, so the gap from 100 to B_1 is a very small one. It's going to be bigger from B_1 to B_2 and keep getting bigger and bigger because each time the guy's paying 8.05, but what he owes, the balance that he owes on, that he's basically borrowed the money on is a smaller and smaller number, so he's overpaying the 7 percent interest by a bigger and bigger amount and the balance goes down by more and more each time. All right, to put it another way, if you take the first thing is, B_1 is X times 1.07,1.07 squared, 1.07 to the 29. B_2 is X 1.07 blah, blah, blah, X times 1.07 to the 28th. So the difference between this and this is the last payment which is 1 over 1.07 to the 29th. The difference between this and this is the last payment which is 1 over 1.07 to the 30th. And so as that final maturity gets smaller and smaller the gap gets bigger and bigger, so I'm just saying the same thing in different ways. So are there any questions about this? Did I go too fast or are you with me? Somebody ask a question if you're lost. Yes? Student: Why don't we discount B_1? Prof: Why do I what? Student: Discount B_1? Prof: I'm sorry, why do I--say it louder. Student: Discount. Prof: Why do I discount what? Student: Why don't we because you are subtracting the amount from the 0 >? Prof: Yes this, so let me say this again. You borrowed 100. The coupon is the agreed upon interest, so you should owe the guy 7 dollars, or 107 dollars the next period, right? Not 100 any more. There's 7 percent interest. Now you owe the guy 107, right? But at that moment when you owed him 107 you paid him 8.05. So the guy says, look, I lent you 100, I expect 107 back next period, you pay me 8.05. That's 8.05, so what's left that you owe me? It's 100 minus the 1.05. So 98.4 something, so let me just say it again. You borrowed 100. The next year you owe 107. We've already taken into account the interest rate. It's 107, so we're sitting in next year. We're no longer sitting back here. B_1 is as of next year. So you should really by rights be owed now, the lender should be owed 107 now because he lent 100 last year. The agreed upon interest is 7 percent so he should be getting 107 this year. What is he getting? He's getting 8.05, so what's left is 107 - 8.05 and that's what we have, what's left is 107, is exactly that. Right, so this is 7 he got paid, so if I write it this way 107 he got paid 8.05, so 107 I'm just rewriting the same thing, 107 - 8.05 is going to be the new B_1, which just happens to equal 90 whatever that is, 98.05, something like that, 98.95, right? So this is 1.05, so 1.05 plus this is 100. So 107 - 8.05 is 98.95. You agree with that, right? Student: Yeah. Prof: So what I'm saying is a year later you were owed 107. You were paid 8.05, so obviously what's left that you're owed is the difference, 98.95 and that's exactly what the equation was that I wrote before. Any other questions? So you can always divide a mortgage payment into the interest part-- so any mortgage payment X can be divided into the interest so now let's erase this and I'm saying it in other words. So your payments are X everywhere to the last period and your remaining balance is going to be B_1, B_2, B_3 and B_30 which is obviously equal to 0. So you can always get out of the mortgage by paying--after you make a coupon payment X you can get out of it by paying B_2. So your mortgage payment is going to be divided into the interest, and then the scheduled principal reduction. So here you pay 8.05. The interest was only 7 percent so you've overpaid. So that's why the balance goes down. That's the scheduled balance--It's called principal, but scheduled balance reduction. And if you want you can prepay and pay off part of the remaining balance, any part you want to. So let me say it again. In some period, let's say 3, what could you do in period 3? Well, by the time you've waited to period 3 you've got to pay the coupon X. Now, the coupon X is way in excess of 7 percent times B_2. It's 8 and 7 percent of 100 is less than X. We're already down to a balance of B_2. So the X is bigger than 7 percent of B_2. So 7 percent of B_2 is the interest, but on top of that you paid more than that, so that extra you paid reduced the remaining balance. That's the scheduled reduction in the remaining balance. You paid that off. You had no choice about that, but now in addition, if you want, you can pay the B_3 and get rid of the whole mortgage. That's the rules of a mortgage. Is that clear to everybody? So any mortgage that you get, works by those rules. So we have to figure out the value of the mortgage. Somehow I feel I'm going too fast. Could someone ask a question if you're lost? I need to pick out--yes? Student: So what you just said applies that as time goes on you pay a bigger and bigger chunk of the principal with each successive payment? Prof: Yes. So the mortgage is called an amortizing mortgage. This was a great invention at the time of the Depression, after the Depression. It probably had been invented before, but was used in a big way after that. I don't know the person's name who invented it. First it has the property that you're always paying more. Because you're paying level payments you must always be paying your principal down. That makes the lender safer and safer because it's the same house protecting his loan as collateral. We haven't come to collateral and how the whole world depends on collateral yet, but believe me we're going to get there. And so we haven't gotten to collateral yet, but when we get to it, the lender's protected by the house. The amount that's owed to him started at 100. It's getting lower every period so he's feeling safer and safer. That contrasts to the old lenders during the Depression who were at the most vulnerable right at the end-- oh, I've lost it--most vulnerable right at the end. Here these lenders are getting less and less vulnerable as time goes on. So that's the advantage of an amortizing mortgage. Now, it so happens that the rate of amortization gets faster and faster. So these numbers start at 100 and stay pretty close to 100, and then they go down pretty fast, which is what his point is, and that's absolutely right. And so if you look at the remaining balances here in this chart it started at 100, went to 98, went to 97,96, 95, now 93,92, 90. They're going down faster and faster. If you keep going you're going to see that they start leaping down from 76 to 73,73 to 70. Now they're starting to go from 43 to 38. They're really, by percentages, going way down really fast, 21 to 14 to 7 to 0. So they go down really fast at the end, the remaining balance. But that's just the way the amortizing fixed interest mortgage works. And now we want to think about how to value it, all right? So the payment is 8, the coupon that they agreed on in the mortgage was 7 percent, but that's different from what the interest rate is in the whole economy which is 6 percent, say. So suppose the interest rate is 6 percent. Why would it be that with a 6 percent interest rate today, one year interest rate today, why would it be that if the interest rate was 6 percent today-- too complicated, this tree--if the interest rate were 6 percent today why would it be that the mortgage rate that people would agree to-- so it could be 6 percent--why is it that the mortgage rate people could agree to-- so this is 7.3 percent and this went down to 4.9 percent. That's in that tree. So you tell me, why is it that when the interest rate is 6 percent today-- so everybody knows on average it's going to stay around 6 percent, and here I want to get a loan from a bank to buy a house and I put up my spectacular house as collateral so the bank should feel safe. It's amortizing and all that. They should feel safe as long as they haven't lent me too much money, right? By the way, if my house is only worth 80 dollars and they lend me 100 then the bank is in trouble. If the house is worth 100 and they lend me 100 the bank might be in some vulnerable situation if the house loses value. So banks would have to be stupid, as they were, to make loans of the home value almost equal to the house value, but we're going to come back to that. So suppose the house is worth way more than the 100 they lend me. The amount I'm owing the bank is only going down, so the house is protecting the bank completely, has no worries of me defaulting because it'll just take my house. Let's take that case. The interest rate in the economy is 6 percent and here the bank is charging me 7 percent mortgage rate. That's what we agree on, and of course when it charges me 7 percent mortgage rate I'm going to be paying 8 dollars every month. How could that possibly be fair? Or to put it another way, why does the bank have to charge a mortgage rate that's way above the starting interest rate? Why would it have to do that? Why does it do it and why is everyone willing to pay it? You see what the question is? Back there, yes? Student: You have the option of prepaying it. Prof: Right. I've got this really valuable option, which of course the bank realizes. I can always get out of it. I can pay the remaining balance and get out of it. Now, what am I hoping for when I take my 7 percent mortgage out from the bank? What am I hoping for? How am I going to make money, the homeowner? Yes? Student: If the interest rate rises. Prof: Right, so if there's some tremendous inflation like there might well be now, some tremendous inflation in the next 5 years-- this is a 30-year loan. If in the next 5 years the economy's in so much trouble and we've got all these homeowners under water and we owe so much money to the Chinese we could well see the Fed engineering a gigantic inflation, so the interest rate might go up to 10 percent. I'm continuing to borrow effectively at 7 percent from the bank. How can you see that? Because this remaining balance, remember, the whole way it's structured is, the payments, after a year, the 100 I borrowed goes down to B_1, but it's like a 20 [correction: 29] year mortgage where I've borrowed B_1, again, at 7 percent interest. After the third year, right, just after making my payment the 27 years left of the mortgage are treated explicitly by the law of the contract as if I borrowed B_3 dollars at 7 percent interest. So in other words, a mortgage is like a contract where every year I get to re-borrow at 7 percent, but I'm borrowing a smaller and smaller amount. So I perpetually get to borrow at 7 percent, but I have the option of canceling the whole thing by paying off the remaining balance. So I'm hoping that the interest rate's going to go to 12 percent and I'm going to be borrowing still at 7 percent, borrowing at 7 percent and reinvesting it at 12 percent. I'll make a killing. I'm praying for interest rates to go up. Now, most homeowners think that they're praying for interest rates to go down, but they just have it all backwards. They think if interest rates go down they'll get a lower mortgage with a lower interest. They don't realize that the present value of their future payments, are going to go up. So they should be hoping for the interest rates to go up. They should be hoping for a big inflation and that's when they're going to make money. And the option that the homeowner gains if interest rates go up and the homeowner can always get out of the mortgage and pay it off if the interest rates go down by paying off the remaining balance, that's tremendously valuable. So how do we compute that value? We have to do it by backward induction. You can intuitively see there's some value, but you don't know exactly what it is until you do it by backward induction. So here the payments are always 8. The payments we said were 8.05 and 8.05 and then at the end 8.05. So we know that at the end the present value of what the bank is going to owe, the present value of how much the homeowner is going to have to pay, let's do it that way, it going to be 0. So we know that at this point the value that's left is 0 because there are no payments after this final--that's year 30. There are no payments after that. So assume that we've figured out the value and we're working backwards. So we are at some node like this one where we know the interest rate and we want to figure out what the value is here just after the coupon payment is made. So what's the value? Well, the homeowner has the option of making--remaining balance, remember, was B_1, B_2 and this is B_30. So at this node here this is 0, this is times 0. So we have B_0 = 100. At time 1 the homeowner, he's made the payment here, so at time 1 he could just pay B_1 and be out of the whole thing, or he could make his payment. So if he makes his payment then he owes the 8.05-- sorry, he's just made his payment, so he could either get out of the whole thing by paying B_1, or he could wait to see what happens next period. So half the time he's going to go up, so he's going to have to pay 8.05 and then he's going to have a decision then to make, but we're working by backward induction. We've already solved out for what the value of his decision is there. So it's V_Sup half the time he's going to have to pay 8.05. He's going to be down here, and then he's going to have the remaining-- he's going to have to decide whether to pay off the remaining balance or not, and V_Sdown is that decision, because we've already figured out whether he should prepay or not here. So that's it. It couldn't be simpler. At every node after the coupon payment is made the guy has the choice of paying or, I mean, of prepaying, paying off the remaining balance or waiting until the next period, and then he has to pay the coupon if he waits until next period, and if he doesn't pay the coupon then... Student: What happened to the interest rate? Prof: Oh, what happened to the interest rate? Well, I forgot it. So thank you. So I have to put this in brackets and multiply by 1 over 1.049. That's what happened to the interest rate. I just forgot it. So either he pays the remaining balance or he waits, and of course he has to discount it by the interest rate there which is 1 over 1.049 times 1 half times what happens over here 1 half times what happens over here. And that's it, and that's what I've written down in the nodes. So here are the interest rate nodes and here are the present value--so here's the non-callable mortgage. So the non-callable mortgage, if the homeowner was so stupid that he never prepaid and the mortgage interest rate is 7 percent and the interest rate starts at 6 percent that's obviously great for the bank. The guy's stupidly always going to pay, never prepays, the bank makes 109 dollars, but if the guy is much smarter than that he's going to call. And now, lo and behold, the value's only 95.55. The option is so valuable that even though the interest rate is 6 percent, the mortgage rate is 7 percent, the banker's incredibly overcharging him, and the guy will never default, still the bank is getting a terrible deal because the option's so valuable to the guy. So what is a bank going to do in that case? What would a bank do? I mean, if you were the banker what would you do? The interest rate is 6 percent. You can't control the interest rates. That's the whole economy. Everybody's patience, and impatience and all the Fisher stuff, is determining all these interest rates. What would you do? You wouldn't charge 7 percent as your mortgage rate. You'd have to charge a higher mortgage rate. Maybe you'd charge 8 percent, and so we could just change the whole thing to 8 percent and redo it, and you'll see that the guy will do better. So the mortgage rate, let's put it as .075 instead of .07. So now the annual payment's gone up and everything is going to change. And so the interest rate process is the same. If the guy never prepays it's now worth 114, and if the guy does prepay optimally, well, you still haven't gotten it high enough. You have to make it 8 percent, maybe. So the interest rate looks like it'll have to get to a lot above 6 percent. Maybe it'll have to go to 8 percent. Maybe 8 percent isn't enough. Well, on average--let's just try .08 and now we can see how that worked out. Interest rate process is the same. Look at this. If the guy never prepays it's worth 120. If he does prepay it's still not enough. So it's going to have to be 9 percent or something. Now, typically if the interest rate is 6 percent the mortgage rate will be something like 7 and 1 half percent, not the 9 percent or 10 percent I'd have to get up to. So why do you think that is? Yes? Student: Maybe there are enough dumb people who don't prepay to make up for the smart people who do? Prof: Exactly. You have to count on the dumb people. That's an important fact of life. You not only have to count on them, you have to count them. So you have to figure out what fraction of the population is this that's only going to pay you 98 in the end, and what fraction of the population is this, they're going to pay you 120 in the end. And if you knew which of the guys were the 120 guys, what fraction were the 120 guys and what fraction were the 98 guys you'd know what the thing was worth. So how far am I going? All right, so if you're a mortgage hedge fund, my company is a mortgage hedge fund. That's what we started out with. We quickly did these calculations and now-- all right, so if you look at the data you're going to find-- oh, by the way, Sunday I'm having, remember, this extra class Sunday night to tell you a little bit about the real world, so I'm going to save the stories of all the data and stuff until then, but basically we look at how people have behaved in the past. So were doing this tree and we're figuring out, from this tree you can figure out when the people should have prepaid or not. Actually the next tree, if you have 1 dollar's worth of principal, if you assume that the original principal was 1 dollar instead of 100 and you always figure out at every node what would 1 dollar's worth of principal be there, you can find out in an easy way when people should prepay. So here you can see where all the 1s are is when they should have prepaid. I don't have time now to explain that, but anyway just a slight modification of the tree shows you when they should prepay. So you can look at when people should prepay and you can look in the data at how many of the people do prepay. So you can go house by house. It's public information. Are these people prepaying or aren't they prepaying? How smart are they? And you can deduce from having watched them in the past miss opportunity after opportunity to prepay you know that these guys-- now, it's not a matter of being stupid, in fact the smartest people might be the ones not prepaying, they're not paying attention or maybe it's a real hassle for them to prepay. So we're going to come to the reasons why they won't prepay. So you have to calibrate how many people are behaving optimally and how many people aren't, and then you can judge how high you have to set the interest rate to make a reasonable profit. And I'm going to talk more about that next time.
Quantitative_Finance_by_Yale_University	4_Efficiency_Assets_and_Time.txt	Prof: So we have begun by talking about general equilibrium, and this was the background to the course so that you're all familiar. Those of you who haven't taken freshman economics or intermediate economics, what's the background that's required for the course? And the fact that general equilibrium is a part of finance is, as I say, a bit of an innovation because most finance courses are taught entirely independently of economic theory. But the two greatest Yale economists and two greatest Yale financial economists had finance and economics integrated, and I believe that's the only right way of looking at the problem. And as I said at the very beginning, I think the events of the last few years have confirmed that view. So let's take up the question today of why is the free market supposedly so good. So we worked out two examples last time, and the two examples are very similar to the first problem set that you did. In the first example you've got two agents A and B, and whenever we write agents A and B we really mean a million agents just like A and a million agents just like B. The heart of perfect competition in the economy is that there's lots of people, and so we can't--yeah, I think from now on hand them in at the end of class. So we mean a million people of type A and a million people type B. So the utility function of A, the welfare function of A is written there, and the welfare function of B is written and they each begin with endowments. So when these two million people come together they're going to be doing the same thing that you saw in the class on the first day. They're going to be haggling, and arguing, and the buyers are going to always say "the stuff's not worth very much and why should they pay you so much," and the sellers are going to say "it's worth a tremendous amount and they should pay even more," and eventually they're going to come to prices. And we discovered last time that the way of describing what prices and what final allocations they come to is by writing down a system of equations, and you did that all in your homework and we came up with this outcome. So similarly we did another problem in the last class and we wrote down different welfare functions or utility functions and different endowments and again we got the equilibrium. So we said that one of the amazing things is that these system of equations, the six equations for each economy that you solved in class always have a solution. So the people who discovered that discovered it at the Cowles Foundation. They were Ken Arrow, Gerard Debreu who was a Yale assistant professor, Ken Arrow who was visiting the Cowles Foundation in Chicago but was a Stanford professor, and Lionel McKenzie who actually taught at Rochester. The economic equations always have a solution. So what's so good about that economic solution? Adam Smith talked about the invisible hand, but there was no mathematics in Adam Smith. So why do we think equilibrium is such a good thing? After all, you saw in the example that there were three pairs of people who forlornly couldn't trade at all. So clearly not everybody gets to trade, discrimination happens. Some people get the stuff. Other people don't get the stuff. Well, the first approach of economists was that equilibrium maximizes the sum of utilities. So let's see how that works in this example. So this example's very special because everybody thinks that the good Y has constant marginal utility of 1. So that's going to play a big role in our optimization in maximizing the sum of utility. So if you want to maximize the sum of utilities you have to maximize (100X^(A) - 碼^(A) squared) (30X^(B) - 碼^(B) squared) (Y^(A) Y^(B)) such that X^(A) X^(B) = 84 which is the sum of 4 and 80 and Y^(A) Y^(B) = 6,000. So the claim is that if all these two million people meet in a room like this and start shouting at each other, and trading and offering deals and stuff, it's going to come down to a final allocation which we've written over there were A gets 77 of the first good and B gets 7 of the first good, and that final allocation is going to maximize the sum of utilities. So why should that be the case? In fact in this example it is the case. Well why is it the case? Because there's constant marginal utility of Y, so we don't have to worry about the Y allocation at all because if you increase Y^(A) and decrease Y^(B) they still have to add up to 6,000. You're going to be lowering A's utility and raising B's utility by the same amount so you won't have changed the sum of utilities. So the Y's are totally irrelevant to this maximizing the sum of utilities. So all we have to do is make sure that the X allocation, maximize the sum of utilities for the good X. So that you can see must be the case because we have to maximize the sum of two people's utilities or two million utilities. You can always plug in X^(B) as a function of X^(A), namely 84 [clarification: X^(B) = 84 - X^(A)]. So let's write it as a function of X^(A), and we can replace this maximization by recognizing that X^(B) is just a function of X^(A). In fact, it's a very special function where the derivative of X^(B) with respect to X^(A)-- so let's call the function, we'll call it that to denote that it's a function-- happens to equal -1. So we want to maximize this over X^(A) taking into account that X^(B) is just a function of X^(A), because to maximize you have to keep feasible. So we've now ignored all the constraints. Constraints have now disappeared provided we keep track of the fact that X^(B) is a function of X^(A). So why is it the case that the equilibrium 77 and 7 maximizes this? Well, the key is diminishing marginal utility. We know that the utility function for-- here's X--utility function for A is quadratic so it looks something like that, and the utility function for B also looks something like that. And so if you look at this function entirely as a function of A it's also going to look like that. So by diminishing marginal utility, the function, the sum of utilities is concave. Concave, remember, is a picture like that. So what is the essence of a picture like that? It means that setting derivative equal to zero implies you are at max. So that's not true of any function. If you have a function like that and then it goes up like that you could have the derivative of zero here and not really be at the max, but because there's diminishing marginal utility more and more of X does less and less good so it turns down. So all you have to do is figure out that the derivative is zero, which it is at this point, and then you know you're at the maximum. But that at X^(A) = 77 has to be the case because if you plug in X^(A) = 77 and you take the derivative of all this with respect to X^(A) of this whole thing, taking into account as before that X^(B) is a function of X^(A), you just get (100 - X^(A)) now it's just going to be (30 - X^(B)) times the derivative of X^(B) with respect to X^(A). Why is that? Because you know the chain rule, if I differentiate everything with respect to X^(A) and X^(B) is a function of X^(A) it's just 30 because I'm taking the derivative with respect to X^(B). So it's 30 times the derivative of X^(B) with respect to X^(A) minus the derivative with respect to X^(B) is X^(B) times the derivative of X^(B) with respect to X^(A), so it's that. But if you plug in X^(A) = 77 and X^(B) = 7, DX^(B), DX^(A) is -1 you just get 23 - 23 = 0, because the marginal utility of A is equal to the marginal utility of B at equilibrium. The sum of utilities is maximized, and that's the end of the story. So that you noticed in the problem set, something like that. You may not have given exactly this argument. That's what you were supposed to have sort of discovered in doing the problem set and now we've confirmed what you already pretty much knew. So are there any questions about that? It's just the simple generalization of our football ticket example where the football tickets end up in the hands of the people who want them the most, and A happens to like a lot of tickets, not just one, and so A's going to keep buying tickets until he's bought 77 of them. And by then the next football ticket is worth less than 23 to him. B, she likes football tickets a little less. She's not going to buy as many. By the time she gets down to 7 football tickets she's going to think--so she hasn't bought nearly as many. When she's gotten to 7 football tickets she's going to think the next one's worth less than 23. And since the price is 23 they're going to both stop there, but they're each going to stop at the same point where the last ticket is worth the same to each of them, and all the previous football tickets each bought is worth more to each of them. So there's no way of rearranging the tickets because if you did you'd have to take a football ticket that was worth more than 23 from one of them and give that ticket to the other one who by then would think it was worth less than 23. So that's the argument. Okay. So economists were beside themselves with their brilliance in having proved this theorem and given a mathematical form to the invisible hand. Whenever you take a verbal argument like Adam Smith and turn it into a mathematical argument you've understood it better. You understand why it's true and you also start to understand why in some circumstances it might not be true. So for 50 years, let's say between 30 and 50 years this was the fundamental argument of economics and economic equilibrium that equilibrium was a good thing because it maximized the sum of utilities. But then little by little, starting with Irving Fisher and a bunch of people at the same time and a little bit later, so Hicks and Samuelson are famous for this, they began to wonder what kind of crazy utility functions are these where there's some mysterious good that has constant marginal utility of 1. So in modern terms how could you justify it? You could say, "Well, maybe there's a machine where we can calibrate exactly how happy people are and we can measure it. So for example, we can measure how aroused their skin is. The skin texture changes as you become less and more aroused. Maybe we could measure that. With MRIs we can measure brain waves. Maybe you can calibrate how many brain waves are spinning around and how happy somebody is, and maybe there's some mysterious good like food that has constant marginal utility." Well, that doesn't seem very persuasive to me and it wasn't to the economists of the beginning of the twentieth century. They all argued, starting with Irving Fisher, that it made no sense to think that we could actually measure utility, and more than that it made even less sense there'd be some good that had constant marginal utility of 1. So Fisher put everything on a symmetric footing and said, "Let's think of the two goods, X and Y, as more or less symmetric. I mean, there's no reason why one has to have some special role." So let's look at this equilibrium which we got the same way, and you did this on a problem set solving for equilibrium. Does this maximize the sum of utilities? Well, the answer is if it did maximize the sum of utilities at the final allocation we couldn't gain anything by switching, reducing 9 fifths a little bit and increasing 6 fifths a little bit. But what is the sum of utilities? So if you write W^(A) W^(B) it's going to be for one thing (3 fourths log X^(A)) (2 thirds log X^(B)). So let's look at the marginal utility to X^(A)--of good A. That's 3 fourths, so marginal utility of A,X marginal utility of B,X = 3 fourths times 1 over 9 fifths which is 5 ninths. That equals 15 over 36, which is 5 over 18 if I've done that right. It doesn't sound right. Student: It's 5 over 12. Prof: 5 over 12. Thank you. That sounds better. But let's look at--so this is the margin utility of X^(A) is 5 twelfths. What's the marginal utility to B of X? Well, it equals 2 thirds times 1 over 6 fifths, which is 5 sixths, which is 10 over 18, which is 5 over 9. So these two numbers are different. The marginal utility to B is bigger than the margin utility--of X--is bigger than the margin utility to A of X. So clearly the final equilibrium allocation doesn't maximize the sum of utilities. By switching some goods from A to B you could make both people better off [clarification: you could increase the sum of both peoples' utilities, though one person would end up worse off in the process]. So that was a shock to economists. It meant that the argument they'd relied on, the thing which they were using to persuade policy people that the free markets were a good thing, is a false argument. It rests on a premise that's indefensible, namely that there's constant marginal utility and everybody can measure it. So they needed some other definition, some other way of capturing the mathematical idea that the invisible hand is a good thing. And the reason I'm spending so much time emphasizing this, even though you've seen this before, is because if economists made a mistake once what makes you think they haven't made another mistake? So now let's give the argument that in a weaker sense the invisible hand holds, that is that the free market comes to a very socially desirable equilibrium. And later in the course we're going to find that that argument is also too narrow. So my point that I'm going to gradually get to is that economists have constantly taken too narrow and too special a view of the world, and as you enlarge the view of the world you have, not by making things mathematically simpler, actually you have to make them mathematically slightly more complicated, as you enlarge the view of the world you have you get closer to the truth and you start to find that the free market isn't quite as wonderful as you thought at first and therefore there's room for government regulation. So it's not, as Paul Krugman argued, that economists are transfixed by mathematics and seduced into simple conclusions that the free market is perfect. On the contrary I would say they were afraid of too much mathematics, and by looking too narrowly they didn't realize what they could have just by being mathematically more sophisticated. So it's a failure of sophistication, not too much sophistication. So what did the economists argue? So the chief among them, Hicks, Samuelson, Pareto and Fisher, all these people basically came to the same conclusion. They said, "Well, it makes no sense to talk about the sum of utilities." Let's talk about Pareto Efficiency. So what's the general problem? The general problem is you start with an economy made up of all these individuals. Let's call them W^(A) and W^(B), but it could be as many as we want so let's just say W^(i)-- and E^(i), so E^(i) is the endowment of X and E^(i) of Y. So that's the economy. You start from the economy and you go to equilibrium. And equilibrium is a price vector P_X P_Y and allocations X^(i), Y^(i), i in I, such that summation over all the i's of X^(i) equals the summation for all the i's of E^(i)_X. So i's final consumption of X, plus j's final consumption of X, plus everybody else's final consumption of X, those are the sum of the X^(i)'s, is equal to the sum of everybody's endowment. And similarly for the Y's, [equals the sum] of E^(i)_Y and such that everybody is doing what's in their personal interest which is maximizing W^(i) of X, Y, so, the max of W^(i) of X, Y such that [(P_X times X) (P_Y times Y)] = [(P_X times E^(i)_X) (P_Y times E^(i)_Y)] is solved by X^(i), Y^(i) for all i. That's the definition of equilibrium. Everybody individually optimizes looking at his own budget set, the hell with everybody else, does the best in his interest, chooses X^(i), Y^(i) at the going prices, supply equals demand, that's how you get the final allocation. So that's the definition of equilibrium and now we're trying to argue that's a good thing. So what's our criterion? Well, what Pareto and Edgeworth and everybody else decided is, "Let's look at the welfare functions W^(A) and W^(B)." So if you take some allocation like the original allocation 2-1 and 1-2 you'll have a welfare of each person, (3 fourths log 2) (one quarter log 1) that's the welfare of A, and the welfare of B will be (2 thirds log 1) (1 third log 2), so that'll be some point here. So this is welfare B, welfare A at initial endowment. And then if you look at the welfare at the final allocation, so, (3 fourths log 9 fifths) (1 quarter log 3 halves) you know it's going to be something like this. It's got to be up here. It's going to be better for both people. How do you know that? Because A had the choice of just buying his initial endowment--that's always affordable and he chose not to do it. He chose to do something else and he was better off and the same with B, so clearly the equilibrium allocation is going to be better than the initial endowment. And so the Pareto criterion is that an allocation X^(i)-hat, Y^(i)-hat, Pareto dominates an allocation-- so this is for all I--X^(i), let's put the i's on the top. If and only if everybody's better off: W^(i) (X^(i)-hat, Y^(i)-hat) is bigger than W^(i)(X^(i), Y^(i)). So we started with an allocation, the E allocation here, and then we moved to competitive equilibrium here and everybody was better off. So the equilibrium allocation Pareto dominates the initial allocation. But now the question is maybe there's some other allocation besides the competitive equilibrium allocation that dominates the equilibrium allocation. So the theorem is that if P, (X^(i) Y^(i)), i in I is an equilibrium for the economy E-- remember we defined the economy E, I better put E here-- then no allocation (X^(i)-hat, Y^(i)-hat), i in I, Pareto dominates (X^(i), Y^(i)) if summation X^(i)-hat equals summation E^(i)_X and summation-- got a little too tight here, sorry about this, Y^(i)-hat equals, this is over i, equals summation E^(i)_Y. So I can read this, it's really bad. It's a critical line right in the corner. So I'll just say it in words and then read it literally. So this allocation dominates this one. The competitive equilibrium dominated the initial endowment, but maybe there's some other way of rearranging the goods that gets you even further out here. The theorem says that's impossible. So it says if you start with a competitive equilibrium, with an allocation (X^(i), Y^(i)) for the economy E, the no allocation like that one, no allocation (X^(i)-hat, Y^(i)-hat) can Pareto dominate it. This couldn't happen. You'd have to be down here somewhere. That couldn't happen provided this other allocation used up the resources that were available. So the sum of the X's in this allocation is the sum of the initial endowments, and the sum of the Y's in this allocation is the sum of the initial endowments over the people. So of course if you add more goods to the economy you can make everybody better off, but using the existing goods in the economy, which is the sum of the E^(i)_X's and the sum of the E^(i)_Y's, there's no way to make everyone better off than at the competitive equilibrium. So it says literally if P (X^(i), Y^(i)) is an equilibrium for the economy E, which is that, which includes the initial endowments, the no allocation (X^(i)-hat, Y^(i)-hat) Pareto dominates (X^(I), Y^(I)) if the sum over I of X^(i)-hat equals the sum over i of E^(i)_X, and if the sum of the Y^(i)-hats over i equals the sum of the E^(i)_Y's. That's the theorem. So we've totally weakened the definition of equilibrium. So it might be that if this is the competitive allocation if you look at this line this is same sum of utilities, because if this slope is -1 and here's the utility to B and the utility to A everything on this line has the same utility. So that theorem would say anything else that's feasible had to be down here. The sum is less than that. But here we're not saying that. We're no longer saying that. Maybe you can increase the sum. From this equilibrium you could increase the sum by taking something away from A and giving it to B. You could increase the sum. So that would have been here. You increase the sum, so you no longer have maximized the sum, but the fact is to make B better off you had to make A worse off and that's the new criterion, Pareto Efficiency. So that's the theorem and now we're going to prove it so that you can see the whole logic of the free market just amounts to that. So are there any questions about this? You all supposedly saw this before, but that doesn't mean you really did. So does anyone have a question what's going on? This is a very basic incredibly important idea. All right, so I'll give you one more chance. Somebody must have a question. Yes? Student: Could you just re-say the theorem a little bit more slowly? Prof: Yes. Why don't I draw a picture, which is what I was going to do anyway? So let's draw a picture, and I'll bring the theorem back after having drawn the picture. So the picture is going to be due to Edgeworth. So he invented the indifference curve and he invented it in order to draw this picture. It was an incredibly clever picture. So he says, "Let's look at this economy," the one on the right that we start with. We put X^(A) here and X^(B) here and you notice that A begins with an endowment of (2,1). So let's put his endowment (2,1) here. So this is E^(A)_X = 2 and this is E^(A)_Y = 1, right? That makes sense. Now we can draw his indifference curves through that. So his indifference curves he likes X more than he likes Y, so the indifference curves are going to be sort of vertical. He doesn't like to give up X very much, so his indifference curves are going to look sort of like this. And the most important indifferent curves are the ones where he gets better off than he was before. So now in the end there's going to be a budget set which is X is way more expensive than Y, so there's going to be a budget set that looked like this. That's sort of the budget set that he faces. And he's not going to choose this. It turns out he chooses something like here which is he chooses a little bit less of X, 9 fifths, and a little bit more of Y. So here's X^(A) = 9 fifths which is a little less than 2, and X^(B) he chose was, I can't read it, 3 halves which is more than 1. Are you with me? You asked the question. Does this picture make sense? Student: Yes. Prof: So he obviously did better than he did before, but we've got another guy to worry about. So how can you put the second guy in the same diagram? Well, let's just add the total endowment. Where's the total endowment? Well, it's 3 units of each. So here we've got 2. So this is 1,2, this must be 3. So the total endowment of good X is 3,2 1 is 3 and a good Y is 3 as well. Here's 1, here's 2, here's 3. This is supposed to be a square. The aggregate endowment is here. This is the total endowment, 3 of each. What are the feasible allocations? So this is an extremely clever insight of Edgeworth's. He said, "Look, the total endowment is (3,3). If I tell you that A has got (2,1) (that's this point) what's left over, B must be consuming." So B's consuming the distance from here to here which is obviously (1,2). And if A ends up over here at 9 fifths, 3 halves, that's from here to here is 9 fifths and 3 halves, since the total is (3,3) B's obviously consuming what's left over, so he's consuming this difference. So whatever A does you can see in the diagram looking at it the normal way, but if you just sort of twist your mind a little bit and look from this direction, once you know what A's doing you can figure out what B's doing, so each of these points defines a feasible allocation. And now what we want to say, the theorem says, look at the utilities that A and B got out of this allocation. A is on this indifference curve. You know what he's doing. B you know is coming from here. We know how he's doing. So look at the allocation they got. You can't make both people better off than that by choosing some other point in this square. So let's look at it from B's point of view. From B's point of view B likes more of everything. So if A gets less B's going to get more. So from B's point of view the further out you go this way the better it is for B. So the axes for B looks like that. So he's going to have some indifference curve that--B's indifference curve has to look like this. So here's where B started here, and then B's going to be better off doing like this. So B's indifference curve looks something like that. Those are B's indifference curves. So the further out you go this way the better off B is, so as you shrink what A gets, that obviously means B's getting more, and so B's getting happier and happier. So what is the definition of Pareto Efficiency? Whatever point we pick like this one to begin with: is there a way of making both people better off. Well the answer is the competitive equilibrium makes both people better off. Why is that? If you can see it from back there, the reason is that A went from this white indifference curve to a better indifference curve over here. B, whose budget line is the same budget line looked at from his point of view, he went from his indifference curve over here to one here. So he went from this yellow indifference curve to a better one, so both of them got better off going to this final allocation than they started with. And of course that had to be true because A could always have chosen to stay where he was at (2,1). He moved to (9 fifths, 3 halves) because it was better, and B could have stayed where she was at (1,2). She chose to go to (6 fifths, 3 halves) because it made her better off, so both of them must be better off at the final allocation than they were to begin with. What does the theorem say? The theorem says--remember, in pictures, it says whatever point we pick here that defines something for A and defines something for B, then we can look at the utility welfare functions of both and see what indifference curves they're on. The theorem says there's no other point in this whole diagram which puts both A and B on a higher indifference curve for each of them than they were at the competitive equilibrium. So if I read the definition again it says, if I start with an economy there with the endowments and the utility functions, so the endowments and the indifference curves, and I compute the competitive equilibrium like we did over there, then no allocation, that means no point in that box could make everybody better off than they were at the competitive equilibrium provided that new point is in the box. So it makes the sum of the X's equal to the sum of the endowments, and the sum of the Y's equal to the sum of the endowments of Y. This is the end of the proof. We already gave the proof according to Edgeworth. So what's the proof according to Edgeworth? He says, "It's all a matter of looking at it the right way." It's easy to look at the picture from A's point of view. You just look at the X-axis and the Y-axis. This is the Y-axis. What is this? This is X^(A)_Y. It was 3 halves. So this is the Y-axis going this way. This is the Y-axis and this is the X-axis going this way. For A it's very simple to look at the Y-axis and the X-axis for A. A's got its indifference curve getting better and better. So from A's point of view it's very simple, you look at the endowment, you draw the budget line through it, which is some linear line, and then A picks the best point on that budget set drawing the tangent, which is the white indifference curve to this point right here. That's the best he can do. Now the trick is to see that from B's point of view up here things look very similar because B's endowment is also at this point. He's got 1 unit up here of X and 2 units of Y. Why does he have that? Because the two together added up to 3, so if this is what A's endowment was then of course what's left over is B's endowment. So B has to go here. Now what does the budget set look like for B? Well it's also a linear thing with the same slope and it goes through this point. So from his point of view this pink line is also his budget set. It goes from here all the way down to where it hits his Y-axis down here. They've got the same budget set just looked at from opposite sides. Now what is competitive equilibrium and supply equals demand mean? It means that when A chooses this point as the best point, which happened to have been (9 fifths, 3 halves), then B is happy to choose what's left over as his best point. So his optimal point, his indifference curve that's tangent to his budget set has to be the same point looked at from his origin instead of A's origin. That's the trick. So that's the key insight that Edgeworth had, his beautiful picture, and now the point is that if the white indifference curve looks like that, anything that makes A better off has to be on this side of the white indifference curve and the yellow indifference curve, which is B's indifference curve, anything that makes her better off has to be on this side of the yellow curve, but the white curve goes that way and the yellow curve goes that way. So there's no point that's simultaneously above A's indifference curve and also above B's indifference curve. So therefore nothing could Pareto dominate it. So that's the Edgeworth proof. Yes? Student: So no matter what our point's going to be on our pink budget line because that's > down. That's all the goods we have. Prof: Right. The pink budget line describes what you can afford to buy, describes the budget equation, this equation, so everyone's going to choose on the pink line. This point is feasible. B gets almost nothing and A gets almost everything. B's never going to let himself be forced down there because B can choose something on the pink line, so he's always going to choose something better than that. So that's proof number one. I'm just going to give proof number two. Most of you have seen this before, but I'm going to give another proof and then I'm going to see whether you really understand what all this means. So here's a second proof. This is a much better proof. I'm going to write this algebraically. The proof of Arrow 1951 and Debreu 1951 separately, so this is called the Fundamental Theorem of Economics, First Welfare Theorem of Economics. So all this pictorial stuff makes so many assumptions, there are only two kinds of traders, there are only two goods. They are consuming only on the boundaries. I mean, they're never consuming on the boundaries it's always in this, you know, there are just so many special assumptions and everything is two by two. It's just special case. So let's give a much more general proof of this theorem. So here we've got--two goods won't play any role. There could be any number of goods. There are two goods only here, but there are many traders, lots and lots of traders. So, what's the proof that (X^(i) hat, Y^(i) hat) couldn't Pareto dominate it? So supposed that we've got--this is equal to summation X^(i)-hat, and this is equal to summation Y^(i)-hat. So we've got another allocation which is feasible. So could it be that this other feasible allocations of X^(i)-hat's and Y^(i)-hats, could that make everybody better off? Could that make each i better off than (X^(i), Y^(i))? And this proof is so short and so beautiful, so elegant, and so convincing that it's mesmerized people now for over 50 years and it prevents them from seeing that there could be an even a more general situations where things aren't so great. So what is the proof? It's two lines. If (X^(i)-hat, Y^(i)-hat) is really better for i, then I claim--line one, W^(i) of (X^(i)-hat, Y^(i)-hat). Sorry, this is line zero. This is just repeating what's the case. W^(i) of X^(i)-hat, Y^(i)-hat greater than W^(i)(X^(i), Y^(i)). That's for all i. That's the claim. Could this happen that you've got a feasible (X^(i)-hat, Y^(i)-hat) and it makes everybody better off than (X^(i), Y^(i)). Could this happen? The answer's no. Line one is, if that were true then it would have to be the case that P_X times X^(i)-hat P_Y times Y^(i)-hat had to be greater than P_X times E^(i)_X P_Y times E^(i)_Y. Why is that? Because the budget set of Mr. i says he spends all his money on X and Y in his budget set and does the best he can. (X^(i), Y^(i)) solves this problem. So if this thing really makes him better off than what he chose, it can't be that it was affordable--otherwise he would have bought this instead. So it has to be that for i, this bundle cost more than he can afford. That's why he didn't choose it. So this relies on agent rationality. Everybody given his choices, he doesn't care about the rest of the world, but given his choice everybody's doing the best thing he can. Shiller would say, "People make mistakes. They're crazy. They have no idea what they're doing. They're stupid. Some guy tells them a story in the bar one night and they totally change their life around," so he'd say all this isn't true. All right, but anyway I actually believe that people have more sense about deciding for themselves what's good for them than third parties do about deciding what's good for them. So I don't want to challenge this. So if you don't challenge this you conclude that if something makes everybody better off each person must have found this allocation unaffordable otherwise he would have chosen it. [Audio dropped] over i of E^(i)_Y. So all I did was--that's true for every single person i. So I could add this inequality for i, plus this inequality for j, plus this inequality for all the people and then I use the distributive law to take the sum inside and I have this. But that is impossible and that's the end of the proof because the sum of this X^(i)-hat is equal to this sum. That was what we had supposed. You're just rearranging all the goods that are really there and this sum is the same as this sum. So therefore since the new allocation just rearranges the endowment differently from the equilibrium, and rearranges the X's maybe differently from the equilibrium, it has to be that actually this thing on the left is equal to this thing on the right. It's identical to it so it can't be greater and that's the contradiction. That's the end of the proof. So it's two lines, two lines to prove what Adam Smith spent 400 pages arguing that the free market is a good thing. So this is the basis for the idea that we shouldn't regulate, we shouldn't regulate, we shouldn't regulate. Sounds pretty convincing, so any questions about this? Anything you'd like to say? Are you convinced by this? What are some reasons you don't believe this, some obvious reasons? Yes? Student: Well, even if this proof makes sense a lot of regulation policies have to do with changing the prices of things anyway so we're not necessarily > with them at market > Prof: I'm glad you asked that question because it betrays a misunderstanding, so I'm glad you asked that question. So this theorem is correct given the assumptions. There's a little bit mistake in the reasoning he made. I want to repeat his question, change it a little bit so maybe he'll deny what this is what he was saying. But I believe what he just said is what really happens in a lot of regulation is they come in and they change the prices. They tax a good, they prevent people from trading so much so the price changes. They subsidize something. Something happens so that you get different prices, and of course at those different prices you get a different allocation. That's all true so far. And then he said because they're at different prices you can't compare the original equilibrium allocation to the new equilibrium allocation. Well, that's where he shortchanged this proof, this proof says however you get to a new allocation (X^(i)-hat, Y^(i)-hat), maybe it's because the government has intervened and changed all the prices and done a bunch of other stuff, but in the end after all that intervention the government is going to get you to a new allocation (X^(i)-hat, Y^(i)-hat), and that new allocation can't be better than the original one. So that's the force of the argument. No matter what the government does in the end the upshot is a new allocation (X^(i)-hat, Y^(i)-hat). We don't have to think about [how] it got there. That's where it got and according to this argument it can't be better. So the argument is correct and elegant. There must be something missing to the argument, some assumption you don't really believe if you doubt the argument. Yes? Student: What if you want an allocation that's better for one party even at the expense of the other party? Prof: What if you want an allocation? Student: It's socially desirable to have an allocation that's better for one party even if that comes at the expense of another party. Prof: So one argument you could say is that it may be in the equilibrium that A--so who's better off here? You notice that this equilibrium A ends up with more of everything than B does. So you could say this equilibrium is not very socially desirable because A ends up with more of everything than B does or at least as much of everything as B does, and that seems unjust and unfair and so we don't like the allocation, and so maybe we should move something from A to B. So that's an argument on the basis of justice. It says we can find juster allocations that are somehow socially more desirable, but this argument of Pareto Efficiency is about efficiency. Maybe you could hurt A to help B because that serves your desire for fairness, but that doesn't say anything about how efficient the allocation is. It's still true that the original allocation was efficient in the sense you couldn't make anyone better off. So the economists would say in order to hurt A and help B what you should do is take some of A's endowment away from him and give it to her and then let them trade to a new competitive equilibrium where she began with more than him. And so the just thing to do is to rearrange the resources at the beginning and still let people trade to a final allocation. So that's an argument from fairness, but it doesn't interfere, it doesn't contradict the economic argument that fair or unfair it's still efficient. We've done as well as we could making everyone as happy as we can. Maybe we can hurt someone and help someone else but we can't help everyone at the same time, whereas most regulation the argument in favor of regulation is you're helping everybody by regulating, and this says you can't ever do that. So what's missing? What's some of the assumptions? This should be an elementary question for you. Yes? Student: Is it violating one of the three assumptions that > , the market theory? Prof: No, it's got all those assumptions so there's something about the model that's too narrow and this should be easy. You're going to tell me obvious things where it's too narrow, so I'm going to just say where we're going. You're supposed to be telling me now obvious ways this is too narrow. I'm going to say, "You're right. You're right. You're right, but finance is different. We don't have to worry about those problems supposedly." So go ahead back there, you. Student: Externalities. Prof: So one critical shortcoming of this argument is that there are externalities. Suppose that X is cigarettes, and A buying and smoking more cigarettes makes B sick. So that's not part of this. Why is that not part of this? Because B's utility depends only on what B's consuming, not what A's doing. So there's no place in this model. It's too narrow to include externalities, so it doesn't capture the fact that he, by smoking, might make her sick by smoking so many cigarettes and that's not in here. And if you put the idea that B's utility, her utility might depend on what he's doing and not what she's doing the theorem won't be true. So there's a reason to tax pollution, and to tax cigarettes and all those things because of externalities. So that's a fundamental problem. Yes? Student: It's also assuming that all of our indifference curves are aligned in the same shape. Prof: Well, we're assuming diminishing marginal utility, but each person has a different indifference curve, so yes. We assume that they are all curved away from the origin, so we assume diminishing marginal utility. But I think that I'm almost prepared to believe, diminishing marginal utility. It's not literally true. Moving from one ticket to two tickets may be a huge gain in utility because now you can bring your friend along. Getting one ticket might not be worth much because you don't want to go alone. Getting the second one may add a huge amount of utility. That's an increasing marginal utility, but eventually after you've got enough tickets it's going to be diminishing marginal utility. So I believe on the whole that diminishing marginal utility is not such a bad assumption, but this clearly relies on that, so you're right but I don't think that's the critical problem. What else is there? Yes? Student: Credit markets. Prof: What? Student: Credit. Prof: Credit markets, now we're starting to talk a little bit about finance, so just hold that thought for one second. Anything else you can think of besides externalities that's terrible for--so let me transition this way. So of course people notice externalities. Another kind of regulation is perfect competition. We assumed everyone took the prices as given. There was no monopolist setting the price and refusing to bargain with people and stuff like that. So regulation could come about in order to enforce the competitive equilibrium to allow for perfect competition, so we assumed that already. That's one place for regulation, and a second place is because of these externalities. So for 50 to 100 years everybody has accepted those two arguments. Clearly there's a place for regulating free markets, ensuring free markets and stopping trusts and monopolies, and for stopping externalities. But then people said finance is different. There aren't any externalities. You're just trading stocks and bonds. There's no pollution. Nobody's going to get sick because someone else has a stock or a bond. Some people might be jealous but we're not really going to take that into account. We don't want to honor those kinds of feelings of jealousy. So the argument seemed to be when you get to finance you don't have to worry about externalities, and yes you have to worry about perfect competition but once you've got perfect competition that's the end of the story. So the rest of the course now is going to be, if you forget about externalities because you forget about pollution because we're trading pieces of paper, they're not polluting anything, why shouldn't the financial markets be efficient? Why doesn't this argument apply to the financial markets, and one of the critical financial markets is the credit market. So can you understand the credit market on just these terms and therefore argue that the market's efficient? So we're going to spend a large part of the course talking about that. So unless you had some particular point to raise now, I'm going to just use your comment as a good introduction to the next part of the course. So far there's nothing that seems to directly involve finance in what we've been talking about. So where does the finance come in? So Irving Fisher was the person who created the first really general equilibrium model of finance. So he was a Yale undergraduate. He was a superstar Yale undergraduate. He graduated first in his class from Yale. He was a math major. He decided that he wanted to build a financial equilibrium model. There were no economists there at his time. We're talking, in the late 1800s, and so he went to Gibbs, the famous physicist, one of America's most famous physicists at the time and said, "Can you advise an economics PhD?" And Gibbs said, "Well, if it's mathematical enough, it has a model and something, yes I can do it." And so Fisher's PhD dissertation was basically reinventing this general equilibrium model that I've just described and then making a machine to calculate equilibrium with water and pumps and water seeking its own level and solving for equilibrium. And we had this machine up until the 1970s in the Cowles Foundation when it got stolen. Some engineer named Sreenivasan about ten years ago was ready to rebuild the machine-- because we have the dissertation where it explains very carefully how Fisher built his machine, and he was going to rebuild it. And then he was offered ElBaradei's job. ElBaradei is the guy, the nuclear inspector who goes to Iraq and says they're building nuclear stuff or they're not building this. Anyway, so he was offered that job, and so he left Yale and then decided not to take the job after all. So we've still got ElBaradei in the job. But anyway, he left Yale and so we never got the machine built. He was a great guy. Anyway, so Fisher after writing his dissertation stayed at Yale as an assistant professor and he got tenure. He became the most famous economist probably in the country for a while. He invented finance, as I'm about to tell you, and in a way this model of finance I'm about to present which was in retrospect clearly the most interesting model of finance of its time, and he was a financial economist. He also was an entrepreneur, so you'll see later that he started his own company. It was a proto-computer company called Remington and he managed to make $10 million dollars for his company in the early 1900s. And he was a friend of Roosevelt's and he kept advising Roosevelt during the Depression to print more money. He said, "Print more money. Print more money. Print more money," and the Yale Library has all these letters he sent to Roosevelt. It also has Roosevelt's responses where you can tell that Roosevelt is paying no attention to him, but Fisher's ego seemed to be so big. Roosevelt says, "I'm very glad that the good professor has made such worthy recommendations and we'll certainly take them seriously." And then Fisher writes back and says, "I'm glad you're going to follow what I suggested." So anyway, Fisher, convinced that the economy was going to turn around, poured all his money into this computer company Remington. The company in the great stock market crash nearly went bankrupt and was leveraged. So he had to go to his wife who was very wealthy and borrow her money, and they lost that money. Then he went to her parents and borrowed all their money and lost that money. And finally he had lost everything of his money, his wife's money and his wife's parents' money and they were about to take his house from him, foreclose on his house, and so Yale was forced to buy his house for him so he could continue to teach. So he set a bad precedent for economists at Yale because whenever any economist at Yale has financial advice to give, someone always quotes Irving Fisher's 1929 line that the economy had reached a permanently high plateau. But anyway, despite all that his theories are well worth studying. He was famous for a few other things. Shiller is clearly trying to imitate Fisher. Fisher wrote a huge number of books, 50 books about everything. So he got tuberculosis and he survived and he wrote a series of books on good living and good health and how to combat tuberculosis. So he said you had to exercise, you had to get fresh air, and these were huge bestsellers. Then he said that drinking was a terrible thing. So he did an experiment in class where he would have his students do pushups, then he'd give them all a martini. Then he'd count how many pushups they could do. Then he'd give them a second martini and count how many pushups they could do. And he found that there was a 10% reduction for each martini. And so he said that prohibition--since the average business person had two drinks at lunch--that prohibition would increase output by 20%. And so he was one of the leading proponents of prohibition. So after the stock market crash he helped form the Cowles Foundation. So Cowles, who was a Yale undergraduate, had run a very famous macro forecasting company in the 1920s. And in 1929 the stock market crashed. There were a whole series of these. They sent newsletters. The same kind of stuff they do now. He, unlike all the others, after the fact realized that he hadn't anticipated anything about the crash, much like nobody anticipated it now. And he was so embarrassed he went and collected, not only his old recommendations themselves, but all his competitors' and so he published a famous paper in which he argued that economists had no idea what they were talking about, in fact that they were frauds. And so he went to his old economist Irving Fisher at Yale and said, "Look, I just believe that economics without mathematics has no meaning. I want to start a mathematical wing of economics and I've got a lot of money." His family owned The Chicago Tribune and The Seattle Times and a whole bunch of other newspapers and there was a famous fashion model in the family, Fleur Cowles and stuff like that. So anyway, so with Cowles' money Fisher started the Econometric Society which is the most famous mathematical society in economics, Econometrica, which is the most famous journal in economics, and the Cowles Foundation which--they started off in Colorado Springs because Fisher said, "Oh, the weather's so good there everyone will want to go there and it's good for them." So nobody would go there so they had to move it to Chicago where the Tribune was and it was in Chicago from 1930 to 1955, and then in 1955 it moved to Yale. And since then the Cowles Foundation has been at Yale, and you'll hear a lot more about it later. But anyway, so Cowles [correction: Fisher] with that background he set out to figure out how to turn economics-- in fact he invented economics, this model of equilibrium to study finance, but so far we don't have any finance in the model. So how can you put it in? Well, what is missing? What do I need to put in the model in order to turn it into finance? What would you say is missing? How would you turn this into finance? What other key thing--yes? Student: You need some element of time. Prof: So the first thing--of course you may have read ahead in the notes, but that's a brilliant insight if it's yours. You need time in the model. So far we just had apples and oranges or something being traded. So the first thing is Fisher said you need to put time in the model. What else is critically missing in this model, one other thing, the major other thing? Yeah? Student: Risk. Prof: What? Student: Risk. Prof: Well, that's good. There's risk. That's missing entirely. So Fisher actually couldn't figure out how to put that in the model, but we're going to get to that. That's very good. What else is missing? Yeah? Student: Impatience. Prof: Fisher, you'll see, had something to say about time and impatience that people always care more about the present than the future. But what other fundamental thing about--what is finance all about? When you think about finance what do you think about? Student: Savings or credit rates. Prof: So you think about credit, as she said, credit, interest rates, and what else? Student: Return. Prof: Return, that's quite related to that. So all this has to go in the model, but what fundamental object when you think--the first thing you think about finance what do you think of? Yes? Student: Money. Prof: Money, so that's not what I had in mind, but I'm glad you think about money. He's right. That is what most people think about, so money. So in this course we're not going to provide a theory of money. So Fisher did provide this theory of money and that's what he was talking to Roosevelt about all the time. We're going to talk about inflation and stuff like that, but we're not going to explain where the inflation comes from. So inflation is going to very important, but we're not going to talk about a theory of money. So what else is missing, something really basic though? Yes? Student: Institutions. Prof: So there are no banks and things like that, institutions. And still something. Come on what's the... Student: Loaning. Prof: What? Student: Loaning funds. Prof: Loaning funds, well somebody said credit. That's sort of loaning funds and interest rates. Student: Collateral. Prof: Collateral, that's something. I'm going to add that. Thank you. What a brilliant idea. What basic thing? Come on. Yes? Student: Wealth. Prof: Wealth, that's in the model. Where's wealth? It's already there. So when you take your endowment and you multiply it by the prices in your budget set that's your wealth. So we've got wealth. Student: Capital. Prof: Capital, so capital--and what is capital? What do you mean by capital? If it's money, I already told you that's not quite going to be there. Student: Contract. Prof: Contract, so we're getting there. Student: Assets. Prof: Assets, so assets--that's the main thing so I'm going to write it over here, assets. After all finance is a lot about the stock market, bond markets, mortgage markets. Those are all assets that you buy that pay dividends later. So assets are things that pay dividends at a later time. That's the critical thing that's missing. And when we talk about finance we want to know, what should the value of the stock market be? How much should a mortgage be worth? So those are the things we have to add. Now, how are we going to add them? It sounds like you might have to just totally redo the theory and start from scratch and do something totally different. How horrible that would be. It would mean I also wasted three lectures. So Fisher said, "You don't really have to change very much at all." So he said, "Number one, time." How do you put time in the model? Simply think of Y as the same good as X but one period later. So Fisher said, "Time isn't such a big deal. We've already got two goods. These crazy marginalists before me they had good X, which was interesting, and this very boring good Y and so it's not so clear how you can have time and everything in the model, but I've already got two interesting goods, X and Y. They're both entering with the same symmetric properties. Neither one of them seems more interesting or more important than the other one, so in fact maybe they're the same good. It's just--X and Y is the same good, it's one comes one period later." Now next class, we're going to talk about you're not going to value them the same amount. The utility for X and Y won't be the same. So here A obviously thinks more of X than he does of Y, and by the way, B, she also thinks more of X than she does about Y. So why is that? Well, if Y is the same as X but a year later--people are impatient. So the reason why A might like X better than Y and B also is not because they're different goods, but because they're impatient. So we're going to come to that later. So we can have the idea that they're two different time periods in the economy simply by change of notation and not introducing anything new at all. Well, what about assets? So I'm going to come back to that in the next class. What about assets? How can you introduce assets in to the economy? Well, Fisher says, "What is the essence of an asset? The essence of an asset is that it's something that you hold today because later it's going to deliver you money or goods or something." And we're not going to talk about money so we're imagining these are all real assets. So they're going to deliver goods in the future. So the definition of an asset is an asset, remember, we have to make it mathematical, so Fisher started this society to make economics mathematical. So an asset is literally something that delivers goods in the future. So an asset is defined by its payoffs, D_X and D_Y. So we can call that asset alpha, an asset alpha is defined by its payoffs, D_X and D_Y. So it's going to pay a certain amount of X and a certain amount of Y. That's all there is. Now, we're going to ask, do people actually know what the payoff of Y's going to be? If Y's in the future that means it hasn't happened yet. Do we really know what Y's going to be? And so maybe we know less about one asset and more about another asset, so maybe one asset is riskier than another asset. So someone said risk, obviously that's going to be a very fundamental question. But before we come to risk, if we don't have any risk yet, because Fisher didn't know how to put it in and we're going to start with his model where there's no risk, then if there's just today and tomorrow and everybody's rational, everybody, since there's no uncertainty, everybody wants to be able to anticipate exactly what the dividend's going to be. So the asset is no different from what its dividend is going to be. Maybe it's paying something today and also it's going to pay something tomorrow, so assets are defined by their dividends, nothing more than that. So the model now becomes a model where we have the W^(I) and then we have the goods as before, the endowments of the goods, but we've added a new thing which is we've added the assets D alpha X and D alpha Y. So the alpha's over all the assets, and we have to add everybody's ownership of the assets to begin with. So we have to have theta. I'm going to call it theta bar alpha, theta bar i alpha. So how much of asset alpha does i own? So that's the economy that we're going to start with. So we've made the model a bit more complicated. We started where we did before with utilities and endowments of goods. Now we're adding assets which payoff more goods, and of course people begin owning trees and stuff like that. So a tree is an asset. It's going to pay apples later on and various different people own various different trees. So to the old economy we add something new. And now Fisher's ingenious insight was that if you think about this, which we will for a little while, you'll be able to discover that you can simplify this economy back down to the economy we began with. So you can start talking about assets and interest and all kinds of others things using the same analysis as before. So with my last thought here, what does interest have to do with P_X over P_Y? What is P_X over P_Y? Suppose they're both apples. So X is an apple today. Y is an apple next year. What is P_X over P_Y? It says how much an apple is worth today relative to how much an apple is worth tomorrow. So this is going to turn out to be 1 the real interest rate, Fisher would call it. Because if P_X is more than P_Y, let's say P_X is 20% more than P_Y what it means is by giving up one apple today you can get 1.2 apples tomorrow. That's just what happens when you put money in the bank. You give up something today you get exactly the same thing back next period but more of it. So you see just by having time and the prices like we had before you're going to see very quickly how interest, assets, everything is going to start coming into play very quickly. So I didn't put the problem set on the web yet because I wasn't sure how far we'll get, but I'll put it on in a couple hours and we'll start again on Thursday.
Quantitative_Finance_by_Yale_University	3_Computing_Equilibrium.txt	Prof: Now, the course, just to summarize again, the course is the standard financial theory course that was made popular over the last ten years in a bunch of business schools, and those guys who developed this material basically thought that markets were great and finance was almost a separate part-- could be walled off from much of economics. So here at Yale we've never taught finance that way. We've always taught it as a part of economics and the crisis recently, I think, has made it clear that that's probably the way one should really think about the problem. So it's become very fashionable now to say that financial theorists had everything all wrong and to ask how it is that they got everything all wrong. Why didn't they anticipate the crash? And the two standard critiques of standard financial economics are a) it didn't allow for psychology, and you'll hear about that from Shiller next semester, and b) it didn't take into account collateral. And it was all done in a very special case, a knife-edge case. If you looked at it a little more broadly you would realize that the kind of crisis we've had now is not such an unfathomable thing. In fact it's happened many times before. So that's the perspective I'm going to take in this class. So to put it a different way, Krugman, very recently in the New York Times, you may have read his magazine article, wrote exactly that, that there are two problems. The financial theory has failed us. Why has it failed us? Well, because it didn't have psychology and it didn't have collateral. And he didn't talk much about the collateral which is obviously something he's not thought very much about before. But together with the collateral he sort of said it's too much--how did he put it? He said, "Too much seduction by mathematics. The financial economists were seduced by their own mathematics into believing stuff that a sensible person who didn't pay so much attention to mathematics wouldn't do." Well, although the critique in this course is going to be partly based on collateral the rest of what Krugman said I completely disagree with. I regard that as a kind of Taliban approach to economics. The more technology and firepower you use the more you're going to be misled. That's what the Taliban believe, and they want to get rid of modern technology and return to first principles. So I think, in fact, the problem with modern finance was not too much mathematics, but too little mathematics, and they made these very special simplifying assumptions and didn't realize how important the assumptions were to the conclusions. So we're going to reexamine all that and that's what we're starting at now. We're going to consider, first of all, the argument that free markets work best. So we started with a little example. Oh, by the way, the first problem set, if I didn't mention it, is due Tuesday. So you need to bring it to class and there will be a box with each of your section leaders' names on it. So supposedly you've been able to sign up for sections by now. Is that right? Anyway, it's on the web, so you pick a section and sign up for it. If you wait too long your section will fill up the time. So there are eight sections. You ought to be able to find one of them that fits your schedule. And you need to turn it in on Tuesday in class, by the end of class. Maybe you can scribble something during the class, but by the end of the class we're going to take the problem sets and after that it's too late to hand them in. So all of you are going to have problems, you're going to have midnight sessions, all night things that you're going to have to do for some other course, or grandmothers are going to die. All sorts of things are going to happen, but we don't take the problem sets late. So there will be ten problem sets. We're only going to count nine of the grades so you'll have one free pass, and that's what life is. And it's just too complicated to keep track of people handing them late all the time. The answers are going to go on the web right after the class, and so it's just in the past we negotiated with every person who was late and it's just too complicated. And when you make a simple rule grandmothers don't die anymore. So anyway, that's how we're going to work it in the class. You just have to turn it in. And there are ten of them. Only nine count. If you miss one altogether it's really not going to change your grade anyway. If you miss half of them that's going to have some effect on your grade, and so I don't encourage you to do that, but I'm sure you won't do that. So I think that's all the preliminaries. There are two midterms, one in the middle of the class and one right at the end. Anyway, the question we want to spend the whole of the class on today is whether the free market is really such a great idea. And the quintessential example in which it is a great idea is the one we did in class on the very first day. We had a bunch of football tickets and there were buyers each of whom knew his own valuation and sellers each of whom knew her own valuation and we threw everybody together and just very briefly explained the rules. By the way, the only important rule was--there were two important rules. You had to announce publically and loudly what price you were offering. That's very important. You don't have any secret deals. That would have screwed everything up. And secondly, we had a rule about once you make a deal what happens. How does the thing actually get transferred? So one of the TAs stood by and wrote it down, and the two people exchanged the footballs and agreed to it and walked off stage. So the actual mechanics of the transaction to make sure that the person turning over the money actually gets the football ticket, that of course is incredibly important and that's the thing that gets left out often in finance. That's the collateral business that we're going to come to later. How do you know that the guy's actually going to pay you what he promises? Well, he's got to put up collateral so that you can trust him. So without that there would have been a big problem, and we're going to come talk about that later. In the old days when you bought a stock someone on a bicycle would carry the certificate from one place-- someone would carry the check from one guy to another guy and then the bicyclist would get the stock certificates and ride the bike back to the buyer. So it was one broker to another broker. Sometimes it took a couple of hours, so there was a spacing in between when the guy gave over the money and when the guy got the stock back, and you have to allow for that. Maybe it would take a couple days to process on everybody's books. So there's a thing called ex-dividend. When you buy a stock the old buyer continues to get the dividends for a while-- the old owner--until a particular date after which the new buyer starts getting the dividends if there are any. And everybody has to understand that, because you have to allow for the actual trading technology. So all those things are going to come up later, and they were in the background of this example. But never mind that. The point now is that these people, everybody just knew their own valuation, not anybody else's valuation, and chaos ensued, hardly any rules, and miraculously almost instantly within less than two minutes they figured out what to do and they managed to get the football tickets into the hands of the people who liked them the most. And I'm going to just say that slightly more mathematically. You could model what everybody did as having a utility function for football tickets. So the top person, Mr. 44 gets utility of 44 for having one ticket and tickets beyond that don't give him any extra utility, just still utility 44. Similarly Miss 6 there at the bottom she had utility 6 for a football ticket, but there's also money in the background. So the welfare function depended on the football tickets and money and was U(X) M. So why does that capture what went on? Because Mr. 44, knowing that the football ticket's worth 44, he would say to himself, "Should I get a ticket or not get a ticket?" Well, if the price is under 44 the amount of money he gives up and loses is going to be less than the amount of utility he gains for the football ticket so therefore he'll buy the ticket. So this utility function U(X) M captures the idea, represents the goals of the people involved in the experiment. Each of them has a different U of X, but all of them are of the form U(X) M. And so the conclusion was of the experiment and of the theory, supply equals demand, the conclusion is that the football tickets are going to end up in the hands of the people who like them the best. So what does that mean? That means that in equilibrium the final allocation maximizes total welfare. Now what does that mean? Well, each person, i, has a different utility function, and so if you add up over all the people i you get the total welfare of every single person, the economy's total welfare. I'm now about to prove--but it should be obvious--that total welfare is maximized at that equilibrium that you actually found in class, almost. There was just one tiny, tiny deviation from the theory. Nobody made a mistake, by the way. I think I mentioned this many times. I've done this experiment before and Mr. 12 gets so upset that he can't buy any ticket and he's standing there embarrassed that everyone else has traded and he's still sitting there with no football ticket-- he ends up bidding 30 or something to get a football ticket. Nobody made a mistake this time, and so it happened almost as the theory predicted. So let's just think of the theoretical outcome. In the theoretical outcome where the price is 25 and those top eight people have it that final allocation maximizes total welfare. Why is that? Well, whatever the money distribution was you couldn't change total welfare, because if i gives up some of his money to her, to j, the total amount of money is still the same, and if you add up the welfares of all the people you're just going to get the total amount of money on the right and it won't make any difference. So therefore to maximize welfare all you have to do is maximize the sum of-- you have to put the football tickets in the hands of the people who want them the most. That's going to maximize welfare, because that maximizes the sum of the U_i of X's and rearranging the M's doesn't matter. So we found in equilibrium--that equilibrium maximized total welfare. So that was the original argument for why equilibrium was such a great idea. The greatest good to the greatest number became mathematical. It maximizes the sum of the welfare, so the sum utilities they called it. That was the utilitarian view of economics, utilitarian view. And that's sort of the view that prevailed in 1871. All right now, they made one generalization from that-- we found before, which is that if you think of not eight different buyers, but one buyer, or maybe two different buyers where the utility functions are this concave function, so they're U_I(X) M where U_I of 1 could be 44 and U_I of 2 could be 44 40 which is 84. That consolidated person would behave exactly like the individual people who'd buy as many tickets as they would collectively and so nothing would change. The football tickets would still end up in the hands of the people who wanted them the most. Maybe it would be one guy, who held three tickets, instead of three different people, but the tickets would still be in the hands of the highest valuation holders and so you would get exactly the same conclusion. One last lesson from that example is that the price turned out to have nothing to do with the total value of football tickets. The price turned out to be equal, more or less, to what the marginal buyer and the marginal seller thought it was worth. So Mr. 26 and Miss 24, they're the ones who controlled the price, what 44 thought was totally irrelevant, so that was why it was called the marginal revolution in economics. So Adam Smith who was so puzzled because he said water is so valuable and has such a low price, and diamonds are so useless really when it comes down to it and they have such a high price the answer to his puzzle is simply yes. Water, at the beginning Miss 44 would be 44,000, whereas if we had a same model for diamonds, diamonds would also be very big at the beginning. But the point is there's so much water in the economy that the marginal value of an extra gallon of water is not very high. The marginal value of water is low even though the total value, which is the area under the demand curve, is very high. So that's the lesson that we learned in the first class. And now we want to generalize this to a much more sophisticated model, but one you can still compute very easily, and we're going to see how these special assumptions don't quite work so well. Yes? Please interrupt me at anytime with questions. Student: So could you explain again how you said that the welfare function and the utility function somehow involve three or four people together. Prof: Yes. So her question is--I said very quickly which you'll see later, I pressed the button too soon. If I press down and it's halfway up does that just break the whole thing? Anyway, so her question is she would like to know, again, why it is that I can sort of combine people into one person and what do I mean by that. So what I meant by that is if I have two people, Mr. 44 and Mr. 40--I'm taking the buyers to be hes and the sellers to be hers--I have two guys, 44 and 40, and I set any price. If the price is above 44 neither of them will want to buy. If it's between 44 and 40 just Mr. 40 will buy [correction: just Mr. 44], and if it's below 40 both of them will buy, but each of those guys is only interested in one ticket. Mr. 44's utility is U_I of 1 is 44. U_I of 2 is still 44. He doesn't get anything out of a second ticket. Suppose now I had a third person, a bigger person whose utility U_K of 1 is 44 and U_K of 2 is 84,44 40. So that person, now, is a bigger guy. He's interested in more tickets. That's what I mean by bigger. He's going to behave himself exactly the same way the other two separate people behaved collectively. So if the price is above 44 he won't buy either ticket. If it's 50 and he buys one ticket he'll have lost 50 and he'll have gained 44 in utils, so he will have been worse off than when he started, and he certainly won't buy two. He would be even worse off. If the price is between 44 and 40 he'll say to himself, this is the marginal revolution, "If I buy the first ticket I pay 42 and I get 44 out of it, so I've gained two utils, but now if I think about buying a second ticket for 42 and I only get 40 out of it I'm going to start losing, so I'll stop with one ticket. So that guy will behave exactly the same way the two people separately behave, so whether it's two guys separately or one guy together it doesn't make any difference. Their total action's exactly the same. And in the end the football tickets have ended in the hands of the people who liked them the most. Maybe I need a lot more water than you do, but if I need it much more than you do then all those gallons, maybe the first twenty gallons I drank I needed more than your first gallon and after that you started needing water as much as I did, something like that. So the tickets or the water ends up in the hands of whoever needs it most, and it may be that there is more than one unit in each person's hands. Any other questions before I raise the thing again? All right, so that sounds all very convincing, but it's not going to turn out to be quite so convincing. So let's try and generalize this model to a more sophisticated thing. And so I'm following an example which is in the notes. So you find that if you read the notes--oh, so the textbooks. Because the approach I take and that we take a Yale is quite different than the standard approach you're not going to be able to follow a textbook. That's why I give you a whole list of textbooks. I encourage you to read them. They're great books. They're famous people. Most of them are quite good friends of mine so I endorse them all, but they're differently presented than this course and that's why you need to rely on the notes a little bit. So let's just take this first example. Suppose now that we have two goods, but they're going to be continuous. You don't have to have just one football ticket or two football tickets. We have two goods which we're going to call X and Y, and we've got two agents, A & B. And so W^(A) of X and Y, that's the welfare function like we had before, is going to be whatever I had, 100X - 1 half X squared Y. And now the endowments of goods, which I was a little bit fast and loose about before, E^(A) of X, E^(A) of Y, that's the endowment of A, how much he has to begin with of X and Y. I say it's 4 and 5,000. And then let's make another person, W^(B), his welfare function or let's say his and her welfare function is 30X - 1 half X squared Y, and her endowment E^(B) of X and E^(B) of Y equals 80 and 1,000. So this is supposed to be shorthand for an economy in which there are thousands of people, millions of people, every person characterized by the utility they get, the goals they have over the consumption goods, and their starting endowments, and they're all going to be thrown together and expected to trade. Another example, we can do another example, let's say. We're going to work out both of these, the same kind of examples you're going to the do in the problem set. Another example, I'm sorry I can't remember my examples. I won't need to look at these after I write the examples down. So another one is W^(C)(X, Y) = 3 quarters log X 1 quarter log Y, and E^(C), the endowment of C, equals 2 and 1. And meanwhile I have another person D of X and Y whose endowment [correction: utility] is 2 thirds log X 1 third log Y and her endowment 1,2. And of course I could have had an economy in which they were all there at the same time, but I'm just going to do two examples. So you see the economy consists of many people, many goods maybe, many people and each with different endowments and different utilities, and if you throw them all together what's going to happen? And so we have a theory now, a theory of equilibrium that explains what happens. And we can use a few tricks, which I'm going to teach you now, to actually solve concretely for what's going to happen in each of these cases, and it's very simple. And the next step is going to be to add finance to it and financial variables, but at the bottom we still want to have economic variables. See here we've got the consumption of two different goods X and Y and we want to see what's going to happen. All right, so equilibrium is always defined by turning things into equations. So we said the equations here are going to be that. So what is A going to do? Well, the endogenous variables are going to be P_X, P_Y, X^(A), Y^(A), X^(B) and Y^(B). That's what everybody has to decide. In the end A has to decide, the prices have to emerge for X and Y. We're assuming, again, that these people, by the way--I have one agent A and one agent B, I really mean there's a million agents just like A and a million agents just like B and they're all shouting and screaming at each other and they're in some kind of market. So if there's only one agent of each type there'd be bargaining and threats and it'd be very complicated, but with lots of people of each type, that's what I'm talking about--so in our football ticket example there were sixteen people competing with each other and you don't really need much more than three, or four, or five on a side, at least four, to get competition. So with enough competition the theory says the prices are going to emerge and people are going to look at the prices and decide how much they want to buy. What do they want to end up consuming? So A has to make his decisions and B has to make her decisions. And so those are the endogenous variables. The exogenous variables were all of the 80,1,000,1 half, 1 times y, 100 times x, all those numbers are exogenous. The utility functions, the endowments, are exogenous. So these are all the exogenous things. So the theory is going to say, how do you go from exogenous to endogenous and it's going to be just a bunch of equations, so what do they each want to do? So A is going to maximize W^(A) of X and Y such that, as we said, the critical insight, the budget constraint-- [clarification: here, writes but does not say out loud P_X X] P_Y Y is less than or equal to P_X times E^(A)_X P_Y times E^(A)_Y), but we know what these numbers are. E^(A)_X is 4 and E^(A)_Y is 5,000. So A takes it for granted--theory says this, it's very shocking--but it says A takes it for granted that he can sell all his endowment if he wanted to, 4 units of X and 5,000 units of Y and get the money from doing that and use the money to spend on his final consumptions-- let's call this X^(A) and Y^(A)-- of X^(A) and Y^(A). So let's leave out the A's here for a minute because those are the choices he has. He's wants to max over X and Y, so there are many possibilities. It has to satisfy this budget constraint. And similarly Y is going to be maximizing over X and Y, W^(B) of X, Y such that P_X X P_Y Y less than or equal to P_X times 80 P_Y times 1,000. I think I remembered the numbers finally. So, and now what we want to do is we want to solve for these variables so that when A, taking P_X and P_Y as given, maximizes his utility function, he'll choose X^(A) and X^(B), and B will choose Y^(A) and Y^(B) such that demand equals supply. And so I'm going to write, over here, maybe, demand equals supply. So we know that in the end so whatever these choices are they're going to lead to him choosing X^(A) and Y^(A) and her choosing X^(B) and Y^(B). And it's got to be that X^(A) X^(B) = E^(A)_X E^(A)_X which equals 4 80 which equals 84. And it's got to be that Y^(A) Y^(B) has to equal e^(A)_Y e^(B)_Y which equals 5,000 1,000, which equals 6,000. I hope I've remembered everything. So all right, so those are two of the equations. Supply has to equal demand, and now let's just do a little trick here to get some of the other equations. A is going to spend all his money. What's the point in not spending money--because the more X he has and the more Y he has, certainly the more Y he has, the better off he is. So he's not going to waste money. So this is going to turn out to be an equality here. Okay, so that's actually an equation, not just a variable. So P_X times X^(A) (now the actual solution) P_Y times Y^(A) has to equal P_X times 4 P_Y times 5,000. That's an equation, and then similarly Y, she's not going to waste her money. She's going to spend it all it she's optimizing, so this will turn into an equality. And so this will give P_X times X^(B) P_Y times Y^(B) = P_X times 80 P_Y times 1,000. So we've got four equations, and now we have to do the marginal equation, the crucial marginal equation. So what does that say? We talked about this last time. You've all seen it before so I can go quickly, but this was the critical insight that took years to develop. Marx couldn't figure it out. Until his dying day he was trying to understand what these marginalist guys were doing. So the idea is that if you've optimized by choosing X^(A) and Y^(A), if he's optimized choosing X^(A) and Y^(A), it has to be that the last dollar he spent-- he was indifferent between where he spent it. Otherwise he would have moved a dollar from one thing to the other thing. So it has to be that the marginal utility of X at X^(A) and Y^(A) divided by the price of X, so what is that? What is the marginal utility of X? That's the derivative of X, 100 - 2 times 1 half, 100 - X, has to equal the marginal utility to A of Y-- divided by the--sorry, I meant to leave room here. Equals the marginal utility of A of Y evaluated at X^(A) and Y^(A), divided by the price of Y. So that equals 1. Marginal utility of Y is just 1. The derivative of Y is 1. And then we have to write the same thing for B. The marginal utility of X for X^(B) and Y^(B) divided by the price of X. So what is for B? It's (30 - X) divided by P_X. Not very good board management. Has to equal, and this is also going to turn out to be 1 over P_Y equals marginal utility of B of Y, at X^(B), Y^(B), all over P_Y. So those are the equations. Now, does that make sense to everybody? I think I need to pause for a minute. I'm going to do exactly the same thing with that other system, but let's just see if we can figure this out. So equilibrium is this very involved thing. What everybody does depends on what everybody else is going to do because how much should you pay for something depends on how much you think you can get it by offering it to some other guy. If there are a million A's and a million B's, you're dealing with one of the B's, maybe the other B will give you a better deal. So you have to think about what the other people are doing before you can decide what to do yourself. All that is captured by the idea of the prices. Somehow people get into their minds what the best deal they can get is. That's the prices, P_X and P_Y. Given those prices, A, each agent, looks as his budget set or her budget set and decides what to do. And what should they do? They should equate marginal utilities. That's the key insight. The marginal utility per dollar of X has to equal the marginal utility per dollar of Y. That just says that the budget set is tangent to the indifference curve. That's what that says. So you take the ratio of marginal utilities--it equals the ratio of prices. And cross multiplying, it says the marginal utility per dollar, the slope of the indifference curve is marginal utility, let's say, of X over marginal utility of Y and the slope of the budget set is P_X over P_Y. So if I just put the P_X down here and the marginal utility up there that just says the marginal utility of X divided by P_X equals the marginal utility of Y divided by P_Y. That's something that you could waste a huge amount of time on. I don't have to do it because I know that you all have seen it before, and the one guy who hasn't seen it before is going to figure it out himself. So we have a tremendous advantage here. I can just skip over that immediately and make use of that fact. So that's the critical insight. You've taken this incredibly complicated system and reduced it to a bunch of equations which you can put on a computer, which is about--what I'm about to do, and solve it with a flick of a button. So are there any questions here--let me pause again--with how I got these equations? So it's a little bit complicated, but of course once you've understood it it's not so complicated. Now, who first thought of all this stuff? The amazing thing is, incidentally, these equations always have a solution. If you take typical equations in any field, physics, mathematics, just random equations, they're not going to be solvable. X squared 1 = 0, that's just one equation, doesn't have a solution. And if you have simultaneous equations why should there be a solution? The economic system always has a solution. This is an astonishing fact first proved by Arrow, my thesis advisor, Debreu who did it at Yale as an assistant professor, and didn't get tenure, and later won the Nobel Prize, which has happened several times at Yale-- Arrow, Debreu, and McKenzie all separately, although these two guys ended up writing a joint paper, anyway, they found that this system always has a solution. There's something special about the economic system that has a solution that has to do with diminishing marginal utility, which we're not going to talk about in this class, but it's quite a fascinating thing. And they based their argument on an argument that Nash had given for games. And this whole thing is very related to Nash equilibrium. And I'm sure you've heard of Nash and many of you have maybe seen the movie, A Beautiful Mind. Well, about five years ago, a couple of years after the movie came out, Nash is still very much alive and not quite as wacky as he used to be, and so the Indian Game Theory Society opened. It was founded believe it not, just five years ago despite all the brilliant Indian economists. The Game Theory Society was founded about five years ago and they had an opening conference where six people gave talks including Nash. I was one of the people who gave a talk, and there were thousands of people who showed up, mostly because of the movie, I mean, there was just thousands and thousands of people. So afterwards we went on tour, traveling to a bunch of different cities, and every city we went to we'd get off the train or the limousine or something there'd be a throng of people there waiting to meet Nash and there'd always be a press conference. And after the press conference there'd be a picture on the front page of whatever city, and these were all great cities, a city we'd gone to, and always there was Nash and everybody else was cropped out of the picture. But anyway, in one of these first conferences, I'm just illustrating Nash equilibrium here, somebody said, some reporter says, "We've seen the movie, but can you really tell us in a word what is Nash equilibrium, competitive equilibrium, just say in a word what does it mean, what does it mean for us? And so each of us took a try at trying to explain what Nash equilibrium was including Nash. It didn't go too well, the explanations, until they got to Aumann. So he was also one of the people who spoke, and he subsequently won the Nobel Prize. But anyway, at the time he hadn't won it yet and he's Israeli. He's also a great figure. And so Aumann says, "That question reminds me,"-- I can't do his Israeli accent--"that question reminds me of the first press conference Khrushchev"-- who you might remember was Premier of the Soviet Union. This was in the time of Kennedy and thumping the table and the Cold War and stuff-- "the first press conference Khrushchev gave to western reporters and somebody said, 'Can you tell me in a word, describe in a word the health of the Russian economy,' and Khrushchev says, 'Good.' And then the reporter says, 'I didn't really mean one word. Take two words and tell us, what is the health of the Russian economy?' And Khrushchev says, 'Not good.'" So Aumann says, "Equilibrium in one word is interaction, in two words, rational interaction." So his definition managed to get into the newspapers and none of ours did. So that pretty much summarizes it. It's interaction, but rational interaction. So, and it's captured by the idea that everybody anticipates the prices and those prices are going to really lead to the market's clearing. So they're all anticipating the right prices and behaving as optimally as they can, choosing the best thing in their budget sets. I put this on a computer and solved it, which we're going to do in a second, but there's a trick to solving this by hand, so I might as well just do the tricks by hand because on an exam, for example, I'm not going to be able to give-- you're going to use the computer, it's very simple. You'll see in one minute you can solve this on a computer, but by hand it's worth knowing how to do and you probably know how to do this, but let me describe it. So the first thing to observe is that the prices don't really matter up to scalar multiples. Walras, by the way, was the first who made this argument. So Walras was one of the marginalists in 1871 from Lausanne. So he says, "Look, doubling the prices isn't going to do anything. It's just like changing dollars into cents." If you look at everybody's budget set and double P_X and P_Y you're doubling both sides of the equation. You're not doing anything. So if P_X and P_Y are part of an equilibrium, 2P_X and 2P_Y will also be part of the equilibrium because the prices only appear here in the budget set and doubling them all doesn't do anything. So really you might as well assume that P_X equals 1. So he says, "Well, that gets rid of one variable. You've got six variables and six equations so you can all solve them, but there's so many it seems too complicated. But now you got rid of one variable, well you can also get rid of one equation," he says. So how can you get rid of one equation? Well, suppose we clear the X market. We find X^(A), X^(B), Y^(A) and Y^(B) and P_X and P_Y and all the equations are satisfied, one through five. All these equations are satisfied, one, three, four, five and six are all satisfied. We haven't checked equation two though, whether that market's going to clear. And Walras said, "Well, it has to clear. The last market we don't need to worry about." Why is that? Because if X^(A) X^(B) = E^(A) E^(B) that means collectively all the agents are spending on good X exactly all the money that they're collectively getting by selling good X. That's what the top equation says because when you multiply through the whole thing by P_X the total amount people are spending on good X is equal to the total amount agents are getting by selling all the good X. So since everybody's spending all their money that must mean the rest of their money collectively is just all their money they're getting from selling good Y. They must be spending it all collectively on buying good Y. That means the next equation automatically has to hold because everybody spent all his money so therefore all the money collectively that was spent on good X equals to what's purchased [correction: revenue received in sales] of good X because supply equals demand for good X. So good Y it has to be that all the people, the income that they're getting on spending [correction; selling] good Y, all of that was spent on buying Y collectively, not any person, each person that's selling Y and buying X or something, but collectively all the money we've just deduced spent on [correction: received by selling] Y had to go to buying Y, so therefore the Y market is clearing too. So once you've cleared all the other markets you know that the last market has to clear. So without loss of generality don't worry about last market. So that reduced it to five equations and five unknowns, so that helped. We got rid of one equation and we got rid of one unknown. So we got rid of the top equation, let's say, and P_X. One of those two equations, the market clearing equations, doesn't matter as long as we do all the others, and one of the prices we can fix at 1. So as we can fix P_Y, let's say, at 1, we might as well fix P_Y at 1. This becomes a much simpler equation. This now I can replace with 1, and this I can replace with 1. We already know what the price is of Y, it's 1. But now things get very, very simple because you have (100-X) over P_X = 1, so I just write that again, (100-X) over P_X = 1. So I bring the P_X to the other side and I have 100-X = this is X^(A)-- equals P_X. Another way of writing that is X^(A) = 100-P_X. Then from this bottom equation I've got 30-P_X--30 minus--X^(B), sorry. These are A's and this was B. I forgot the superscript. So (30-X^(B)) over P_X) has to equal--well, the marginal utility is 1 and the price is 1 so that equals 1. So I just have 30-X^(B) = P_X, or, in other words I have X^(B) (just writing this-- bring it to the other side) = 30-P_X. So you look at the demand. This is what Walras did. He said, "Forget about all these equations just look at demand and see where demand equals supply." So here, given the price P_X and P_Y we know without loss of generality P_Y is 1. So given P_X this is how much A is going to demand of X. And given P_X this is how much B is going to demand. And we know in equilibrium by that top equation that plus that has to equal 84. So now I can solve it. So I know that 100-P--well, I'm just going to solve it quickly. So it's 130-2P_X = 84, which implies that 46,2P_X = 46 implies that P_X = 23. Once you have P_X = 23 then you can figure out what X^(A) is, because 100-X^(A) has to be P_X so that implies that X^(A) is 23 and it implies that X^(B) is-- no, X^(A) is 77, right, where is X^(A)? X^(A) is 100-P_X, so if P_X is 23 X^(A) has to be 77. It implies that X^(B), I can do X^(B) from over here. 30-P_X is 7, and sure enough 77 7 really do equal 84. So we've cleared the top market. And now we don't have to worry about the other market. We can figure out what X^(B) is. How do we figure out what X^(B) is? We go into this budget set. At a price of 23 he's going to consume 77. That's going to cost a bunch of money, and this is how much income he has, and we subtract if off, and P_Y is 1, we can figure out what Y is. So we can figure out from this Y^(A) and Y^(B), and we know that that's going to clear the market, so we've solved the problem. But we can do this on a computer. All right, so are there any questions how I did this? I'm going to do it one more time with this model and then I'm going to do it on a computer. And so this is the kind of problem that hopefully will be second nature to you after you do the problem set. It's a very elementary thing. Of course the first time you do it, it seems very complicated, but it's a very mechanical elementary thing, but it's going to give us a lot of insight into the economy, so any questions? Yes? Student: I was just wondering what those two lines said. I think the first word says assume. I just can't read it. Prof: Assume, this says, without loss of generality that P_X = 1. Student: And the second line? Prof: Except that I took P_Y. This is P_Y not P_X. P_Y = 1. And the second line, this one says, so without loss of generality P_Y is 1, so having put P_Y = 1 here I then looked at these equations, (100-X^(A)) over P_X = 1 over P_Y, but I took P_Y to be one so that's 1 over 1 which is 1. And I took this equation which is (30-X^(B)) over P_X = 1 over P_Y, so (30-X^(B)) over P_X = 1 over P_Y, but that's 1/1 which is 1, so I wrote that. So this is how I got my two critical equations. These two equations here, this and that, went down to this. And then I just rewrote this one as X^(A) is 100-P_X and this one you can write as X^(B) is 30-P_X. So 100-P_X, 30-P_X and then I added X^(A) to X^(B) and I got 130-2P_X = 84 and I got P_X. Yeah? Student: So we can set P_Y to any number? Prof: Any number. Student: And get the same results? Prof: Yes. You'll just multiply the pries. If you set P_Y to be 2 you'd have gotten P_X to be 46 and you get the same answer. Student: So they're like relative prices? Prof: So the only thing that matters is relative prices. So this is what Walras pointed out. If you change dollars to cents you're going to multiply every price by 100, but the relative price of oranges and tomatoes is going to be the same as it was before. So the theory only produces relative prices. Any other questions? There was someone else raising their hand. Nope? All right, let's just do it one more time so you see you get the hang of this and then we're going to talk about why the market's so good and we're going to see things are getting a little bit more complicated. So let's do this one. This one is going to work--oh, so I wasn't very clever here. Aha, maybe I could be clever, more clever. So how do we do this one? Well, we have to write down all the equations. So what are they going to be? They're going to be the same as before, X^(A) X^(B) = E^(A)_X E^(B)_X. [correction: as pointed out later, should be X^(C) X^(D) = E^(C)_X E^(D)_X]. That's supply and demand but this is just 2 1 = 3, and over here we have--it's not A and B any more. It's C and D, I guess I called them, C and D. And now we have for the second one, we have Y^(C) Y^(D) = E^(C)_Y endowment of D of Y = 1 2 = 3. All right, so that's supply and demand. Then we have to do the budget sets. They're going to be simple. P_X times X^(C) P_Y times Y^(C) has to equal P_X times 2 P_Y times 1. All right? And then budget set for D is P_X times X^(D) P_Y times Y^(D) = P_X times 1 P_Y times 2. And finally we have to do the marginal business. So what's the marginal business? So somebody tell me this. So we need the marginal utility of A over the price of X. What's that? What's the marginal utility of X to Mr. A? Student: 3 fourths X. Prof: 3 fourths what? Student: X. Prof: That's what you said 3 fourths X, exactly, divided by P_X. So how did I do that? I took the derivative of 3 fourths times log X. This is the only thing you have to know. The derivative of log X is 1 over X, and that's going to be equal to the marginal utility of [clarification: at the point] X_A, Y_A with respect to Y over P_Y and that's equal to what? Student: 1 fourth Y. Prof: 1 fourth Y. Student: Are your A's C's? Prof: Yes, my A's are C's. Thank you. I'm glad you pointed that out. Thanks. So it's embarrassing to make all these mistakes, but you'll find in 30 years you'll start making mistakes too. So that's that equation and then we have to do the same thing for Y. And I should have been more clever and left more room, but I didn't. But anyway, the last equation is going to be marginal utility. So what is the last equation? Marginal utility of D, of X, over P_X = what? 2 thirds times 1 over Y [correction: X] divided by P_X = what? I'm not going to write out marginal utility of -Y over P_Y is what? Student: > Prof: [1 third times 1 over] Y^(D), [all] divided by P_Y. So those are the equations. So now we're going to put these on a computer, but we can solve these by hand again, and were going to see it's very useful to be able to do this. Almost, so there's another trick to doing this. So the trick is we can take one of them to be 1, whichever we want to do. Take P_Y to be 1 or P_X to be 1. So take P_X = 1. Here you see things are a little bit more symmetric. There, there was the special Y that had constant margin utility just like in our football tickets example. Here there's nothing that is constant marginal utility. X and Y are much more symmetric. So this move to more symmetry without the special X if very important, and the guy who first did that was actually Irving Fisher at Yale who you're going to hear a lot about very soon. So it's a little bit more complicated this time. So here's the critical equation, this one let's say. So now I'm going to solve this. So how can I do this? I want to do the same trick as before. I now want to solve--so let's take P_Y to be 1 like I did before, take P_Y to be 1. So let's just solve this equation, solve for X. It's not going to be so easy to do this. So now there's a tremendous trick here. What does this say if I rewrite this? I can bring the X down here and I get P_X times X. And I can bring the Y down here and I get P_Y times Y. So it says that the amount you spend on X relative to 3 quarters is equal to the amount--this is by the way Mr. C--the amount C spends on X relative to 3 quarters is equal to the amount he spends on Y relative to 1 quarter, but the total spending on X and Y has got to be all his income. So basically it says that he spends 3 quarters of his income on X and 1 quarter on Y. That's the crucial insight. So you can solve these logarithmic examples very easily by that trick. So it's evident from marginal utility equation that C will spend 3 quarters of his income on X, and D will spend 2 thirds of her income on X. By the same argument she's going to have 2 thirds-- I can bring X^(D) down and her spending on X relative to 2 thirds is equal to her spending on Y relative to 1 third, but she's spending all her income on X and Y. So clearly 2 thirds of it is being spent on X and 1 third of it Y. So that property of the log utilities is no accident. They were invented for exactly that purpose. So this is a story you probably heard, but there is a famous--I'm from Illinois-- there was a famous Senator Douglas from Illinois, there have been several Douglas' from Illinois. One of them debated Lincoln. Maybe he wasn't from Illinois. Lincoln was from Illinois. There was a famous senator named Douglas from Illinois after the Civil War and he noticed that farmers' labor tended to get 2 thirds or 3 quarters of all the income and capital the rest. So he said, "What kind of utility function would make me always spend the same fraction of my money on a particular good." And so he went to his college math teacher, Cobb, and asked him if he could invent a utility function which had the property that you always spent a fixed proportion of your money on each good, and so Cobb invented the Cobb-Douglas utility function and this is where it is. This is just the sum of logs. So it's called Cobb-Douglas utility. So it has that property, this property, that each person in this Cobb-Douglas utility spends a fixed proportion of her money on each of the goods, a different proportion on each of the goods and different people have different proportions, but any single person can always spend a given proportion 3 quarters on X and 1 quarter on Y, 2 thirds on X, 1 quarter on Y. And because of that it's very easy to solve for equilibrium. So we go, X^(A) is going to be 3 quarters. What is her income? Her income is P_X times 2 P_Y times 1. So her income has to be that. She's going to spend 3 quarters of her income on X, so I could write X^(A) as that. So this is C. And X^(D) is going to be, she's spending 2 thirds of her income on X and 1 third on Y, so her endowments are 1 unit of X and 2 units of Y. So this is her income, P_X times 1 P_Y times 2, and so she's spending 2 thirds of it on X so therefore P_X times X^(D), that's the amount of money she spends on X, that's what she spends on X, has to be that, so X^(D) is that. And if I add these two, when I add them up I have to get 2 1 = 3. So I can just now solve this. Well, I can do a trick and pick one of my--either P_X or P_Y to be 1, so either one. I keep going back and forth. It doesn't make any difference. Let's try P_Y as 1, can take that to be 1. And now I can solve it. So this is just 3 quarters, times (P_X times 2 1 divided by P_X. Then the other one is 2 thirds (P_X times 1 2) divided by P_X. So I can add those, and when I add those it equals 3. So I know that 3P_X, if I multiply through by P_X I get 3P_X = 3 halves-- hopefully I did this right--3 halves P_X-- this'll be very embarrassing if I didn't-- 3 halves P_X 3 quarters 2 thirds P_X 4 thirds = 3P_X. Oh, is this right? So who can do this in their heads? 3 halves P_X from that is 3 halves P_X, so 3 halves - 2 thirds, 3 halves is 9 sixths - 4 sixths is 5 sixths. It looks like 5 sixths P_X. Does anyone believe that? If I do this in terms of 6 that's 9 sixths and that's 4 over 6, that's 13 over 6 and that's 18 over 6, so it's 5 over 6 P_X. That looks right, and 3 quarters 4 thirds if I go to 12ths that's 9 twelfths and 16 twelfths is 25 twelfths, so this looks like 5 halves. So that means P_X = 5 halves. So there I've got the answer. Does that look right to you? Is this clear what I did here? I just took for this trick all I did was I solved for--so let's just repeat what I did. Just like over there I reduced it to simultaneous equations in a mechanical way, in a very simple straightforward mechanical way which the first time you see looks very complicated, but it's very simple, in fact, after you've done it once. Then it allows you to take these very complicated models and say something concrete. So I've got all the peoples'--their welfare functions and their endowments. So I say in equilibrium what has to happen. Whatever they decide to eat C and D what he eats plus what she eats has to be the endowment. The total endowment is 3. So the total consumption of X has to be 3. The total consumption of Y between what he eats and what she eats also has to be three. Now each of them is going to spend all their money. He's going to spend all his money. She's going to spend all her money. Because it's Cobb-Douglas, because it's logarithmic, and you do this marginal utility stuff you find out, and this was the only trick, so this is a non-obvious trick which some senator and professional mathematician had to invent, Cobb-Douglas is designed so that you can say right away with those utility functions D is clearly going to spend 2 thirds of her money buying X, and C is going to spend 3 quarters of his money buying X. It's just obvious from the first order conditions, from this marginal utility conditions, they're called first order conditions, from this equating marginal utilities. That was the crucial trick. So that's a trick that you have to internalize and from now on that's all you have to know that C's going to spend 3 quarters of his money on X, 1 quarter of his money on Y and D's going to spend 2 thirds of her money on X and 1 third on Y, but supply has to equal demand. So what is C? What is he actually buying? Here's his total money. He has two units of X and one unit of Y. So he's selling his units of X at the price P_X, and his units of Y at the price P_Y, and he's spending 3 quarters of it on X. So how much X is he actually buying? This is the amount of money he's spending on X. Divide by the price of P_X, that's how much money he buys of X. She, D, she's going to spend, here's her income which is not quite the same as his, because her endowment is different, that's her income. She spends 2 thirds of it on X, so the amount of X she wants to buy is the amount of money she spends on it divided by the price. That's how much she wants to buy. Now I just have to add X^(C) X^(D) and it's very hard for me to do at the board and you to follow there, but of course if you stare at the page for a minute at home it'll be very simple to follow. I do Walras' trick. I said I can always take P_Y to be 1, and if I take P_Y to be 1 I'm going to get this income is P_X [times] 2 times [correction: plus] 1 times 1 which is just 1, so 3 quarters of this divided by P_X, that's what he's buying. She's buying 2 thirds of her income which is P_X times 1 1 times 2 which is plus two, divided by P_X, that's what she's buying, and I just add this to this and do a little algebra. So I just add and do a little algebra and lo and behold P_X is equal to 5 halves. So I happened to remember that's the right number so I actually did this right. So P_X is equal to 5 halves, and we've solved the whole problem. So if P_X is equal to 5 halves how much is she actually buying of X? Well, I could always plug this back in, plug in P_X is equal to 5 halves and find out that's 5 1 is 6, times 3 quarters, divided by 5 halves. That would tell me how much X_C she was buying. So and I could plug in 5 halves for P_X and I'd get how much D was buying of X and I could also plug P_X = 5 halves and PY = 1, and find out what they were doing of good D. So you can solve it by hand very easily, but let's just solve it by computer instead unless there's a question. Ha, I stopped it. Any questions about what I did here? Yes? Student: So we just maximized utility so there's no other allocation of utilities any greater? Prof: Well, now we haven't gotten here yet. I've run over a little bit, so I'm going to finish the class by repeating this calculation on a computer just by pressing a button and you'll see what the answer is. But then we have to examine the question, have we really maximized utility here, and to give away the punch line, that utility was very special. It was constant marginal utility of 1 in a particular good Y. That's what made this example as almost identical to the football ticket example. The final equilibrium is going to maximize the sum of utilities. Here, this equilibrium is not going to maximize the sum of utilities. There's no reason it should maximize the sum of utilities. And so you need a different definition of why the free market is such a good thing. So economists made a tremendous mistake. They thought that the original criterion for a good market is you maximize the sum of utilities. That's not even true in an example like this one, so we need a different definition which we call Pareto efficiency that illustrates why the market's good. But if they made a mistake once it stands to reason they could make a mistake another time. So there's something special even about this example. When we put in financial variables I'm going to argue you shouldn't expect to get the optimal outcome all the time, but that'll be next class. Yes? Student: Beyond like arithmetic use is there any reason you would choose to assume P_Y or P_X is 1 or it's arbitrary? Prof: No. There's no reason to pick P_X or P_Y to be 1, whichever one you want you can choose to be 1, and I keep going back. I can never make up my mind which one to do, so yeah, just whatever it works out. This one it clearly worked out arithmetically easy to take P_Y = 1 because the marginal utility of Y was 1 and that canceled everything out. Here I could have taken either one price to be 1 and it wouldn't have helped. So I picked P_Y to be 1 again. In the last five minutes let's just show how to solve this by computer. So this is something you also are going to be able to do. And it sounds like, "Oh, there's so many complicated things. There's these new equations," if you do this for the problem set, after you've done it once for the problem set-- you may have a little trouble with the problem set, the TAs will help you, but after you do it once this will be very simple. Now, doing it by computer is also very simple. And it's going to sound complicated, but as all you young people know if any old guy can figure out how to work a computer you can do it vastly quicker. So let's just take the second example here. And we have five minutes left. That's all it'll take. So this is Excel. Now, Excel is this program that's made zillions of dollars. The inventor of Excel, by the way, was the inventor of Lotus. Oh, what was the guy's name? His sister was in my class at Yale. He was two years ahead of me. Not Gabor, Mitch Gabor, [correction: Mitch Kapor] something like that was his name. Anyway, she was in my class, and he was two years ahead of me. And he invented this thing called Lotus, which made a lot of money. And then it got bought out by a few people. And then Excel just basically copied the entire thing, Microsoft, and made a fortune and had to pay him off for plagiarizing the thing. But anyway, it's basically Mitch Gabor was the inventor, a Yale undergraduate two years ahead of me. So he's a billionaire now. So let's just solve the problem. Let's do the second one because I may not have time for the first one. So what did I do? I said let's write down the exogenous variables first, sorry let's just go up a little. So the exogenous variables are the endowment of X, of the two goods, A and B, that's 2 and 1, and B is 1 and 2. Now what are the variables? P_X, P_Y, X^(A), Y^(A), X^(B) and Y^(B), we don't what those are. So I've plugged in P_X and P_Y. I'll guess both of them are 1, which is obviously going to be wrong, and I'll guess that people just end up with their endowments, which is obviously not right. So then I look at the budget set. So those are my guesses. These are the endogenous variables and wild guesses about the solution. Now, what are the equations? Well, we wrote them down. There's the budget set of A, so that's just the budget set of A. So how do you write these equations down? You simply name the--it's up here if you haven't used Excel before, up here. You write down the letter, say B35 that's P_X, so B35 times B31. That's P_X, is B35 times endowment X^(A). That's the income. I wrote the income first. That's the income A has minus how much she spends or he spends. B35 times B37, B35 remember is the price of X, B37 is how much he buys. So that's just the budget set. So for each of these equations, the marginal utility, I just did the same thing. Remember the 3 quarters, over P_X times X = 1 quarter over P_Y times Y, so this [difference] should be equal to zero. Instead of saying this equals that I subtract the right hand side from the left hand side. So you want all these equations to be equal to zero. I just wrote down the six equations. And so Excel now tells me that of course the budget set is going to be satisfied automatically because people are consuming their endowments. And the budget set of B is automatically satisfied because I just had them choosing their endowments. And markets are going to clear, of course, because everybody's choosing their endowments, but they're not optimizing. So this marginal utility stuff is all screwed up. So what do I do on the right? For every error in the equation I square it. So I've squared all the errors. So these are my equations I need to satisfy, one, two, three, four, five, six equations. One, two, three, four, five, six, and I summed the squares. So if I make the sum of the squares zeros each of those has to be zero. So Excel, now, can minimize the sum of squared errors. Excel is going to search over all endogenous variables, P_X through Y^(B) to find the things that makes this number as small as possible. Once this number becomes zero it means all the ones above it have to be zero because they're all squared numbers adding up to that, and so I will find the solution. So you see that all you have to do--if you've done this before of course it's obvious, if you haven't it's just so simple to write the equation. Supply and demand I just name the box, B32 that's the endowment of Y^(A) the endowment of Y^(B) equals the consumption of A plus the consumption of B. That's the difference we want to make zero. So here's how you solve it. There's a thing called solver. So you go to tools and you hit solver, and now solver says you want to take a target cell. I cheated. I already knew what it was, C47. So it's the target cell. I hit minimize, so I want to minimize that. And now what cells do I change? Well, I have to tell Excel what to search over. So now Excel, what are the cells? I could say P_X, P_Y, you know, all the endogenous variables, but I know I can fix P_X to be 1 so I'm going to forget that one and I'm going to say just these five, right? I don't need all six of them, just five because I can always take P_X to be 1. So the solver now knows it wants to minimize this number, which is the squared errors of all the equations I want to hold equal, it's going to minimize that by searching over all those numbers. It's not very smart about searching for it, and sometimes it never finds an answer. We know there always is an answer, and so how do you solve it? You just hit solve and it's going to search and do it. And what should the answer be? If I fix P_X to be 1, remember the answer was when P_Y is 1, X turns out to be 5 halves. If I fix P_X to be one, what should P_Y be? The solution we got before was P_X = 5 halves and P_Y is 1. Now I'm going to fix P_X to be 1, so what should Y be? X was 5 halves times Y, so Y should be .4, so if this solves right we should get P_Y to be .4. So I just hit solve and voila I get P_Y to be .4. I find X^(A) is 1.8. I find all the numbers. I just solved it just like that instantly. So you can see how useful it's going to be to use solver and do these problems. Student: If you change the endowments does that change it? Prof: Of course. If I change the endowments I'll get a different answer, and if I increase the endowments yes it does and that's very important. Student: > increasing it > Prof: If I double everybody's endowment? Student: If you double one endowment. Prof: If I double one endowment that's going to change things around. If I double everybody's endowment it won't change anything, yeah.
Quantitative_Finance_by_Yale_University	11_Social_Security.txt	Prof: Okay, today we're going to talk a little bit more about Social Security. Social Security, remember, is the biggest program the government runs. Its annual expenditures are slightly bigger than the military expenditures every year, and those two things are way bigger than everything else. It's been the biggest program the government's run since the New Deal, since Franklin Delano Roosevelt put it into effect in the late 1930s, and it seems to be broke. So it lasted for 70 years, and now it seems on the verge of going broke. So what happened and how can we fix it? And as I said, this has been a topic of conversation, presidential conversation, at least since 2000. There were a bunch of commissions before that, looking at the problem, and what I said last time was, the general public and our politicians seem completely confused about what's going on. So we need to figure out, how could it be that the program went broke? Should that have been a surprise, and how can we fix it? And the three standard things everybody says is, President Bush and many people like him saying, "Well, the system's going broke. The rate of return young people like you are going to get is less than 2 percent a year. That's terrible. Any bond, any stock, you can expect a much higher return than that, so the program's just awful. We should stop it or privatize it." I'll explain what privatizing means. In that way, your money, instead of going to old people, will be put in the stock market and you'll get a higher rate of return and you'll do much better. Then a second thing people say is, "Well, the thing lasted all this time. I mean, what's really gone different? What could possibly have caused the change? It must be those dastardly baby boom generation-ers, like me, who are headed towards retirement in another 20 or 30 years, and they're going to bankrupt the system. There are going to be so many of those old geezers hanging around needing to get paid, that young people like you won't be able to carry the burden, and so it's our fault." And then there are the people, the naysayers, Gore chief among them, but many others, Obama now similarly saying, slightly similar things, saying, "Well, privatization doesn't make any sense. It's logically impossible, because if you take the taxes that the young people are paying, and tell them, those Social Security taxes, they can invest in private accounts, the stock market, with their own name on it, then how are we going to give money to the old people now? So you'll just be screwing the old generation." So privatization is impossible. So those are the three most standard things people say. All three of them have some truth to them, but on the whole, they're substantially wrong, completely wrong, and once we clarify what stage the system is in, we'll be able to think about what the right solution is. I'm going to tell you my solution which, as I said, is not universally admired, but I'll see what you think about it. So the program came into effect in what was the greatest or the biggest of the New Deal advances made by FDR. And I just thought I'd play you this tape of him signing it into law, and behind him is the Secretary of Labor, Frances Perkins, who you'll see in a second, played a huge role in this, since she was the first woman in the Cabinet. And by the way, in my generation, there are many women named Frances, because their parents named them after her. So here's the--let's see if this works. > Franklin D. Roosevelt: Today a hope of many years' standing is in large part fulfilled. The civilization of the past hundred years, with its startling industrial changes, has tended more and more to make life insecure. Young people have come to wonder what would be their lot when they came to old age. The man with a job has wondered how long the job would last. This Social Security measure gives at least some protection to thirty millions of our citizens who will reap direct benefits through unemployment compensation, through old-age pensions and through increased services for the protection of children and the prevention of ill health. We can never insure one hundred percent of the population against one hundred percent of the hazards and vicissitudes of life, but we have tried to frame a law which will give some measure of protection to the average citizen and to his family against the loss of a job and against poverty-ridden old age. It seems to me that if the Senate and the House of Representatives in this long and arduous session have done nothing more than pass this security bill, Social Security Act, the session would be regarded as historic for all time. > Prof: Okay, well, it was regarded as historic for all time, and let me now explain what Social Security does, and what the rules are. And I have to open another file. I forgot where I put--I hope it's--I wonder whether it's--sorry, I opened the wrong year, I see. I'm living in the past. Sorry, that was last year's. Okay, so we went through all this last time. So, after passing legislation, a massive publicity campaign was launched, convincing people that this was a good idea. And not everybody thought it was such a good idea, by the way. And so, you know, this is an example of the advertisements that were plastered everybody, you know, telling you about how much you were going to get, money after you retired. Now what was the idea of Social Security? The idea was that lots of people, when they were young, didn't really have the foresight to imagine what life was going to be like when they were old. In fact, in the late 1930s, the most destitute of Americans were the old, and so the idea was to force them to save when they were young, and then the money would be there--would be invested in US Treasury bonds and accumulate interest, and the money would be there when they got old. So it was imagined to be a prefunded system, prefunded meaning the money comes in and it's that money which is going to then pay people later when they get to old age. And the idea was, you were going to collect enough taxes so that when you got to be old, you would get 40 percent--every year, you would be receiving, the average person, recipient, retiree, would be receiving 40 percent of the average wage of the average young worker. And, you know, the idea is that when you're older, you have less expenses. You probably already own your house, your children are out of the house, so 40 percent should be enough to keep you going. It was certainly more than the average old person had at the time. Now this you would get for your entire life, so when Roosevelt called it insurance, what was the main thing that you were insuring? Well, there's a side part of the program which he mentioned, which is insuring people of disabilities, things like that. But that's a 1--out of the 12.4 percent tax, it's something like 1.8 percent. But the main part of the program is insurance against what? Yes? Student: Living too long. Prof: Living too long. So you get the money your entire life, no matter how long you live, so you're being insured against living too long. Exactly. So what happened was, of course in the first year, a lot of people were starting to pay taxes. And in the second year, they were paying more taxes, and of course, they were still not retired yet, so they weren't actually giving out the money to anybody, and this fund was starting to accumulate. So Frances Perkins said, "Well, what are we doing here? The whole point is that we've got all these old people, you know. It's just the Depression. We haven't come out of the Depression yet."--World War II hasn't started. It won't, for the US, start for a few more years, by the way. "So there are all these old people sitting here, totally destitute, and we've got all this money also just sitting here. It really doesn't make sense," she said. "What we ought to do is take the money the young people are paying in and give it to the old people who are already there. That way we are going to be saving these old people and the young people, when they get old, they'll be saved themselves, because there'll be more young people coming along afterwards who can pay taxes in when they're young, and today's young, when they're old, will then collect those taxes. They'll be reimbursed for what they contributed when they were young." Well, so Roosevelt resisted for a while. Frances Perkins was apparently, incredibly persuasive person. One person at the time named Witt, who was on the Social Security commission, tried to tell her that was going to lead to budget problems. She said that he was a half-Witt, and that we had a more urgent problem. Not that she doubted him, but the problem was more urgent, and so that was the only way to solve the problem, the current crisis. So they finally agreed to move the system from a prefunded system, to a pay as you go system. So the money coming in from current workers is used to pay directly to the old workers. So I don't want to get into all these little variations that got made. So the program's called the Old Age Survivors and Disability Insurance Plan. The insurance is mainly for living too long, but also in case you get disabled, or in case you have children and you're disabled, you die, they get something. Okay, so it's a combination of insurance, disability, but the main insurance is for living a long time. So as I said, the tax now is 12.4 percent, up to a cap of 106,800 dollars. So if you make more than 106,800 dollars, you pay, you know, 13,000 or something, and then nothing more on Social Security. Okay, so the Social Security tax stops at 106,800. So the income tax, I'm losing track of what it is, and whether we're going to go back to the old one, but let's say it was 38 percent, 39 percent, something like that, if you had to pay that income tax and on top of it pay Social Security tax of 12.4 percent, you'd be over 50 percent taxed. So needless to say, some of the people who think we can solve our Social Security problem by eliminating the cap would be imposing a gigantic marginal tax rate on a lot of people who don't have a marginal tax rate-- who have already high marginal tax rate. That would make it sky high, so that's been resisted. So 94 percent of workers are below the cap anyway, so we're talking about the top 6 percent, most of which--you'll be in that top 6 percent, so you won't have to pay on the margin Social Security tax. So there's the taxes, 12.4 percent, and then there are the benefits. Now how do the benefits work? How are they determined? So the tax, as I said, you just take your income below 106,000 and you pay 12.4 percent tax. So how do the benefits work? This is a little bit complicated, but it's actually a very interesting plan. What they do is they look at your entire lifetime earnings. You're not going to get benefits till after you retire, so you've got your whole life history behind you, and they say, "Let's look at, every year, what the fraction of your wage was relative to the economy wide average." So it's your relative earning. So when you're young, it's probably going to be .8, .9. If you go to Yale, it's probably going to be 1.5,2, you know, soon thereafter, all right? Okay, and it might get even higher, but anyway, so that's the relative earning you have every year. So then they say, "Let's average your 35 best relative earning years and just take the sum and divide by 35." So what is your average lifetime relative wage, you know? For the average person, it's going to be 1. For some people, it might be .8, for some people, it might be 2 or 3 or 10, okay. Now the first--all right, so you've got your average relative lifetime wage. What do you make when you retire? Well, when you hit an age, which, you know, they're adjusting now, but it used to be 65, when you hit 65, they compute the average wage--sorry. When you hit 65, you're going to be paid a fraction of the average wage in the economy when you're 65. So what is the fraction that you're paid? Well, that depends on what your historical average wage was. So let's just see what the function is. So, if your average wage was 1, equal to the average wage of the economy, your entire, over those 35 years, so you're the average guy, then you get, you see, that's near .4. It's actually .44, so you get 44 percent of the average wage at the time you retire, okay? If on the other hand, you made 10 percent of the-- your relative wage historically was 10 percent of the average wage in the economy, you would get 9 percent of the average wage at the time you retire. So you can see that this is what's called a concave function, just like our utility function, those diminishing marginal returns. So it means that if you're earning very little through your life, you're going to get a much better deal. You're going to be paid--the ratio of relative wage historically to what you get of the young people's wage is going to be .9, then the slope drops to .32, then it drops to .15 and after you're double-- it's actually, I think, 1.99--after you're double the average-- if your historical average wage was more than twice the average wage in the whole economy, it doesn't do you any good. Might as well have been twice. If it's 4 times, 10 times, you don't get any increase. Okay, so you can see why it makes some sense to have a cap to the taxation, because people who are making 10 times the average wage, you know, let's say they're making a million dollars nowadays, they aren't going to see any benefit from having contributed so much to Social Security. Their benefits would be just the same as if they only made 200,000 dollars a year. Okay, so anyway, you see that there's a connection between how much you made when you were young, how much you get paid when you're old, but the connection is a concave thing. So it redistributes income. People who had very low average wages when they were working get a better deal from Social Security than people who had high relative wages while they were working. And that's a cornerstone of the idea. It's meant to help protect the people who are very poor. And so it doesn't pay everybody equally. Still, you get some return from having contributed more, but definitely you don't get a completely fair return, because the whole idea is to redistribute wealth and help the least well off. Okay, so that's one of the cornerstones of Social Security. All right, going back, now what happens to you after the first year you retire? After the first year you retire, so when you're 65, you're getting 40 percent of the average wage, if you're the average worker throughout your life. You know, it's 44 percent, something like that. After that, your Social Security benefit is indexed to inflation, so it grows at the rate of inflation. The wage is probably growing faster than the rate of inflation. So as you get to be 75,80 and 85, your average benefit is down to 36 percent of the average wage of the workers when you're 85, but it starts off at 44 percent, assuming you were average your whole life. It'll be 44 percent and gradually decline if wages grow faster than prices. So it's insuring you against living long, because the benefit carries on forever. It's insuring you against inflation, because it's inflation corrected. It's in a way insuring you against feeling like a loser, because you're always going to start off with a fraction of the new average wage. So if your children, if the whole country grows incredibly fast and your children are incredibly wealthy and getting high average wages and every young person's making a lot, the old won't feel totally left out. They'll be keeping up with them, 40 percent of them anyway, and similarly, if the young have a horrible time and aren't making very much money, the benefits to the old also go way down, because they're getting 44 percent of a much lower number. So it's every generation in it together and redistributing wealth from the richer to the less rich, protecting you against long life, making sure that you have some money no matter how long you live. That's the idea of the system. So are there any questions about how this mechanically works? Okay. Now it's very hard to do this in the market, by the way. If you wanted to, for example now, think to yourself, "Oh, I'd like to protect myself against my old age. I'm three years out of Yale and I've fallen into an incredible job that's paying me a huge fortune. I might want to retire early and be a writer the rest of my life." You can't easily find an annuity in the private market that's going to tell you that when you hit 65, it will continue paying you for the rest of your life. You can actually find them, but they're incredibly bad deals. The reason that they're bad deals is that the people who would have to take the money now and give it back to you when you're old, first of all you have to worry whether they're going to be around and still be able to pay you when you get old. And secondly, they're worried that the only people who come to them are people whose families live 100 years, and so they're going to have to pay a lot longer than they would for the average person. So they're afraid of getting a bad selection, that is, a selection of super healthy people wanting to make that deal. And so they basically assume that you're going to live to 100 and so they're giving you a very low annuity year by year. So Social Security is doing something that's very hard to obtain in the market. Now, so what went wrong? Oh, I should say a couple other things about it, some interesting things. You can choose to retire early if you want. If you retire before 65 and you want to get your payments starting earlier, they say, "Okay, you can do that, but we're going to cut the payments every year," and they make some actuarial calculation so that it's fair, based on how long the average person lives. So if you start at 63, you get 2 extra years, but they know if you live the average amount of time, how much to cut it down, so that on average, you'll get the same amount as if you did the normal thing retiring at 65. They've actually raised this age to 67. Now another thing is the spousal benefit. This is actually quite amusing, I think. So I had a secretary 20 years ago who got married three times. So she consulted me about this. If you're a spouse, you know, traditionally, one of the spouses wouldn't work, typically the woman. And so the wife has the right to 50 percent of her husband's-- or the husband has the right--one spouse has a right to 50 percent of the benefits of the other spouse, just by virtue of being married or having been married. So the rule is that if you've been married for more than 10 years, then you can either take your own Social Security benefits, or if they're bigger, you can take 50 percent of your spouse's. And if you've been married to several different guys, say, and you're not married to any of them anymore, you can pick the guy who had the highest income and get 50 percent of it. So she tracked down her first husband she hadn't talked to in 30 years, and anyway. So okay, and there are a bunch of other rules. Anyway, that's not really the heart of the matter. The heart of the matter is--just to give you an idea of the size. This was in 2005. So 157 million workers are paying into it. There are 48 million beneficiaries. It's a gigantic program. So imagine the cost of keeping track of just who's alive, you know. When somebody dies, they're supposed to stop collecting Social Security. How do they know that the guy's died? I mean, that by itself is not an easy thing to keep track of. They have to send the checks to everybody. Somebody moves, they have to figure out where to send the check to the new address. They have to get the taxes, they have to make sure people are paying the right amount. It's a huge thing involving basically the entire population, a couple hundred million people almost, either getting taxes, paying taxes or receiving benefits, you know, over 200 million people. It's an incredible amount of paperwork and moving stuff around and figuring stuff out. So how much does it cost? How much money do they waste running the whole thing? Less than 1 percent of the benefits. Okay, so it's one of the most efficiently run programs, maybe the most efficiently run program government has ever devised. So it isn't that the thing is going broke, as you might believe listening to George Bush, because somehow they're pissing away the money and just losing it. That's not the reason. Something else is happening, because they don't waste much money running the program. Okay, this gives you an idea just of the size of it. So this is 2005, so you have to add 20 percent or something or 15 percent. So the benefits, the contributions, 593 billion. Remember, there's a tax rule of 12.4 percent. Then you have to pay out the benefits, which is some other rule, depending on what you earned in the past, so there's no connection between the two. And in fact, the contributions are bigger than the benefits, so the trust fund is growing. Now look at the administrative expenses, tiny. And there are some, the railroad, when the law was first passed, railroads were in trouble, so in order to get some senator to vote for it, they had to hand money over to the railroad. So anything, something's going on with the railroads. But the other benefit is the trust fund makes returns, because it's a 2 trillion dollar trust fund. It was a little smaller than that 2005, so it's earning interest. That's part of the extra returns. You see why the surplus is quite big now, but it's headed to be quite small. Okay, so now what is the argument about? What is the crisis of Social Security? What do the Democrats and the Republicans say? Well, you've just heard what the program is. How attractive do you think it is, and do you really think it's such a good program? So the main thing is, it's going broke. Okay, so now why is it going broke? It's not broke now. It's making more money than it's paying out. But in the future, it's very obvious, you can just look at the demography. It's very obvious that it's going to-- the benefit formula is so big, and there are going to be so many people retired that the payments you make to the old, when I'm retired, are going to be way bigger than the payments that the young are making in taxes, provided the rules stay the same. So that's the main problem. Somehow the system got out of whack and we have to figure out how to put it back together. Now it's no surprise in one sense that there's an imbalance, because there's nothing about the rules that balanced it. I mean, the taxes you pay--we'll look at this in a second--that's just some formula, 12.4 percent. What's that got to do with the benefits you're paying? Well, the benefits are 40 percent, on average of what young people are making. So basically, somehow the system must have assumed that there would be three young people for every old person. So the young people paying 12 percent each, the old guy getting 40 percent, you know, 3 times 12.4, it's close to 40 percent. So if the ratio of young to old, young workers to old retirees getting benefits is 3 to 1, then the systems going to sort of be in balance. But if that ratio is very different from that, the system--for example, two young people for every old person-- the system's going to be way out of balance. And the formula has nothing to do with how many children people are having or anything like that. So it's not so surprising it's gotten out of balance. But we're going to see, there's a much more fundamental reason why it's out of balance. Okay, so the first problem is, it's not in balance, but there are many other problems. So why do Democrats like it so much? Democrats say, "Oh, it's wonderful. We're helping poor people. We're redistributing things on the basis of lifetime earnings. We're sharing risks between generations. We're all in this together." As I said, if the young people have bad wages, then the old get less benefits. If the young are booming along, making huge wages, then the old guys keep up with them, so there's less--so it's not only insurance, but it's less jealousy and less disparity in the population. And then you're protected against long life, you're protected against inflation, and you can't blunder away your money, because you have no choice about where your investment goes. The government's taken care of it, so if you're a bad investor, you can't suddenly find that you've lost all your money. So now what do Republicans say? And surprisingly--well, anyway, you'll be surprised where I come out on this, I think. So Republicans say, "This stuff is much less good than it sounds at first glance. For one thing, there are no property rights. I mean, who's to say what I'm going to get when I'm old? Nobody even knows what they're going to get when they're old. I defy you," a Republican would say, "to tell me exactly what your benefits are going to be, or even to explain to me how they're calculated." "Virtually nobody in the population can do that. That's just not right, and you have no control over them. So what's going to happen?" a Republican would say. "One of these days, the Democrats are going to say, 'Oh, the system's broke. We can't afford to pay everything, so we're going to cut all the benefits in half' or something." So a Republican would say, "You know, they're not even my benefits. In order for me to really feel good about participating in Social Security, I want to know that when I put the money in, what I'm getting out, and I want to own it. I don't want it to be some vague promise that can be taken away from me, and probably will be taken away from me." Okay, so it's a matter of property rights and transparency. Then another thing is, even if you did know this formula that I just explained, people who want to retire and want to figure out how to plan for their retirement, what does a normal person do? He says, "How much money have I got in the bank? I've saved on my work; I've got 100,000 dollars in the bank. Please tell me what the value today is of my future Social Security benefits. If those are 8 million dollars, then I know that my 100,000 dollars, I don't want to waste too much time trying to accumulate money out of my savings, because I'll never catch up to 8 million dollars. If it's 50,000 dollars, today's market value of my future Social Security benefits, I know that I'd better be putting in a lot of money today. And I know how much money today is, how big my savings are, relative to what the market value is of my Social Security benefits." So the Republicans say people just don't have any idea what the value of their benefits are, even if they happen to know the formula I just explained, nobody really can calculate what it is. Then thirdly, the rich are giving money to the poor. Everybody knows Social Security is doing that. Can you tell me, what's the effective tax rate? Let's say I'm in the top tax bracket. What is my effective tax rate on Social Security? What fraction of my taxes are being taken away from me because my benefits are going to be less good, because I was one of the highest earners? There's virtually no one in the country who's able to answer that question. A Republican would say, "What kind of a program is this if nobody knows? Okay," they'll say, "we may sign on to the idea that the rich should give some of their money to the poor, but at least tell us how much of our money we're giving to the poor. We don't even know." And then the Republicans say, "We'd like equity-like returns. You know, why is it--" This is what George Bush said. "Why is it that our returns are going to be 2 percent? I'd like to know that my money is being invested in the stock market and earning what I could get in the stock market." Anyway, Republicans, savvy investors like to think that the money that they're being forced to save can get the same rate of return as they could get for themselves. Why should they be cheated in a government--never mind that they have to give away part of the money. The part that they're not giving away at least ought to earn equity returns. And then Republicans tend to think that choice is a good thing, not a bad thing, and so if you let people decide how to invest, it'll be better for them than if you-- even if some of the people make mistakes. Okay, so those are the two--maybe some of you can add some other criticisms. Yeah? Student: Wouldn't any system that insures against living longer than expected, that annuity type system, have that problem in terms of caring >? You'd be unable to calculate the present value, precisely because you're unable to predict how long you live. So any system that successfully > is supposed to perform, that's just an inherent issue. Prof: Yes. So no, I don't think so, because--so his question is, since we don't know how long we're going to live, and the program continues to insure you for your entire life and pay you for your entire life, how can you figure out what the market value of that is? Well, the fact is, there is no general market. So you're right, there is no general market you can look at now today, that will tell you, suppose we pay a fixed amount of money for the average person in the economy, what's the present value of that? However, that doesn't mean we couldn't have a market like that. And so my solution is going to involve precisely a market like that. So to answer his question, it's not inherently impossible to attach a market price to paying somebody for the rest of his life. After all, you could imagine Social Security now, paying, let's say 50 million people, the people who are now retired, each of them is going to be paid for the rest of his life according to a rule, which we all understand. It just goes up with inflation. So you could say, suppose you owned 1 percent of all those payments, what would the value of that be? You could trade a security like that. Somebody could say, "I want to buy today a security that gives me 1 percent of all the payments everybody's going to get," or it could be 1 percent of all of the payments every 70 year old today is going to get from Social Security. That's a well-defined thing and it could trade in the market. You're going to see that the market, as soon as we start talking about this, there is an incredible number of derivative instruments, they're called, that trade in the market. That could be a new one, and then there would be a market price. You're going to see, when I propose my plan, that it involves something like that. Any other questions about the rules of Social Security or whether you think they're bad or good for some other reason? I've tried to list the ones that struck me as the most important. Yeah? Student: What does it mean by a return? Does it mean that you invest in government bonds and then you get back taxes from another part of the government? Prof: Equity-like returns? Is this what you're referring to? Student: > define the return. Isn't the interest you're getting just taxes from another part of government? Prof: Okay, so you can always do this calculation, which has historically been done, and I'm going to show you those numbers in a second. You can always look at how many tax--let's take someone my father's age. My father actually died, but a couple of years ago, my father, he could look back at his whole life, and he could look at how much money he paid in Social Security taxes when he was young. Then he could look at what benefits he got every year until that point. Let's say it was the day after he died. I could look at what he got every year until he died. So then I could just--that's just a sequence of cash flows. We know how to calculate the internal rate of return of that sequence. That's his rate of return. And I showed you in the graph a long time ago that that was actually done historically. We've done that. Leamer did that here. He did that for every generation. Every birth cohort, the average person, what their return was, and you see, it was very high to begin with and it become pitiful. If you forecast the future for you, it's going to be less than 2 percent. So Bush is saying, "Why should you, young Yale undergraduate, why should you be satisfied with less than 2 percent? Instead of paying those taxes to Social Security, you put them in the stock market, you get lots more than 2 percent probably, so why be satisfied with 2 percent?" And Gore would say, "Well, now we've got this pay as you go system, you can't possibly put it in the stock market, because then the old people aren't going to get it." Okay, any other questions? Any other reasons you think the program is good or bad, Social Security. What's your feeling about whether we should get rid of it or not or privatize it or change it? Yeah. Student: It discriminates against people who are predisposed to die early. It favors couples whose ages are really far apart. It's extremely > Prof: Yes. He's saying other problems with Social Security is that it discriminates. It doesn't treat everybody equally. His first example was, people who you can reasonably expect to die sooner are going to get a less good deal than people you can reasonably expect to live longer. So what is the most basic class that's being discriminated against, therefore? Who among you can you predict are going to live less long than others among you, at least historically? Presumably that will stay true. Student: Men. Prof: Men. Okay, so men live 6 years less long than women, so men are getting a bad deal. Now black men, historically--although this is rapidly changing, but black men lived even less long, even worse by a considerable degree, so you'd think it discriminated against black men. Black men also tended to be poorer on average though, so they were getting a better return per year than rich white men. But anyway, a black man with the same earnings got a much worse deal historically on Social Security than a white man with the same earnings, because on average, the black man died before the white man. That probably had a lot to do with healthcare and nutrition and stuff like that, and this is rapidly changing. But anyway, certainly it seems like men are going to get a worse deal than women. So yeah, there are all kinds of little problems with Social Security like that. Anything else? He mentioned a couple of others too. I regard those as less critical though, than the problem of the thing going broke, and these things which have split the country. It's been impossible--so basically, everybody thinks this is a logical contradiction. You can't do what the Republicans want, at the same time, do what the Democrats want. So what should you do? Anything else anyone wants to say? Someone else had their hand up before. All right. So why did the system become such a mess? How did it go broke? How should we have expected it to go broke? Did it all happen because there was the baby boom? All right, so I want to tell a little parable. It has nothing to do with the baby boom. Okay, so imagine that--and I'm saying it in terms of fathers and sons, but I could say mothers and daughters. So historically, it was men working most of the time, but let's do mothers and daughters. So suppose a mother is old now and sick and she needs an incredibly expensive operation, a million dollars to save her or to extend her life. She doesn't have the money, so she goes to her daughter and she says, "I need a million dollars." And of course, the daughter who loves her wants to come up with the million dollars to pay for her. But, you know, that's a lot for her to pay. So she thinks to herself, "My mother not only gave me life, but let's face it, without her, my daughter wouldn't have any life and her daughter wouldn't have any life and her granddaughter wouldn't have any life. My mother's responsible for not just me, but for all these generations after me. Why should I be the one to pay the entire benefit of my mother's operation? So you know what I'm going to do? I'll give her the million dollars, but when I get old, I'm going to go to my daughter and say, 'Daughter of mine, I sacrificed for your grandmother, my mother. I put up a million dollars to save her. I'm broke now. Maybe I don't need an operation, but I'm basically totally broke because I spent so much money rescuing my mother. Why don't you do the same for me that I did for my mother and give me a million dollars? And by the way, you could use the same argument with your daughter, and so it's really not so bad, because you're going to get the money back when you're old.'" And so the granddaughter agrees and pays the daughter, and then when she gets old, she does the same thing. It goes on for generation after generation. Now let's say it went on forever. How did this happen? Did nobody lose anything and we paid for the operation to begin with? Is this some kind of Ponzi scheme or something? Where did the million-dollar operation get financed? How did that happen? Who paid for it? Yes? Student: Don't you pay the opportunity cost > million dollars and > individual lifetime when the money could have gone and made money itself rather than spending on the operation? Prof: Well, you got a million dollars back, remember, when you were old. Student: > nothing more than a million dollars > Prof: Okay, exactly. So that's the whole point. The point is that the daughter--just to repeat what he said. The first daughter paid a million dollars when she was young. Yes, she got the million dollars back, but when she was old, and that's a long time later. So for that whole time, she made a 0 percent interest. Now maybe the interest rate was, let's say, over that many years, we're talking about 30 years or 40 years, a large amount of time. So the interest rate could easily, over 40 years, you divide 40 into 72, you know, it's like 1 and 3 quarters or something. So if the real interest rate was 1 and 3 quarters, something like that, you could easily imagine, that was the doubling rule, that 100 dollars could have been turned into 200. So the first daughter who took her 100 dollars could have had 200 by the time she was old. She only got 100 when she was old. So in present value terms, she gave up 100 when she was young. She got, in present value terms, 50 dollars when she was old. So she gave away 50 dollars. She paid for half the operation. Now where did the rest of the 50 dollars come from? Well, the granddaughter gave 100 when she was young, got 100 when she was old, so in present value terms, she also lost 50 dollars, exactly the same amount as the first daughter. She gave up the same thing. Her contribution was just as big. Of course, it came a lot later, so in present value terms, at the time of the operation, the granddaughter's contribution is discounted twice, so it's 1 half of 1 half. So she only contributed in present value terms 25 dollars to the operation. And then the great granddaughter, she herself looks at it as a 50 dollar contribution, but from the point of view of the original operation, it's discounted 3 times, so by 8, so it's 12 and 1 half. So 50 25 12 and 1 half 6 and 1 quarter, blah, blah, blah, forever, adds up to the 100. So basically, this parable shows how a daughter could share the cost of her mother's operation among all the descendants, pay completely for the operation with each generation making the same contribution, the same sacrifice. Of course, the generations who make it earlier are helping the mother more, but the point is, every generation has made exactly the same sacrifice and that's how the original mother's operation got paid for. Now what happens in generation 10, the great great great great great great granddaughter is going to say, "You know, I never even heard of this original mother. I couldn't care less about her operation. It wasn't a very good operation anyway, because she died three years later, because medicine was so bad at the time. So why should I be paying my contribution to that original mother's operation? Yes, I know that she's responsible for my life, but you know, I don't know anything about her. I don't even know her name any more. How come I have to keep paying for it? So I just want to stop." Now why is it going to be actually difficult for that generation to stop? "I just don't want to give my money to that first generation. I couldn't care less. Let's stop right now." Yes? Student: She's not giving the money to her great great grandmother; she's giving it to her own mother. Prof: Her own mother, exactly. So you can't stop just in the middle because it's like the gift is being re-enacted every generation. So the new generation that stops, even if they understand where the whole thing began, they're not going to screw the original mother. They're going to screw their own mother, which they probably don't want to do, so they're not going to want to stop the thing. So to say the parable very shortly, the first generation that got taxes-- got benefits without contributing anything, that was a huge amount of money that they got. Every generation after that lost money, but that was all a way to pay the first generation, and you can't stop the cycle without screwing your own parents. So it's very difficult for the thing to be stopped. Now you could make it a little bit more realistic by saying every generation, wages grow every generation, say between 1 and 2 percent in real terms. That's the historical rate of growth. By the way, it hasn't been so great lately, but anyway, historically, say 1 to 2 percent real growth of wages. So on an annualized basis, if you did the same thing with each generation paying 12 percent of their youthful wages, you would find that--now we're coming closer to reality-- that every generation was going to get between 1 and 2 percent return on their contributions, because the young would contribute 12 dollars out of 100 say, but their daughter, that lady's daughter, 30 years later, the wages would have grown by 1 to 2 percent every year for those 30 years. So 12 percent of that bigger number would go to that daughter, and so there would be a rate of return between 1 and 2 percent. And that's exactly what Bush and everybody else is predicting. So now you understand where the 1 to 2 percent comes from that you're going to get. If the population is stable, the ratio of young to old, the rate of return on Social Security is going to be equal to the rate of growth of wages. So it's not 0 as in the first parable, because wages are actually growing. It's between 1 and 2 percent, which is a bad return compared to the rate of interest, and that's why every generation is losing. Okay, so let's do one more thing. So the baby boom, does the baby boom make things worse or better? How can you think about it? It's so simple minded to think this way. It's amazing; the public is so confused about this. Suppose you have a baby boom generation. So you're going on with all these mothers, we're back to the mother and the daughter with 1 million. So let's say there's one mother, one daughter, one person in every generation. All of a sudden, there's a baby boom generation, but of course, to be old, you have to be young first. So let's say in some generation after a bunch of times, there are 2 daughters instead of 1 daughter. Each of them is not going to pay--if the tax rate stays the same and the young daughters now each pay 1, the mother who's alive then only needs 1 when she gets old. So 2 daughters now have 1 to contribute, so half of their money goes to paying off the mother when she's old, just like would have usually happened. But the baby generation, because it's young first, that means when I was young, my generation was making a huge amount of money. We're doing it now. That's why there's a surplus. There's this gigantic surplus being put in to Social Security, and so when my generation gets old, the dollar that didn't have to go to the mother, because there was an extra dollar there, that could be earning the rate of interest. And so at the end, when we get old, there are going to be 2 of us, and there's only going to be 1 child next generation to contribute 1, and we're going to be expecting 1. But see, the 1 that was put in when we were young has now grown to 2. You've got 2 there, plus another 1, that's 3, so there actually should be a surplus, not a deficit. Did you follow that? Did that go too fast? So I'm saying that every generation, you give 1, you get 1, you give 1, you get 1, you give 1, you get 1. All of a sudden, there are 2 people, so they're each giving 1, so none of them is worse off than before. When they get old, they're going to need 2. You've only got 1 person contributing. So here's the baby boom, double the size of all the other generations. When they're old, it looks like a problem. Who's going to take care of these people? There're not enough young people to take care of them. But remember, they were young before they were old. So since this mother only needs 1 and there are 2 of these daughters, the extra 1 could be invested and the 1 that's invested is going to make a rate of return and become more than 1, like close to 2. And so you'll have the 1 from the new daughter, plus almost 2 that was saved, that was in the Social Security trust fund and earning interest. So you'll actually have 3 dollars to make up for the 2, and so it's not a problem at all that you have this baby boom. In fact, it's a benefit that we had the baby boom. So basically, what did the baby boom do? It staved off the original problem. So let's just think about this one more time. Suppose that you have a slightly more realistic example, the kind you're going to do in the problem set. Suppose that you've got--people live from 20 to 80 and they pay taxes and work from 20 to 60 and they retire from 60 to 80. Everybody's paying 12 dollars in Social Security taxes when working, and there's a 0 rate of interest, and they're getting 24-- maybe I have a rate--they're getting 24 dollars when they're retired, in benefits. Okay, so the system balances every year, because in every generation, these are the birth years, the thing started in 1938, and then they collected taxes for a little while. Frances Perkins got in action and so they decided to go to pay as you go. To--let's just assume it started pay as you go from the very beginning. So in 1940, you see in 1940, the people who are 60, the 1880 generation, would have two decades to live. So these guys--oh, I'm sorry, I never put this. Not that it mattered, but it would have been a little better. So these guys, the 60 year olds here, and these 70 year olds, the 70 year olds and the 60 year olds are collecting money. Now the original start of Social Security was a little fuzzy. They didn't want to pay people who had never contributed, so these 70 year olds weren't really getting anything. Okay, let's just keep for the simple, steady state. So the point is, the 60 year olds are collecting 24 dollars. The 70 year olds are collecting 24 dollars, and each of these generations, the 50,40, 30s and 20s, they're all paying 12 dollars. So the contributions are exactly matching the benefits. So the system is perfectly in balance. Now what happens the next decade? You've got the new 70 year olds. It's this next generation, plus these guys, who have now turned 70, who had been contributing before. Now they're in their 60s, sorry, they're in these 60s. These guys in their 70s, these guys in their 60s, and then here are the contributors. This new generation has now come on board to contribute. So again, there's balance every generation. Okay, but now who are the winners and the losers? Well, you know, it's much worse than it sounded at first glance, because people live longer than 1 year. So you see these people, in the '40s, all these guys were gaining. So this generation of 1870, they have almost an infinite rate of return. They made no contributions. These guys, they also made no contributions and they're getting huge returns, because they're getting them, you know, 20 years of returns. But it's worse than that, because when we go to the next generation, these guys, they actually contributed when they were in their 50s, but that wasn't very long before they retired and they got 24 dollars of benefits and 24 dollars of benefits, having paid only 12 dollars of taxes. Of course, this came later, but 48 compared to 12, they got a gigantic rate of return. You go to the next generation, and they're making out like bandits too, because they only contributed twice. Okay so in the '40s, a bunch of people were making money, getting benefits, who didn't make any contributions. In the '50s, a bunch of people were making--getting benefits who made no contributions. In the '60s, there are still people getting benefits who made no contributions. It's not till you get to the '80s, once people are fully retired, having made 40 years of contributions. So from 40 to 80, it's not until the '80s that the people who are getting benefits were all people who fully contributed. Okay, so all these people were getting an incredibly good deal. We had 40 years of people getting extra returns. If you just do the distributive law of arithmetic, and you realize that all these things go off to infinity because they're discounted, you can sum them in either direction. You can sum down the columns, and that's always 0. The benefits and the contributions always net to 0, but therefore, if you add up the rows, which is what each generation gets, they also have to add up to 0. But you see, there's so many original generations. This one got a huge benefit. This one got huge benefits. The present value of their contributions relative to their benefits is incredibly positive for that generation. For this generation, it's still incredibly positive. Remember, this is 12,12, and this is 24,24. For this generation, it's probably still positive. Not till you get to here has it become--well, not till you get to here does something change. So this is a positive number, this is a big positive number. This is a gigantic positive number. This is a huge positive number. You add up over all these things positive. The rest of these generations have to be negative to just balance the thing at 0. So that's why every generation from here down to here is going to have to earn a negative return, basically in steady state, they'd all earn the same negative present value, or the same bad rate of return. And there were so many generations that got positive amounts of money. So in today's dollars, can you tell me how much money that we gave away to these early generations? Can you take a guess, just order of magnitude? So I'm asking in today's dollars, today's present value dollars. Whatever the number is, you have to assume it grew at the rate of interest since then. So what do you think that is? Student: Couple trillion. Prof: Couple trillion. Does someone want to guess? Reasonable guess, but someone want to make another guess? Just so you get an idea of the size of the program. Does anybody know what GNP is in the country? Student: $15 trillion. Prof: Okay, $14 trillion, something like that is GNP. So what do you guess this number is? Okay, it's $17 trillion. He guessed $2 trillion. It's $17 trillion. So we made a staggering transfer of income to these people at the beginning, and now somebody's got to pay for that and it's not a trivial thing to pay for, because $17 trillion, if everybody gave, every corporation, every person in the whole country gave away all the money they made for a year, we still wouldn't pay it down. So that's a big amount that's hanging over everybody, and that's what the Social Security problem is. We gave away so much money at the beginning, if we keep the system in balance, we have to gradually give all the money back. And we can't stop it, because then some old guys are going to get screwed. So there's no way of stopping the thing and each generation has to lose. So the reason why you're getting such low rates of return is because the system was designed--Frances Perkins knew what she was doing. She wanted to help all those old people in the '40s. Now she was out of power in the '50s and '60s, you know, when we were still helping all those people. But the point is, there was a tremendous transfer of wealth, so there were entire generations of that era, and that's the reason why everybody's getting such a bad rate of return now. It's not because the money's being lost or thrown away. So what I'm telling you now is not controversial. I don't think many people understand it, but everyone who does understand it agrees with it. When come to my solution, they're not going to agree. But anyway, so what I'm telling you, just to compute, in the problem set you have to compute an example. So let's just see how this would work. So suppose from the point of view of a 10 year old, just doing the example I did, suppose there's a 15 percent rate of interest, and you're going to contribute in your 20s, 12 dollars, 12 percent, so no growth in the economy. So it's 12 dollars all the time when you're in your 20s, 30s, 40s and 50s. So what would you do from the point of view age 10? That's 10 years before your 20s. You're going to contribute 12 dollars in your 20s. You discount it at the 15 percent rate of interest. You're going to be contributing 12 dollars in your 30s, so you discount it at 15 percent twice, and in your 40s, you're giving up 12 dollars, you're discounting it to 15 percent 3 times, and in your 50s, you're doing it, 12 dollars, so you're discounting it 4 times. So that's the present value. From the point of view of a young girl, looking at what you're going to be forced to contribute over your life, those are the taxes you can expect to pay in present value terms. Now of course, when you get old, in your 60s and 70s, you're going to get benefits, 24 dollars, much higher than the taxes you paid. But by then, it's 5 decades later, so you're discounting it 5 times, and when you're in your 70s, you're discounting it 6 times. So you have to discount by 6, so the present value of that is way less than the present value of this. So you see that the loss in present value terms is going to be 11 dollars, 11 dollars out of 34, which is what your benefits were. So your loss is something like 34 percent. So this is just--I made up these numbers. The actual loss, which I computed for the real economy, is around 25 percent. So that's how big each generation, 1 quarter of the typical--so here it's 34 percent. 1 quarter to 1 third in this example of each generation's Social Security taxes are simply being lost, frittered away, and basically used to pay off the debt from the original generation. Now if you want to look at the total present value loss, starting in the 1930s, for people born in the 1930s, you have to look at every generation's losing the same 11.95 and so you take the infinite future of generations, and they're losing 79.68, if you add up to infinity, and of course, that's the gain that was given to the original generations. Okay, so that's the kind of example you're going to work out, except for with realistic numbers. Okay, and so I just do--you're going to do that anyway. All right, so that's it. So now, if you look at which generation's got the most money, at the beginning, there weren't many people in Social Security, and so the amount of money that they got, the benefits that the really old got, there were so few of them that if you add it up, it wasn't that big. So the generation that benefited the most was my father's generation and James Tobin's generation. Tobin, as we'll see in a second, he used to tell me all the time-- he was Yale's most famous economist, and I happen to be the James Tobin professor, so I have quite a fondness for him. I also went to the same high school he went to in Illinois. Anyway, he used to tell me that the problem with Social Security was, we didn't have enough--I didn't have enough children, and I would tell him the problem with Social Security was we gave him, his birth date, too much money, and that's why we're all suffering now. So you can see all the generations and which ones, which generation got the most amount of money. So that I also calculated. Now this parable is not exactly accurate. So you know, in the parable, we should have had a crisis in 1970, it should have been, or 1980. I told you the people in 1980 should already have realized-- the generation starting to work in 1980, so born in 1960, a lot younger than you are, they should already have realized that they're getting a bad deal in Social Security, and so we should have had all this come much sooner. So what kept the problem from manifesting itself until now? Well, what kept the problem from manifesting itself until now is actually quite easy to see, is there were a lot more young people per old in the historical generations. Now we're leveling off and everybody thinks we're going to be 2 young people for every old. The story I sort of told, working from 40 to 60 and retired from 60 to 80 in a stable population, that's coming close to what we're converging to. So there are going to be 2 young for every old, where there used to be 3,4 and 5. Now how could there have been so many young for all the old? Well, you know, women at the beginning, in this period, they were working. Women were surging into the labor force. There were a huge number of young women working, but their mothers actually weren't working. They had not worked and so they were getting half their husband's benefits, not the full benefit that these daughters who were working their whole lives are going to get. They're not going to take half their husband's benefits. They're going to take all their own benefits, which are going to be a lot higher. So then there was the baby boom generation. The baby boom generation, far from causing the problem, has deferred the problem. There are all these surpluses, because we were working so long. I don't want to get into all the details. People are living longer now too, so that's another problem. Too much complication here. Okay, so what can you do about this? Well, there are obvious things to do, which are bad. So one thing you could do is, you could say, if we're supposed to be paying the average young [correction: old] person 40 percent of the new generation's wages, and there are only going to be 2 young people for every old person, we could maybe shave the 40 percent down a little bit. Let's make the Social Security tax 18 percent instead of 12 percent. So you could raise it by 6 percent. Nobody wants to actually do that, because an increase of 6 percent in a tax rate is an astronomical increase and you can read in the newspapers how loath Congress is to raising taxes. Another obvious thing you could do is, you could raise retirement age. So instead of saying it's 65, because people will live till 80, make it start at 67, so you'll only have to pay them for 13 years instead of 15 years. In this example, 18 years instead of 20 years. So you could keep raising the retirement age. The problem with that is--not the retirement age, the age you start collecting Social Security. The problem with that of course is that people are retiring not later and later, even younger and younger, believe it or not, and so you're getting this huge gap between when people retire and when they start getting Social Security. So there's a limit to how--obviously you should do a little bit of that, but there's a limit of how much of that you can do. So you need to make not just a parametric reform, you know, like adjusting a number, changing the tax rate a little bit, but I believe you need a fundamental reform, and the Republicans have proposed one. They've said, "Let's privatize. Let's change the whole system." Okay, so what does it mean to privatize? How are they going to do that? So what Bush had in mind was the following: he said, "What is privatization? It involves three things. It's the creation of individual accounts, so your name goes on it. So it's your account, your money and no one can take it from you. It's your money and your money's what's going to pay for your own benefits, so it's prefunded. So it's individual accounts and prefunded, and it's diversification. You're supposed to invest not just in government bonds, but in the stock market, whatever else you want." So those are the three cornerstones, at least the way I've explained them, of privatization. Three things that it accomplishes. It gives you your name on the money. It's your money. That's the money that's going to pay you when you get old, prefunding, and you can invest in a wider range of assets, especially the stock market, which is what everybody seems to want to put their money in, or at least used to, until we had this last crash. On the other hand, the stock market's going up a lot, so people are getting less nervous about it. So those things are different, they're not the same. So how is Bush going to handle this? How would you think he was going to do this? How could you possibly--so Bush said, "I want to privatize. I want the 12 percent that you pay in Social Security taxes, I want 4 percent of that for you to be able to put that in your private account in the stock market with your name on it." So Gore said, "Well, that's ridiculous. If it's only 8 percent then, left to give to the old people, the old people are going to get cheated, so how is Bush going to handle that?" What did you think he was going to do? Student: Borrow the > Prof: Could you say that again? It sounds right, but I couldn't-- Student: Borrow to make up the shortfall. Prof: Exactly. So I don't know what Gore was thinking, especially since I was supposedly advising Gore about Social Security. But he just said in the debate, "That's impossible. You'll just screw all the old people." Okay, so you're supposed to be giving 12 percent, you know, 12 here, -12 here, and then getting some return over here. And now Bush is saying, "I only want to give you 8 dollars, and the other 4 you put in your Social Security account, and then you're going to get maybe a much bigger return here-- sorry, in your stock market account, in Social Security, so you can't take it out." So Bush would say, "Yes, let people put their names on it, force them to save and contribute the whole 12 dollars." Bush agrees that you've got to force young people to save, because they're not going to do it otherwise. So you put the 4 dollars in their private account, but it's their name on it, and then it grows to some huge number, you know, 20 instead of just doubling by the time they get old. And so that huge account is their money. So that's what Bush would say. So Gore would say, "If you take these 4 dollars and give it to them, how are you going to pay the old people who need the 12 right up here? The old people are supposed to get 12. How are you going to give them their 12 when the young aren't handing over the 12 anymore? They're only handing over 8." Well, it's not like Bush and his advisors didn't think about that. That would be a colossal blunder. Of course they thought about that. So what were they going to do? They were going to have the government go out and borrow the other 4, so the government contributes 4 that it borrows. And now of course over here, the government's going to have to owe 8, because it's got to pay back the 4 it owed in 30 years, at we're assuming, 100 percent interest over 30 years, has got to pay back the 8. You're all with me. So where are they going to get the 8? Who are they going to get the 8 from? What? Student: Taxpayers. Prof: Which taxpayer? Student: All of them. Prof: Everybody. Really? Student: The same people who are paying the Social Security. Prof: Okay, these people. So if you chose to take 4 of your dollars out of Social Security and put it into your Social Security stock market trust fund, your personal trust fund, the deal is, you have to pay the interest at the end of 30 years. So this 8 comes out of your 20. So these people pay back the 8. So basically, to say it in a different way, the way you get to invest in the stock market, according to the Bush privatization rules, is these people effectively, they're giving the 12 dollars anyway to the old, but they get to borrow 4 dollars and put it in their private stock market account. And then they have to pay back the amount they borrowed with interest, which is 8. But if the stock market does better than the interest rate, then of course they make out better. They get 20 - 8, which is 12. Okay, so is that clear how he did it? So it's not a logical impossibility. The problem with the Bush plan, of course, is that if the money you put in the stock market earns the same rate of return that you would have gotten anyway, if the stock market earns the same rate of return, 100 percent over all those years as the bond market, then this private stash you have just goes back to paying off the government debt and you haven't gained anything in the stock market. You get the same Social Security benefits you would have had anyway. So these guys who opt into the privatization program, let me repeat the Bush plan. If you opt into the privatization program, you effectively do everything you did before in Social Security. You pay your taxes that go to the old people. You get the benefits just like you did before, but on top of it, you have the right to borrow 4 dollars from the government, invest it in stocks, and then at the end, you have to pay back the government out of your stock market return. So you're betting on whether the stock market is going to do better than the bond market. That's effectively what the plan was. Okay, so it's not a logical impossibility like Gore said. On the other hand, if you don't think the stock market's going to do better than the bond market, you could end up being worse off. You could put in 4 dollars here, get only 6, and then you'd have to owe the government 8. Where's the government going to get the other 2 dollars from? It's going to reduce your Social Security contributions [correction: benefits] by 2. So that's the government plan. So in the problem set, I gave you three problems. You can only do two of them now. The last one I didn't get far enough to have you do. So just do two of them, and I'm going to give my own plan next time and also do a little mathematics. It's going to turn out that it's quite interesting to math this up a little bit.
Quantitative_Finance_by_Yale_University	23_The_Mutual_Fund_Theorem_and_Covariance_Pricing_Theorems.txt	Prof: Okay, I think I should begin. So we're at the point in the course now where we're talking about the Capital Asset Pricing Model and the economists' understanding of risk aversion and its consequence for the financial sector. So much of what economists know was already known to businessmen, because it's common sense, and even to literary writers like Shakespeare, who was himself quite a successful businessman. So you might remember that Shakespeare already had the idea of diversification. In the Merchant of Venice, Antonio says "Each boat on a different ocean." He said it a bit more poetically than that, "each sail on a different argosy" or something. I've forgotten what it was, but each boat on a different ocean. So he wasn't very worried because he was diversified. He also had the idea of risk and return. Nothing ventured, nothing gained. Nothing ventured, so ventured means risk. Nothing gained. So another way of saying this diversification is "Don't put all your eggs in one basket." So what have economists done that wasn't already known to every business person and every clever literary writer? Well, economists have quantified this and turned this into a usable, practical piece of advice. So the diversification theorem in CAPM-- so I should have moved CAPM. I should have called this Shakespeare and this CAPM. CAPM becomes the mutual fund theorem. So the mutual fund theorem has very practical advice. It says if you're investing in the stock market, don't try to pick out individual stocks. Hold every stock in proportion to its value in the whole economy. If you want to be more venturesome, don't pick riskier stocks. Just simply leave less money in the bank. So divide all your money between the index and the bank. It says, hold all your money in stocks in the same proportion everyone else is holding them. Hold the market, in other words. Hold an index like the S&P 500, of all the stocks, in proportion to how big they are. And if you want to get more venturesome--if you're cautious, put some of your money in the index and some of it in the bank. If you want to be more venturesome, take some money out of the bank and put it into the stocks. But in the index. If you want to be even more venturesome than that, borrow the money to put the money into the stock market. That's called leverage. But you should, according to this theory, not try to pick stocks. So if you're interested in risk, you shouldn't pick high technology startup companies. You should pick the same mixture of blue chip companies like General Electric and these startup companies that everybody else is choosing. So that's what it means to diversify. Hold a little bit of everything in the same proportion as everyone else. So it's much more precise, much more surprising than Shakespeare's advice. Then the second thing, risk and reward, it says that the price of a security, so we'll call it pi_J say, which we used to think of as the expectation-- of course, you need the probabilities-- of the payoff of the security J, discounted. That's what we would have thought the price was. So this is called the covariance pricing theorem. The shocking thing is, it's not the expectation discounted, which is what we thought it was before. We know that you have to adjust for risk somehow, which we haven't taken into account before. But what's so shocking is, you might have thought you'd subtract maybe something times the variance of the return of asset J, but that's not going to be the case. It's going to be, surprisingly, subtracting something times the covariance, with the market, of asset J. So you penalize--the price of a stock should go lower if it gets riskier. Its risk is not defined by what its variance is, but by what its covariance is with the market. So I want to develop these two ideas in this lecture, spend the whole lecture on just developing these two ideas, which are the modern mathematical version of what Shakespeare already knew 400 years ago, but made much more concrete, much more precise, with the mathematics wholly behind them. So what have we got here? We imagine a world, the situation I'm going to describe, is the one we had last time, where we know that there are different things that can happen. These are the states with different probabilities, so there's states. s = 1 to big S and each of them have probabilities, with probabilities gamma_s. Of course, the sum of the gamma_s = 1. So everybody knows the probabilities of the states and then they know what the payoff is of the different assets. So here's A^(1), here's A^(2), here's A^(J) say, and they know what the payoffs are going to be, A^(1) in state 1, A^(1) in state 2, A^(1) in state S, A^(2) in state 1, A^(2) in state S, A^(J) in state 1, A^(J) in state 2, A^(J) in state S. So given these probabilities and given the payoffs, you can compute the expectation of each thing. You can compute the expectation of A^(J), say. It's just the summation from s = 1 to S of gamma_s A^(J)_s. You can also compute the variance, so I'll write that sometimes as A bar^(J). You can compute the variance of A^(J), which is the summation, s = 1 to S, remember, of gamma_s A^(J)_s - A bar^(j) squared. Okay, and you could also compute the covariance of any 2, A^(J) and A^(K) as summation gamma_s A^(J)_s - A bar^(J) times (this is s = 1 to S) of A^(K)_s - A bar^(K) K. So those three numbers, the expectation, the variance and the covariance between any pairs, those are numbers that anybody could compute, knowing the payoffs of the assets and knowing the probabilities. And what the theory is going to say, the capital asset pricing model, that model is going to explain how the prices of all the assets depend on their expectation, their variances and their covariances, under the assumption that people have quadratic utilities, or more generally, assume people only care about the mean-- that's the expectation--and variance of final consumption. So we wrote that last time. We said if you had quadratic utility for consumption in every state, you could summarize these thousands-- there could be millions of states and thousands of securities. You add them all together, what you hold, it only depends on the end about what the expectation and the variance of your final portfolio is. You like expectation and you hate variance. So under that hypothesis, we're going to have a very concrete interpretation of what Shakespeare was talking about from the beginning, which is going to allow us to quantify what you should do, how people in the market are doing. We'll be able to answer a series of questions. And then we'll be able to test the theory too. So now the theory I'm about to explain was developed in 1950. It began in 1950 when Koopmans was a professor at the Cowles Foundation, the director of the Cowles Foundation, was in Chicago. I told you, the Cowles Foundation was started by Alfred Cowles, who'd been a Yale undergraduate, and his family owned the Chicago Tribune and a bunch of other newspapers. And he ran a macroeconomic forecasting company in 1929, right after the crash. He was embarrassed to realize that he had predicted that everything was going to be fine, and he sent around questionnaires and read everybody else's, his competitors' newspapers, and realized they'd been predicting everything was going to be fine too, except for one guy, Jones, the Dow Jones guy. Except for that, everybody had been making the same rosy predictions. So he decided the whole subject of economic forecasting, in fact, economics altogether was a fraud, and he wanted to put money in encouraging the use of mathematics in economics, instead of the touchy-feely more qualitative analysis that was the norm at the time. So he went to see Irving Fisher, who was the great Yale economist, and said, "What should I do with all the money? Where should I put this institute, and who should I invite to the institute?" So Fisher and he set up the whole thing and it started in Colorado Springs, because Fisher believed in fresh air, and he wrote a lot of books about fresh air and how it staved off tuberculosis and things like that. And no one wanted to go to Colorado Springs, so they moved it to Chicago where the family was originally from, the Cowles family. The director then in the '50s was someone named Koopmans, and Koopmans had this idea of trying to examine risk by making people with quadratic utilities. And he said, "Okay, student Markowitz, why don't you try to develop a theory?" And Markowitz began the theory of the capital asset pricing model. Now the theory, just to get a little ahead of the story, Markowitz went quite a ways, won a Nobel prize many years later for what he did, but didn't quite get to the end. And while he was working on it, Koopmans didn't want to be director any more of Cowles, and he invited Tobin, the great Yale economist, to come and be director of Cowles. And Tobin got there and the people at the University of Chicago said to Tobin, "Well, we're glad you're coming. You'll be right next to us, but don't try and get us mixed up with all those mathematical people at the Cowles Foundation. They're all crazy. We would like to keep that high tech mathematics out of our department. That's just Cowles' crazy idea." So Tobin refused the job, came back to Yale, and Markowitz was so angry--not Markowitz. Koopmans, his advisor, was so angry that he went to Cowles and said, "They're not treating us right at the University of Chicago. Let's move the entire Cowles Foundation to Yale." So in 1955, they moved it to Yale. But in these conversations Tobin had with Koopmans and the Cowles Foundation, he got to know what Markowitz was doing, and so he added the final crowning achievement to-- the mutual fund theorem--to the Markowitz setup, and he subsequently won the Nobel Prize for that. In fact, the New York Times said in its description of what he won the Nobel Prize for, the New York Times said, "James Tobin won the Nobel prize for showing that you shouldn't put all your eggs in one basket." So anyway, that's the theory that I have to explain now, that it's a little bit less trivial than just saying, "Don't put all your eggs in one basket. So, the idea is that you like expectation, you hate variance. So the first thing we're going to do is notice that covariance--I'm sorry, standard deviation is defined as the square root of variance. So to say that you don't like variance means you don't like standard deviation. They're the same thing, but you're going to see, it makes the diagrams much prettier. So if we had a portfolio that you could choose among some combination of putting your money in the A's, you'd get some expectation of some standard deviation for your total portfolio. And people like more expectation and like less standard deviation. So the indifference curves are going in that direction, unlike the usual picture. That was the first step. Now the first thing we noticed last time, this was three weeks ago or so, we made an extremely important observation. We said, what is the covariance of part of your money in X, the variance of part of your money in X and the rest of your money-- let's say you have 1 dollar--so t in X and (1 - t) in Y? For example, 1 half in X and 1 half in Y. Well that is by definition the same as the covariance of this portfolio with itself, and now we know this from this theorem, from this definition of covariance, that if you look at the covariance of J with K, so fixing K--this is just linear. This is a constant, multiplying the differences from J and its expectation. So this is a linear in each variable, so therefore this is going to equal the covariance of tX with tX twice the covariance of t-- so the covariance of tX and (1 - t)Y, the covariance of (1 - t)Y and tX (1 - t) squared (so I'll put that one over here) the covariance of (1 - tY) with itself. So I've taken this with this, then this with that, then that with that and that with the thing on the end. But it's linear again, so I can pull out all these things. So that's the formula. Now what we noticed is that if 2 stocks, X and Y, are independent, their covariance is 0. So I'm assuming you remember that, so those terms just go away. And then it's also linear, so this is just going to equal t squared, covariance of X with X, which is just the variance of X. So assume XY independent, then that is what allows me to cancel these two terms like that. So I get t squared times the covariance of X (1 - t) squared times the variance of Y. If I take t = 1 half, I know that the variance of 1 half X 1 half Y = 1 quarter times the variance of X 1 quarter times the variance of Y. We derived this three weeks ago. I'm just repeating it. So the amazing thing is, if X and Y have the same expectation and the same variance, but are independent of each other, by splitting your money between two independent things, you're obviously going to have the same expectation, but only half the variance. And that last step is, the variance of X = variance of Y. So amazingly--or it's not so amazing, I guess, if you've thought about it--but if you haven't thought about it, you've got 2 equal risks. Neither one is better than the other, so why bother with one rather than the other? They're both the same. But if they're independent, you should put half your money in each of them. You get the same expectation, but you're going to get only half the variance. So if you have 2 dice, let's say the first die will give you--you pay 100 dollars for a dice, you can get 100 the number of dots showing. So if it gets a 1 that's 101 dollars, you get a 6, it's 106 dollars. So if you held 1 dice, 1 die, you'd get on average 103 and 1 half dollars. You could pay 100, get 1 die, which on average paid 103 and 1 half. Instead, you could put 50 dollars in the first die, get half of that, 50 dollars in the second die, get half of that. So on average, you're still getting 103 and 1 half, but the variance you get is going to be half of what it was before. So in this picture, you start off with X and Y with the same standard deviation and the same expectation, but they're independent and now you put half your money in each and you cut the variance in half, which means you divide--the standard deviation is the square root-- so you divide it by the square root of 2. So you've improved. You've moved to the left. You've gotten less standard deviation without constricting your expectation at all. So that's the most important thing to notice. I'm going to say one more thing, one more way. I'm going to go back to this formula, which is where the variance was, here. Now suppose--let's look at that formula. Suppose I take 2 stocks, which I'm going to switch now, X and Y. That was most unfortunate. But suppose I take 2 stocks and I'm at the point where all my money is in Y. So I'm going to take the case t = 0. So if I took t = 0, I would just have the variance of Y. That's actually quite good, the variance of Y. So I'd have all my money in Y. I'd have this standard deviation and this expectation. Now what happens if the two are independent, X and Y? Let's drop the fact that they have the same variance now. Maybe X has way more variance than Y does. So look, X is much riskier than Y. Maybe X has a higher expectation than Y, but it's so risky. People who are risk averse wouldn't ever want to subject themselves to all this risk, say. So maybe they should just stick with Y, you would think. But no, the answer is, you shouldn't, because what happens if you start to mix some of your money in Y-- take a little out of Y and put a little bit into X? Your expectation, if you take a little money out of Y and put a little into X, your expectation's going to go up, because it's going to be the average of X and Y. So the expectation's going up. But then you say, "Oh, but my variance is going up." So I wouldn't want to do it, but no, that's wrong. The variance isn't going up, because they're independent. Even though X has a way higher variance than Y, mixing a little between the two lowers your variance. So how could that be? Seems quite shocking. Well, let's take the derivative of this with respect to having all your money originally in Y. So this is the variance of putting t dollars in X and 1 - t in Y. So we simply take the derivative of that, which I've done here, I suppose. Why don't I just write it out? Take the derivative of that, d/dt of this = 2t times the variance of X 2 times (1 - t) times (okay, but this is a -, so I take the derivative) it's 2 times this times - 1, so - 2T, 2 times (1 - t), variance of Y. Let's evaluate that at t = 0. The first term is 0, the t is 0, so this doesn't matter. The second term, t is 0, so this is - 2 times the variance of Y. It's going down. The variance is actually going down here. So just as this says, the variance starts down. Eventually, it has to end up here, so as you move your money, all of it originally in Y and start moving some of it into X, your variance is going to go down. So those two things put together are the argument for diversification. If they're independent and identical, then you should put half your money in each. But even if they're not identical, you shouldn't stick to Y. You should mix Y with some X. So there's why diversification is such a good idea. So it's not all diversification. It's diversification of independent risks. There's a bit of a mathematical nuance. Diversification of independent risks is bound to help you. Everybody should diversify a little bit, because you can reduce your risk. That's the first important thought. Now I don't want to do too much in the mathematics. So I prove in the notes, but I won't do it here, suppose we didn't assume X and Y were independent. Suppose X and Y were arbitrarily chosen. They have big covariance, whatever you want. Then what is going to happen when you combine your money between X and Y. So there's a proof, which I'm not going to give, because I'm a little bit behind, so the proof is this. Suppose we have exactly the same situation, where you started with Y and you've got X, and you could think of moving you money in between X and Y. Well, it turns out, if they're perfectly correlated, so really they're the same thing, Y is just 80 percent of X, it's the same stock, so moving back between them is not really changing-- X is just a scalar improvement on Y, so it has more expectation and more standard deviation. If that were the case, you'd just move on that straight line that connects the two points. I must have a way of doing this. Yes, if they were perfectly correlated, you would just be moving along this line by putting your money in between. If they're independent, you're going to move along that line. But no matter how correlated they are, as long as they're not perfectly correlated, it's going to turn out the curve you get by moving between them is going to look like that. If they're negatively correlated, then you can really improve yourself and get a curve that looks like that. Independent will be like this, positively correlated, but not perfectly will be like that, and perfectly positively correlated, no diversification gains, you get the straight line, but you're always above the straight line. So that's a kind of--anyway, it takes a little bit of algebra to prove that, you know, the Cauchy-Schwarz inequality, but I'm going to skip that. But anyway, that's a mathematical fact. You see in the independent case, we proved that the line has to start going that way and eventually it has to end up here, so it should be no surprise that it looks like that in the independent case. And then it turns out that every other case is sort of in between that or at the other extreme. It always has this bowed out shape. So there's always gains to diversification, something you're getting out of diversification. The risk is somehow going down by mixing things up. That's it, that's the mathematics and that's the general principle. Now, what can you get out of this? I want to derive these two famous theorems, which we already saw in action in the example that we calculated, but it seemed like a miracle. So what did we find in the example we calculated last time in class? We found that--we only had two stocks, but if there had been hundreds of stocks and millions of states of nature, and each person had a different utility, different risk aversion, but all quadratic, and you calculated the competitive equilibrium, assuming there were Arrow securities, it would end up that every consumer held the same mix of all these stocks, positive or negative amounts of the bond. So the mutual fund theorem turned out to be true, that the best thing everybody could do was hold the same amount, the same proportion of stocks and bonds, and maybe more or less of the riskless asset, maybe even negative of the riskless asset. So I want to show you why that's true now. Then we're going to have to talk about whether we really believe it or not. So let's see what an implication is. Suppose now what I do is I write down--I have all these stocks, X, Y and Z. So you can imagine--you have a certain amount of money--so you can imagine putting your money--so let's suppose that I've written down all the stocks. The prices are given. Let's say prices of stocks are in equilibrium. So I've solved for the equilibrium like we did last time, and I write down X, Q, Y and Z. These are the expectation and standard deviation per dollar of the stocks, or per I dollars of the stock. Maybe the person has exactly I dollars, so let's say it's I dollars of each stock, what their expectation, return and standard deviation would be. If 1 dollar, you get some expectation, standard deviation, 10 dollars of the same stock, you'd be able to buy 10 shares, which means you would-- 10 times as many shares, which means you'd have 10 times the expectation and 10 times the standard deviation. So whatever the guy's income is, they'll fix the returns as per his income, because he's going to spend all his income on these stocks. So what could he do? He could put all his money into X, he'd end up here, or all his money into Y, he'd end up here, or all his money into Z, and he'd end up here. But maybe he wants to divide part of his money in Y, part in Z and part in Y. He'll be somewhere like here. Or maybe he wants to instead put part of his money in Z and part of it in X. Well, he could end up here. But why should he stop there? Maybe he wants to take some combination of the money that was in Z and X and combine it with some combination of things that was in Z and Y, combine this and this. That would get him out to here. So there are lots of different combinations he could hold. So graphically, it looks like that. Mathematically, what's he trying to do? He's trying to--so R now. I've replaced A with R. So R^(j) is just going to = A^(j) divided by the price of j, maybe times I. So R^(j) will be the--let's just say it's A^(j) divided by pi_j. So R^(j) is the return per dollar you put in the asset. R^(j) is the payoff of the asset per dollar. Let's stick with that. Let's say the guy has a dollar to spend, so it's the return per dollar. So those are all his possibilities. Now what does he want to do? He wants to choose his money, how much money he's going to put in each asset, which is omega_1 through omega_J. That's the money he's going to put in each asset. And if he does that, he's going to have a portfolio, which I'll write as R_omega, so it's going to have a certain expectation, a certain variance. So the question is, how should he divide his money between the assets, and here's the kind of stuff he could imagine doing. Looks very complicated, but it's going to turn out to be very simple. So are there any questions about what we're doing so far? I want to get a simple rule to tell you, practical advice about what to do. Markowitz posed this problem. This is the Markowitz problem, okay? It turns out, by this argument, you see if I keep combining things over and over again, I'm getting this sort of blob. But the blob is always pushing itself further and further out. It's always convex, because given any two points, I can always do the thing to the left of it. So if I could do this and I could do this, and I look at the line connecting them, I can always be above that line by spreading my money between those two assets. Or given this combination of assets that produces this expectation and standard deviation, and given that one up there, I could combine the two and do better than the straight line connecting them, do to the left of it. So therefore, all of the combinations put together have to, geometrically, look like this in the end. So I'm going to do this algebraically in a second. They have to look like that if I did every possible variation. It couldn't end up with a picture where after I do every possible variation-- if this is the expectation, this is the standard deviation, I couldn't get something that looked like that, because I would just combine this thing with this thing. Whatever portfolio produced this, whatever portfolio produced that, I'd put half my money into each of the stocks that this told me to do, half the money into each of the stocks this told me to do. I'd still end up investing 1 dollar and instead of getting the line, I'd get something that looked like that. So I couldn't have the thing going in like that. It has to go out. But then of course, I can combine this and this and get that, and so I'm going to end up with this kind of shape. Now I'm going to prove that algebraically. But if I had that kind of shape, then what would the guy do? He'd choose something like that, where he's tangent. That's what Markowitz basically did, except he did it algebraically. So that's what Markowitz did. That doesn't seem to have gotten us very far. You notice that different people are going to make different choices. If somebody is incredibly worried--someone's not very worried about the standard deviation and cares a lot about expectation, they're going to have a flatter indifference curve. So instead of looking like that, it will be a flatter thing. And so if it's flatter, the guy who cares-- sorry, if it's flatter, it means he cares about expectation and not standard deviation, because a little bit of expectation can compensate him for a lot more standard deviation, so his indifference curve is flatter. He's going to choose further up. So he's going to choose a point like way up there. So he's going to get a higher expectation and higher standard deviation. Someone who's more risk averse is going to choose where that point is. So that's qualitatively what's going on. So Markowitz played around with this, played around with this. Then Tobin appears on the scene. Tobin says, "All this gets so much easier if you have a riskless asset." Let's suppose that there's a bond. You haven't mentioned the bond yet. Let's suppose we have a bond that pays something for sure, and we're going to ignore inflation, Tobin said, which is a big problem. We should come back to that if we have time. We're going to ignore inflation, so US Treasury's going to pay a certain amount of money for sure. So it has an expectation like this, but no standard deviation. It's 0. Now why is this so important? Let's imagine combining this riskless bond with some other stock X, 1 dollar's worth of X. 1 dollar's worth of the riskless bond gets you 1.06 say. 1 dollar's worth of X gets you much--you know, maybe your average is 1.12, but you're also running a big risk. What happens if you put your money part way in between them? So suppose you put part of your money in X, and the rest of your money in the riskless bond. What's your expectation going to be? Your expectation, let's say X is 12 percent and Y is 6 percent, 1.06 and 1.12, the average is going to be 1.09 if you put half your money in both. But what is the standard deviation going to be? I claim it's just going to be on this straight line. Why is that? Because the riskless thing has covariance 0. If X is riskless, its covariance is going to be 0 with Y. So these terms are going to disappear. Look at the covariance. If X--ifY is the riskless bond, it pays always its expectation. So these numbers are always 0. Therefore the covariance of that thing with anything, the covariance of Y with any X is going to be 0. And not only that, but the variance of Y itself is also 0. So all you get is, for the variance of the t dollars in X and 1 - t dollars in Y, you just get t squared times the variance of X. But then when you take the standard deviation, it's just t times the standard deviation of X. So in other words, the standard deviation of the mixture of Y and X lies right on the line. So unlike--to put it another way, something that has no variance is perfectly correlated with everything else, it makes no difference. When the other thing goes up or down, it doesn't tell you--you still know what Y's going to be. So unlike everything else, where you have this bow shaped thing, the riskless asset just connects everything to a straight line. So if there were a riskless asset and you could do this with some X and here was a Z, you could also do that, or you could do that. Is this clear? Okay, so the punch line, which we're now going to see algebraically, the punch line is--and by the way, if I combine, what does it mean to extend that line? I should have extended that line. That was a huge mistake. Suppose instead of--so here's all the money in the riskless asset. Here's half the money in the riskless asset and half in X. Here's all my money in X. What would happen if I extended the line here? What would that correspond to? I'm now at a point on the extension of the line. How do I get that? Student: You borrow money and invest it in X. Prof: Right. That's negative Y and bigger than 1 in X. So negative 1 half of X 1 and 1 half of Y, that's still 1 dollar. I sold X short and so I'm just going to continue the line that way. So I shouldn't have stopped here. I could have kept going. So it's putting money in the bank and sharing it between a single stock puts me on this line. Borrowing money from the bank to put in a stock is called leveraging my return, puts me on the extension of the line. We're going to come back to that in a second. So knowing that, now what should I do? Is there something really simple? Well, what would you do here, faced with this choice? Which combination of stocks and bonds would you hold? I say it's really simple. You just look for a line through the riskless point that's tangent to this blurb, which happens to be here, and now you should choose your point anywhere along this line, independent of what your mean-variance utilities are. No matter how risk averse you are or how risk loving you are, you should choose somewhere along this line. Why is that? Well, I've drawn, with this blob, I've drawn all the possible combinations I could get by mixing different risky assets. What I left out of the picture is all the combinations I could get by adding the riskless asset. I've got all the risky asset combinations. That's the blob. Now I want to do--adding the riskless asset means I can take part of my money in here and part in there. So in particular, I can put part of my money here and part of my money there, or I can go short. So whatever this combination was, that's the best thing I can do, because now I can get everything along this line. Nothing else can do better. What other combination could there be? It has to be the riskless asset a bunch of risky assets. But combining the risky assets just puts me in the blob. So it might put me here in the blob. And then once I combine that with the riskless asset, I'll be on that line. This line is always below that line, so this is the best possible thing I can do. No combination of the riskless asset and any other combination of risky assets, that'll always put me on some line from here, through some point in the blob, which is going to be below this tangent point. So this is the best thing I can do. And it's independent of whether I was risk averse or a risk lover. If I'm risk averse and want to play it safe, my utility function--I forgot what those looked like. My indifference curves--I'll be here. I'll put most of my money in the bank and not very many in the risky stock. If I'm more of a risk lover, I'll be maybe here, and I'll choose to put a good fraction of my money in the stock and only a little in the bank. If I'm really reckless, I'll borrow money and put it in the stock market and be way up there. But everybody will do the same thing, no matter what their preferences are. They'll all be along the same line. So that's the mutual fund theorem. Why is that the mutual fund theorem? Because it says everybody should invest in the same index of stocks and put more or less money in the bank. So every single person ought to be doing the same thing. This is the mutual fund that everybody should hold. Whatever combination of stocks that got me to this point is the mutual fund that everybody should hold, and combine that with putting money in the bank. Okay, so let's just prove that algebraically, in a special case, which is going to illustrate the point, the idea of it anyway. I'm doing a very special case here, but just to illustrate it algebraically. So suppose that the Rs are, as we said, the returns, up here, per dollar of stock. The R_0 I've now added and that's going to be the riskless asset that pays like 1 dollar 6 all the time, if the interest rate is 6 percent. So now you have your money, you have I dollars. You're the investor with I dollars. You can divide that money into the riskless asset or any one of the J assets. So here you've got R^(0). You can get that return, R^(1) up to R^(J) and you can put money, omega_0, omega_1, omega_J, but of course, this all has to add up to I. So how should you do it? Well, you care about your expectation and you hate variance, so I'm doing just a special case to make it illustrate the idea. Suppose I write down your utility as if it were the expectation, - alpha times the variance. It could be a more complicated function. We said already that the quadratic utilities give you expectation - alpha expectation squared, - some other alpha times the variance. That's the utility we derive from quadratic-- when people have quadratic utilities over consumption, their induced utility of portfolios is this thing. So it's not exactly the one I've written down, but the argument would be just the same and this is shorter and simpler. So just to illustrate the flavor of it, let's say all you care about is your expectation - some constant, how risk averse you are, times the variance. Now let's suppose, to keep it even simpler, that the assets are all independent. The theory doesn't rely on that. I'm just saying, suppose it were so we can algebraically get it without having to work very hard. So you're maximizing your expectations, so the bar above means the expectation. So what's your expectation of omega dollars in here, omega_1 in here and omega_J in here? Just omega_0 times the expectation of this. So your expectation then is going to be omega_0 times R^(0) bar (that's the expectation of that) omega_1, R bar^(1) omega_J, R bar^(J). These are the top for some reason. That's your expectation. Now what's your variance, the thing that you don't like? Your variance is going to be--is going to be the variance of these. They're independent. So the variance is just going to be what I've written. So call the variance of R^(J) sigma, so it's going to be sigma_0 squared (that's the variance of sigma_0) times omega_0 squared, (remember, because for variance you have to square if you multiply by something) omega_1 squared sigma_1 squared, omega_J squared sigma_J squared. Now of course, remember that the variance of the riskless thing is 0, so that's actually 0. This is the variance you have to watch out for. This is the expectation you want. How should you pick omega_0, omega_1, omega_J, when your penalty for having too much variance is alpha? So different investors have different risk aversions so they have different alphas. Should they be led, as Markowitz thought, without the riskless asset, remember, with the blob like this, one guy was going to pick here, another guy was going to pick there. They'd all do very different things. Tobin added this riskless asset, and lo and behold, now everyone should do the same thing. So why is that? We just reduce this algebraically, solve it algebraically. So the constraint is a nuisance. To maximize something with the constraint's a nuisance, so if you just notice that if you satisfy the constraint, omega_0 has to equal I - the sum of the omega_js. So if I substitute for omega_0 right up there, I substitute I - the sum of the js. Then I'm going to get R bar^(0) times I - R bar^(0) times omega_1, - R bar^(0) times omega_2. But I can feed that into the other thing, so I get R^(0) times the I, and then the R^(1) term is going to be R bar^(1) times omega_1 - the thing that came from subtracting the omega_1 there in I-- by replacing omega_0 with (I - omega_1 - omega_J), etc. So I'm going to notice--all these other terms now, I get rid of the constraint and all the other terms get replaced. R bar^(2) gets replaced by R bar^(2) - R bar^(0). I've dropped sigma_0 because it's 0. So I'm maximizing something without a constraint by plugging in the constraint to omega_0. So I have to choose my omega_1 through omega_J and then omega_0 is determined from that. But I'm maximizing one thing, so just take the derivative with respect to each omega_i and set it = to 0. So with respect to omega_1, say, it's going to be R bar^(1) - R bar^(0) - 2 alpha sigma-- I'm differentiating with respect to omega_1 so it's 2 alpha omega_1 times sigma_1 squared. 2 alpha omega_1 times sigma_1 squared = 0. So therefore omega_1 = R^(1) - R^(0) over 2 alpha sigma_1 squared. But if I did it now with respect to 2 or to 3 or to 4, nothing--I would get the same formula, just with a j instead of a 1. So that's the formula everybody picks and notice it depends on what alpha is. So people with different alphas are going to put different amounts of money in omega_j. But it depends on alpha in a very trivial way. So if I took the fraction, the relative amounts of money I put in i and j and divided this by omega_i, by omega_j, I would get that the alphas and the 2s canceled out. So everybody would put R^(i) - R bar^(0) divided by sigma_i squared, R bar^(j) - R^(0) over sigma_j squared. That number doesn't depend on who the person is, so the relative amounts of money put in i and j are independent of what your alpha is, independent of the person. So unlike this old Markowitz case, the Tobin case looks like that, and everybody chooses the same combination of risky assets and then this safe asset. So it may be that different people put different combinations of safe and risky, but everybody's proportion of risky assets is proportional to everybody else's. That's what we just proved algebraically. So graphically, a sort of general proof, algebraically, a special case. And then if you were in a graduate class, you'd get an algebraic proof in general, which is actually much faster than either of these, but you have to know a little linear algebra. And so that's the proof. It's a very simple thing. It's a remarkable thing, and here's the famous Tobin diagram. Everybody should do that, put their money in the same combination of risky assets and the riskless asset. Are there any questions about this? It's kind of shocking. I could swear that most people think, maybe even rightly, if you really want to go for it, put your money in the young Microsoft or something. It could be a tremendous success or it could go out of business. That's what you should do, but no, this says not at all. If you really want to go for it, take the same index that everybody, the S&P 500 and just leverage it. Borrow a lot of money and go out that straight line, way out to there, to the right. Don't put your money in Microsoft. Just leverage the hell out of the S&P 500. Okay, so after this theory was created--I'm going to tease out all the implications of it. After this theory was created, the mutual fund business took off. Vanguard and all of these places, what did they do? They said, "Look, economic science has taught us, the best you can do is not try to pick individual stocks. The best you can do is to hold the same index, the whole market. "Now of course, it's very expensive for you to hold the whole market. Are you going to go to a broker and tell him 'Buy me 3 shares of this and 7 shares of that and 9 shares of that, 14 shares of that'? It'll take the guy forever to buy all that stuff and you have to pay a commission on every single thing you buy. It's going to cost you so much money to do what economic science says. Come to us at Vanguard. We'll buy the whole market for you, call it our index fund and charge you almost no commission at all, just a tiny little bit, because we're doing it in such bulk, everyone's--we've got lots of investors like you. They're all buying the same thing. We have huge volume, so we're going to get a really small brokerage fee, so you should put your money in with us." So that's what everybody started to do. So all these mutual funds and money managers, they all grew up, originally by guaranteeing to produce an index fund, the very same thing economic science recommended, at almost no cost. If you read Swensen's book, his first, most important piece of advice: if you are a standard investor who doesn't know how to manipulate all the complicated instruments on Wall Street and has transactions costs and things like that, put all your money into an index. That's what he recommends doing. And he says everyone else who tells you otherwise is just trying to steal your money, rip you off. So that's the main financial advice that economists give now. It's Shakespeare's advice. Don't put all your eggs in one basket, but it's very specific. Put it in an index where you buy everything in the same proportion. Now of course, if you're buying everything in the same proportion and everybody's doing that, what does this have to be? I forgot to say that. If everybody's buying every stock in the same proportion, that proportion must be the market, because that's what everybody's holding. So this doesn't turn out to be any old portfolio. It's the market portfolio. So the index, that's a huge conclusion here, the index that they should offer is not just some magical index that's better than everything else, because if everyone's doing the right thing, everyone's choosing the same index-- that's what we proved--if everyone's choosing the same index, it must be the market index, because that's all there is to choose. Supply has to equal demand. So therefore the advice is to put all your money into the market index, not just an index, the market index maybe put money in a bank. Or even borrow from a bank to put it into the market index. That's the first surprising theorem that Tobin proved and it had dramatic--so it created the indexed investments. It created Vanguard. So these people who run these companies, I forgot the guy's name who runs Vanguard. He's always giving these speeches. So that's how he describes how he got his start in his business. All he says is, "I take all the recommendations of economic science," he says, "and I allow people to carry them out. That's why I'm doing great good for society. Everybody else, all these hedge funds and stuff, they're ruining society. I am just doing what Tobin told us to do." That's his basic speech. So Markowitz was a little bit more precise even than that. Markowitz' formula and Tobin's special case, he not only told you what to do. He told you, "do what everyone else is doing." He told you what that should be. So let's suppose that I've got 2 stocks, i and j, with the same return, same expected return, but one has standard deviation 3 times higher than the other. So in my picture here, that standard picture, we've got the standard deviation, we've got the expectation. We've got 1 stock here and we've got another stock here with 3 times the standard deviation. So you might have thought, "Well, these 2 stocks, same expected return, what's the difference? Put all my money in one or the other, doesn't matter." A little bit further thought would say, "Well, this one is much better than that one. I've got smaller standard deviation, so I should put all my money into this one." But then on further thought, given that these two are independent, what should you do? How should you allocate your money between this stock and that stock? What does the formula tell you to do? It's very clear. Well, the ratio of money in one stock to the other stock looks like this ratio. But I've told you that the expectations of the 2 stocks are the same. So those things are the same. I've told you that one has 3 times the standard deviation than the other, so therefore, what should you do? Yeah. Student: Hold 9 times as much as the one with the lower-- Prof: Exactly. You should put 90 percent in this stock, 10 percent in that stock. That's it, because if one sigma's 3 times the other, and you square it, it's going to be 9 times the other, and so obviously you have to figure out what's in the numerator and what's in the denominator. But clearly, you're going to put more of your money in the lower standard deviation, so it's 90/10. So it's very concrete advice. So the first concrete advice is, the first concrete thing we've gotten out of this is, buy the index. Now the index typically in America, they're easy to buy, are indexes of stocks. But you know, the second piece of advice is, and this is also Swensen's second most important point-- I'm quoting Swensen because we're here at Yale, not because he's the only one to recognize these things, but he was a student of Tobin--so the second important point is that you should not just buy the index, because the indexes are the wrong index. The index should be the index of everything. It should include American stocks, Chinese stocks, French stocks, Greek stocks, Israeli stocks. You should have all stocks in the index, but you can't really very easily buy all those other things. You can only very easily buy index of American things. It's getting easier and easier now to buy the global index. But anyway, you should buy the global index. That's what this says. So every time you find a new independent risk you should look for it. So you should buy the global index, seek out independent risks. So what did Swensen do? One of his most important things was, Yale is always looking globally to find independent risks. So let's go back to the--so you should always find independent risks, and you suffer if you don't. So you see, by putting 90 percent here and 10 percent here, Markowitz is telling you, you're going to do better. What else do I have to say? So let's go back to our dice example. Suppose that you had 1 dice. Now by the way, I want to introduce one more term, which I'll call the Sharpe ratio. So the slope of this line--so it's the Tobin diagram. It should be called the Tobin ratio, but this other guy at Stanford snuck in and managed to give his name to it. He ended up getting a Nobel prize too. So here this line, the slope of this line, this is the riskless asset--the slope of this line, what is the slope of this line? So this is standard deviation, this is expectation. The slope, what's the slope? Well, it's the expectation of whatever you're holding, X, - the riskless asset divided by the standard deviation of X. That's the Sharpe ratio of X. So you notice that every point you could conceivably choose, which is somewhere in this blob, then connect it to the riskless asset-- so every point on this line obviously has the same Sharpe ratio. If you leveraged your position and went to here, you wouldn't change your Sharpe ratio. It has the same slope. If you put half your money in the bank and half in the riskless asset, you'd be here, same Sharpe ratio. Anything else you could do has a lower Sharpe ratio. So another thing to say is that an investor managing all his money should maximize the Sharpe ratio. You could in fact tell if somebody had screwed up. Instead of doing the global index, they just did the American index, pick something here, you could look at the slope of where they ended up and it would be a worse slope and a worse Sharpe ratio. You could even judge people, how they're doing, by looking at their Sharpe ratio. So let's take the case of the 2 dice. Suppose you had 1 die. So if you had 1 die, remember, if you invest 100 dollars, you could get 101,102, through 106. Let's say the interest rate is 3 percent. So you could get 101,102, 103,104, 105,106, with 1 sixth probability of each. So the average of that is obviously 103.5, right, because 1 and 6 is 7, and divide by 2, is 103.5. So the expected payoff for putting your money into 1 dice is the average return, is 1.035. The riskless return is going to be 1.03, so it's .035 - .03, .005. And now what's the standard deviation? What's the variance of this? Well, you could take 101 - 103.5 squared, 103 - 103.5 squared, etc. and take the square root of it, and you'd get .017. So you notice the chance of losing money, by the way, is 50 percent. 50 percent of the time, you're going to lose money, and your Sharpe ratio is .005 over .017. So that's about 3--no, it's about .3. Now that happens to be the Sharpe ratio of the stock market, just about. Shockingly low, isn't it, if you look at the history of the stock market-- so it depends what year you start and what year you end, if you do it right after a crash or before a crash, but just to pick vague numbers it's 9 percent and let's say the interest rate is 4 percent, something like that. It could be 5 percent or 3 percent. Depends again the period. Maybe it's 2 percent, but somewhere like that. And the standard deviation of the stock market is 16 percent or 12 percent, again depending on what period. But always around 12 to 18 percent, let's say 16 percent. That's the one I like to use, because it's percent a day. So that's = to 5 percent over 16 percent, which is about 1 third. It's about .3. That's exactly what this dice has, about .3. So that's all you can get out of the stock market. Not a very good Sharpe ratio. So you could measure Swensen's Sharpe ratio. You could measure Ellington's Sharpe ratio and see what they are. You can see who you think is a better manager. So I won't tell you those numbers just yet. But now let's suppose, what else could I do? So let's suppose you put your money in two dice. That's the whole point of this. Suppose you put half your money in the first dice and half your money in the second die. Now what are the chances--what's going to happen? Well, again, your expected return hasn't changed. It's still .035, but the Sharpe ratio has drastically changed. In fact, you could see that. What are the chances of ending up with 101 dollars now, if you put half your money in each, the worst case? It's not 1 in 6. You have to get the worst case in both dice. So to get 101 dollars, it's 1 in 36. It's vastly less likely that you end up with this extreme bad outcome once you put half the money in each die. So if you compute the standard deviation, it's going to be a lot smaller number. It's going to be .012. So the Sharpe ratio's gone from .3 to .4, just by finding the second die. So what you should be doing is looking, like Swensen does, like everybody does, for those independent risks that the rest of the market is too stupid to see. Even after they got the idea of the index, for 20 years, they didn't realize the index should mean everything, not just in America. So you'd have a huge opportunity to do better than the rest of the managers. While everyone else is screwing around on this line, you can be screwing around on that line. So you could run the same risk this guy did. So Swensen says, you could leverage-- not that he does, but if you're Harvard and you're on this thing instead of this thing, you could leverage and go up here and say, "Look, I've got the same standard deviation everybody else does, and look at my returns. They're so much higher than everybody else's." So that's what Harvard is trying to do. They're trying to globally diversify, cut down their standard deviation and then leverage, and compared to everybody else, get a higher return with the same standard deviation. So that's the first implication of the theory. Now the second implication is the best part. Let's hope I get to it. I'm going to skip over leverage. The second story is coming right up. How are these things priced? I have to get to the second part of Shakespeare. What can we say about the pricing of individual stocks? It looks like an individual stock is going to be worth more if it contributes no variance, less variance. But that turns out to be completely wrong. It's shocking that that's wrong. So why is this? The crucial thing is, remember back to our first principles. What is price = to? What is the key ingredient of price? What is it always = to in basic economics? Student: Supply and demand. Prof: Supply and demand, okay. But an individual's going to buy so that price is = to his marginal utility, right? So we have to figure out--what we've shown so far is that everybody is holding the market. Everybody's holding a market, maybe with some riskless asset. So they're holding the market, plus maybe they're long or short the bonds, but that's not creating any covariance. So if I'm holding the market and I hold a little bit more of a stock, so if I could pay a little bit more and buy t units of stock X, what good would it do me? Well, the expectation, the change in expectation, with t dollars of X would be, as I increase t a little bit, the derivative of my expectation is just the expectation of X. So by holding the new stock, I get expectation of--I get a little more. I get t times the expectation of X, I hope. By coming up with t extra dollars, I could increase my expectation by t times the expectation of X obviously. But what would happen to my variance? If I look at the variance of this, what happens to my variance? Which is = (for variance I could write) is the covariance of this with itself, tX M. So everybody's supposed to hold M some riskless thing, negative or positive in the bond. But the negative or positive in the bond is riskless asset. That contributes nothing to the covariance. I might as well just look at the covariance of a little bit of money in X with the market. And what's that covariance going to be? Well, it's covariance of t, tX and, tX, covariance of tX and M (these are definitely not 0 anymore) covariance of-- so it's 2,2t, covariance of tX and M. And then it's the, covariance of M with itself. So it's the covariance of tX with itself, tX with tX, twice the covariance of tX with M and then this tX with M, 2 covariance tX with M, and the covariance of M with itself. Now I want to differentiate that thing with respect to t. If I put just a little bit of money, that's being on the margin, what's the marginal effect on my variance? I hate variance, but see the mistake people have made in the past is they said, "People hate variance. Therefore a stock that has a lot of variance is bad." Absolutely wrong reasoning. That was Adam Smith's puzzle about water and diamonds. You know, why is water less expensive than diamonds when water's so much more important? It's not how important the whole thing is; it's how important one tiny extra drop of it is, the marginal utility. So if you add a tiny bit of X to what you're already holding, which might involve a bunch of X already, so you add a tiny bit more of X to what you're already holding, what's going to be the change in your variance? So it's the derivative of this with respect to t, when t = 0. So this, by the way, = t squared, variance of X 2 covariance--2t times the covariance of X and M the variance of M. I'm differentiating this with respect to t. Right? Because I've just rewritten the same thing. That's just t squared, the variance of X. The t comes out, 2t covariance of X with M, and here's the variance of M. But if I differentiate with respect to t, I get 2t variance of X (remember, it's the derivative of t when t is 0), 2t variance of X 2 covariance of X and M 0, because the variance of M doesn't depend on t. So at t = 0, this is also 0. So you see the change in my variance, when I add a little more of X, is twice the covariance of X and M. So what is it that X adds? It adds some expectation and it also adds some variance, but not according to the variance of X, according to the covariance of X with M. When I add some more--the price of water is how much extra utility I get, given what I've already got. I've already got a huge amount of water. That's why an extra amount of water's not doing much for me. That's why the price is low. So X itself might be very dangerous, but if it's independent of all the other stuff, M, that you're holding, in fact, you're only adding a drop of it, it won't change your variance hardly at all. So this is 0. It's the covariance. So that's the crucial idea, that the marginal contribution of every stock depends on its expectation and its covariance, not its variance. And the expectation is good and the covariance is bad. And all of this is linear, because it's differentiable, so it just says that--this is the change in covariance. So remember the guy, the marginal utility of expectation. How am I doing in time? 1 more minute. Marginal utility of expectation times the expectation of X, that's the change, when you add 1 dollar's worth-- a tiny bit of X, your expectation goes up by the expectation of X. So this is the marginal utility of expectation, which is the good thing, - the marginal utility of variance. That's the bad thing. And what's the change? The thing that affects--the contribution to variance is the covariance of X with M. So the punch line is, everybody has a linear tradeoff between expectation and covariance. So for any fixed person, it's just a constant times the expectation of X - a constant times--this doesn't depend on the portfolio. This is the marginal utility at his consumption. Marginal utility of expectation at his consumption. You face him with any possible new thing that he could buy, just like a consumer in the first day of class. He could buy apples, he could buy oranges, he could buy pears. The marginal utility of each one of those at the point he's already chosen to consume. This is a number that's fixed, this is a number that's fixed. Whatever X I put in here, that's what I get. So there's a linear tradeoff between expectation and covariance. Expectation good, covariance bad. So the final picture is that in equilibrium, what you should have is every stock--this is called the security market line. This is the expectation of X. This is the covariance of X with M. So what we've found is that it should look like this. There has to be a linear relationship. In order to want the stock--if it's got a higher covariance, that means it's adding bad stuff. You wouldn't want it unless it had a higher expectation. So here's the riskless asset right here. So this is a different diagram than the Tobin diagram. It's expectation and covariance. Every stock is along this line. Should be priced along this line. So let me end with a puzzle, the one we started with on the first day of class. If I have two companies, General Motors and AIDS--an anti AIDS company. Some scientist at Yale discovers a cure for AIDS. He calls it AIDS. He discovers a cure for AIDS. If the thing works, he'll make a fortune. If the thing doesn't work, of course, it's going to go bankrupt and pay anyone no money. Let's say we calculate the expected profits of General Electric. General Motors is too junky now. General Electric. Let's say the expected profits of General Electric = the expected profits of the anti-AIDS company. Which will sell for a higher price? Student: General Electric. Prof: Will sell for a higher price. Why? Student: > the variability of the outcome. Prof: Okay, that's what you should have said at the beginning of class, but not at the end of class. Who's saying that? Down here. Who said that? Who just said that? I don't want to embarrass anyone. All right, you're anonymous. I didn't see who it was, so exactly. That's what you would have thought before this class began. Everybody hates variance. The AIDS company is so risky, you could get a fortune or 0. You couldn't get riskier than that. General Electric is not going to go bankrupt very easily and it's not going to suddenly multiply its value by 100 times either. It's much more solid. So which would you pay more for? Everyone at the beginning of the class, I think, would have said like he did, whoever he is, would have said "General Electric, you'd pay more for." But the answer's not General Electric. Why is that? Yes? Student: Because the cure for AIDS actually working is uncorrelated with the state of the economy, > Prof: Exactly. That's the shocking fact. That's the shocking conclusion. So Shakespeare, yes, "Nothing ventured, nothing gained." You have to take a risk to expect a higher return. Everyone would have thought that's the anti-AIDS company. No it's not, and Shakespeare couldn't possibly have figured this out. It's General Electric is the one with the higher risk, because it's correlated with the market. It's correlated with the market. Obviously if people are rich, they're going to buy more refrigerators and engines and stuff like that. If business isn't doing very well, they're not going to buy that stuff. It's very correlated with the market. Anti-AIDS, if it cures AIDS, people are going to buy it. If they've got AIDS, they're going to buy it no matter what, otherwise they won't, so it's uncorrelated with the market. So therefore the price of the AIDS company is going to be its expected payoff, discounted. The price of General Motors [correction: General Electric] is going to be much less, because it's going to be punished for having a correlation with the market. Therefore the return on General Electric is going to be much higher, because the same expected payoff and a lower price, your return's going to be higher in General Electric. That's the shocking thing that Shakespeare couldn't have noticed. So yes, we're just doing what Shakespeare said in the beginning, but in a way he couldn't possibly have done without any mathematics. Okay, now the problem set, you'll have to see if you can do the problem set. It's due on Tuesday.
Quantitative_Finance_by_Yale_University	24_Risk_Return_and_Social_Security.txt	Prof: Anyhow, so today I'm going to try and wrap up a few loose ends. So I'm going to try and talk about the high water mark of finance which is basically CAPM and Black-Scholes, both of which we've almost talked about, almost finished talking about, and I'm going to talk in the middle about Social Security which we never finished, my Social Security plan. So I hope to deal with all three of these things today. So just to wrap up the CAPM, the CAPM had two main ideas. The first idea was diversification and the second main idea, as we said, was the tradeoff between risk and return. Shakespeare had both of these ideas. He understood that you're safer if you've got each of your boats on a different ocean, and he understood that if you're going to take a high risk you'd better get a high return otherwise nobody is willing to take it. And so he made that very clear. In fact I think the whole point of the play is about economics, The Merchant of Venice, and he made both of these principles very clear, but he couldn't quantify them and he couldn't mathematize them, and the Capital Asset Pricing Model gives a mathematical, quantifiable form to both and a quite shocking recommendation in both cases. So just to draw those two pictures, for those of you who didn't hear it last night, if you do Tobin's famous picture, this is the Markowitz-Tobin Capital Market Line they called it. It's very important to keep straight what's on the diagram. There's the standard deviation of any asset per dollar. So here I'm writing the price. So it's per dollar, and here is the expectation of the asset per dollar. So pi of Y, I'm calling that the price. So this is per dollar. And I'm not going to go over what we derived before, but we noticed that if you took all the risky assets, any risky asset's going to have per dollar, if it's priced, some standard deviation and some expectation. You can write down all the risky assets, and you can combine them, and you'll get a possibility set that looks like this. So the diversification already shows up in this picture because if you combine this asset and this asset you're going to get possibilities by putting half of your money in each, not on the straight line between them, but on some curved line that's much better because you're reducing your risk. So Markowitz already had that curve and this picture in mind. Tobin added the riskless asset, which he put here, and then he said, well, if there's a riskless asset everybody's going to do the same thing and everyone's going to choose the same point. It's better for everybody, so this is the optimal risky portfolio and it has to be equal to the market, because if everybody's smart enough to figure out what to do they're all going to do the same thing, and whatever everybody holds that's by definition the market. So Tobin showed that everybody should choose something on this capital market line and so everybody should split his money between the market and a riskless asset. Put your money in the bank or own the entire market. That was his recommendation and that was the beginning of the whole idea of index investing. So that was the first idea, first, most important idea. Now, how could you test this? Well, you could simply test every fund in history and compare so called experts and see if those guys could get you above this line. So by the way, the slope of the line, one more thing, is the slope equals Sharpe ratio. So everybody's trying to get the highest Sharpe ratio they can, and if you have this portfolio you've made a mistake, you haven't held the optimal one, then the slope of your performance will be a lower Sharpe ratio than that. The slope of this, which is the Sharpe ratio of that point, is worse than the slope of that, which is the Sharpe ratio of this point. And the Sharpe ratio, remember, is (the expectation per dollar minus what you can get in the riskless asset per dollar) divided by the started deviation of Y per dollar, let's say. So that's just the slope of this line. So we can measure performance of a portfolio manger by the Sharpe ratio. Everyone should try and get the highest Sharpe ratio. The upshot of diversification is you should buy a little bit of every stock in the economy no matter how small, no matter how big, no matter how safe, no matter how risky, you should spread your money across everything. That's the recommendation of Tobin. And it relies, of course, on everybody else being rational, so everybody else is choosing the right thing. Then you can just piggyback and do what everybody else is doing. So that's the first thing. Very shocking, as I said, at first glance you'd think someone who loves risk would just invest in risky stocks and people who are very risk averse would just invest in safe stocks. Tobin says, no, no, no, no. If you're risk averse you should just put most of your money in the bank and hold a little bit of every stock. So you're here somewhere. If you're very risk tolerant you shouldn't just concentrate on the risky stocks. You should buy the same proportion of all stocks as everyone else, but you should borrow the money to do it and maybe way up here. And people who borrow money to invest that's called leveraging. So that's idea number one, the crucial idea. There are a lot of ideas mixed in that, and as I said, you can test it by seeing if anyone can beat the market-- is there anyone historically that has had a higher Sharpe ratio than the market. In 1967 when all of this was being tested there was a famous book called A Random Walk Down Wall Street written by Malkiel, which I recommend you read. He gives the history of tests of whether people could beat the market. Of course many people beat the market for short periods of time. Then they totally collapse. And then some people beat the market for 20 years in a row and then retire, but there are so few of those people that it looks like just by random dumb luck you could get almost those people. On the other hand there are some people like Warren Buffet who seem to beat the market for 40 or 50 years. It's really hard to believe that that's all just luck. And so that's one test of the thing. The second idea of the Capital Asset Pricing Model is risk and return. And so now if we assume--so all this graph, by the way, assumed quadratic utilities, quadratic or mean variance utilities, quadratic utility and common probabilities. So everybody knew what the probabilities were of the different states, so you know how to measure the covariance and the variance and all that because you know what the probabilities are to measure over. So here, having assumed that, it turns out that you just apply the principle that we saw the first few days of class, that the price is going to equal the marginal utility, not the total utility. Price is going to equal marginal utility and if the price equals the marginal utility the marginal utility is going to be-- depends, according to this assumption of quadratic utilities as we showed, depends on expectation. So this is the price of Y, so let's just call it pi of Y like I did before. It depends on the expectation of Y and it depends on the covariance of Y with the market. We've assumed with quadratic utilities that people only care about the mean and the variance, so you'd have expected the marginal utility of any single asset to depend on its mean and its variance, but it's the marginal utility. It's what it adds to what you've already got. So it adds expectation because expectation's additive, but when you add another stock to what you already have, the variance of the whole portfolio changes according to the covariance of the new thing with what you already had, and everybody already had the market. So given that you know that the price, mathematically therefore, the price has to equal something times the expectation of Y plus something times the covariance of Y with the market. But that's true for all Y. In particular it's true for the riskless asset. So the riskless asset pays 1 for sure, has no covariance with anything like the market, and its price is 1 over (1 r). So therefore A has to be 1 over (1 r). So we know that this has to be (1 r). And then B could be whatever it is. The covariance, by the way, is going to be bad, so this is minus. And then B, you have to figure B out. So you don't know what B is a priori. You don't know what the interest rate is either. You had to see that in the market. Once you know the price of one asset, and you know its correlation with the market, if you knew this price, and you know the expectation of Y, and you know the covariance with the market that will tell you B. So once you've given one price of a risky asset, like of the market as a whole, you're going to be able to figure out the price of every other asset because from that one price you can deduce B, and once you have B you can price everything. So that's the second idea, risk and return. And you can see it graphically and more dramatically, because if I take that same equation, this is called the covariance pricing formula, you take that and divide by pi of Y you get 1 equals expectation of Y divided by the price of Y-- dividing both sides by pi of Y-- minus B times the covariance of (Y over the price of Y) with M. So that just tells me the expectation and the covariance of a dollar's worth, just like this was a dollar's worth. This was per dollar and this is per dollar, so if you put the covariance of Y and the pi of Y down here, and M over here, and here you put expectation Y over pi of Y, this just says this is just a constant, and this is a constant, so it says this and this are linearly related. These are all securities who have price 1. There has to be a linear relationship between their expectation per dollar and their covariance per dollar with the market. And as the covariance gets higher the return gets higher. So if you take a stock with a high covariance it's going to have to have a high expected return. That's exactly what Shakespeare said. If it's more risky people won't hold it unless it's got a higher return, which means you can buy it for a cheap price. So its price is less than its expectation. But the difference with Shakespeare is we've quantified risk. It's not what you would have thought, variance, it's covariance. And that's it. Those are the two big ideas and you could test-- so this is called the Security Market Line, and you could test this by asking is every stock-- so if you look at every stock last year, you look at its covariance, you put a point here, then you look this year at its expected return, of course some stocks are going to be wild, but you average over a bunch of stock and a bunch of years. Do you get things that lie in a straight line or close to a straight line? And Sharpe, in 1967, found that amazingly when you did that you got--so I described last night exactly what his test was. You got something that looked incredibly close to a straight line like that. So this was the greatest triumph in the history of the social sciences, it was called, because you had huge amounts of data, huge capacity to test things, a shocking conclusion, a shockingly precise theory to test, and it fit the line so incredibly closely. And it just swept, it made a huge impression in finance and in economics and lots of Nobel Prizes were given for this. Sharpe won a Nobel Prize. Markowitz won a Nobel Prize. Tobin won a Nobel Prize. Lintner died. He would have won a Nobel Prize too. So this was the first major triumph, the most important triumph of finance, the Capital Asset Pricing Model. Now, as it happens, as the theory's been tested over and over again every year since 1967 it's performed more and more poorly. And so now when you do this you get points that look like this, and like that, and like this, and they don't seem to lie on a straight line at all, and it's pretty shocking how up until '67 or the early '70s that it seemed to work out perfectly and now it doesn't work very well. And this business they've also discovered, according to this you couldn't beat the market. So how do you test whether something beats the market? You can pick a bunch of people and say, "Could they beat the market," or you can actually just make up a strategy yourself like buy only new stocks. Just every year buy the stocks that have come onto the S&P 500 for the first time, or just buy the stocks that are the biggest 10 percent. And it turns out some of those strategies actually do beat the market. So I don't have time to go into the details, you know, that is they lie above or below here. So the theory has come into--so theory and doubt. And so what I'm going to talk about next week is, and it certainly doesn't explain the current crisis, so I want next week to explain crisis. So next week I'm going to end by giving another theory which is going to explain the crisis and be different from this one, but of course it hasn't been tested over 30 years or 50 years like CAPM. CAPM looked great for the first 20 years, so whatever I say next week will probably turn out to be 90 percent wrong, but at the moment it looks pretty good. And I didn't want to spend half the course on it in case in 20 years it seemed to be ridiculous. But anyway, I'm going to present it anyway to those of you who want to hear it next week, and it'll be, I think, understandable and down to earth and it'll invoke a very basic thing. Nowhere in this model did we take into account, you know, when we say people leverage that means they're borrowing money and choosing to go up here. We haven't taken into account that they have to pay the money back, and who's going to trust them to pay the money back? And forcing them to do something to guarantee they're going to pay the money back is going to change the theory in a critical way, which I'll get to next week. Now, one last thing about the theory, as I say, you test it by seeing--nobody should be above this line and nobody should be above this line, but of course you can find people above this line. Swensen, to take a famous Yale example, is above this line. And you can find people above this line, Ellington. So Ellington, let's say, above this line. All right, so hedge funds. Let's call it an anonymous hedge fund since we're on camera now, hedge fund, hedge fund E. So the question is, is that luck, they just did it a few years in both cases like 15 years apiece, or does it mean something? All right, well, so you can measure the, you know, if you believe this theory and you just say, okay, let's say the theory's 99 percent true, it's just that there are a few people who really do beat the market, then you can decide by looking at these graphs just how good is Swensen relative to the market? How good is this hedge fund relative to the market? And so you have a way of calibrating and measuring how well people do. So I don't have time to get into that, but I would measure the quality of a hedge fund by its marginal Sharpe ratio. How much does having access to this hedge fund, if you added it to your portfolio, increase your portfolio hedge ratio [correction: Sharpe ratio]? That's, I think, the right measure of how good a hedge fund is. And the right measure of how good Swensen is, is, what's his Sharpe ratio? And so there's a different criterion. I keep emphasizing this. Swensen is managing an entire portfolio so you have to measure him on how's he done for Yale, because Yale's not going to combine him with something else. It's just holding what he holds. So it's his Sharpe ratio. But Ellington, you're going to combine Ellington with some other stuff. So Swensen might invest in Ellington, but ten million other things. And so you have to say how much is Ellington going to help Swensen's Sharpe ratio? So instead of Swensen's Sharpe ratio how much is Ellington going to help the market Sharpe ratio? So that's how you should measure a hedge fund, its marginal Sharpe ratio, and Swensen by his Sharpe ratio. So I'd say measure Swensen performance by Sharpe ratio, measure hedge fund performance by marginal Sharpe ratio, because you'd be crazy to put all your money in a hedge fund. The only people who do it are the partners of the hedge fund who are sort of forced to do it because that's how they can persuade investors that they're really paying attention to their fund, because all their money's at risk. So that's it. That's the basic bottom line. So are there any questions before I now move on from this? We talked about this last night and we talked about it for the last two lectures. All right, so it's a high water mark as I say; incredibly precise prediction and incredibly close to the facts, at least in 1967 but not after that. Now, I want to move to an aside of Social Security before I come back to Black-Scholes which is the last high water mark of the standard theory. Remember the upshot of what we've talked about so far. The upshot of this is that the market will get a higher return. Oh, by the way, I'd say one other thing. What is the standard critique of this theory? So of course everybody else has seen that the theory doesn't work. So what is their explanation for why? What's the old explanation for why the theory isn't working so well now? The explanation is that in the old days what was thought of as the market was just all American stocks. But now it's pretty obvious, in fact it should have been obvious from the beginning. And so Swensen realized it early on that Markowitz's advice is to diversify, diversify, diversify, not just into all American stocks, into everything all over the world and all kinds of assets that aren't stocks at all. So what you measure as the market shouldn't just be American stocks. It should be the world portfolio, but how do you measure the world portfolio? That's hard to do, and so people have tried to maintain that the reason the theory doesn't work is because we've got the wrong M in all these equations. So that would be a nice way of fixing the theory. I doubt if that's going to help in the end. So my problem about collateral is a different look at it. But anyhow, so the market according to the theory will get a higher return than bonds, and of course that's true. The market has a very high positive covariance with itself so a very low price up here. It's high covariance with itself, so a low price. Compared to its expectation the price is low, so you're paying much less than the expectation. So then when you see what actually happens it's going to look much higher than that. It's not just this. The price is lower therefore the final outcome's going to be much bigger on average. So to put it another way, if you had two possibilities which you knew were equally likely, 1 half and 1 half, and the market paid off something good here and something bad here, so everybody's rich here and everybody's poor here. The price of the Arrow security of this state is going to be much lower than the price of the Arrow security of this state. So this state is going to have a price, let's say .8, and this one might have a price .2 because here the bad state, that's when everybody's poor, so you're going to, you know, this formula basically tells you that if you're paying off here you're negatively correlated with the market, you're going to have to pay a very high price for it because you're hedging. By buying this security you're balancing off what you have with the market. By buying the market, people don't like that because it adds more risk to what you already have. And so people don't like it so they're not going pay very much, so the price will be much less than the actual probability of 1 half. So that's the conclusion of what we've done. I want to now connect this to Social Security. So you remember in our Social Security model we had land that went here, here, here, paid 1,1, 1,1, 1, and we had these people, overlapping generations-people like that. And we discovered a very important thing. The reason why Social Security seems to be broke is because we gave away so much money to the people in the first generation. It's not that Social Security wastes money like George Bush seems to imply whenever he talks about it. It's not like they just throw it away. It's that we gave a huge gift to the people in the '40s, the '50s and the '60s and so everyone after that has to pay for that gift. But there's a little bit more to George Bush's story than I've allowed so far, which is that he wants to put the money into stocks. And we know that stocks are going to get a higher return than bonds. That's the whole point of this theory. You put money in stocks, the expected return on stocks is higher than the expected return on bonds. So if you want to make this mathematical we have to add the possibility of risk and stocks and it looks like it's going to be hopelessly complicated, but we can do it very easily. So I'm going to reproduce the same picture with uncertainty in stocks in it, and then we're going to come back to Social Security and spend 15 minutes talking about what's the right plan for Social Security. So how could I take this simple model, which already seemed complicated, it's already a pretty complicated model, had no uncertainty, and now put uncertainty in it? Well, I'm going to suppose that land--so this is the land dividends I'm now going to describe. And by the way, I had people with endowments here. They were (3,1) and (3,1). Remember, this is their endowments, but we didn't say where those endowments came from. So I'm going to take the land dividends. I'm going to suppose the dividend of the land today is 1, but things might get better or worse in the future. Maybe the dividend goes to 2 or down to 1 half, say. I'm taking some extreme case where it doubles or halves, and maybe after that it could double again or it could go back to 1 and here it could go to 1 or it could go to 1 quarter. So what dividends are doing is a random walk. If the economy starts getting more productive then it's in a better position, and from that point things get even more productive or maybe go back to where they were. If things get worse they're worse, but maybe things will start to get better again or continue to get worse. So this is what I imagine as my process of dividends. So if you own the land you get all these dividends in the whole infinite future, all right? And now let's say that there's labor as well, so labor income. So I have to make an assumption about labor income. So I'm going to assume only young work. So here we kind of made the same assumption. You get a lot when you're young and not much when you're old. I'm going to assume only the young work, and I'm going to assume that this productivity gains or losses, and by the way, you might think you never go backwards. Maybe it goes from 1 to 2 or 1 to 1.1. So it's always growing, but random. But I'm just going to keep it here since I solved this example last night. I might as well stick to that one, but there's no reason why--I could have made the thing always, no matter what, either stay the same or get better. That might have been a better example to do, more realistic because we don't really have tremendous productivity declines, but anyway, all I mean to do is to put some randomness here. So only young work and wages proportional to dividends, so let's just assume this, so I'm assuming--this is what's called neutral technical change. So presumably the reason why productivity is going up, the dividends are getting higher, is there are more discoveries improving the product of the land, but they're probably also improving the product of labor, and so let's say they have same effect on both. So I'm going to assume that labor is actually--put the 1 above. Let's say labor always gets 3 times what dividends are. So this is a 6 and this will be 3 halves, and this will be 12 and 3 again and 3 quarters, so that's what labor is getting, so labor income. I shouldn't have switched colors, labor income. So that's my complicated world, way more complicated than it was before. So if you own the land you get all the dividends in the future. People live two periods, so I'm going to assume that utility-- so you're going to live when you're young and then when you're old and up and when you're old and down. So you're going to live--let's say a guy born here, he's young here, or she's young here. She can work here, and then she's going to be old here and here, but when she's old it's not clear how good her investment's going to turn out. So this is going to just be our simple log. I'll call this 1 half log Y 1 quarter log Z_up 1 quarter log Z_down. So you don't discount the future, let's say, you just take log of consumption today plus probability 1 half of log consumption in the up state, 1 half log consumption in the down state. So the probabilities here are 1 half. These are the objective probabilities. So maybe I should have written the utility--maybe better it would have been to write the utility like that. That's what people know, what the probabilities are. So that's it. That's my set up. So what should the economy do? What should people do? You see, if you buy--if you're some person like this woman here, she could decide to hold bonds, and she could get whatever the interest rate turns out to be, which we're going to compute in a minute, or she could hold stock in which case she's going to get-- let's start her off here, maybe. She could buy land; buy stock. Now we don't know what the price is yet. We have to compute that. But if she buys the stock she'll get a dividend of 2 here and be able to sell the land for a high price, because from here on it's obviously pretty productive, better than it was back here, or she might get unlucky and the price might, you know, the dividend might be really terrible, just 1 half, and not only that but the land she sells when she's old is also going to have a really lousy price. So if she holds land she's going to get a high dividend and a high capital return, or else a low dividend and a low capital return. It's really risky for her, or she could just buy a bond at whatever interest rate it turns out to be and get something safe. So what should she do, and will that be a good thing for the economy or can we make everybody better off by using Social Security? So how can we solve this? So it looks like a really complicated model to solve because we've got a generation born here, another one born here, the same generation might be born up here under different circumstances, and then this generation here could be born under any of three different circumstances, so there's a lot to solve for. But what we know is that when we compute the Arrow price, starting from any point, this Arrow price is going to be bigger than 1 half and this one's going to be less than 1 half because the economy is doing much worse down here so people know they're all going to get screwed down here and consume a lot less. So to hedge that they're all going to want to buy, they're going to be desperate to buy consumption down here. Of course they can't all do that, so it's got to be the price that's more than 1 half that discourages them from doing that. And they don't really need that much to buy up here because their dividends, they're going to be so rich anyway. So the price of the Arrow security is going to be less than 1 half because there's so much that they have to end up holding and that'll encourage them to buy. I mean, sorry, I said the logic backwards. There's so much that they're going to have to end up consuming because the economy is so productive. How can you get them to plan to consume that much up there? It's by having a low Arrow security price. So even in advance they know that they're going to end up consuming a lot and they're happy to do that because they're willing to buy Arrow securities because they're so cheap. So how do we solve all this? So everybody following the problem? It's quite a complicated problem, but it turns out to have a very simple answer. Yep? Student: So the down state, the price of consumption is high but the price of land is low? Prof: Right, so. Well, so if you start--starting from here the price of consumption-- if you want to buy at this point, consumption at this point, you're going to have to pay more than 1 half to get it, but you know that once you get here the price of land is going to have dropped. So yes, I'm agreeing with you. Student: I understand the first part because the CAPM price... Prof: Right, now why should the price of land be lower here? Remember, the price of land is always in terms of the consumption good that period. Every period I might as well take an apple to have a price of 1. So you see, the land here is producing an entire apple, and on average going forward it's going to be producing 1 apple. The geometric average of all these numbers is 1 starting at this point. Once you've gone down to here production has deteriorated. The land is only producing 1 half an apple here, and in the future instead of producing 12 it's going to produce 3 apples here and only 3 quarters of an apple. So it's crummier land down here, so you're going to pay less for the land. Any other questions? But I'm going to tell you exactly what you'll pay for the land. So we're going to solve this. So need to solve for land price in each state, and interest rate at each state, and price of up Arrow security, and price of down Arrow security at each state. So how can we do all that? Well, first of all you notice that the Arrow securities are always the key. Once you solve for those you can figure out everything else. So we just have to solve for these, the price of the up and down Arrow securities in every state. Oh, this was me in a previous class today. I didn't erase it. I figured the next guy would do it, serves me right. So how can we solve this? Well, we can guess, let's do it up here, guess that these prices, Arrow prices, the same at every state. So what do I mean by that? I mean, here, how many apples would you pay to get an apple here? I'm guessing that that's the same amount you would pay here to get an apple here. And what you'd pay in apples at this point to get an apple down here is going to be the same as this generation would pay to get an apple down here. That's a guess. We have to verify that that's going to work. It seems like everything is sort of homogeneous, and so guess that price of land is proportional to dividends in that state. Well, the whole thing is sort of homogeneous and everything, so if the land here is 4 times as good as the land here, the land here is 4 times as good as the land here, because the dividends are always 4 times higher if you go up one thing. So this is 4 times that, that's 4 times that. So why not guess that the price of land is 4 times here than it is here, 4 times higher here than it is here. Sounds possible, anyway, and of course these are going to turn out to be correct guesses. So once you make these guesses it's going to be very simple to find the equilibrium, and then we can verify that the guesses are correct. So what does this guy want to do here? So assume you only work when you're young. So what's your income? What's anybody's income like this young guy here? Young at time 1, so this is time 1 here, time 2, time 3, time 4, so at time 1 their income is 3 because that's what their wage was. They work when they're young and they've got three. That's it. They don't own the land when they're born. They're going to buy the land but they don't own it now, and so what do they want to do? They want to consume when they're young, their utility, remember? So what's their budget set? Their budget set is they can consume Y, that's consuming here, or they can consume here or here. So they can consume P_up times Z_up P_down times Z_down. That's what they can do with those Arrow securities. So what are they trying to maximize? They're trying to maximize 1 half log Y 1 quarter log Z_up 1 quarter log Z_down. That's what they're trying to do. So what do we have to do? We have to clear this market and this market given what the young are going to do in the next period, but let's see what this guy's going to do when he's young. Everybody is going to face a similar, basically a scaled up version of this problem. So this is what the guy is doing here. He's got an income of 3 and there's the price of up and down Arrow securities. That's going to tell him what to consume here and what to plan to consume up here and down here. Student: Do you change your utility function? Prof: So utility function is the same one as this. I just multiplied through by 1 half, right? So I put 1 half, 1 quarter, 1 quarter to get that. So I've just multiplied it all by a constant. So now the coefficients add up to 1; 1 half, 1 quarter and 1 quarter. That's his budget constraint, but what's the budget constraint going to be of a guy down here? It's exactly the same. He's going to maximize the same utility function and his budget constraint, since the prices of the Arrow securities are the same, the only difference is going to be that he's only got 3 halves here. So they're pretty similar problems. So let's see what the guy at time 1 is going to do. That's going to imply that Y = (Cobb-Douglas) 1 half times (his income) 3 divided by the price of Y which is just 1, so 1 half of 3 over 1 which is 3 halves. And what's he going do when he's old? Z_up is going to be--well, his Cobb-Douglas is 1 quarter, and then his income is still 3, and then the price is P_up of the Arrow security. In the down case he's going to have 1 quarter times 3 (that's his income) divided by P_down. So to clear this market what do we have to do? We have to clear the market by doing what? Z_up, that's this guy, so 1 quarter (so this is the old guy) times 3 divided by P_up. That's what this guy wants to consume up here, plus what the young are going to do there, but we know what the young are going to do here. This young person is doing exactly what this guy did, except instead of having a starting wealth of 3 he has a starting wealth of 6. So instead of consuming young 3 halves he's going to consume young 6 halves. So this is going to be plus 3. He's going to consume half of his wages just like this guy consumed half of his wages when he was young. So this new young guy, the young guys are always going to consume in the first period half of what their wages are. That's what this equation tells us. If this is your budget set, this is your income, this is what your budget set is and this is what you're maximizing. This is a very special Cobb-Douglas case where you have endowments only in one good, so it's clear that in that good you'll always consume the Cobb-Douglas coefficient fraction of it, 1 half of that, so 3 halves. And this guy's going to consume 1 half of 6 which is 3. So the old up here are going to consume that number. The young are going to consume 3, and what's the total that's available for them to consume? What's available? Student: 6. Prof: No, more. Student: 8. Prof: 8; the young got 6 apples and the land paid 2 apples in dividends, so the total number of apples is 8. So that's it. And so we can solve that and that's going to imply that multiplying-- so that's 5 and multiplying by 4 is 20, so P_U, of course I'm going to screw this up now. P_U is 3 over 20, because if you put 3 over 20 in here you get the 3s cancel and you get 20 over 4 which is 5, and 5 3 is 8, so it's 3 over 20. Now meanwhile, what are we going to have in the up state? In the up state... Student: In the down state. Prof: Down state. That was the up state. In the down state the guy's going to do 1 quarter 3 over P_D. What is this other guy going to do? The young person here is going to consume what? So in the downstate what are we going to have? The equation of the downstate is going to be-- so this one 1 quarter 3 divided by P_down plus what's this guy going to consume when he's young? Well, his income, his wages are 3 halves and he's going to consume half of that so it's 3 quarters, right, because when you're young you always end up consuming half of your wages, so 3 quarters and that has to equal-- what's the total? 2? 2, so what does that leave us? That leaves us 3 quarters, that's 5 fourths, so let's see. So 5 fourths equals 3 quarters over P_D, so P_D is going to equal 3 fifths, right, because the 4s drop out and you put P_D up and the 5 down, it's 3 fifths. So that's it. So now we've got--we've figured out the prices. So this Arrow security was 1 half. I mean, the probabilities are 1 half, 1 half, but the prices, the Arrow security prices, are going to be less than 1 half and more than 1 half. I forgot what they were already, 3 twentieths, 3 over 20 and 3 over 5. Those are the Arrow prices. By the way, you notice they don't add up to 1. So what's the interest rate? So if you want to get--a riskless bond pays 1 in each of these two states, so how much is that worth, 1 over (1 r) equals (You have to buy both Arrow securities. We've done this before.) 3 twentieths 3 fifths which equals 15 twentieths, which equals 3 fourths, so therefore 1 r = 4 thirds. So r is 33 percent. So that's what we did. We've got the probabilities, 3 twentieths and 3 fifths. Just as we thought the price of the down Arrow security is going to be much bigger than the price of the up Arrow security even though objectively they have 50/50 probability, and why is that? Because everyone who's rational is going to realize that they have to plan to consume much more up here than down here, but they're not going to want to do that unless the price is much cheaper. So that's how we got the price. So now what's the price of land? That's the only last thing we have to figure out, so the price of land. So the price of land at time 1 equals what? Well, what if you buy the land? What do you get? You get 3 twentieths, then you get the dividend which is 2, but then you get to sell the land which is P_land^(up). And then plus if you get the down state you get a dividend--so the down state is worth 3 fifths to you, right? And then what do you get? What's your dividend? 1 half the price of the land you can sell, P_land^(down). So that's what the price of land is at 1. It depends, of course, on what you can sell the price of land for in the future, but we made a guess here that the price of land is just proportional to the price of the dividend. So whatever the price of land is here when the dividend is 1 it should be twice as high here and half as high here. So therefore this, instead of looking at it as the price of land went up it's going to be twice the price that land was at the very beginning. So it's just 2 times the price of land at the very beginning times that same price. And this price of land at down, the dividend is half, so the land is sort of half as good from here on out as it was in the beginning, so let's guess the price of land is half of what it was at the beginning. But now you see we've just got P_land in terms of other stuff and so we can solve for it. So the price of land is going to equal--well, now it's complicated. So 3 tenths 3 tenths times the price of land 3 tenths 3 tenths times the price of land, and so that means the price of land minus 6 tenths. So 4 tenths the price of land is going to equal 6 tenths. So the price of land is 3 halves at the beginning. So we figured out the price of land here. Price of land is 3 halves at the very beginning. So we've solved for the whole equilibrium. It took a long time, but I'm at the end of this story now. So let's just review what we did. And so I don't think it's that complicated a story. The story is that you've got land which has risky dividends. So instead of having one straight line of what can happen in the future we've got this infinitely expanding tree. So it's very hard to imagine solving it, but then we've built in somewhat special assumptions. We've got all this homogeneity and that allows us to solve it because it's the same problem getting repeated over and over again, just like we did before. So the price of land turns out to be 3 halves. So what is this guy going to do? He's going to take his land, his income which is 3, eat half of it, which was 3 halves, that's what we said he always does when he's young, spend half his income on consumption, the rest of his income, 3 halves, he uses to buy all the land. Now, with the land he gets a payoff of 2, but he gets to sell the land now for double the price he bought it, namely for 3. So 2 3 is 5 and that, by the way, the price of up was 3 twentieths so this is 5, right, because if I put in 3 twentieths up here that's the Arrow price of up, then Z_up is going to be 5. And so that's exactly how we got it. With the land he gets the dividend of 2 plus he sells the land for 3. That's 5, so he does consume 5. Z_down, incidentally, the price of down was 3 fifths. So the consumption of down--what's consumption of down going to be? Student: 5 fourths. Prof: 5 fourths, thank you. That'll be 5 fourths, so let's see that that's going to work out too. So the guy buys the land, he gets his dividend of 1 half, and then he sells the land for half of this price which is 3 quarters, and 1 half plus 3 quarters is 5 fourths, exactly what he's supposed to have. So you see it works out that everybody's doing exactly what they're supposed to and all the markets are clearing. Anyhow, the point is not so much the numbers, the point is the following; that sure enough, just as we said before, the price of Arrow securities are going to be expensive when things are going down and cheap when things are going up. The upshot of that is the return on stocks, like land, is going to be very high. You put in 3 halves and what happens with the 3 halves? With probability 1 half, that's what you put in, with probability 1 half you get 2 plus you get to sell the land for 3, which is 5. And with the other probability 1 half you get--the dividend is 1 half, plus you sell the land for 3 quarters. That's what you're eating, 5 and 5 fourths. That's equal to 5 halves 5 fourths 5--I don't know what this is. What is this? 1 half 3 quarters is 5 fourths times 1 half... Student: 5 eighths. Prof: It's 5 eighths divided by 3 halves. So this is a very high number. So what is this? 4 times that, that's 25 over 8 divided by 3 over 2 which is... Student: 25 over 12. Prof: Is what? Student: 25 over 12. Prof: 25 over 12, is that what you said? Student: 25 over 12. Prof: 25 over 12, I'm just believing you now. So that is over 200%, right? So your return is 100%. Whatever you put in you've more than doubled your money in expectation, whereas the interest rate, we said, was 33 and 1 third percent. So of course you're getting a tremendous return by putting your money into capital because that's the whole point of the theory. It's risky. The whole economy is going to be rich or poor together, so the price of capital, on the margin it's a very risky thing to do. It just adds to this inequality in your consumption. So the price is going to be low. You're going to get a very high return. That's all I wanted to do. I just solved it out concretely so you can see very clearly that you get a high return in the good state and-- you get a high return on capital, much higher than the riskless rate of interest. So there we are. We're back at the beginning now where George Bush--we can see that somewhere in the middle here things are really disastrous. These people who are getting Social Security, which means they're getting a fixed amount here and here are doing really badly, at least in expected return, compared to what they would do in the stock market. And so what should we do about that, and is it true that just because stocks make a higher return, we should privatize? So what do you think now? Where are we in this argument? Has anything materially changed? So George Bush is saying, and many Republicans say, that we should let people, you know, get them invested in stocks. There's a higher expected return. So what do we think about that? What do you think about that? This is a real policy issue here. We've got this problem in America. Right now we've got this huge deficit in Social Security. The rate of return has gotten really poor for your generation. You're looking forward to not making very much money, and now we know theoretically, confirming what we've seen in the past, stocks are making higher returns than bonds, and Social Security is paying people a fraction of the wages of the young. So let me remind you of the arguments. So the issue has come up because Social Security is running out of money. So it came up because of this problem. There's going to be a deficit. If we continue to pay people at the same rules that we've used up until now we're not going to be able to afford to do it much longer, so we're going to have to lower what we pay the people going forward, lower it in some clever way like they don't get money until they're older. Instead of 65 make them wait until 70, or do something like that to pay them less. That's one way of balancing things. And because we're going to have to make changes like that, that's why the whole issue of Social Security has come up, and now deeper thinkers are questioning the whole idea of Social Security. So let me just remind you that America was ahead of everyone in the world when we created Social Security under Roosevelt. Nobody had anything like it. Then everybody in the rest of the world gradually copied us, and now everybody's facing the same problem we are, which we know why you have to face it. You're giving away stuff to the people at the beginning and so they're facing it by changing Social Security in some crazy way or another, and we haven't changed anything at all, but obviously we have to, and the question is how should we change it and what's the right thing to do. And just to remind you, again, of the issues, the Democrats and Republicans seem to be totally opposed to each other. The Democrats say, "Oh, we want to continue to give people who have done poorly in their lives a better deal on Social Security because we want to redistribute. We want to help the poor." The Republicans, actually some of them agree with that, but some of them don't agree with that, but anyway, even the ones who agree that's not the most important thing they think of in Social Security. Then the Democrats say, "Social Security is so important because we're sharing risks across generations. If the next generation has poor wages so they end up down here with bad wages, you know, the economy takes a turn south with bad wages, then the old people should suffer along with them. And if the young do better with high wages because things went up then the old should also get better Social Security dividends," and that's what the current situation promises. It's also indexed according to inflation, all right, so once you retire then you're protected against changes in inflation. And then another important thing of Democrats, you don't have an opportunity to make a mistake. If you invest in stocks and stuff like that and the stock market suddenly collapses you're not going to lose money in Social Security because Social Security depends on the wage of the next generation, and that moves much slower than the stock. The Republicans, on the other hand, say, "This is just terrible. Nobody knows what their property rights are in Social Security. No one actually understands how much money they're getting when they're old. They just know now it's going to be bad compared to what they're paying in taxes, but you don't even know what it is, so how can that be good? It's not transparent, but not only that, whatever you think it is now it's going to turn out to be worse because in ten years somebody's going to say, 'Oh, the system's not balanced. We have to delay benefits or something to put it back into balance, and we're going to take away what you thought you were going to get.'" So Republicans say, "That's horrible. Nobody knows really exactly what it is, and they get an idea of what it might be, but it could always be taken away. Really what they want to know is, 'What's the value of my Social Security account, and I want it to be mine. I can also then tell what the redistribution is. If I know what I'm paying in taxes and I know the value of the benefits I'm getting I can see that my taxes are much more than my benefits. And if I happen to be a nice guy and think it's a good idea to have redistribution, fine. But if I'm a bad, you know, not a bad guy, if I just don't believe in that much redistribution I should be aware of it and have the chance to vote against it.'" Also, a key thing is these Republicans say, "People should get equity like returns, not this wages of the next generation, those grow slowly. Stocks might have a much higher return on average. People should get equity like return, so let's put them in the stock market." And then Republicans think choice is always great. Even if people make mistakes it's their own mistake, so let them make mistakes. So those are the opposite sides of the argument. They seem totally at odds with each other and impossible to reconcile. So I want to now tell you my plan. So everyone's got the problem straight. We're running out of money and the philosophies of the two groups seem to be totally opposed, so what should we do about it? All right, so my plan, in five minutes because I want to end with Black-Scholes, my plan in five minutes is, okay, to make a few observations. First of all, yes it's true that you get a higher return on stocks than you get on bonds, but you face a higher risk. So it's not like you get it for free. It's a bigger risk. So that's number one. So no, actually, point zero is you've still got the problem because you gave money to all those people in the '40s, and the '50s, and the '60s, and the '70s. That money is gone. We've essentially borrowed to give them money and somebody's got to pay back that debt. And so there's no way around that. There's this huge 17 trillion dollar debt hanging out there that we have to pay back and you can't get around that. So putting the money into equities, or wherever you put the money there's still that tremendous debt. Now the question is--so you can't just make the problem go away by saying that equities have a higher return. Bonds also have a higher return than the return people are getting on Social Security because the Social Security return includes the tax that you're paying to make up for the original generation. So that's the first thing. So the next thing is maybe it's not such a big difference, this equities and not equities, because notice in this model when the stock is paying higher, when the stock dividends are higher, 2 instead of 1, the price of stocks goes up. That's a great return from the stock market, but the wages were also higher here as well. So in fact I claim that in the long run, and it's amazing that the Republicans haven't noticed this, in the long run over 30 or 40 years it's obvious that the stock market and wages are correlated. I mean, if the stock market collapses that's disaster for America and you can be sure the wages are going to go down too. If our stock market's booming and America's incredibly successful it's a sure thing that in 40 years if the stock market is just booming along wages are going to be higher as well. So if you get the wages of the generation 30 years from now in the Democratic plan you're actually getting equity like returns, but you're getting an advantage which is that the wages move slowly. So although the stocks are bouncing up and down, so somebody who retires in the year 2007 if he held stock and sold it when he retired he could get a huge pension, where someone who retired in 2008 and sold the stock just when he retired he would be crushed because the stock market lost 50 percent. So that will never happen if you just pay according to wages because they're much more stable. But wages in the long run are correlated with stocks in the long run. In the short run they just don't fluctuate at much. So what is my plan? So those are just some preliminary observations and I'll give you the plan. Then as I said this is obviously controversial. I think I've identified the problem in a scientific way. That is, everyone would agree with me if they knew enough economics, but now my plan, even people who do know as much as me might disagree with me, but this is what I would--okay so here's the plan. As I said, other plans just say, "Well, things are bad. Let's just keep the same system." So there are two basic ideas. The Democratic idea is, "Let's just keep adjusting at the margin. We'll make up for it by giving people money later. We'll do all kinds of things like that. Maybe we'll raise some tax, reduce some benefits, balance the system." The Republicans want to junk the whole thing and privatize and let people, you know, force them to save, but put it in the stock market in their own account. Now, here's my plan. I don't have time to talk about Bush's plan. So here's my plan. Number one, the fact that we gave all this money away to people in the '40s, and '50s, and '60s and '70s, why should that be the responsibility of the workers today? I mean, our government decided it was a good idea. Roosevelt and Frances Perkins decided we had to rescue the old of the '40s, and our Congresses kept that up for the next 20 or 30 years even though the old weren't in such dire shape, but they kept it up. Maybe that was a good idea. It's probably a very good idea, but because we have that huge debt why should workers be the only people responsible for paying back that debt? I would start by imposing a legacy tax on everybody, not for Social Security, just for the debt we accumulated by giving it to those old generations. So I believe that would be something like 1 percent. I wrote 2 to 3 percent, but I think it's closer to 1 percent, actually, on all income. If I did it on all income it would be like 1 percent and that fund would pay off for the Social Security legacy. So then if we were starting the system afresh how should we do it? And some countries like Chile decided they're going to start afresh. So how should we start afresh having gotten rid of this old debt that was hanging over our heads? Well, what would I do? I would have what I call Progressive Personal Accounts. So I like all the Republican ideas of knowing what you've got, making it yours, and making it transparent. I think that's all an extremely good idea, but why should it be that that comes from putting your money into stocks? I mean, stocks, this is an old fashioned security and it's incredibly risky. From one year to the next it totally changes. I like the idea of indexing something to wages. So I want to create a new security that I called Personal Annuitized Average Wage Security. So what this does, this is a security that just pays proportional to the wage in the whole country at the year you retire. So whenever you earn money on Social Security--I'm running out of time so I'm going to skip over this pretty quickly. So if you earn 1 dollar and you pay, let's say, 12 percent in Social Securities taxes, that income, I'm going to say that's your income, it's your 12 percent. You're going to be forced to save it, and what you're forced to do is to buy these securities. So it's a new kind of security that pays proportional to the wage. So it might pay 1 percent of the average wage. So it would pay 12 cents here, 3 cents here, and 3 quarters of a cent there. That's the wage in the economy and it would pay 1 percent of that. And how much of it would you get to buy, as much as you could afford to buy with your security, with your tax contribution. Now, that almost replicates the current system. The only difference is that it doesn't replicate the current system, there's nothing progressive about it yet. So what I would do is I would make it a progressive tax. If you're making a hugely high income I wouldn't give you the whole 12 percent. I would take part of it. And if you're making a really low income I would have the government subsidize it a little bit. So instead of getting 12 percent of your low income you'd get a little more than 12 percent. If you had a high income your 12 percent tax the government would take 1 of those 12 away from you and you'd only have 11 percent that you got to put in your personal account. Now, but it has a tremendous advantage, this system, which is that if you can price the PAAWS, if you know what the market price of PAAWS is then you're balancing the system, because every time you hand somebody money you don't make some crazy promise that when you get to be old I'm going to pay you such and such dollars like the current system is. You're letting the guy, or the woman, let's say, who's working; she is buying her own Social Security benefits. So the benefits have an equal value to what she's paying for. So you've balanced the system. The legacy tax you got rid of by having the tax on everybody of 1 or 2 percent, and the balancing the system going forward is occurring because you're forcing people to buy their Social Security benefits. So anyway that's my, in a nutshell, my system. And the last thing is how are you going to get PAAWS priced by the market? Well, I'm going to get the market to trade them, and I think that would be a tremendous boon to the economy if we had these securities paid. Why is that? So how would I do that? I'd force everybody to invest only in PAAWS, which I claim are like stocks in the long run, but in the short run they're less risky, so it's a better investment vehicle, but they'd have to sell exactly 10 percent of their PAAWS into the market, and with that 10 percent of money they could hold stocks or whatever else they wanted to, and those 10 percent would all be pooled together and traded in the market. And the market then would have an idea of--a new instrument to price what they think future wages are going to be. So anybody giving a pension plan that's indexed to future wages would know what the market price of those things are, so it would dramatically help pension plans as well. Anyway, that's my idea for Social Security. So I have four minutes left and I want to end with one last thought, one last idea, which is Black-Scholes. Now, we've already done Black-Scholes in a few problem sets. So what is the idea of Black-Scholes? It's just like the idea of the example we gave. By the way, if you do come next week and you want to question me about my Social Security plan and criticize it I'd be thrilled to be criticized because you can't learn anything unless you're criticized and I think I can defend it too. But anyhow, this is an idea which obviously hasn't caught on yet because Social Security reform stopped. We've got worse problems to worry about, but if we get through this crisis the very next thing on Obama's agenda is going to be reforming Social Security. So I'm ready. So let me just end with Black-Scholes. So in 1972 Black and Scholes wrote a famous paper. And what did they do? They started off by saying, this model we had, you see, of the stock market which follows a geometric random walk, it can go up by a certain percentage or down by a certain percentage. We've used that with interest rates too. They can go up or down by a certain percentage. Here the stocks can go up or down by a certain percentage. We saw that you could solve models like that very easily. So Black and Scholes, Fischer Black who is a great economist, and Myron Scholes who won the Nobel Prize, but was not as mathematical as Fischer Black. Anyway, he started the hedge fund Long Term Capital. Myron Scholes was one of the people. They looked in 1972 at the returns each day on the S&P 500, and they binned them up like this. So here are the number of times the return was between .47 percent and some other number. And then they compared that to a normally distributed random variable, and look how close to normally distributed it is. It's practically like that. So this thing over here is exactly normally distributed, and this is the frequency graph of what actually happened that year, incredibly close to normally distributed. If you take the cumulative occurrence of each thing and compare it to the normal it's incredibly close to the normal. So they said, "Gosh, isn't it great, this model of things going up or down by a certain percentage every year, maybe with a drift, that's exactly the model the stock market seems to follow, and maybe interest rates follow that sort of model too," and that's why we've worked with all those models. Well, it turns out if you make those assumptions and then you try to solve for option prices you can do it very quickly through some formula, which I'm not going to have time to present. It'll only take one minute, but I'm going to skip that. So what happened then? So this was the second high point of, you know, there's the CAPM model and then the Black-Scholes model. You've done problems with Black-Scholes now in the problem set to figure out the value of a call option. So I'm just pointing out that you could put it in a spread sheet like I've done, which will be on the web. And you can do daily returns, and fix the standard deviation and stuff, and do backward induction incredibly quickly, and figure out the value of the call option, even get a closed form formula for it, and then explain why call option prices have the form that they do. So it was a great triumph and it relied on things being normally distributed. I'm down to 30 seconds. So what happened? If you do the same thing recently--so you do exactly the same thing and bin everything up like Fischer Black did, not in 1972--shit, sorry. Not in 1972 but the last five years, say, they only did one year, but you do the last five. Actually I did this a couple years ago, so from seven years ago to two years ago. If the pink thing is normally distributed and we do the same binning that Black and Scholes did, look everyday at what the return is and stick it in a bin and just do the frequency thing, what do you see? You see that there are a lot more times where in reality the move was very small, but there are a lot more times in reality where the move was very big. So this is precisely what you call a fat tail, that you get smaller moves than the normally distributed ones but also bigger moves than the normally distributed ones. So you can have some big negative moves. And so we know we've had some huge negative shocks. So I'm ending now with this thought that finance produced remarkable theories, remarkably precise predictions, and for decades at a time it seemed those were borne out in practice. But then looking back 50 years later or 30 years later on these discoveries we see that they don't do quite as well as they seem to be doing at first glance. So something's missing in the theory, and I think the subject is so exciting because it's so connected to the world. Everybody talks about finance nowadays. Anyone in the world is spending half their time thinking about finance and the theory is still up in the air because the old classics of the theory no longer hold. And so it's an exciting time to be developing a new theory and maybe you'll think about it in the future. So I'll see you, some of you, next week.
Quantitative_Finance_by_Yale_University	1_Why_Finance.txt	Prof: So anyway, the course I'm going to teach is called Financial Theory. I'm going to teach an actual class. I'm going to spend the first half of the class talking about the course and why you might be interested in it, and then I'm going to start with the course. There are not that many lectures available in the semester so I'm not going to waste this one. So the first half of the class is going to be about why to study it and the mechanics of the course, and the second half of the lecture is going to be actually the first part of the course. It'll give you maybe an idea of whether you'll find the course interesting too. So I think I'll turn this--I won't have too much PowerPoint here. So you should know that finance was not taught until ten years ago at Yale. It was regarded by the deans and the classically minded faculty of the arts and sciences as a vocational subject not worthy of being taught to Yale undergraduates. It was growing more and more famous, however, in the world and there was a band of business school professors, Fischer Black, Robert Merton, William Sharpe, Steve Ross, Myron Scholes, Merton Miller, who had a huge following in business schools teaching the subject, and whose students went off to Wall Street, and more or less dominated the investment banking parts of Wall Street, and became extremely successful. Finance became the most highly paid profession. It became the most highly paid faculty in the university, although they were all in business schools. There are more physics PhDs working in finance now than there are working in physics. So this merry band of financial theory professors didn't really believe in regulation. They believed markets left unfettered worked best of all. They believed in what they called efficient markets and the idea that asset prices reflect all the available possible information. So an implication of that is that if you want to find out whether a company's doing well or not you don't have to take the trouble to read all their financial reports, just look at their stock price. If you wanted to know whether a country's doing well or not you don't have to study its entire political system and current events, just look at the general stock market of the country and that'll tell you. They believed that you could make as good returns in the market as a lay person as you could as an expert because all the experts were competing to try and get the best possible price, and so the price itself reflected all their knowledge and wisdom and opinions and so the lay person could take advantage of that by buying stocks. Everybody should be an investor, they felt. A monkey throwing darts at a dart board would do as well as any of the greatest experts. Now, their own theory was basically contradicted by their own experience because all of them seemed to go out into the world and invest, and almost all of them made extraordinary returns and made a huge amount of money all of which made them even less popular in the faculty of arts and sciences. So, a critical part of their theory was that the markets were so efficient, driven by people like them who are competing to exploit every advantage, and therefore compete away every advantage, and by doing that put all the information they have into the prices. The implication of that theory is that there's an extraordinarily clever way of computing the value of most investment assets, and about deciding when a financial decision's a good thing to do or not, and that was the heart of what they taught in these business schools, these algorithms for valuing assets and making optimal financial decisions. One striking thing is that the people they studied, the business people and the investment bankers they studied adopted their language. So this had never happened in academia before. I mean, anthropologists study primitive tribes and different kinds of people all the time and not one of them, I venture to say, has ever taken over all the language invented by anthropologists to behave themselves in their own societies, but the business people that these professors were studying ended up using exactly the language created in academia. Now, Yale was very different. There was no divide between economists and finance people, the business school finance people. At Yale the greatest economists in Yale's history were actually very interested in finance. Maybe they were financial economists to begin with. So the greatest Yale economist of the first half of the twentieth century was Irving Fisher who you hear a lot about. He wrote, possibly, the first economics PhD at Yale. There was no economist to teach him so he had to write his PhD with Gibbs, maybe the greatest American physicist of the time. There's a building, as you know, on Science Hill named after Gibbs, and you'll hear more about his dissertation in the 1890s, but he was a mathematical economist, an econometrician but he invented almost all of this economics in order to study finance. The most famous Yale economist of the second half of the twentieth century was James Tobin, a famous macroeconomist, the most famous macroeconomist, possibly, of the second half of the twentieth century after Keynes, a great Keynesian. But he got the Nobel Prize for work he did on finance in economics. Finance was incredibly interesting to him. So Bob Shiller and I went to Yale and we basically said to the deans, "There's a long tradition of finance and economics hand-in-hand at Yale, and so it's not a vocational subject. It's actually central to economics, and central to understanding the economy, and central to understanding the global economy. So we'd like to teach it to Yale undergraduates, and we believe a few of them will actually take the course," and so they agreed to let us do it, and so we've been teaching it now for the last ten years. So as you know Shiller has been very critical of the business efficient markets tradition. He feels that these finance professors left something essential out of the whole story. What they left out was psychology. They left out the idea of fads, and rumors, and narratives, which he thinks has as big an effect on prices as the hard information about profits that the business school professors imagined drove profits. I myself have been quite critical of the financial theory. I started off as a straight pure mathematical economist. To me economics was almost a branch of logic and philosophy that happened to tell you something about the world. So I got my PhD with Ken Arrow, who you'll hear a lot about very shortly. And I came to Yale, I'd been a Yale undergraduate, I came back to Yale and I joined the Cowles Foundation. And the Cowles Foundation's motto was basically, "Can we make economics more mathematical? Economics, a social science, ought to be amenable to mathematical analysis just like physics or chemistry is," and people didn't believe this at first. And the Cowles Foundation, which you'll hear a lot about in these lectures, led the revolution in economics transforming it from a verbal subject, political economy, into a mathematical subject. Well, I decided around 1989 that since I did mathematical economics, and there were all these finance people doing all kinds of mathematical things on Wall Street and doing it very successfully, I thought I might just check out what they were doing. So it might be fun to see what they were up to. So I went to Wall Street and I joined--most people I knew, in fact, professors I knew went to Goldman Sachs. There was a famous finance professor, who I had mentioned before, named Fischer Black who was there at the time and he attracted a lot of people. And so that was the traditional thing to do, but I decided to go to a littler firm called Kidder Peabody, and it was the seventh biggest investment bank at the time. And one thing led to another, and they decided that they wanted to reorganize their research department in fixed income. And since I was a professor there, and I did mathematical economics, and I was there for the whole year somebody said, the director of the Fixed Income Department said, "Why don't you take charge of it and hire a new Fixed Income Research Department for me. So I did, and ultimately there were seventy-five people in the department. All the time I was a professor at Yale. And after five years Kidder Peabody, even though it was a hundred thirty-five years old, formed by a famous family, the name should sound-- Peabody--familiar to you, it closed down after a hundred thirty-five years, five years after I got there. I had to invite the seventy-five people I'd hired into my office and say, "You're fired." And then I went next door to the office next to mine and the guy there said, "You're fired." And so that was my first taste of Wall Street. And after that six of us founded a hedge fund called Ellington Capital Management, which was a mortgage hedge fund, and we had-- I'll tell you a lot about it. It started after the Kidder closing as a rather small hedge fund, but it grew into a very big mortgage hedge fund, in fact the biggest mortgage hedge fund in the country. (Although recently we found out that practically everybody who trades mortgages is basically a hedge fund. Fannie Mae, Freddie Mac, they'll all basically hedge funds, so it doesn't mean anything anymore to say that you're a big mortgage hedge fund.) But anyway, we almost went out of business in '98 a subject, a story I'll tell you at great length, and then we just suffered through this disastrous last year or two, but we're still here. So these experiences, of course, have colored my understanding of Wall Street and my approach to the subject. So I took on, in my theoretical work, finance and economic theory on its own terms. I didn't think like Shiller to introduce psychology into economics I just take it on in its own terms, in its own mathematical terms. And what I found was that there are two things missing in the Standard Theory. One is that it implicitly assumes you can buy insurance for everything. It's the assumption that's called complete markets. And secondly it leaves out collateral entirely so you'll never see, almost in any single economics textbook, the idea of collateral or leverage. And those, I think, the idea that you can't get insurance for everything and that you need collateral, you know, you have to be able to convince someone you're going to pay them back if you borrow money and collateral is the most convincing way of persuading him he's going to be paid back, the lender. Those two things were missing from the Standard Theory, so I built a theory around incomplete markets and leverage, which is a critique of the Standard Theory. So in a way Shiller and I have been vindicated by the crash. I mean, so let me just show you a picture here. Well, maybe I will, you know, how bad the crash was. So let's look at the Dow Jones. The Dow Jones is an average of thirty stocks and what their value is. We'll talk more about it later. But here it is back to 1913 moving along breezily going up and up and up, you know, there are a few blips which we'll come to later like this one in 1929, and then--but look what happened lately. Look at that. The Dow Jones was up at 14,000 and it dropped to 6,500, something like that, more than a fifty percent drop and now it's gone fifty percent up again. So if you believe these finance professors you'd have to say that everybody realized that future profits in America were going to be less than half what they thought they were going to be before and that's why the stock market dropped. And then miraculously when it hit a bottom everybody figured, "Oh, my gosh, we misunderstood things. Actually it's not nearly that bad and things are fifty percent higher because now people think that profits really weren't going to go, you know, didn't drop in half, didn't drop by fifty percent, they only dropped by twenty-five percent. And that was the only way, according to the old theory, to explain what happened. Now Shiller would just say, "Well, everybody's--they're crazy. They got this into their head that the world was just going to be great and then some rumor started, and things were so high, and the narrative changed and they thought things were terrible," and this his story. And I'm not sure how he gets it to go up again. They changed their mind again. By the way it's a little bit better to look at the Dow correcting for inflation and then you see that the 1929 crash looks-- and this is on a log scale, remember before the Depression the stock market was so low. It's grown so much over a hundred years that it hardly seemed like anything was happening. Well, now in log scale--going up two of these is multiplying by ten-- you see that in the Depression in 1929 through the early '30s the stock market fell. I don't remember what it is. It looks like it's almost two things. It looks like it's eighty or ninety percent, and the fall this time has been much smaller, fifty percent, not ninety percent. So it's a whole thing down but not two things down. It's not a whole thing down. It's less than that. A whole thing down would be the square root of ten or a third. It didn't go down two thirds. It went down less than two thirds. It went down fifty percent, so the actual percentage drop was much worse in the Depression than it is now. We're going to come back to all these things. What else can we get out of these numbers? I just want you to notice a couple other things. So these numbers are all very interesting. If you're mathematical these are the sorts of things you pay attention to. So these efficient markets guys, they looked at the change in price every month. So there's a lot to say for their theory. They said, "Look, it goes up and down randomly." In fact we'll see that there are all kinds of tests about whether you can predict it's going to go up tomorrow on the basis of how it did yesterday, and the answer's no. It's very difficult to predict whether the stock market is going up or down. It seems to be random. Well, it's random and they used to think it was normally distributed. A lot of people argued it was normally distributed, but it's hard. You never get these gigantic outliers if things are normally distributed. They're just way too unlikely to happen. So Mandelbrot, who was a Yale professor who retired a couple years ago, although he wasn't when he formed his theories, the inventor of fractals, he said this couldn't possibly be a random walk in the traditional Brownian motion sense of the word because you'd never get these big outliers, but he offered no explanation for why they might be there, and I don't know if Shiller has an explanation either. I mean, is it that people suddenly get shocked one day and then the next week they change their mind and things aren't so bad after all? But you'll see that the theory of collateral and margins does explain these kinds of things. Let's just look at the Dow. We just looked at the Dow. Let's look at another, the S&P 500. Where's the S&P 500? Here's the S&P 500 data. Here's the history of the S&P 500. It looks very similar to the Dow, except we have longer history back to 1871, so I just want to point out one more thing in the S&P 500. So this is an average of five-hundred stocks, not just thirty, but it's more or less the same. But let's look at the same thing taking the logarithm and check for inflation. So you see here that there are these four cycles. Things seemed low in 1871. They go up and they go down. Then you've got another up and a down. Then you've got another up and a down. Then you've another up and a down. Four times the same thing has happened. Now this could be just meaningless accidents, but it will turn out that the demography of the country, the baby boom cycle, we haven't had just one baby boom we've had four of them, so this cycle of stock prices, which they're each time a generation long, happens to correspond exactly to the rise, the different age distribution in the population. So another theory of the stock market, which wouldn't have been entertained by these original financial theorists, is that demography has something to do with the stock market, not information about profits and returns but the distribution of ages in the population. So I'm not saying this theory is correct, although I was one of the proponents of it, but it shows that there's room, I think, in finance for economic things, for demography to matter, for leverage to matter and not just for expectations about future profits. So let me show you another picture. So this is a second way in which Shiller became famous. He said, "Well, look at housing prices," the Case Shiller Housing Index. So he's also famous because he had the idea of collecting housing prices. So it's quite amazing, every town has to record, by law you have to record in the town directory, and they're often on the internet, what the price is of every sale of every house. So everybody has it and it's all publicly available on the internet, or most of it is publicly available on the internet. And nobody thought to gather all this information together and take the average and write down an index until Shiller did it. So here's the Shiller Index. All right, so you can see that housing prices were pretty stable throughout the '80s and then in and around 2000 they started taking off, so this is when the stock market was taking off too. So Shiller says this is irrational exuberance. People just went crazy. They somehow think things can never go down, and they're just going to keep going up, and they keep buying because they think things are going to go up, and it's crazy. Psychology--eventually a new narrative is going to start. Somebody's going to say, "Oh, they've been going up so long they can't continue to go up. Things have to go down," and things went down. I think there's something to psychology so there was something missing in the original finance story. The finance guys, by the way, they would say, "Well, the rise is not so surprising. Look at the mortgage rates. (This is the interest rate you have to pay if you get a mortgage.) There's been an incredible decline in mortgage rates over the years, so it's less costly to buy housing. If you take the present value of your expenditures you just have to pay less. You pay over a long period of time, and so the interest rate is less, so the value of the houses is worth more because you're discounting the future benefits at a lower rate. (You'll hear all about discounting later.) So there's no mystery." On the other hand nothing happened to interest rates. They kept getting lower so there's no reason why the market should have crashed. So, again, this seems like a vindication for Shiller. Now, it also, in a way, is a vindication for my theory which is non-psychological. So I'm distrustful a little bit of psychology because it can be anything, although I agree it's important. So my theory is when you take a loan you have to negotiate two things, the interest rate and how much collateral you put up. Who's going to trust you to pay back? When you buy a house they say, "You can't just borrow the whole value of the house." They say, "Well, make a down payment of twenty percent. Borrow eighty percent of the value of a house." And so what I say is that instead of paying all your attention to the interest rate think about the collateral rate. Why is it twenty percent that you have to put down? Maybe it should be ten percent or forty percent. Well, in fact, that number changes all the time. So here what I've done is--the pink line from 2000 to the future, that pink line is Shiller's Housing Index inverted. So you notice the scale on the right is the housing prices, but I've inverted it, and on the left I have the down payment percentage. These are non-agency loans. We'll come back to the graph later-- I don't have time to explain exactly how I got it-- but what you see is that from 2000 onwards the down payment people were asked to make to buy their house got lower, and lower, and lower, and lower and it got down to three percent. You could put down three percent of the value of the house and borrow the other ninety-seven percent of the value of the house to buy it. So amazingly the prices go up and down just with what's called the leverage. So why is it called leverage? Because the cash you put down payment, say ten percent, you can lever it up and own an asset that's worth a hundred even though you put down ten dollars. So you're leveraged 10:1. If you put down three dollars and you get a hundred dollar house you've leveraged it 30:1 or 33:1. So that's why it's called leverage. So anyway, the point is that leverage went way up. The margins kept going down and down and down and just at the peak of the housing cycle, which is the bottom of that curve, that's when collateral started getting tougher and people started asking for more money down again, and sure enough the prices turned around. So if you look at the prices of mortgages, again, the inverse on the right, and you look at the margins on the left, not for buying houses but for buying securities-- I don't have time to explain this whole graph, but the blue line is the buying securities. So '98 is a big crisis, the margins spike up, I don't have pricing data back until then. That's the blue line. And now from 2007 to 2009 you see the margins spiking up. So to buy a toxic mortgage security investors don't pay cash, they borrow part of the money to buy it. They used to put down only five percent to buy it. Now they have to put down seventy percent to buy it on average. Well, what happened to prices? Prices--this is the inverse of prices--in 2007 they started to collapse. So this going up means prices are collapsing. So once again, the margins--tougher margins means lower prices and as the margins came down recently the prices have gone up recently. So it's an alternative theory. So what else do I want to show you? So it doesn't mean that the standard financial theory is wrong. After all, I helped run a hedge fund. Six of us founded it and we've been in business for fifteen years. We must believe in standard financial theory because that's how we've been making a lot of our money. We exploit all those algorithms and those are the things I'm going to teach you, so I certainly believe it and it's very important to teach you that again this semester, but there's more to the theory than just that. I want to show you one more thing in the Dow Jones or the S&P which I forgot to mention. And where is this? Oh, I can't get it out of that. Let's try Dow. Okay, so Dow. Where was the peak of the Dow? It was right over here. Now what was the date? The date's supposed to flash here. So it's October 1st 2007. So that's when people started to realize something was wrong with the world and things headed down. Until then nothing bad seemed to be happening in the world, but suppose that you look not at the Dow, suppose you looked--sorry. Here's a graph, suppose you looked at the sub-prime mortgage index. So you see it's a hundred. You'll understand what these things are. So a hundred means nobody thinks there's going to be a default. Over here January 2007, that's ten months before the stock market starts to go down--before it hits its peak. The stock market is still going up here. A month later, this is April 2007, a month later the sub-prime index starts to collapse. You see it goes from a hundred to sixty. We're already--In February or March 2007. So that means the people, those experts trading mortgages, already realized there was a calamity about to happen. This was long before anyone else perceived anything happening, long before the stock market moved, long before the government did anything to correct the problem. So just as financial theory says if you pay attention to the prices you can learn a lot about the world. The people trading those things--their life depends on fixing the right prices. Probably they know stuff that you don't know. The prices are going to reflect their opinion. If the price collapsed part of the reason it collapsed, maybe margins and something had something to do with it, but part of the reason it collapsed was because they knew something bad was happening. So for two and half years we've known there's going to be a major catastrophe in the mortgage market. To go from a hundred to sixty and since to twenty is a total calamity. So you know that there are one point seven million people who have already been thrown out of their houses. Another three and a half million aren't paying their debts and are seriously delinquent. Probably all of them will be thrown out of their houses, and another four or five million after them might default and have to be thrown out of their houses. So it's a major catastrophe and the market told us and warned us about it two and a half years ago and nobody's done anything about it, basically, until now as we'll find out. So it's not that I think financial theory, the standard financial theory is wrong I think it's incredibly useful. I just think it has to be supplemented by a more general and richer theory. Maybe I should show you how my hedge fund has done just so that you don't think that it was a total failure. Oh dear, where is my returns? Here we go, EMG returns, it's sort of interesting. So Kidder Peabody went out of business in 1994. There was a tremendous crash in the market, a low of the leverage cycle. The purple is Ellington, that's the hedge fund. You'll see that these are other investment opportunities. The S&P 500 is the green thing which looked like it was doing great for a while. Emerging markets is the blue one, and high yield is the green one, and then there are bunch of other things like treasuries, and this is Libor which is what banks lend to each other at. So this says if you put your money into any of those strategies, in Libor, keep lending your money each month to a bank and seeing what interest you get and seeing how much money you accumulate, or putting your money in Ellington and looking at the purple, or putting your dollar into the stock market and see what happens, the S&P 500, this is what happens. So you see there was a crash here. You're fired, you're fired. So we start Ellington and Ellington does great, and so we have all these years we're doing great. Then '98 there's another crash. Look what happened. Overnight, practically, we lost a huge amount of money. We almost went out of business. Long Term Capital, which, by the way, was run partly by two Nobel Prize winners, Merton Miller, not Merton Miller, Myron Scholes and Robert Merton, two of the guys I mentioned who were the leaders of the financial crisis [correction: leading finance academics], they bankrupted their company and they went out of business. And why did they go out of business? Because they weren't aware of the leverage cycle, in my view. Anyway, so the prices collapsed. Then look it, all these returns shoot up again and the world seems to be doing great, the stock market, everybody's doing great. Then there's another crisis in 2007. Everything plummets all together this time and then everything is going up again. So it's hard to see this and to live through that. So I remember in '98, for example, when there was a margin call. Our lenders called and said, "We want more money. We don't believe that the assets are worth as much as they were and so the collateral is not covering the loan anymore." And we said, "You can't make a margin call. It's not legal. You promised not to change the margins on us for six months. You can't make a margin call." And they said, "Well, blah, blah, blah, we don't really know about that. We're making a margin call." So we called up Warren Buffett and we said, "This is terrible. They're making a margin call. They can't do this. We have great bonds. There's nothing wrong with the bonds. They're going to force us to sell all the bonds to pay them the money, and how can they force us to do that? They shouldn't force us to do that. We've got great bonds, it's a great business, it's a great company and they're going to run us out of business. You can't let this happen. Warren Buffett why don't you buy part of the company and save us and you'll get rich and it'll be great." He said, "Say that again." And we said, "Well, they're going to force us to sell all the bonds on Tuesday to meet their margin call and we'll get terrible prices for the bonds and we'll be driven out of business, even though they're great bonds, just because they're making a margin call. You can't let this happen to us. Buy part of the business and save us and you'll get rich. You'll own part of a great company." And he said, "Hell, it sounds like I should just show up on Tuesday and buy the bonds." So we survived. I'll tell you more about what we did. We survived that, no thanks to Warren Buffett, although he had a pretty good idea, and then we survived the last crash. So we survived all these crashes, but the fact is things go up, they crash, they go up, they crash, they go up. Could it all be my fault? I decided it can't be all my fault. It's got to be there's something more basic at work and that's why I'm going to tell you about the leverage cycle. Now, of course, I realize that my pet theories may not turn out to be right, although I think more and more people are starting to think there's something to it. So I'm not going to spend a huge portion of the course just talking about my pet theories. I mean, I recognize that I have to teach partly what's standard. So the course is going to be divided in the following way. I'm going to talk about the standard no-arbitrage Financial Theory, and I'm going to talk about it theoretically and mathematically and from a practical point of view, because helping to run the hedge fund-- lots of the things that I'll be teaching are things that we actually confronted in the hedge fund. And so you'll get the standard financial theory course taught from a hedge fund perspective both theoretically and from a practical point of view. On the other hand, I've lived now through three mortgage crises and so it seems silly for me not to describe how the mortgage market works, even through you'll find almost none of that in any standard finance textbooks, how the mortgage market works, and what's going on, and what happened in the crises, and how we survived and how other people didn't. And I'll talk about the leverage cycle. I'll also spend some time--I think it's quite important--on the mathematical logic of the invisible hand argument. That's the most important argument in economics that the free market does good for the economy and a huge number of people believe it. And part of that argument and part of the sort of hazy knowledge of that argument is what drives resistance to a lot of government programs. I mean, the government can only screw things up is what people generally believe. Is it a prejudice or is there some actual argument behind that?. Well, I want to go over that argument and show you precisely how it works and how it doesn't work in the financial sphere. And then, I want to talk about Social Security. That's one more program. That's the biggest program in the budget. It's as big as defense and the two of those are much bigger than everything else, vastly bigger than every other thing in the budget. So I want to talk about Social Security and should it be privatized and should it be reformed and why did it go bankrupt. It's also an interesting mathematical problem because Social Security critically involves the belief that things will go on forever, so there's an infinity in it. Each generation the young are paying for the old. Nobody would do that if they thought they were going to be the last generation paying to the old, and when they got old nobody would help them. So Social Security rests on this world going on forever which makes it mathematically interesting. Anyway, so I got interested in it from a theoretical point of view and then I got put on all these National Academy panels on Social Security and privatizing. And so I know quite a bit about it so I might as well talk about something I know about, so that's why I'm going to talk about that. All right, so this is too hard for you to read so let's do this. So let me just give you a few examples. Uh-oh, I hope I didn't do a terrible thing. No. So let me just give you a few examples here of the kinds, just so you realize there's something to the Standard Theory. There's a lot to it. So I'm going to give you ten examples very quickly, of the Standard Theory. So these are things that I'm guessing you'll have, at least some of them, trouble figuring out how to answer now, but by the end of the course this should be totally obvious to you. So suppose you win the lottery, forty million dollars, it's a hundred million dollars, the lottery. Now they always give you the choice. Do you want to take five million a year over twenty years or just get forty million dollars right now? Which would you do and how do you think about what to do? So now you get tenure at Yale at the age of 50, say. You're making a hundred fifty thousand dollars a year and you think professors-- it's going to go up with the rate of inflation, and that's about it for the next twenty years until you retire. So that's twenty years of that and then you're going to live another twenty years when you're going to be making nothing. So how much of the hundred-fifty-thousand, and let's say inflation is three percent, and what you'd like to do is consume inflation corrected the same amount every year after you retire and before you retire, and so how much of the hundred-fifty-thousand should you spend this year and how much should you save? You'll learn very quickly how to do a problem like that. Now, President Levin wrote a few months ago, the end of last year if you remember, he said that, "Well, the crisis was bad. Yale was going to weather it, but Yale had lost twenty-five percent, probably, of its endowment. That's five-billion dollars almost of the twenty-three-billion dollar endowment. So how much should he choose to cut? It's his decision. How much should Yale reduce spending every year? The total spending at Yale is a little over two-billion. So the endowment goes down by five-billion what cuts should you take to the budget. Should faculty salaries be cut, be frozen, should you get three TAs instead of four TAs? What should you do? How big a cut should you take? Now, the same question faced Yale in 1996 or so. I've forgotten exactly the year. Ten or twelve years ago the previous president, Benno Schmidt, he suddenly noticed that there was deferred maintenance, as he called it, a billion dollars to fix the Yale buildings. That's why, incidentally, every year another college gets fixed. They decided there was deferred maintenance of a billion dollars. A hundred million dollars every year for ten years had to be spent. The whole endowment then was three billion, and now we had a one billion dollar deferred maintenance problem. The budget was about one billion then. So how much should you cut the Yale budget at that time? So Benno Schmidt said, "I'm firing fifteen percent of the faculty." He announced he was firing fifteen percent of the faculty. That was on the front page of the New York Times, "Yale to fire faculty." Well, did he make the right decision? Rick Levin took over as president three months later, so probably not. What mistake did he make in his calculations? What should he have done? What was the right response? We're going to talk about it. It's not that hard a problem. Now, let's take a slightly more complicated one. You're a bookie. The World Series is coming up. The Yankees are playing the Dodgers, let's say, and you know that the teams are evenly matched and you've got a bunch of friends who you know every game will be willing to bet at even odds on either side because they think it's a tossup. Well, one of your customers comes to you and says, he's a Yankee fan, he's sure the Yankees are going to win the series. He's willing to put up three hundred thousand dollars to bet on the Yankees. So if the Yankees win he gets two hundred thousand, but if the Yankees lose he loses three hundred thousand. So 3:2 odds he's willing to bet on the Yankees winning the series. Well, you say, "This guy's sort of a sucker here. I can take big advantage of him. On the other hand it's a lot of money, two hundred thousand I might lose if I have to pay off and the Yankees win. So even though I think that my expected profit is positive, because he's putting up three hundred thousand to make only two hundred when they're even odds, in fact--the fact is it's such a big number I'm a little worried about that." So what do you do? So what can you do? You've got these friends who are willing to bet at even odds each game by game, so how much money--Presumably the first night you're going to bet with one of your friends. You take the guy's bet, the customer, you take his three hundred thousand. You promise to deliver him five hundred back if the Yankees win and to keep it if the Yankees lose. What should you do with your friends? Should you bet on the Yankees with your friends? Should you bet on the Dodgers with your friends and how much should you bet at even odds the first night? So the answer is, well, I don't want to give all the answer now, but so there's a way of skillfully betting with your friends and not betting two hundred or three hundred thousand the first night with your friends at even odds. You bet some different number than that, which you'll figure out how much to bet so that if you keep betting through the course of the World Series you can never lose a penny. How do you know how much that is? Well, that's the kind of clever thing that these finance guys developed and you're going to know how to do. So let's do another example like that. I'm running out of time a little bit, but an example. Suppose there's a deck of cards, twenty-six red and twenty-six black cards. Somebody offers to play a game with you. They say, "If you want to pick a card and it's black I'll give you a dollar. If it's red you give me a dollar." So if I'm picking, I'm in the black, I get a dollar, it's in the red I lose a dollar, I have to throw away the card after I pick it. The guy says, "By the way, you can quit whenever you want." So should you pick the first card? It looks like an even chance of winning or losing. Let's say you pick the first card, it's black, you win a dollar. Now the guy says, "Do you want to do it again?" You picked a black one so there's twenty-six red left and twenty-five black. So now the deck is stacked against you. Should you pick another card? Well, it doesn't sound like you should pick another card. But you should pick another card and I can even tell you how many cards to pick. Even if you keep getting blacks you should keep picking and picking. So how could that be? It sounds kind of shocking. Well, it's going to turn out to be very simple for you to solve half way through the course. So, a more basic question. There are thirty year mortgages now you can get for five and three-quarter percent interest. There are fifteen-year mortgages you can get for less, like five point three percent interest. One's lower than the other. Should you take the fifteen-year mortgage or the thirty year mortgage? How do you even think about that? Why do they offer one at a lower price than the other? One more example, suppose you're a bank and you hold a bunch of mortgages. That means the people in the houses, you've lent them the money, they're promising to pay you back. And you value all those mortgages at a hundred million dollars. The interest rates go down. The government lowers the interest rates. Half of them take advantage to refinance. They pay you back what they owe and they refinance into a new mortgage. So now you've only got half the people left. Let's say all the people had the same size mortgage and everything. Half the people are left. That shrunken pool, half as big as the original pool, is that worth fifty-million, half of what it was before, or more than fifty-million, or less than fifty-million? How would you decide that? Again, this is a question which might be a little puzzling now, but actually you should be able to get the sign of that today even, and we'll start to analyze it. So that's what mortgage traders have to do. They see interest rates went down. A bunch of people acted. The people who are left in the pool are different from the people who started in the pool. Now we've got to revalue everything and rethink it all, so how should we do that? Let's say you run a hedge fund and some investor comes to you and says, "Oh, things are terrible. Look at all the money you lost for me last year. I know you're doing great this year and you've made it all back that you lost last year, but I don't want to run that risk. So I want to give you my money, a billion dollars, I want to get these superior returns you seem to earn, but you have to guarantee that you don't lose me a penny. I don't want to run any risk. I want a principal guarantee (it's called) that when I give you a hundred dollars you'll always return my hundred dollars, and hopefully much more, but never less than a hundred dollars." So is there any way to do that? You know that you've got a great strategy, but of course it's risky. You could lose money. You've lost money a bunch of times before. So how can you guarantee the guy that he'll get all his money back and still have room to run your strategy? Well, it sounds like you can't do it, but of course a lot of people want to invest that way, so there must be a way to do. So you'll figure out--we'll learn how to do that. So, three more short ones. A scientist discovers a potential cure for AIDS. If it works he's going to make a fortune. He started a company. He's a Yale scientist, he's--medical school, started this startup company. Yale, of course, is going to take all his profits, but anyway it's his startup company and if his thing really works he's going to make a fortune. If it doesn't work it's going to be totally zero. You calculate, and let's say you believe your calculation, that the expected profits that he'll make if it works, the probability of it working times the profit, that expected profit is equal to the profits of all of General Electric. Should his company be worth more than General Electric, the same as General Electric, or less than General Electric since it's got the same expected profits? Well, I can tell you the answer to this one because I think most of you would think, first you'd think, "Well, maybe the same." Then you'd say, "Well, this AIDS thing it's so risky. It's either going to be way up here or nothing, and that's so risky, and General Electric is so solid, probably General Electric is worth more." But the answer is the AIDS Company is worth more. So how could that be? So another question, suppose you believed in this efficient market stuff and you rank all the stocks at the end of this year from top to bottom of which stock had the highest return over the year. It's 2010, let's say 2010, this year's a weird year. So let's say you do it in 2010. All the stocks the highest return to the lowest return. Now, suppose you did the same thing in 2011 with the same stocks? Would you expect to get the same order, or the reverse order, or random order? Now again, if you believe in efficient markets and the market's really functioning, the prices are fair and all, I'll bet most of you will say, you won't know, but you might say it should be random the next time, because firms only did better or worse by luck, but that's not right either. So you're going to know how to answer that question by the end of the class. One last one, the Yale endowment over the last fifteen years has gotten something like a fifteen percent annualized return. A hedge fund, that I won't name, has gotten eleven percent over the last fifteen years counting all its losses and stuff like that. So is it obvious that the Yale endowment has done better than the hedge fund? Would you say that the Yale manager is better than the hedge fund manager? Its return was fifteen percent. The hedge fund only got eleven percent. So I'm asking the question, and I would say that David Swensen would think about it the same way I think about it. So suppose I even told you that the Yale hedge fund had lower volatility-- the Yale hedge fund?--the Yale endowment had lower volatility than the hedge fund, which it surely does, would that convince you now that the Yale endowment had been managed better than the hedge fund? Well, we're going to answer this question again, and you're going to see that the answer's a little surprising. It won't be so surprising--I wouldn't have brought it up otherwise. But anyway, that's the kind of thing that in finance you're taught to think about. So the crisis of 2007, which we're going to spend a long time talking about, I just want to get back to that subject. So that list of questions were the kinds of things that I used to teach for years before I was confident about my theory of crises, and this is the kind of questions you have to face all the time in hedge funds, and decisions you have to make, and things you have to tell investors, and so that's the basic part of the course, but I want to say more. So I want to talk about the crisis of 2007-2009. It started as a mortgage crisis. Now, how could it be that everything goes wrong in mortgages? I mean, they're four thousand years old. The Babylonians invented mortgages. What is a mortgage? You lend somebody money. They put up collateral. They don't pay you take the house or you take the guys life, he's a slave or something, but it's the same thing. You borrow money and the guy promises you can confiscate something if he doesn't pay. Four thousand years and we screwed it up. How could that be? And why should a screw up in the mortgage market have such a big effect on the rest of the economy? Were sub-prime mortgages a terrible idea? Was there some logic to it? And how did we get out of the crisis? How is it, that everybody was saying this is the worst crisis since the Depression, may be another Depression and things seem to have turned around. What is it that we did to get things to turn around? I don't think we're out of it yet, but things are a lot better than they were a year ago. So what is it that the government did to turn things around? It didn't do nearly enough, I think, but it did something. What exactly did it do? Now, Shiller would talk about the whole thing was irrational exuberance. I'm going to say it's all the leverage cycle, but anyway so that's the mortgage crisis. Now, are free markets good? I want to talk about the argument. The argument was first made by Adam Smith about the invisible hand. The modern mathematical argument is Ken Arrow's, my thesis advisor. And of course everybody knows that monopoly and pollution and things like that interfere with the free market and they have to be regulated. But the financial markets, there's no monopoly. As long as there's no monopoly and there's no pollution shouldn't the free market function there? So I want to go over that argument and show you what was missing in it, as I said before, and then lastly we're going to talk about Social Security and how could that system be going bankrupt. I mean, it just seems shocking. There's a two-trillion dollar trust fund that's going to run out in 2024 or something and after that the system will be broke. So how did it happen? Why is it broke? What can we do to fix it? So George Bush said, "Well, it's terrible. Even if we manage to sort of get the trust fund rehabilitated young people like you are going to get a two percent rate of return. If you put your money in the stock market, even allowing for the last crash, over the long haul, the returns have been six percent. So it's terrible, Social Security. Something's wrong with the system. We should privatize it and let young people like you put your money in stocks instead." Well, Gore, in the debate in 2000 said, "You can't do that because then the old people who are expecting their money can't get paid." And both of them agreed that it was all the baby-boomers' fault. People like me we're getting old, we're going to retire. That's why the system's going to get broke. So that's the conventional wisdom. All three of those things are wrong, so we're going to find out why. So in summary, why study finance? It's to understand the financial system, which is really part of the economic system. It's to make informed choices. Is privatizing Social Security a good or bad thing? Is regulation of financial markets a good thing? The language that you learn is the language that's spoken on Wall Street, and was created by professors and yet practitioners use it. For me it's incredibly fun, all these little puzzles. As J.P. Morgan said, "Money's just a way of keeping score." You have to figure out what something's worth in the end and if you get it right you've solved the puzzle right and it'll help you make good financial decisions in a pensioned career. That's the standard reason to take Finance. Now, the prerequisites of the course, so I want to make this clear, you don't really need ECON 115. It would be helpful because this logic of the free market being good or bad, that was already started in ECON 115. That's what they call it now, right? It's still called 115. I used to teach it but I haven't done it for years. So anyway, what you really need is mathematical self-confidence. It's not going to be high math. It's going to be simple math, but it's relentless over and over again. And I can tell you that every year there's the five percent of you, let's five or ten out of the hundred-twenty are going to just get bored doing problem after problem and you're probably not that, you know, those ten maybe haven't that much experience doing it, don't feel very confident doing it, stop coming to the class and then really have no idea what's going on. My sister is probably much smarter than I am, but she doesn't like math. She wouldn't take this course. So if you're not confident doing little mathematical problems just don't take the course. You'll save yourself a lot of trouble. I don't know how to say this any better. I want to warn you not to do it. It's easy math, but it never stops. Every week there's going to be a problem set. The exam--there are problem sets. The exam is doing problems just like the problem sets, but if you don't like that, you know, to me finance is a quantitative subject. What's so beautiful about it in one aspect I really like is that you have these complicated different things you have to weigh, but at the end you have to come up with one number. What is the price you're willing to pay for something? It's very concrete. I'm going to take advantage of the concreteness by turning every question into a number. I hate it when you get on the one hand and on the other hand. It's a number. So if you don't like numbers it's not a good course to take. So what are the kinds of things you have to know? You have to understand the distributive law of arithmetic (which, I have little kids and I see that's not so easy to understand). Anyway, and then you have to understand the idea of a function which is a contingent plan. Simultaneous equations; that's what we do for equilibrium in arbitrage. Taking a derivative, that's marginal utility. The idea of diminishing marginal utility, a concave function looks like that. That's risk aversion. Bankers invented the logarithm, compound interest, so you have to know what taking a logarithm and exponential means, and you have to understand how to take probability weighted averages of things. And we're going to use Excel for a lot of the problems which we'll teach you. By the end of a day you'll be better at it than I am. So my office hours are four to six. My secretary assistant is Rendé, there's an accent missing as she always tells me, Wilson. She just started three days ago but I'm sure she'll be great. There are going to be two lectures a week and a TA section. So every Tuesday there'll be a problem set starting this Tuesday due the next Tuesday. There will be two midterms. There's a lot of stuff to learn and so I found, everybody I think agrees who's taken the course, if you take the midterm it'll focus your mind and make it a lot easier, so I give two of them so you only have half the course to study. It makes the final much easier to study for. I recognize that some of you will have problems on one of them, like especially the first mid-term, and if you do vastly worse on one exam than the rest I'll tend to ignore that, but most people don't, by the way, do vastly worse on one exam than the rest. So the final's forty, the problem set's twenty, and the two midterms are twenty percent. Tuesday to Thursday, and so all the TA sessions are Thursday to Monday so they're going to start next Thursday. So you see the classes are Tuesday-Thursday then the next Tuesday. There's a long time in-between here so all the TA sessions will meet there. So they're at the same moment in the class. There are all these textbooks, all by the Nobel Prize winners, all by those financial greats. You can buy any one of them, but I have my own lecture notes because as I say I teach a slightly unconventional course and there's a huge list of books on the crisis. Some of them are incredibly interesting and fun, and so they're all on the reading list you can take a look at. I mean, there's never been a more fun time to read this stuff now. So course improvements, anyway. So that's it. Are there any questions about how the course runs, or how I will run it, or whether you think you should take the course, or whether your preparations--So if you haven't taken ECON 15 it's okay, 115, but you've got to be confident that you can solve problems, otherwise don't do it. Any questions? Yes? Student: So the first problem set will be assigned next Tuesday? Prof: Yeah, so next Tuesday it's going to be due the Tuesday after. So I know that's early, but you probably already know whether you're going to take the course or not. Yes? Student: Will you teach this next year? Prof: Will I teach it next year? Actually I probably won't because I'm going to go on leave, but I might, but probably not. Someone else will teach it. Yep? Student: Which of the books do you suggest we buy? Prof: They're all good. They're all famous people who've written. They're trying to sell copies so they're pitched at a quite low level, but they're very good. Anyone of them is good. Merton's book is good. Steve Ross is a friend of mine. He used to teach at Yale, so his book is good. So any one of those is very good, but they're not quite at the same mathematical level because they're trying to sell thousands of books, and they stick pretty closely to this financial view of the world that everything is efficient. Yes? Student: Will the taped lectures be available online? Prof: That's a good question. I don't think so. No, they're shaking their head. So it won't be in time for you, but it will be if you want to look back in your old age, "I was there. I saw the leverage cycle." Sorry. Yes? Student: Are the lecture slides posted before or after the lecture? Prof: Oh, the lecture notes are all posted already before the class. So the first twelve of them are there, and I'm changing them each year so there'll be some changes. So last year's first twelve are there and they might change a little bit, but you can already get an idea of what they're about. This first lecture is not on, but the rest of them are. Any other questions? Yes? Student: When do we sign up for the TA sections? Prof: Oh, you should be signing up now. I don't know how to do this. It's online or something, right? You sign up online. Yeah, so you should pick your sections. We might add another section if all of you stay, but probably you won't, but if we do we'll add another TA section. Yes? Student: What's the grade distribution? Prof: The grade distribution? I don't know. The standard Yale junior level course grade distribution which is when I was at Yale things were much tougher, so it's the standard distribution. I don't remember it offhand. But I'll tell you all about the distribution at the midterm. So there will be a midterm before--you'll have chance to drop the course after the midterm and then there will be another midterm right at the end of the course. Yes? Student: What level of math and type of math should we be comfortable with to take the course? Prof: I was trying to say that. I'm glad you asked me again. So I went over the things that you have to know. If you have 3x-4x^(2) you have to be able to take the derivative of that which is 3-8x. If you've got the log natural of x you have to take the derivative. It's one over x. If you've got 3x 5=10 and 2x-7=12 you have to be able to solve that simultaneous equation. So that's the kind of thing you have to do, and you have to be able to do it quickly and with total confidence that you're doing it right. And for many of you that's no problem, but for some of you who are maybe even smarter than everybody else that's a problem, and so you'll have to judge yourself whether you can do that comfortably so you don't have to worry about the mechanics of doing that. You can think conceptually about what the question is asking. When does this end, ten of or quarter of? Student: Ten of. Prof: Ten of, so we have 13 minutes. I want to end with one experiment. So (Teaching Assistant), can you help me with this? So this is something we're not going to have time to figure out the answer to. So I need sixteen volunteers. How about the first two rows? Why don't you just volunteer. You'll survive, and I know it's a drag but you'll do it. What I'm going to do now is I'm going to run an auction. So please stand up and eight of you go this side and eight come over here. That's okay, you'll be okay. I know everyone's reluctant to do this. So I only need sixteen. (TA), help me count them. Two, four, six, eight, you guys have to come the other way. The TAs aren't going to participate. You're not in this, right? No. Two, four, six, eight so we only need eight, you both sat down. So would you like to participate? Come on. We could use another woman here. Two, four, six, eight, there are eight of them? So can you mix these up? There are going to be eight sellers and eight, we say seller, right? Buyer, so shuffle them up and hand one to each. So we've got eight, and these are the football, they're selling. So we've got eight sellers and eight buyers, and I don't know whether you've ever seen this experiment before, but shuffle them, right? Student: They're all sellers though. Prof: They're all sellers, but you've got to shuffle them. On the other side there's a number. So we've got eight sellers here and eight buyers. So each seller knows what his football ticket is worth, or hers, so please take one. Student: I have a seller one. Prof: Oh, you have a seller one? That's bad. Student: Yes. Prof: I'm blind. Student: Thank you. Prof: Buyer, thank you. Does this say buyer and buyer? You should be one short. Here's an extra. So there are eight sellers and eight buyers. They've got the football tickets. Each of them knows what the football ticket is worth to her. There are three women here and only two, so these are the "hers". She knows exactly what it's worth to her. So say it's fifteen. The football ticket's worth fifteen. Now if she can sell it for more than fifteen she's going to do it. She's going to make a profit. If she sells it for less than fifteen she's not a very good trader. She's not going to do that. She's going to say, "If I can get more than the football ticket is worth I'm going to sell it. If I can't get more than it's worth I won't sell it." So everybody knows what the football ticket is worth to herself. All these guys, they know what the ticket is worth to them. So say someone thinks it's worth thirty that guy's going to say, "If I can get it for less than thirty, like for fifteen, I'm going to get it. That'll give me a profit of fifteen. If I can only get it for forty I'm sure not going to do that because I'm paying more than I think it's worth. So you all got that? You have a reservation value yourself. You don't want to pay more than it's worth because then you're losing money, and they want to sell it for more than they think it's worth because then they're making money. So nobody knows anybody else's valuation. The information is distributed completely randomly across the class. Now this is a famous experiment. I'm not the first one to run it, although I've done it for ten years. I do it in my graduate class, in my undergraduate class, the undergraduates, by the way, always do better than the graduate students. So this knowledge is distributed in the whole environment, and we're going to see what happens when I start a chaotic interaction between all of these sixteen people. What's going to happen? And you would think it'd be total chaos and nothing sensible is going to happen. And if that does happen it'll be very embarrassing for me. But what the efficient markets guys would say is, "Something amazing is going to happen. The market is going to discover what everybody thinks it's worth and figure out exactly the best and right thing to do and that's what's going to happen." Now, it's hard to believe that with this little preparation that you've had, zero, zero training, zero experience, and you're only going to have two minutes to do this. So see the class has got eight minutes to go. You're going to miss the grand finale. Anyway, so you've only got eight minutes to go. So with only two minutes of training they're going to get to a result, which if I had to do it myself and read all the numbers and sort them out and sort through them would take me much more than two minutes, and all this is going to happen in two minutes. It's hard to believe. It probably won't happen this time. So here are the rules. I'm going to put you all together. Start inching your way towards each other, and try not--now, when I say go, which won't be for two minutes you're going to start yelling out an offer. So if you think it's worth fifteen and you're a seller you're not going to sell it for fifteen. You're going to say give me twenty, or give me thirty, or give me twenty-five. You're going to try and get as much as you can. You have to yell it out. The buyers are going to be making their offers. When two of you see that there's a deal you have to shake hands, exchange the football, and leave, and tell your numbers to (TA). Where's (TA)? (TA), you're going to stand outside the group that way. So once you make a deal you just leave and tell what's happened to (TA) who's now standing back here, back there. So it has to be public outcry. It's very important that you're yelling these things publically and all the other people can hear you, and you've only got two minutes. Now two minutes sounds like an incredibly short period of time, which it is, but it's much longer than you think, wait, quiet here. You shouldn't trade--I'm giving you valuable advice-- you should not trade in the first ten or fifteen seconds because you have to hear what everybody else is offering. If you trade right away you're probably doing something really stupid. Two minutes, though, it sounds short, is actually a very long period of time. So be patient. Try to get the best possible price and we'll see what happens. Any questions about what you're doing? And now, in the heat of the moment you might be so frustrated that you can't sell when you think it's worth fifteen that you sell it for ten. I'm going to expose you in front of all these people if you do that, so keep track of what you think the thing is worth. All right, any questions anybody about what is going on? So you have two minutes. Is there a second hand there? I can't see it. No? Student: It's on the ten, or coming to. Prof: Where is it? Student: Now it's on the three. Student: It's moving. Prof: It's on the three. I think I see something. When it gets to the four we're going to start. So start, go. > Prof: Oh, no collusion. No collusion. > Prof: Come out and tell (TA). If you made a deal tell (TA). > Prof: How much time is left? One minute left, plenty of time, one minute. Any other deal made? Write down the price and the two, what price they agreed. How much time? Twenty-five seconds, stay cool. How much time? How much time? I can't see. Fifteen. Stay cool. Don't make any mistakes, ten, five, four, three, two, one, stop. Did you get all the numbers? > Prof: Give me back the tickets. Student: Was this designed to make us look bad on camera? Prof: Give me back the tickets. Student: You designed this to make us look bad on camera. Prof: No, you're going to look great on camera, you are. Give me all the tickets back. (TA), you getting done there? Teaching Assistant: Yeah. Prof: All the tickets. I need them all back, all the stuff. God, you're big folders here. These tickets have lasted ten years until you guys took over. They're all crumpled up. All the tickets, I need them all back. You can sit down now. Everybody's reported in? Now let's see what happened. You've got them all? Five traded. Teaching Assistant: Five traded. Prof: Five bought and sold. So here's what happened. Here were the numbers. So we have five minutes just to look at this. So all the buyer prices are in blue, forty-four, forty, thirty-six, you should recognize these you buyers, and the red ones were the sellers. So you notice that every seller, for everybody there's a seller who's underneath. So it could have happened that thirty-eight sold to forty-four, and thirty-four sold to forty at thirty-seven, and twenty-eight sold to thirty-six at thirty-two. You could have had eight trades. So what did happen? Nothing like that happened. You had five trades, five pairs of people traded, and there are those three poor schlumps, pairs of people at the end looking despondent, hopeless, unable to trade, worried that they were on camera. Now, let's see, who are the people who traded? So, (TA), name the buyers who bought. Teaching Assistant: I don't know the names. Prof: The prices. Teaching Assistant: The seller got it for nine and managed to sell it for twenty dollars. It was all quick so I don't have everybody's name, because they were all rushing. Prof: You got them. Teaching Assistant: I got them.. Prof: That's everything, great. Teaching Assistant: I just don't have their names. Prof: Here's what happened. Mister seller ten sold to thirty-six at a price of twenty. Mister seller nine sold to buyer twenty, so nine, there is no nine. Teaching Assistant: Six. Prof: Nine sold to twenty at a price of what? Six. Teaching Assistant: Sorry. Prof: That's okay. So seller six sold to twenty at a price of twenty. Student: Yeah, even though it's cheaper > Prof: No, no, buyer twenty paid twenty, so seller six did well. We won't ask who buyer twenty is. Buyer twenty is going to screw everything up. So Buyer fourteen through--I can't read this either. Teaching Assistant: Forty-four. Prof: Buyer fourteen sold to buyer forty-four for twenty, and buyer twenty sold to buyer forty for twenty-two, and seller twenty-four sold to buyer thirty for twenty-five. So five people traded, now which five were they? The sellers were ten, six, fourteen and twenty-four, one, two, three, four, five, the bottom five. The five buyers were thirty-six, twenty, forty-four, forty and thirty. So basically forty-four, forty, thirty-six, thirty, twenty-six didn't buy, twenty bought instead. So if you look at it, so it's not quite the way theory would have predicted, but almost. If you look at it, if you just shuffle the order and you put the sellers, instead of from top to bottom you put them from bottom to top, you get what looks like a demand curve and a supply curve. And so what happened? All these five people ended up selling, one, two, three, four, five, those are exactly the sellers. The price they sold for was all between twenty and twenty-five, and the five buyers were forty-four, forty, thirty-six, thirty. Twenty-six didn't manage to buy, but twenty bought. So what is the theory of the free market? The theory of the free market says, "This chaotic situation where they had less than two minutes to decide what to do could be analyzed as if you put a demand curve together with a supply curve and there was one price that they miraculously knew. Here it should have been twenty-five. It turned out to be twenty or twenty-two that all the trade took place at. At that one price you get all the trades happening. The people have the highest valuation buyers they're the ones who get the tickets. The people with the lowest valuation sellers sell it. So the people who end up with the tickets are these red guys at the top and the blue guys at the top. All the tickets go from the people who value the stuff least to the people who value it more. So the market has done an extraordinary thing in two minutes. So there was one mistake. Mister or miss twenty, whose identity we are protecting, although I'm searching the faces, mister or miss twenty got a very bad deal. She or he, let's say he, bought at twenty when the value was twenty. That was a horrible deal. He didn't get any extra out of it. So he should probably have only bought if the price were lower, and then twenty-six would have bought instead of twenty. So twenty sort of squeezed his way into the market, so twenty-six and twenty between them somehow there was a slight inefficiency. But basically with no training, no background, no practice, these sixteen undergraduates managed to reproduce-- they gathered all the information in the whole economy, and they discovered who were the eight people who valued the tickets the most and they ended up with all the tickets. For me to do it and sort it out would have taken longer. The market solves a complicated problem, and gets information incredibly quickly, and puts things into the hands of the people who value it the most. And the marginal buyer thought it was worth about twenty-five or twenty and that's what the price turned out to be. So anyway, we're going to come back to this parable at the beginning of the next class.
Quantitative_Finance_by_Yale_University	22_Risk_Aversion_and_the_Capital_Asset_Pricing_Theorem.txt	Prof: Okay, but now I want to move to the next topic, which is the topic called the Capital Asset Pricing Model, and it's in some points the high point of the class. It used to be the high point of finance. The theory hasn't worked out as well as people thought in recent times, but it's quite a great achievement and a lot of it was done here at Yale, so I want to explain it to you. So you see we have a problem so far. If everybody's trying to hedge that means everybody's trying to get a completely riskless payoff. It's impossible because, I mean, there's real risk in the economy. And what do we mean by real risk? Well, something in one state is just going to be bad for the whole economy compared to another state. Maybe we'll run out of oil or something like that. It's impossible that everybody can consume the same thing in every state, so it's impossible that everybody can perfectly hedge, but everybody wants to perfectly hedge. So what has to happen? What gives? How does the theory have to change? Well, the theory's going to change in a simple way, which Shakespeare himself already knew and already told us about in The Merchant of Venice. What's going to happen is everybody is going to try and hedge as much as they can by diversifying, but because there's some real risk in the economy, in some states things will be in the aggregate worse than they will be in other states. So what's the consequence of that? The consequence of that is if you're going to buy an asset that pays something that's riskless you're going to pay the discounted expected return of the asset, but if you're going to buy an asset that's risky you're going to need a higher rate of return so the price will be less than the expected discounted payoff. So Shakespeare, remember, said exactly that. When the play begins with Antonio looking melancholy his interlocutor says, Salerio or somebody asks him whether he's worried about his businesses. He says, "No, I've got a different ship--every ship's on a different ocean so I'm diversified. I'm not that worried." So Shakespeare knows about diversification and that's what everybody should do, but then when it comes time to pick the caskets to get to marry the beautiful Portia, who by the way is not just beautiful but she's rich so they're looking for a prize, but they sign a contract that whoever picks the wrong casket not only doesn't get Portia, he can never marry anyone in the future. So what's the purpose of that contract? It's to make it a very risky gamble. And so why did Shakespeare want to make it a risky gamble, so he could explain he understands risk and return. So you remember the conversation where everybody says, "Well, I'm not going to pick this unless, you know, it's only because she's so rich and so beautiful that I'm willing to do this. The return is so high that it's worth the risk to me." So Shakespeare already understood that things that are risky are going to have to be priced less than their expected return-- expected payoff--so the expected return, that is the payoff per dollar put into it looks higher to compensate you for the risk. So Shakespeare almost had the whole story. What's missing from Shakespeare? Well, what is the definition of risk is missing from Shakespeare, and it will turn out that it's going to be a very surprising definition. So the purpose of the model I'm going to explain is, how do you measure risk, and how should that affect the price of things, and how does that affect all the analysis we've done so far? So that's the topic of the next couple lectures. So the first person to confront this problem and propose a solution, a mathematical solution, was the mathematician Bernoulli and his brother. So the Bernoullis were a famous mathematical family, and one of the brothers went off to St. Petersburg where he ended up dying shortly afterwards, but he noticed the following puzzle, and some of you have heard this, it's called the St. Petersburg Paradox. So suppose I offer you a bet. I say I'm going to flip a coin, and I keep flipping the coin until it comes up tails, and I count how many coin flips I've counted until you get tails, and if that's N flips you get 2 to the N dollars. So if you flip it 1 time and it comes up tails right away, which is probability 1 half, you get 2 dollars. If I flip it 2 times and it gets heads and then tails, that's with probability 1 quarter, you've flipped it twice you get 2 to the 2 or 4 dollars. If I flip it three times and I get heads, heads, tails the odds of that are 1 half times 1 half times 1 half, which is 1 eighth, but then you'll get 2 to the 3 dollars. So 4 8 1 over 2 to the N times 2 to the N .... So Bernoulli, the one who died, told his brother Daniel about this and he said, "Well, I've offered this bet to a bunch of people and I asked them, how much would they be willing to pay for this risky asset?" I mean, what would you pay? Let's hear some numbers? How many dollars would you pay if I offered you this bet? I'm just going to keep flipping a fair coin, count the number of flips until a tails and pay you 2 to the N dollars. So this is the expectation which obviously equals infinity. So according to what we've said so far you should pay infinite amount of dollars for it, but Bernoulli couldn't get anyone to offer him that much money. How much would you offer for this bet? I just want to hear some numbers. Student: 1 dollar fifty. Prof: 1 dollar fifty. Anybody else have any-- it's pretty conservative, I mean, that's almost ridiculous, in fact. You're guaranteed 2 dollars no matter what happens, right? So you're paying 1 dollar fifty and you're going to get 2 for sure, so that's a pretty conservative number to say, anybody a little more venturesome than that? You can't do worse than 2 dollars in this bet. Student: 4 dollars. Prof: What? Student: 4 dollars. Prof: 4 dollars. All right, so Bernoulli asked a bunch of people and the average of what they say happens to have been 4 dollars. That's what they said on average. And so Bernoulli said, "Well, this is amazing. The expectation is infinite and they're only willing to pay me a miserable 4 dollars for this." Now, the real reason might have been that they didn't believe Bernoulli was actually going to pay the money, and they'd give up their money and they weren't going to get anything back, but let's ignore that temporarily and take it seriously. Bernoulli said, the solution must be that people don't care about the dollar payoff. They care about the utility of the dollar payoff. So let's put in a utility function. So the utility of the dollar payoff would be [one half] U of 2 1 quarter U of 4 1 eighth U of 8 1 over 2 to the N U of 2 to the N ... And so then he said--well, of course why is that going to help? Well, because if the utility function, say, looks like this--so here's X and here's U of X-- the more dollars you get, maybe it increases utility but by less and less, so you're not really gaining much by getting these numbers way out here. They're not adding really much to utility, so you only care about these small numbers. I mean, it's good to get more, but not much better to have more. So he said, lo and behold, if I put in log natural as my utility function, which this looks like, that's the graph of log natural, and I put this in. Now, you see this is easy to solve, to compute, because log of 2 to the N is N times log of 2. So the log of 2s come out and it's just the sum. It's log of 2 times the sum of 1 over 2 to the N times N. So it's N over 2 to the N. So this is equal to log of 2 times the sum, N equals 1 to the infinity, N over 2 to the N. That's what it turns out, that this thing is that. So it's not just 1 over 2 to the N which would have added up to 1, but N over 2 to the N. So the point is because you have the log function here this actually equals the log of 4. So anyway, I've worked out the arithmetic. It's very simple. You all know how to sum 1 over 2 to the N. You probably don't know how to sum N over 2 to the N. You never thought of doing it before, but the same trick gets you to be able to sum N over 2 to the N. It's obviously more than 1 over 2 to the N, in fact, it's equal to 2. So this sum is equal to 2 and 2 times log of 2 is log of 2 squared which is log of 4. So by plugging in--instead of caring about expectation you care about the expected utility. You can explain why the average person was willing to pay 4 dollars because the expected log of this is equal to the log of 4. This is equal to the log of 4. So Bernoulli thought he'd brilliantly explained his paradox. So this is the other brother, Daniel. The dead brother posed the problem, maybe solved it too for all I know, but the other brother who still lived came up with the solution, maybe with his brother, that people don't look at expected payoffs, they look at expected utility of payoffs, and the utility should have this concave feature that more and more payoff adds on the margin less and less utility. So this function satisfies d squared U (X) / dX squared is less than 0. The second derivative is negative. So the marginal utility is declining as you get more and more. So that was the first advance on how to deal with risk. Now, actually Bernoulli didn't really solve the problem because just saying that you replace the payoff with expected utility of a concave function-- this log wouldn't have really solved the problem, because suppose that Bernoulli had offered instead a bet not of 2 to the N but of 2 to the 2 to the N, a much more generous bet? Then even with logs you would have gotten an infinite number. So basically he should have said that people care about a concave function of payoff where the function is bounded unlike log which is not bounded. But anyway, let's leave that aside. It should be a concave function. So to put it another way, a concave function has the property, if you look at it, let's say it looks like that, that if you have this payoff X_A and this payoff X_B and you've got-- so this is the utility now here, X_A, and this is the utility U of X_B, and this is the utility U of X_A. If you have a 50/50 bet of either getting X_A or getting X_B you're going to end up with this expected utility. Your utility is going to be 1 half of U X_A 1 half of U X_B. That's what we had down here, 1 half of this utility plus half of that utility assuming nothing else can happen. But if you give the person half the amounts of money for sure then he gets this utility which is much bigger than that utility because this is a concave function. The extra you gain by winning the bet, compared to getting the average for sure, the extra you gain doesn't drive the utility up very much because it's flattening out. Whereas losing the bet, even though you're losing the same number of dollars because from here to here is the same as from here to here, the loss of the same number of dollars is more important to you than the gain of an equal amount of dollars, and that's why you'd rather get the middle for sure than having a 50/50 chance of going on the extremes. So Bernoulli pointed the way to the modern theory of risk aversion, which is to just assume--risk aversion in modern economics means people care about expected utility, maybe discounted, expected discounted utility where the utility is concave. So whatever utility function we wrote in here, maybe it shouldn't be log, it should be something else. How would people evaluate this? They'd evaluate it log of 4. In other words, they'd say take whatever that constant utility was, which was log of 4, that produces the same utility as the random gamble. So this random gamble gives this expected utility which is equivalent to having that for sure. So here's the 4. So 4 for sure gives a utility, log of 4, that puts you here which is the same as the expected utility of getting the random gamble. That's the modern theory of risk aversion, and it explains why people would rather have things for sure, but it's now quantifiable because if you can't have something for sure then you know that it's more dangerous, but with this concrete utility function you can find out exactly how much you're willing to pay to transform this risky gamble into a safe gamble. You'd give up this much expectation in order to get the payoff for sure. So we're going to turn a vague theory into something quantifiable and get a surprising conclusion. So that's step one. We now think about people maximizing utility. Well, of course we thought about that from the beginning. The very first class you had utility and diminishing marginal utility. So actually this risk aversion with diminishing marginal utility, fortunately for us, is exactly the same thing we've been thinking about all along anyway, diminishing marginal utility for consumption. So the very assumption of diminishing marginal utility that we made from the beginning is also explaining risk aversion. So it's incredibly fortunate that we don't actually have to change any of our mathematics and we've explained a new phenomenon. Now, the most simple utility function is either the log one or the quadratic. So remember, U (X) = a b X - c X squared. Adding a constant is never going to change anything, so I'm always going to write this as a X - 1 half alpha X squared. That's going to be my utility function, my quadratic utility. It could be like this or it could be like that. If you add a constant which doesn't depend on X that's not changing what anybody does so that's irrelevant, and if I divide it by a constant like B that's not going to change what everybody does so I might as well assume the quadratic utility is X - 1 half alpha X squared, quadratic utility. So that's about as simple as we can get and we're used to working with those kinds of utility functions. Now, why is that such a good convenient thing for us to use? It's because let's suppose now that you've got this random payoff where with probability gamma_1 you're going to get X_1, probability gamma_2 you're going to get X_2, probability gamma_S you're going to get gamma_S [correction: X_S]. So what's the expected utility, the analog of Bernoulli? That means U is going to equal summation, s = 1 to S of (gamma_s X_s- 1 half alpha X_s squared). So that's all we're doing. We're just saying that people don't care about the payoffs. They have to evaluate getting X_1, X_2 or X_S. They're going to multiply the payoff by the expectation but not look at the payoff itself, look at the utility of the payoff. Now, quadratic is very simple and the reason why we're going to get such a beautiful theory out of it is because this number you don't have to keep track of all the X's to express this utility. We're going to be able to summarize it incredibly simply. This is going to equal some function F of the expectation of X and the variance of X. So all we're going to have to worry about is the expectation of X and the variance of X, and so many, many very complicated things we can think about very simply. So more generally if you put the log instead of the quadratic utility we couldn't get this simplification and so the theory would have to be more complicated. So the beautiful theory, the Capital Asset Pricing Model, comes out of using this simple quadratic utility. So why does it get so simplified? Well, if I just write it out, U is going to equal the summation of gamma_s X_s, so this is s = 1 to S (I've let my probabilities be gamma, I don't know why I chose that) - 1 half alpha, summation s = 1 to S, of gamma_s X_s squared. Well, here we have the expectation of X already. Now, what is this 1 F alpha gamma_s X_s squared? Well, if I wrote X_s - the expectation of X and I summed this squared that's equal the variance of X--oops, times gamma_s. That by definition is the variance, but if I wrote this out what would I get? I'd get summation s = 1 to S, gamma_s X_s squared which is what I have over there and then I'd have-- well, what would I have-- minus 2 times summation gamma_s X_s expectation of X summation s = 1 to S of gamma_s expectation of X squared. But what's this? The second term minus 2 times that, the expectation of X is a constant so I can take that out, minus 2 expectation of X, can take this out and notice that summation gamma_s X_s, that's the expectation of X as well. So that's just minus 2 times the expectation of X squared. And so this I can take the expectation of X squared out and the summation of the probabilities is 1. So therefore I just get equal to summation s = 1 to S, gamma_s X_s squared - (expectation of X) squared. So therefore, this up here is equal to the expectation of X. So what have I got here? I've got this term. So I've got the variance of X equals this summation X_s X_s squared - (expectation of X) squared. So this term equals the variance of X (expectation of X) squared. So therefore I've got this minus 1 half alpha (expectation of X) squared - 1 half alpha variance of X. That's what the algebra gives me, so why is that again? Because given quadratic utility up here, that thing--getting old--given the quadratic utility up there I can write it as this in this term. This term is obviously the expectation of X, but this term is just the variance of X plus the expectation of X squared. So when I subtract it I keep the expectation of X minus the (expectation of X) squared. That's the first term, and then I've got minus the variance of X from that term times the 1 half alpha. So you see that depends on the expectation of X in a positive way, assuming alpha's a small number, and in a negative way on the variance of X. So, just as I said, somewhere, I said it was going to turn out like that, and it did right here. The utility is equal to the expectation of X and the variance of X in a positive way on the expectation of X and a negative way on the variance. So now we're ready to start the analysis. So far we've assumed people only care about the expectation and then we said, well, we know they don't only care about the expectations. Hedge funds and everybody else, if they know what they're doing and they're trying to keep their investors happy they're going to hedge. We didn't say why they're going to hedge. We just asserted they like to hedge so their investors don't get mad at them, but really what we had in mind is the investors have some utility function. They don't like risk so the hedge fund is going to try and keep the payoffs steady. But there's a tradeoff. You can't eliminate all risk. So, how much is the hedge fund and the investor going to suffer if all risk isn't eliminated? Now we have a way of quantifying it. People care about the utility and not about just the expected payoff and so you add more risk to them-- you replace a sure thing with a risky thing with the same expectation-- they think it is worse, that much worse. And so we've said that of all the myriad of utility functions-- we could use log, some exponential e to the minus aX, X to the r, there are lots of different utilities we could use-- we're going to deal with the quadratic because it has the simple property that in evaluating an entire risky proposition people care about the expectation, which is what they cared about before, but they're punishing themselves for getting a bad variance. So because that's such a simple thing to say we're going to get a simple conclusion and a very surprising conclusion. So let's now analyze a problem and see what would happen. So the problem I'm going to choose to analyze is this one. I'm going to say that three things can happen in the economy. Anyway, those are the probabilities. Now, there are many firms in the economy A, B and C, and let's say the first firm, I don't want to invent the numbers here so I might as well just write down the ones I picked. The first one's going to be 50,100 and 75. B, the other firm's going to be 150,180 and 365, and C is going to be 300,220 and 60. So those are the three things that can happen in the payoff of the three firms. Let's say there are two agents, agent alpha owns A and also 133.5 units of X_0. And beta owns B & C and--I may have reversed these two guys--66.5 units of X_0. So here we go. So by alpha and beta, I mean, there are a million alpha agents and a million beta agents so everything could be scaled by a million because I want a big economy like we always have. So there we have it. We've got now a risky world. Things can happen. So what are the utilities? Let's say utility now of alpha is going to equal--sorry, I left out the main point. Utility of alpha is going to equal 1 half X_0-- I just made up these numbers, by the way, they're not--so summation s = 1 to 3, gamma_s, that's the gamma_s up there, times X_s - 1 over 400 X_s squared, the states. So there's s_1. So here are the states. This is state 1, s = 1, s = 2 and s = 3. So those are the three possible states just like we had before with this payoff and those are the payoff of all the assets. Alpha owns firm A which is producing that output in the three states, and also owns 133.5 units of X_0. So over here alpha's owning 133.5 and beta's owning 65.5 of consumption at time 0. So this is time 0. This is time 1, the end of the year. So by the end of the year something is going to happen. There's a lot of uncertainty between now and then. Some of the firms are going to be paying off in some of the states and badly in other states and so on. And so the utility function for alpha, so he cares about consumption at time 0 and also in each of the three states, but now he's going to have these quadratic utilities. He's going to say to himself, if I just hung onto my A in state 1 this would be-- if I never traded, I just hung onto A the utility function would be this quadratic thing of 133.5. So it would be 133.5 - 1 over 400, 133.5 squared, plus he would end up with (50 - 1 over 400 times 50 squared) times 1 quarter (100 - 1 over 400 100 squared) times 1 quarter (75 - 1 over 400 75 squared) times 1 half. That would be his utility if he never traded. If he just stuck to A he'd eat his own endowment 133.5 at time 0. Oh, that isn't true. I wrote down the wrong utility at time 0. I said his time 0 utility is 1 half X_0. So it's 1 half 133.5. So we get 1 half 133.5, but in the future he'd get 50 in state 1,100 in state 2, and 75 in state 3, and that's the utility he'd end up with. But that's not very good for him because he's running this gigantic risk. He's got this risk at time, you know--state 1 is a disaster for him if he just sticks to that, so he doesn't want to stick to that. So how should he evaluate the shares of firm A? How should he evaluate the shares of firm B which he could get if he gave up some of A, or how should he evaluate the shares of firm C? What should he do? So beta has a similar utility. Beta's utility, U_beta is going to equal 3 quarters X_0 the summation, s = 1 to 3, (gamma_s times X_s - 1 over 800 X_s squared). So I've made these guys--far from being impatient they seem to prefer consuming in the future until now. That was a poor choice of numbers. This number should be bigger than 1 and this should be bigger than 1, but anyway I put 1 half and 3 quarters. So there's impatience built in except it goes the wrong way. That was just poor choice of numbers, but the rest of it expresses their risk aversion. So alpha is looking at the expected payoff of what he gets to consume in the future, but he's punishing himself by the variance. So you look at this formula you see it's not just the expectation, but he loses something because of the variance. And similarly, beta, he's looking at consumption today, he's adding to that the expectation of his consumption tomorrow for his utility, but he's punishing himself for having variance in the future. So it's exactly what we formalized, Shakespeare's idea of people not liking to be exposed to variance, to uncertainty, which we've quantified by calling variance. Is everyone with me now? Yes? Good, I'm glad you have a question. Student: I don't understand how you got 1 over 400 and 1 over 800. Prof: I just made up those numbers. That's the utility of alpha and that's the utility of beta. I could pick any people I wanted. I just picked those two people. Now, how do they differ? Which person is more afraid of risk than the other? Is alpha or beta more afraid of risk? Student: Alpha. Prof: Alpha is more afraid of risk, right? This 1 over 800 is smaller than 1 over 400, so beta doesn't really care that much about risk, well cares, but is not going to punish himself too much by being exposed to risk. Alpha is not going to punish himself too much, but is going to punish himself somewhat more. So alpha is more risk averse. Alpha is more afraid of risk, it seems. So I've taken two agents who are afraid of risk, one's more afraid than the other, and I've put them in an economy where there are risky things that could happen. And so we now want to work out a more sophisticated version of pricing and of equilibrium than we had before. So let me remind you that what we sort of have been supposing up until now is that the price-- what would the price of A be if we didn't think about risk aversion? So far what we would say--what would you say the price of A is, price of firm A? If we were naive you might say it is 1 quarter-- by the way, I hope I have those probabilities right-- you'd say it is 1 quarter times 50 1 quarter times 100 1 half times 75. Is that what we would have said up until now? Even up until now we would have been more sophisticated than that. Student: Discounted. Prof: Discounted, times discounted. That's what we sort of figured up until now. That's the logical thing to do. Well, but we ignored risk aversion, and we ignored it at our peril because it's obviously important. I mean, Shakespeare, a literary person, he understood already 400 years ago that risk aversion was important, and there are facts that confirm what Shakespeare's intuition is. The stock market historically has had a lot higher return than the bond market. Even with the last stock market crash, of course it came back a lot, averaged since 1926 the stock market's made something like 9 percent a year compared to 2 and 1 half percent in the bond market. So there's a huge disparity and after over such a long period of time it can't just be it was luckier every year after year after year. Somehow people must have realized the stock market is riskier, and so as Shakespeare said they wanted a higher return meaning they were paying a lower price, but how much lower? How can you figure out how much lower? So in this example, in other words, what is the price of A? So this is the wrong price of A, apparently, because it doesn't recognize risk aversion. So that's where we are. So any questions about what the question is? We're about to give an answer. So you see what the question is, that our old methodology for figuring out prices-- that's taking expectation and discounting-- obviously can't be right because it doesn't recognize risk aversion. On the other hand, we always had a utility function in there from the beginning, even a quadratic one, so all we have to do is do what we did before and put in a quadratic utility and we'll probably get the right answer. So that's exactly what we're going to do. So Arrow, in 1951, this is the same guy who proved with Debreu the Pareto efficiency of equilibrium. He was my thesis advisor. He said we can do the same trick that Fisher did, only for some reason he never credited Fisher. I could never quite figure that out. He had some obscure Danish guy he credited. But anyway, apply Fisher trick and assume firm dividends are part of endowments. Look for GE, the general equilibrium, trading outputs, trading goods, then go back to deduce value of firms. Now, what goods are we trading here? That was a conceptual advance. We call them Arrow and then Debreu got involved too. Arrow-Debreu, so Debreu was the Yale Assistant Professor while Arrow was a Stanford Assistant Professor, so Arrow-Debreu State Contingent Commodities. So, just as Fisher said, an apple today and an apple next year, even though they're identical apples, are different commodities with different prices because they come at different places in time. In fact, most people would prefer the apple today to the apple next year. So Arrow said an apple in the top state is a different commodity from the same apple in the second state, so it should have a different price. So we've got just our conventional equilibrium according to Arrow where as long as you have these Arrow state contingent commodities that you can trade-- trading today, you can imagine today buying an apple if state 1 occurs but not having to get the apple if state 2 or state 3 occurs, and that'll have a price P_1. And today you could imagine buying the apple if state 2 occurs, a different price from the apple if state 1 occurs, and also an apple if state 3 occurs, which obviously is going to be more expensive, or it looks like it'll be more expensive than the other apples because it's 50 percent likely to happen, and those are the prices we have to look for. And that's going to solve our problem because the prices of the Arrow securities are going to be different, maybe, from the probabilities and that's what will reflect the fact that when everybody's trying to hedge and not everybody can do it you're going to have to change the tradeoffs. So we've already seen this in our gambling thing, at least the prices. Remember with our bookies the bookies were effectively willing--remember there were two outcomes, the Yankees win or the Phillies win. You could get the bookie who thought the odds were 60/40, by paying 60 cents today the bookie was going to give you 1 dollar if the Yankees won, or paying 40 cents today the bookie will give you 1 dollar if the Phillies won. So we've already had these Arrow contracts, these Arrow securities implicitly in our equilibrium. And those 60/40 odds those were the opinions of the bookie, maybe not the actual probabilities. We said the final betting odds depended on what the other bookies were willing to give. It didn't have to correspond to reality. There might not be a reality even. So here there's a reality, 25,25, 50, but that doesn't mean that the odds, the prices they're going to quote in the market are going to turn out to be that. We have to solve for equilibrium and see what they are. So what's going to happen? Well, we can solve for equilibrium very easily because we've done this a million times before. And I've chosen linear quadratic utilities, the kind we did on the very first day of class, because those are easiest to solve for equilibrium. You don't have to get involved in the budget set or anything complicated. You just set marginal utility equal to price. So we know for alpha, sorry, we know that the marginal utility of alpha at time 0 divided by the price 0 is going to have to equal the marginal utility of alpha at each state s times the price P_s. So the equilibrium, the Arrow-Debreu equilibrium, is going to involve P_0, P_1, P_2 and P_3, the prices of the Arrow securities, the present value prices. P_0 is what you pay today to get the apple today. P_1 is what you pay today to get the apple a year from now in state 1. So these are the present value (that's what Fisher would say) state contingent prices. The state contingent is what Arrow added. Now, you may ask whether there really are these Arrow securities floating in the economy, and we're going to come back to that question, but you could imagine all these Arrow-Debreu state contingent prices and commodities, and those would be the prices we'd solve for equilibrium. So we get this over this, marginal utility of that. So what is this? And similarly for beta, marginal utility^(beta) at 0 over the price of 0 equals marginal utility^(beta)_s over the price of s. So what is this? For alpha, his marginal utility of consumption is 1 half. We might as well assume one of the prices is 1. Let's take this price to be 1. So beta, her marginal utility is 3 quarters and the price is 1. What's his marginal utility in any state s? It is gamma_s times (1 - 1 over 200 times X_s). So I just differentiated this. I got 1 - 2 over 400 times X_s. And what's her marginal utility? It is gamma_s in state s times (1 - 1 over 400 times X_s). So I know in equilibrium that's going to imply that 1 half-- well, now I have to screw around here, so how am I going to--so I've got this thing over here 1 half equals this thing over here. What? Student: Over P_s. Prof: Over P_s. Ah, glad that appeared. I was getting worried there. Thank you. Over P_s, that helps a lot. So that implies that something like X--so this is what alpha is going to do and this is what beta is going to do. So this implies X^(alpha)_s equals what? So if I multiply through by 200, and I bring P_s over gamma_s to the other side, and I do a bunch of stuff, I'm going to guess this is 200 - 100 P_s over gamma_s. How do you think that's going to play in Peoria? Let's see. If I multiply through by P_s over gamma_s I get P_s over gamma_s times 1 half. Then I multiply everything through by 200. So I get 100 P_s over gamma_s, and then I get the 200 here, and the X_s goes to the other side, and the P_s over gamma_s goes to the other side. So it's 200 - 100 P_s over gamma_s. And this one is going to be--X^(beta)_s is going to equal-- well, I have to do the same trick here except I'm going to be multiplying through by 400 and taking 3 quarters which is 300. So it'll be 300 minus--no, that was wrong, 400 - 300 P_s over gamma_s. Because if I multiply through by 400, put P_s over gamma_s on the other side I have 3 quarters P_s over gamma_s times 400, which is 300 P_s over gamma_s. This becomes a 400 and the P_s gamma_s went away so I have that. So I know now if I could figure out what the prices are I know what everybody would demand in every state. So let me pause here. That was the first critical step. So what did I do? I said it's a long story. A lot of years went into this. I said people are risk averse. Shakespeare knew that. We want to quantify it so we say people have concave utility functions. That quantifies risk aversion. We want to make a simple concave utility function. We pick quadratic, but of course we don't know what quadratic. Different people could have different quadratic utility functions. Then we do the Fisher trick and say that any equilibrium, as long as you can buy and sell every contingent commodity in the future, because all the Arrow securities are there, it can always be reduced to general equilibrium just like we did before. And so now you have to feed the endowments into the agents'--I mean the payoffs and the dividends into the agents' endowments. So we haven't done that yet. And then we solve for supply equals demand. So all we have to do is we have to have X^(alpha)_s X^(beta)_s has to equal the endowment of alpha in s plus the endowment of beta in s. All right, so we have to do that for every s. So this is 200 - 100 P_sS over gamma_s equals--now we have to do it in state 1. So it equals whatever they are. So what is endowment of alpha of s plus endowment beta of s? We have to look at each state separately. And lo and behold I picked the numbers so that if you add these all together you get 500, and here you get 280 and 220 is also 500, and here you get 500 again. So lo and behold there is no aggregate risk in the economy, although the individual stocks are risky the aggregate is totally un-risky. So no matter what s is, I could put in 500 here. It's going to turn out that the total endowment of both people, because I've plugged the dividends into their personal endowments, added up the two people, it's 500. So it means that P_s over gamma_s equals... Student: > you forgot. Prof: What? Student: You forgot the second term. Prof: I've forgotten something for sure, what? Student: X^(beta). Prof: Oh, X^(beta). So that's alpha. Thank you. Plus 400 - 300 P_s over gamma_s = 500. So if when I add this up I get 600 - 400 P_s over gamma_s = 500, so then I flip them to the other side and I get P_s over gamma_s = 1 quarter, because 500 from here is 100 and put the 400 on the other side and divide by it I get P_s over gamma_s equals 1 quarter for all s. So what did I find? So it's the same. P_s over gamma_s is the same, same in all states. So what would the price of A be here? What's the price of A in equilibrium? What's the price of A? I'm going to take the price of A should be P_1 times 50 P_2 times 100 P_3 times 75, and what does that equal? Well, P_1 is just 1 quarter times gamma_1, right? P_1 over gamma_1 is 1 quarter. P_2 is 1 quarter times gamma_2, and P_3 is 1 quarter times gamma_3, so I just got this multiplied by 1 quarter. So in fact all I did is I did what I had always done. I took the expected payoff and discounted it. The discount rate is 1 quarter. What's the price of the riskless asset, pi of (1,1, 1), is just going to be 1 quarter, because it's 1 quarter times gamma 1 1 quarter times gamma 2 1 quarter times gamma 3, gamma 1 gamma 2 gamma 3 is 1 so it's 1 quarter. So it implies the riskless interest rate is what? What's the riskless interest rate? Student: 300 percent. Prof: 300 percent. So we're discounting by 1 over 1 quarter because the interest rate is 300 percent. So basically nothing happened. We got all the prices exactly as we would compute them without, you know, just doing expectations we got the right discount rate. All we had to do was figure out the discount rate. So risk hasn't played any role. And why didn't it play any role? Because although alpha started off owning A alone which exposed her--forgot who was her and who was him, let's say her--exposed her to a lot of risk. She's not going to sit there stupidly just holding A. She's going to trade it for B and C for different shares. In fact she's going to end up holding her consumption, this is her consumption, 200 - 100 P_s over gamma_s, this number doesn't depend on s. She's going to consume the same thing in every state, and how can she do that? She can own equal shares of A, B and C. She'll own a share of the whole economy. So in other words, by diversifying alpha and beta each get rid of all risk. So instead of calling it diversifying I could call it hedging, the same thing. She doesn't just hold her A. She mixes B and C with it so that she gets a payoff of consumption that's exactly the same in every state because P_s over gamma_s is independent of the state. She'll always consume the same thing. Everybody can hedge perfectly and there's no problem because there's no aggregate risk that anyone has to be stuck with, and therefore the price is just going to be the same as the probabilities discounted. And that's the theory we've worked with so far. So, so far you could say that everything we did was kosher it's just that when we had these two different probabilities of things happening up or down we thought that the aggregate economy would have the same endowments here as it did there, and therefore the probabilities we used were the objective probabilities discounted. No reason to change them because nobody's going to be forced not to hedge. Everybody'll hedge. So are there any questions about what I've said? I'm sure there should be a question because I can't have said it as clearly as I ought to have. So would somebody like to say something? Yes? Student: > the old price that we found when we hadn't done this, but that also change the new one? Prof: This is the new price with the 1 quarter. This is the correct new price. So the theory so far hasn't changed in any interesting way. We just found the discount rate. It just looks like expected utility, but you shouldn't have expected it to change because the aggregate endowment was 500, the constant in every state. There's no reason why we can't have everybody perfectly hedged and consuming a constant in every state, and in fact that's what we did have, everybody--she consumed the same thing in every state. He consumed the same thing in every state. No reason why they both couldn't hedge themselves perfectly and in equilibrium that's exactly what they did. Any other... Yes? Student: If the total endowments in every state hadn't all added up to 500 would you create an expected endowment or would you just not do the problem? Prof: So the next step is going to be-- what I'm going to do now is I'm going to assume that the endowments don't add up to a constant in every state. Then what's going to happen? So this is not at all obvious how to solve this and what to do, but it's going to turn out to have a beautiful simple answer, shocking, not only be simple but also surprising. So before I do that I'm going to change the endowments so they're not all a constant. Any questions about where we're going? Yeah? Student: Could you just repeat what you said about hedging >? Prof: Yes. Thank you for the question. So I went a little quickly. I said that what we proved by solving for the general equilibrium is that the price in every state was just going to be 1 quarter times the probability. That's what we showed had to happen in equilibrium. Now, what's the consequence of that? The consequences are twofold. Number one, the price of all the assets is the same expectation we naively would have taken before where we used the discount rate 1 quarter. That's the first implication. The second implication is that from the formula for consumption we noticed that she consumes the same amount in all three states because P_s over gamma_s is 1 quarter in all three states. Her consumption is going to be the same in all three states, and his consumption, which will be different from hers, but his will be the same in all three states as well. The two will add up to 500. So then I took a little bit of a leap and I interpreted that conclusion that her consumption doesn't depend on the sate. What's the interpretation of that? She has obviously, somewhere behind the scenes, given up some of her A to get B and C and held them in a mixture so as to get the same consumption in every state. What must the mixture be? Obviously she holds the same proportion of A, B and C because those add up to 500,500, 500. So she must have held the same proportion of A, B and C, a fraction of the market and got a riskless payoff. So she diversified. She didn't just stick with her A. She substituted a little bit of A, a little bit of B and a little bit of C, a different boat on every ocean, and now she runs no risk at all. So she diversified, but in the language we used last time I could call diversification hedging if I wanted to. She just, sort of, sold Arrow securities in the right proportions to turn her A into something that was completely riskless. So whether you call it diversifying or call it hedging she's achieved the same end of totally balancing her consumption. He did the same thing and they both could do it because the aggregate consumption was a constant. Yes? Student: What would an Arrow security actually look like? Prof: In real life? Student: Yeah. Prof: The closest we've come to an Arrow security in real life is a CDS, and this is part of the reason why these economists, Larry Summers, my classmate, and Rubin who was the Secretary of the Treasury, and ran Citi Corp, and who was a Yale law school student and a Harvard undergraduate, and who I've sat on many committees with, they were seduced by the--so what's a CDS? A CDS pays 1 dollar if some bond defaults by 1 dollar. So that isn't an Arrow security because an Arrow security is a much more detailed thing. An Arrow security says I'll pay 1 dollar in state one. An Arrow security says you get an apple in state 1, but state 1, remember, is not described by a single firm, state 1, the states of nature are total descriptions of everything that could happen in the economy. So an Arrow security really says if it stops snowing in Siberia, if Khomeini loses power in Iran, if there's a favorable election outcome in Afghanistan, and if Obama wins reelection, and if the U.S. solves the energy problem then I'll give you 1 dollar. So the Arrow security lists an incredible number of contingent things, every contingency possible and says in that case I'll give you 1 dollar. A CDS says if this thing happens I'll give you 1 dollar whether or not Obama wins election, whether or not America discovers a new source of energy, whether or not Afghanistan turns around. Just so long as the bond defaults I'll give you 1 dollar. So the CDS is an event contingent security. That's the CDS, and an Arrow security is a much more finely specified thing. It's a state contingent--you say everything that happens in the economy, so we'll never get to Arrow securities, but CDS looks like we're on the way to them. And these guys blundered by thinking since CDSs are on the way to Arrow securities we should have as many CDSs and let people trade as much of them as we can, but we're going to get to that in the last lecture about how all this theory, what's wrong with all the theory. So, any other questions before we--so let's now make the change that he suggested up there. Let's now change the economy just a little bit. Let's eliminate C. So this just disappears. So obviously now the total endowment is very contingent. It's 200, it's 280 and it's 440. Now what do we do? So beta owns B. So now what's equilibrium going to be? What do you think is going to happen? We want to quantify this. We want to give a beautiful simple theory that's quantifiable, but what do you anticipate happening to P_1, P_2 and P_3? So everybody's going to say, alpha, she's going to say, look, my A is risky. I don't want to hold my risky thing. I want to start hedging and trading these Arrow securities so I get the same constant in every state. Of course beta who owns B, he's going to do the same thing. So they're both going to be trying to trade Arrow securities. What's going to happen, do you think? Yes? Student: Aren't they both just going to be exposed to whatever the total risk of the economy is in >? Prof: Yeah, there's no way that they can, exactly, there's no way that each of them can be perfectly hedged. So no matter what they do, they're going to be exposed to more risk in state, you know, state 3 is going to be a great state. State 1 is going to be a terrible state, so what do you think that means about the prices? Everybody can't be hedged, and so in fact what'll happen is nobody will be hedged. Although, alpha will be, who hates risk more than beta, will be closer to hedged than beta will be. So beta will end up bearing more of the risk than alpha. And what do you think will happen to the prices of the Arrow securities relative to the probabilities? Yes? Student: It won't be constant. Prof: There won't be a constant ratio of 1 quarter as we had before, but can you be more specific? Student: The price of the securities for state 1 will be greater relative to the probability than the price of the security in state 3. Prof: Exactly. So that's what's going to turn out. The world is short of commodities in state 1, there just aren't many apples. That's the disaster. That's when we can't solve the energy crisis. We're totally screwed. Everybody wants to consume more in that state. Everyone's going to try and hedge against that state. They're all going to be trying to buy Arrow securities in that state, which means that because there aren't as many to buy, there's just not enough apples to go around, the price of Arrow securities in state 1 is going to be high relative to state 3. There's plenty to go around there. So she is going to sell some of her A and get some B to diversify, but B's got so good in state 3 that all of a sudden she's not going to be so worried about state 3 anymore, but state 1 she's still going to be worried about, and there's nothing to be done about that. So the price is going to have to be very expensive in state 1. So all right, that's all blah, blah, blah. Let's solve for equilibrium and see what happens. We can solve immediately. Nothing's changed. The utility functions are the same. None of this changed, so this board doesn't change at all. That's demand. Still depends on P_0, P_1, P_2 and P_3, but now we have to be a little bit more careful in state 1. So demand in every state is 600 - 400 P_1 over gamma_1 equals endowment of alpha endowment of beta. So in state 1, I'm going to now change this to a 1 although with my handwriting it looked like a 1 anyway, what's the aggregate endowment in state 1? The aggregate endowment in state 1 is 200. This is a 1 now. That's 200, so that means P_1 over gamma_1 = 1, right? Because 400 and 400 so it's 1. So you're not discounting the first state at all. You're looking at the probability of it. But what if I go to P_2 over gamma_2? Well, the demand is going to be the same. It's the price that's going to change to make up for the fact that the supply is much different, namely, namely what, 280. So now if I subtract I get 400,280 minus that is 320 divided by 400 which looks like 4 fifths, maybe. 320 over 400 is 4 fifths, right? Because 320 divided by 400 is 4 fifths, so P_2 over gamma_2 is 4 fifths. So they're not proportional anymore. And then P_3 over gamma_3 equals--now the outcome is 440, so if I subtract 440 from this I get 160 divided by 400, what's that? Student: 2 fifths. Prof: 2 fifths, thank you. P_3 over gamma_3 = 2 fifths. So the prices turned out to be quite different. Now, the reason why they're slightly higher on average, of course, than they were before is because there's less consumption in the future. We've suddenly made our future much worse off. So people are more desperate to consume in the future, so that means the prices of future consumption are going to be higher. So we have two effects here. These prices instead of being 1 quarter everywhere are higher, much higher than 1 quarter because the future looks so much worse. The interest rate is going to go down. It's not going to be 300 percent anymore. But more interesting is that the prices are no longer proportional to the probabilities. Just as he said over there the price in state 1 is going to be much higher relative to the probability, namely 100 percent of it, than the price in state 3 which is only 40 percent of it. So that's the conclusion. So now what do we do for our price? What's the price of A? What's the price of A? What do I plug in here? That, so that equals 1 quarter times 50 4 fifths times 1 quarter-- 1 fifth times 100 P_3 was 2 fifths times 1 half 1 fifth times 75 which equals something, 20,35 and 12 and 1 half, 47 and 1 half. Student: Why would you >? Prof: Why did I what? Student: Why would you >? Prof: So what is P_1? P_1 is equal to gamma_1 and gamma_1 is 1 quarter. So that's how I got 1 quarter here. So that's 1 times 1 quarter. P_2 was 3 fifths. What was P_2? Maybe I did it wrong anyway. P_2 was 4 fifths times 1 quarter which is equal to 1 fifth, and P_3 was 2 fifths times 1 half which is equal to 1 fifth. So that's how I got the prices. So all right, so you see that things changed, and we've captured the idea that people can't hedge fully by making the price of the Arrow security in the state where the economy's worse off, much smaller than it was before, I mean, much higher than it was relative to the probability than before. So we haven't gotten close to the punch line, sorry. Yes? Student: Can you repeat the part where you said stuff about the future looks so much worse they need to increase consumption? Prof: Two things happened to the prices compared to before. One is that we no longer have the prices proportional to the probabilities, right? Their proportion is 1,4 fifths, 2 fifths instead of the same constant 1 quarter everywhere, and that's because of the relative scarcity. People are much more worried about the first state than the fourth state and that's why, relative to the probability, the price is much higher than the third state. You agree with that, right? Student: Yes. Prof: But there's a second effect which is that all these numbers, 1,4 fifths, and 2 fifths they're bigger than the 1 quarter, 1 quarter, 1 quarter we had before, but that's obvious. That's because we wiped out the future. Half the endowment in the future disappeared, so naturally people are willing to pay more for the future because they're poorer there. In the first day of class we said that the interest rate, or the third week, the interest rate according to Fisher would go down if you got poorer in the future. So that's part of the reason that's happened. By the way, what is the riskless rate of interest? So P_1 P_2 P_3 equals what now? It's equal to 1 quarter 1 fifth 1 fifth, so 1 quarter 1 fifth 1 fifth. These are the prices, 1 quarter 1 fifth 1 fifth and that's equal to 20, 10,14 over 20, so that's 7 over 10, so therefore the interest rate 1 r = 10 over 7 so r = 3 sevenths which is like 40 percent. So the interest rate went from 300 percent to 40 percent, but that's because we lost all this future consumption. But that's not what I'm concentrating on. Fisher would have already known that. What I'm concentrating on is the fact that the prices are no longer proportional to the probabilities. You're discounting every probability, but adjusting the probability because people are much more worried about the first state than the third state. Student: So people are much more worried about A? Prof: Not A, they're more worried about the first state. The firms are A and B. The states are 1,2 and 3, so they're much more worried about the first state where the payoff is 200, than they are about the third state where the payoff, total dividends in the economy are 440. Are you with me? Student: Yeah. Prof: Oh boy. That sounded so unconvincing. I want to say the punch line. So I've got three more minutes to go. There are two punch lines. I haven't gotten to the stunning conclusion. So far I've said stuff which Arrow and Debreu had already figured out, but now I want to go to the thing that Tobin and Markowitz figured out, which is one more step we haven't noticed yet. Arrow has already figured out that because not everybody could hedge that means that the price of an Arrow security is not exactly equal to the probability. It's relatively high if the economy's poor like in state 1 and relatively lower if the economy's rich like in state 3. That's common sense. Now, what's not common sense is the extraordinary conclusion I'm about to show you. Let's look at what the consumption is; the final consumption of these two people. So if we look at the final consumption of these two people, what's her final consumption, so X_A. In the three states it's 200 - 100 times 1 which is 100. What is it in the second state? It's 200 - 100 times--what was P_s over--times 4 fifths which is, help, 160, maybe. And the last step was 200 - 100 times 2 fifths. 2 fifths is 20 so this is 180. That's hers. And his consumption in the future-- I'll put a tilde, I haven't talked about X_0 yet-- is 400 - 300 times 1 which equals 100, and here's it's 400 - 300 times 4 fifths which is equal to, help! 4 fifths of 300 is 160, and here it's 400 - 300 times 2 fifths which is equal to 280. Is this right? 100,160, who told me it was 160? Yes and what's that? 2 fifths is 120. This is 280. Student: The number > , like 200 - 100 times 4 fifths is like 120. Prof: What? Student: The first > Prof: Which mistake is there here? Student: No, the second > Student: The second 120 > Prof: Is this the wrong one? Student: The wrong one. Student: 160 should be 120. Prof: Here. 200 - 80 is 120. Thank you. So these are all right now? Student: 180 should be > Prof: 180 should be, okay, this is 40 so this should be 160. Thank you. That's it, great. So now what's so shocking about those numbers? That I finally got them right? Thank you. What's shocking is this consumption is just the sum of the aggregate endowment--what's the aggregate endowment? Remember the aggregate endowment is just 200,280 and 440. So let's say you take 1 quarter of this. Let's take 1 quarter of that. That's 50,70--that's 50,70 and 110. So 1 quarter of this plus if you add to that 150 you're going to get all these numbers. So this person, alpha, A, I claim, just holds 50 of the riskless bond, pays 50,50 plus 50,70 and 110. No. Is this the right--let's just check the numbers. Sorry, only one more second. I should have--so 100,120 and 160, that's the right number and that's equal to 50 of the bond plus 1 quarter of this thing. So 50 50 is--1 quarter of this is 50,70 and 110, right? So if you hold 50 of the bond plus 1 quarter of this you get 100. 50 of the bond plus 70 is 120. 50 of the bond plus 110 is 160. And this guy is going to hold 3 quarters of the aggregate endowment plus minus 50 of the bond, so 3 quarters of the aggregate endowment, 3 quarters of this thing, 3 quarters of the aggregate endowment is 150 - 50 is 100. 3 quarters of this is 210 - 50 is 160. 3 quarters of that, is 330 - 50 is 280. So what they've done in equilibrium is everybody, despite having a million stocks to choose from and thousands of states and all that stuff, what everybody does is hold the riskless bond, puts money in the bank and holds the whole stock market. So the first theorem we're going to prove next time is called The Mutual Fund Theorem which is that everybody diversifies by holding the aggregate economy, all stocks in the same proportion, plus money in bank. So that theorem of Shakespeare of diversifying, what did it amount to do? We have a very concrete thing. You hold 10 percent. This person's holding 25 percent of every stock in the whole economy plus putting some money, 50 dollars in the bank. The other person is doing 3 quarters of every stock in the whole economy plus lending the money to the first person. So that's the first of the two amazing results and I'll start next time by explaining it.
Quantitative_Finance_by_Yale_University	19_History_of_the_Mortgage_Market_A_Personal_Narrative.txt	Prof: Hi, this is John Geanakoplos again. Here to give a lecture, that I gave one evening, that we couldn't record. So I'm going to try and reproduce the lecture as faithfully as I can. And I think it's a historical lecture. I hope you find it interesting. It's about the history of the mortgage market. And I call it a personal history because by some accident, I participated at many of the key points in the recent history of the mortgage market. So I started off in 1989. I was professor here at Yale. I was a mathematical economist. I thought of myself as using mathematics to study economics and staying really pretty much as far from the real world as I could. But for some reason, I decided that I wanted to see what was going on on Wall Street. The most interesting mathematical modeling of that day was being done on Wall Street. And mathematical modeling and finance, that is in economics. And so I decided. why not go see it? And so I visited a bunch of investment banks. A number of my friends, including one from Yale, had worked at Goldman Sachs. So that was the natural thing to do. But, I had a little cousin who had just been hired recently, a little bit before that, at Kidder Peabody, which was sort of the number seventh investment bank at the time, in terms of size. And he introduced me to the fellow, Ed Cerullo, who ran fixed income at the time. And they persuaded me that it would be much more interesting to go to Kidder, Peabody and to talk to people like Ed Cerullo, than go to Goldman Sachs and be one of a hundred visiting professors. So I decided that the firm was a little bit smaller, but I would see more of it. And why not do something a little bit different? So they never had an academic visitor, I think, like me spend a year there before. So I went in 1989 to 1990. And while I was there I talked a lot to Ed Cerullo and to the traders and to a bunch of other people. And at the end of the my sabbatical, Ed Cerullo came to me and he said, you know I've come to realize that our fixed income research department isn't very mathematical. Why don't you hire a research department for me? And I'll help you along. But, you find the people, you know the subject, you can judge, your business is judging people doing research, why don't you hire me a research department? So I hired him a research department, which ultimately grew to 75 people. And I returned to Yale. And after I got back to Yale, he called me up and he said, now that you've hired the research department, you have heads of all these different groups, why don't you run the research department? You can do it from Yale, as a consultant. And so I became the head of fixed income research at Kidder Peabody from Yale. And it was quite an experience. I hadn't realized, when I accepted the job, just how many complications would arise. How many people would get job offers from other places and want to leave. And how many models wouldn't work. And then there'd have to be a wild scramble to fix it. But anyway, that placed me at an investment bank, that would become one of the key players in the mortgage market. Now in the mortgage market, well who are the players? They are the homeowners you all know about. They are the banks who are giving mortgage loans. But then there are a number of other players that are invisible to much of the public, which really dominate the market. There's the government agencies, Fannie Mae and Freddie Mac, which you'll hear a lot about. There are the investment banks, like Kidder Peabody and Goldman Sachs and a bunch of others. There are the hedge funds and there are other investors. And this group of people creates a gigantic hierarchy, an invisible market, that's on the same size, the same scale, as the stock market. So I think in that time, 1989,1990, if you'd asked anyone in America practically, what's an important financial market? They would have said, the stock market. What's another important financial market? Corporate bond market. What's another one? Well, foreign exchange market. What's another one? Options market. I don't think anyone would have said the mortgage market. Or at least they wouldn't have said it very early on in their list of important financial markets. But in fact, as I'm going to try and tell you during this class, the mortgage market is not only on the same scale as the stock market, but actually quite a bit more complicated than the stock market. More mathematical than the stock market. And in some ways, more interesting than the stock market. And as we'll see at the end of the course, it was the mortgage market that led to the greatest crisis we've had since the depression. And in fact, caused several similar crises before that. So mortgages appear at the bottom. You have homeowners living in their houses who need to borrow the money to buy the house. Before they can live in the house they have to get the money to buy the house. So they borrow the money by taking out a mortgage. And it's a bank or a thrift or somebody like that who lends the money. That's the first step. So a mortgage is just a promise to pay the loan back over a long period of time using your house as collateral. An important part of mortgages is that you have an option to pre pay the mortgage. I mean, what if you move? The mortgage is, say, a 30-year promise. And after three years, you might want to move. So, if you're gone from the house, the house can no longer serve as collateral because you don't live in it anymore. So there has to be some way of getting out of the mortgage. And so there's an option to pre pay it. Now, in the United States, that option can be used even if you stay in the house. And it turns out to be one of the more problematic aspects of valuing mortgages. And one of the most interesting aspects of valuing mortgages. We'll come to that later. So this idea of a mortgage, those three ideas, were already known to the Babylonians more than 3,000 years ago. So the mortgage is not a recent invention. It wasn't invented after the industrial revolution. It was invented more than 3,000 years ago near the Middle East. So, it's stayed pretty much the same for most of those 3,000 years until the 1930s when the amortizing mortgage was invented. So what happened in the 1930s, that was the time of the Great Depression and farmers had lots of mortgages and they would owe, $7.00 a year, say, as their interest payment. And at the end of 10 or 15 years, they'd have to pay $107, that is they make their interest payment. And they pay back the balance. What's called now a balloon payment. That's how a typical bond works. Well, of course when things got really bad, a lot of them defaulted. And naturally, they chose to default just before the $107 payment. So seeing that, mortgage lenders decided that it would be much safer to make a flat mortgage loan where the payment was say, $8.00 a year for all of thirty years. Now, you pay a little bit more each year for 29 years, but then you continue to pay the $8.00 the 30th year. But you see, if you add up all the extra payments and you realize that there's discounting, the $107 way off in the end isn't really that much money when looked at from the beginning. And so by paying $8.00 every year, you can get the same present discounted value of paying $7.00 29 years and $107 the 30th year. So that's called the amortizing mortgage. It makes the lender much safer because after a bunch of years have gone by, the house presumably has gone up in value. Or even if it hasn't gone up in value, the remaining payments are much less because so many have been made that the balance has been amortized. And so actually to get out of your mortgage, you need to pay less than $100 back. So this amortizing mortgage is something we're going to study mathematically in the next lecture. But now, I just mentioned that was one of the big innovations, which made the mortgage market much safer than before. Well so things continued pretty much the same from the 1930s all the way to the 1970s when we had securitization. Like many of the great financial innovations in history, this one was created by the government. So Fannie Mae and Freddie Mac were government Agencies They were created by the government. They then became eventually separate from the government. But they were given the task, they were created for the purpose, of making mortgage pass-throughs. So we're in the 1970s. So mortgage pass-throughs are the second tier of this hierarchy. So the banks who had lent the mortgage, remember when you take out a mortgage as a homeowner, you're selling your promise. You're getting the money by selling your promise to pay back later. So those promises are collected by the banks. And instead of just sitting on the promises, the banks now, with Fannie Mae and Freddie Mac could sell their promises to Fannie Mae and Freddie Mac. And Fannie Mae and Freddie Mac would put them together in gigantic pools called pass through pools. Why were they called pass-throughs? Because the mortgage payments the homeowners made would go to the banks and the banks would just pass them on to the pools. And then the pools would collect the money and pass that money on to the shareholders. So the ultimate lenders to the homeowners are the people who buy shares in the Fannie and Freddie pools. So the banks appear to the homeowner to be lending the money. But actually, they're not lending it all. They are the middleman. And so they collect the money from the homeowner and they send it on to the actual lender, who's the shareholder of the pool. And the banks are also the servicer, really. They're getting paid a fee for collecting the money and writing threatening letters if the homeowner stops paying. And as we'll see later, throwing the homeowner out of his house if the homeowner doesn't pay. So Fannie and Freddie played an extraordinarily important role in the mortgage market. First of all, not any mortgage could be sold into these pools. They had to meet strict criteria. You had to have a good credit rating. You had to have a job. You had to have all sorts of-- sorry about this, I'm going to have to shut off my cell phone. So the loan to value of the mortgage had to be, that is if the house is worth $100, the loan could only be 80% of it. You had to have a record of the job you had and so on. So this was very standardized and very high performing loans. You could contrast with, say, to the world that you might have seen in the movie It's a Wonderful Life. So in the movie It's a Wonderful Life, you remember Jimmy Stewart runs a thrift and he makes mortgage loans. And people come to him and they say we want a loan. And you know one guy comes and says he wants a loan. Jimmy Stewart says, well do you have any collateral? No, I haven't built the house yet, you know I'm trying to build the house. Do you have a record of employment? No, I just moved here, I don't have a job yet. Do you have someone who can vouch for you? No. Do you have a credit rating? No. There's no such thing as credit rating. So then Jimmy Stewart looks into his eyes and realizes this is a good honest person and gives him a loan. Well, that doesn't happen in the Fannie Mae and Freddie Mac pools. They're very standardized criterion. And that guy, Martini who got the loan from Jimmy Stewart would never have gotten a conforming Fannie or Freddie loan in the 1980s or 1990s. Might have gotten one in the 2000s though, but we'll come back to that. So that kind of market is very much like the kind of market in the Jimmy Stewart movie, It's a Wonderful Life, that gets created in his fantasy. Where you know, the town gets taken over by the evil banker and that evil banker, whose name I've forgotten at the moment, but that evil banker basically is creating the kind of loans, almost, that we're talking about now. Everything's mechanized and standardized. Of course with standardization you get tremendous advantages. For one thing, these loans being pooled together and being of the same general good quality, they allow the lenders, instead of lending to a bunch of homeowners in Peoria like the bank would do, now all those Peoria loans are stuck with a bunch of other loans from all over the country in the same big Fannie pool. And so the lenders, who are the shareholders, have diversified their risk. If the big businesses in Peoria, Illinois go under, it might be that all the homeowners in Peoria will default on their mortgages. But not in the Fannie and Freddie pools, because those are loans from all over the country. So it would have to be that businesses all over the country went bad for those loans all to go bad. So secondly, if you're getting a whole pool and there's an automatic criterion for getting into the pool, you don't have to worry that you're getting the worst loans or the cheatiest loans or something. You know the quality, the general quality, of all the loans. And once you have shares in a pool, you can resell the shares. So a bank who has to study the homeowner and you know have meetings with them. And you know, Jimmy Stewart had to look into his eyes. So Jimmy Stewart may have convinced himself the guy is a good risk, but how could Jimmy Stewart ever sell the loan to somebody else. The other buyer, who hasn't looked into Martini's eyes, he's never going to believe Jimmy Stewart that that's a good loan. So Jimmy Stewart is going to be stuck with that loan for 30 years. In the Fannie and Freddie pools, the shareholder who buys the loans and knows they're standardized knows exactly the same thing as the next guy who might buy his shares from him. So if the shareholder will be willing to pay more for the loan, because he knows that if he needs cash, he doesn't have to wait 30 years, he can just sell his shares to somebody else. So because of the diversification, because of the reduction in adverse selection, and because of this ability to resell the shares, lenders, that is shareholders, are willing to pay more for the mortgages. And so the mortgage rate went down. So, I've estimated that this operation together with the next one I'm going to talk about, has reduced mortgage rates by at least a percent. So if you think the average loan is $200,000, you're talking about $2,000 a year that the average homeowners save by this financial innovation. So securitization seems to have been a great boon. Now in 2002, when I made these slides, I'll just give you an idea of the size of the mortgage market. And you have to double all these numbers today, pretty much. So you see that you know the stock market was around $15 trillion and the mortgages around $7 trillion at the time. And you know that compares to $2 trillion for corporate bonds or $3 trillion for treasuries. You see how big the mortgage market was then, and now it's twice as big. It's the same size basically as the stock market, which hasn't really grown since then. So, I don't have time to talk about this. But, of course, of the mortgage market, some of it is commercial, some of it is residential. The vast majority is residential. But there's a very big commercial mortgage market. I'm going to be talking mostly about the residential mortgage market. Some of these mortgages are in fact held by the banks without selling them to Fannie Mae and Freddie Mac. But a lot of them are securitized just in the way we talked about. And they're going to be private securitizations later that we'll talk about. And so now that securitized part is $10 trillion. I'll give the numbers, recent numbers, later. So actually that may be a little bit big. The $7 trillion, the securitized part of the mortgage market. So in 2002, the agencies dominated the security market. The securitized loans were almost all Fannie Mae and Freddie Mac. There's also another agency called Ginnie Mae, but there was another part of it, which were jumbo loans. So there was a size limit. The loans couldn't be too small and couldn't be too big for these Fannie and Freddie pools. The government was trying to appeal to the middle class. Establish homeownership in the reliable middle class. And so the wealthy who were buying million dollar homes weren't able to get their loans sold into a Fannie or Freddie pool. And so those loans were securitized the same way, but by private agencies and not by banks, by investment banks, and not by the government. And that at the time, in 2002, was half a trillion. We'll come to all these numbers later. When we say today's numbers. So the next innovation after the 1970s, came in the 80s and that's the collateralized mortgage obligation market. CMOs, they are called. So the investment banks like Kidder Peabody and Lehman Brothers, for example, would buy some of these big pools. And then they would cut the pools, which were just pass-throughs. So the pools just passed through the money that the homeowners were giving them. So maybe they were passing through $1,000 a month as the promise. Well, say Kidder Peabody, might buy a pool promising $1,000 a month to the shareholders. And then cut the promise into two pieces. Maybe a floater, which would pay $500 plus the interest rate. And so when the interest rate went up, the payments would go up, that's why it's called a floater. And maybe a second piece called an inverse floater, which is $500 minus the interest rate. So as the interest rate went up, the payments would get smaller. But as the interest rate went down, the payments would get bigger. That's called an inverse floater. So that way the two add up to $1,000. But now, you can appeal to two different buyers. A buyer who needs the money when interest rates go up would buy the floater. A buyer who needs the money when interest rates go down, would buy the inverse floater. So by creating out of plain vanilla promise, two more tailored promises, you can target more sharply a clientele. And therefore get probably more than half the money for each of the two pieces. And that way, of course competition in the CMO market raises the amount people are willing to pay for the pass-throughs. Because they can then buy them and split them up. And sell them for more. So that raises the price of the pass-throughs, which in turn raises the price that the homeowners can sell their mortgage, which in turn lowers the interest rate that the homeowners have to pay. So again, it's another reason why this whole operation of securitization improved the welfare of almost everybody. So, the pieces gradually got more complicated So if there was default or somebody prepaid, as we talked about, used their option to pay early, instead of getting the money you expected, you get extra or less money than you expected. That created risk. And some of these buyers didn't want to bear the risk. So maybe you'd make the pieces $400 plus the interest rate and $400 minus the interest rate. And leave $200 to what might be called a residual piece or a derivative or something. And that $200 would bear the risk. So if someone defaulted, you take it out of the $200 piece and not of the first two pieces. So that split up, again, made the floater and inverse floater safer and encouraged people to buy it. But of course, somebody had to buy the residual piece, which was more complicated. So, as I said, this whole operation was a way of accomplishing two things. It made homeowners able to sell their promises for more. So they effectively were paying a lower interest rate. So it made it easier to move into houses. And that's precisely what the government intended by creating these agencies. It also allowed buyers and investors to get money in the cases they needed it, in the states they needed it. Because the pieces were tailor made for them. So I realized, while I was there at Kidder Peabody, that this whole multi trillion-dollar operation behind the scenes was, as I said, invisible to everybody and was worth writing about. It was bringing great welfare gain to the country and nobody quite knew about it. So for me, it crystalized what the essence of finance is. The essence of finance is you're trying to create promises, the financial system is creating promises, that deliver money to people in circumstances or states as I call it, that they really need the money. But of course, you have to guarantee that the money is going to be paid to them. So in order to do that, you have to have collateral. So this entire system is a way of creating promises and backing them with collateral. So if you remember, here are the potential promises, and maybe some people want money down here. That's when the interest rates go up, they're buying the floaters. Way over there, the money's going down, the interest rates are going down, that's the people who buy the inverse floaters. That's when they're getting most of their money. But these promises, you have a reason to expect to get paid, because they're backed by the collateral. OK, so this is not a very good picture. The houses backed the promises of the homeowner like in Babylonian times. If the homeowner doesn't pay, he loses his house. Then those mortgages themselves, those mortgage promises, are backing the pools, which are selling shares to the shareholders. But those shares are backing the CMOs, which are making more complicated promises. So the collateral you see is used once by the homes, once by the pools, once for the CMOs. And then it will turn out, as we'll see in a few minutes, that the investors who buy are borrowing money, buying on margin, using the CMO pieces they buy, as collateral for their purchases. So the collateral is being used and reused. And so in fact, the entire system is stretching the available collateral as much as possible. So collateral is a very scarce resource. It's very important to running a financial system. Many developing countries don't have any collateral. And therefore they have a primitive financial system. Here, there's a tremendous incentive to stretch the collateral as much as possible. You can stretch it by using it over and over again or by letting the same collateral back many promises. We saw both of those, the tranching, the different CMO pieces, and the pyramiding, the using the same collateral over and over again. So I wrote my first paper, published it, in 1997. I had written it while I was at Kidder Peabody. And one of the questions I asked was, when you take out a loan, not only what interest rate do you have to pay, but how much collateral do you have to put up? And that was a question that nobody seemed to have asked really before, in a general equilibrium model. So that was my first paper on the subject. I want to get back to Kidder Peabody. Kidder Peabody, as I said when I started, was a sleepy number seven ranked investment bank. Didn't dominate any market. But it came to completely dominate the CMO market. So this, as I said, was a multi trillion-dollar market. And if you look at all the pieces that are being promised here, what Kidder decided to do was, things got more and more complicated, there weren't just two pieces, there weren't just three pieces, there were 90 pieces typically at that time. And so a typical investment bank that wanted to buy a pool and sell these CMO pieces. Like let's say, Salomon or First Boston, they were the ones who first did these CMOs. They would try to line up 90 buyers and figure out what each of the 90 were willing to pay. And then when they added up the prices each of the 90 willing to pay, they'd go and if they thought the sum of those was bigger than the price in the pool, they'd go to the pool and buy the pool. And then immediately make a profit by selling off the 90 pieces. Well, at Kidder, the head of mortgages, who by this time by the way, was my young little cousin, who through hard work had worked his way up to running the small CMO operation. He got the idea that what Kidder could do, was to find a buyer for the riskiest piece. The one that I've put in yellow, remember, the residual. Which was maybe called an inverse IO, it had different names, but the riskiest pieces. Once he found the buyer, a place to put the riskiest piece, he would borrow the money to buy the pass through, and hold an inventory of all the other pieces. So he knew, that eventually, we would be able to sell off all the other pieces. And so we had a tremendous advantage. While everyone else was looking for buyers for 90 pieces, we had to find a buyer for one piece or two pieces. So we then had an inventory of 88 pieces, say, to sell. And as we did deal after deal, that inventory would get bigger and bigger. So our sales force would have a much easier time selling a piece. We wouldn't have to call someone up and say, do you want piece number four, that's the one we're trying to get you to buy. We'd call up and say we've got a huge stock of different kinds of pieces, of all kinds, from all kinds of deals. Maybe you're interested in one of them. So it's much easier for a sales force to sell with that situation than it was for the other investment banks to sell. So of course, we lured away some of the best sales people. So of course, the down side to all of that is we had to be very careful that the pieces we held, we knew how to hedge. We had to be very careful that when we held all these pieces, between the time we held them and finally sold them, we didn't lose a lot of money. And sometimes we were the ones who held the most dangerous piece, too. So we had to figure out what were going to be the cash flows of these pieces and how to model them. And that's what we're going to mathematically talk about the next few days. But I'm going to give you a hint of this now. So we had to predict, among other things, what the prepayments would be, OK. And so, if you talked to a macro economist, especially in those days, and you say, what do you think is going to happen in the world? They'll usually say, well I think in the next two quarters, unemployment is going to go up half a percent, and then maybe things are going to get better for the next year, and beyond that it's too hard to tell. So these mortgages are 30-year mortgages. You can't have a prediction that lasts a year and a half, you have to have a 30-year prediction. And the macro economists, by the way, are typically wrong. Even in their two-month prediction or six month predictions. So how can we risk billions of dollars holding an instrument that's 30 years long, which depends on what people are going to do over the next 30 years? Well the answer is you can't make a prediction and expect it to be right. But you can make a conditional prediction. You can say, if interest rates do such and such for the next four years, and housing prices do such and such for the next four years, then in that fifth year, pre payments will be so and so. That's a conditional prediction. It's much easier to make a conditional prediction than an unconditional prediction. It's shocking that so many economists are lured into making unconditional predictions. It's not a business we should be in. We should always be making conditional predictions. Well, I learned that lesson at Kidder. So, you know, the idea of possible worlds is going to play a central role in our course from here on out. And the possible worlds are the paths of interest rates or home prices. And so here's a very short, this is maybe a one year into the future, and we'd have to go 30 years in the future. As you can imagine, and this is just actually a much smaller group of possibilities than we used to consider. But, you see all the possibilities that could unfold over the next 12 months. And you see the blue line is one of those possible paths. So we have to predict, if we knew which path interest rates and housing prices were going to take, like that blue line, could we then predict, at the end of the blue line, what pre payments would be. Of course, if you followed another path down to here, we'd make a different prediction about pre payments. So, the cash flows are the pre payments and defaults. That's what we have to predict. And so, you might say, what good is it to predict a different number on each of these trees. Then basically what you're saying is you don't know what's going to happen. But that's far from the truth. If you know what the payments are on each of the paths and then you can hedge those paths. So for example, suppose the payments are very low here and very high at the top. Well, if you can buy another instrument that pays you something at the bottom, and you pay at the top, you can offset the variation in cash flows and the mortgage by that other instrument and guarantee yourself the same safe payment all the way through. That's the sort of thing that we did it at Kidder Peabody, which we're going to study in great detail. We held these complicated pieces whose payments would vary tremendously. So we ran a huge risk of losing all our money. But then we would hedge them with some other instruments. So in the end, we've got a pretty safe return. And because we knew the return was safe, we felt we could pay up a good amount of money for it. Whereas other buyers who couldn't hedge it, wouldn't want to buy it at all. So, now let's just see how good the predictions were. Here's a typical history of pre payments. So you can see it ranges to 99 from 88, something like that. So it's 10 years, 11 years, of pre payments. So that's the percentage of people who prepay every year. So it's the annualized percentage. So every month, you check how many people paid off their mortgage early, and you assume that rate stayed the same for the whole 12 months, what would the pre payment percentage be? That's what the number measures all the time. You see in some months it's practically zero. These are pre payments for a mortgage issued in 1986 that had an 8% coupon. So all basically, 1986 mortgages with an 8% coupon issued by Fannie Mae or some big pool of them anyway. So you see sometimes the pre payments are very low, sometimes they're incredibly high. How standing at the bottom at the back there, in '88 say, could you possibly have predicted that pre payment going forward? You know with the ups and downs and stuff like that. Well you couldn't, if you made it unconditional. But if you made it conditional, it's not so hard. Because what do you think happened in '93 that made pre payments go up so high? It was interest rates went down. Homeowners had an opportunity to refinance at a lower interest rate with a different mortgage. So of course they did that. And in those other months, when pre payments are very low, the interest rates were higher. So clearly, there's a connection between the mortgage rate you got and your original mortgage and the new rate that you can refinance into. And that is part of your conditional prediction. But another thing that's interesting is burn out. So if you look at two pools, one issued in '95 and one issued in '92, and with exactly the same coupons, you'll see that the older one is always pre paying less than the new one. At least starting from '95 onward. So it's as if the old one burns out. Once it has an opportunity to pre pay, you see a lot of pre payments and then they slow down. So that's another thing people had observed. So you might have thought the standard way of modeling things at that time was to just do a regression. You say, well we figured out that pre payments depend on the new interest rate and how much more in the money you are. And it depends on how long you've been in the money because of the burn out. You try to estimate a curve, like an S curve or something, that depends on parameters, that's on the interest rate, and on the burn out. How long you've been in the money. And according to some parameters that described the S and you tried estimate those parameters. So that would be an old fashioned way of measuring things. But as we're going to see in this course, we look at everything from an agent based approach. So what are the individual agents doing? So, I got the idea of trying to model all you care about is aggregate pre payments, what is the whole pool doing? But I decided, let's try and predict every single homeowner. So let's try to put ourselves in the mind of every homeowner in the country. Why are they pre paying or not pre paying? Well, they're pre paying if they get an opportunity to save some money. But, we know from that graph that lots of people don't prepay. Even when there's a tremendous opportunity, only 60% percent of the people are pre paying in a whole year. So that means the whole year goes by, and only 60% percent of them have prepaid. So every month, 8% or 10% are pre paying. So the other 90% haven't seen their opportunity. They've missed it or they've waited. So clearly, not everybody jumps at the opportunity. So it must be that people are different somehow. Even though they're in exactly the same circumstance in terms of refinancing. So, you have to account for the difference. So, I imagined that different people have a different cost of prepaying. It's a hassle to prepay. Maybe you literally have to pay some money to prepay. Maybe you have to take a day off from your job. Some people have other things to do. They're not that alert because they're paying attention to their kids or they're paying attention to their work. So not everybody has the same alertness. And not everyone follows financial matters as closely as everybody does. So, also over time, people are getting more rational and beginning to understand the market and pre paying more and more. And of course, people hear from their friends. If their friends are all prepaying, it's more likely that they'll think about it and prepay themselves. So I built a model, together with the researchers at Kidder Peabody. And then later we built the model of pre payments based on every individual making a different decision. So an individual is characterized by his cost and his alertness. So different individuals have different costs and different alertness. And by watching how they behave, we can come to guess what the cost and alertness is of each of these people. So you see this model captures all the effects that we talked about already. If you have a pool of people, you can see the vertical is how many people of each types. So there are different costs and different alertnesses. And so at the beginning, when you have a new pool, like on the right, there are a lot of people. And as, they get opportunities to refinance, it's not random people who prepay, it's the people with the highest alertness and the lowest cost who prepay. So over time, as a pool gets older, the distribution of people is going to shift. It's going to be have less hyper alert and low cost people and more high cost and low alert people. That's why the pool is going to slow down. So burn out is naturally explained by an agent based approach. So anyway, as we go through the course, we're going to emphasize this agent based approach. So building a model like that, starting in the 1980s, and making a conditional prediction, you can get a fit that looks like this. So notice, you make some gruesome errors, like over here, that was an expensive, '97, '98, that was an important mistake. But you can fit this kind of pre payment surprisingly well. OK, so that was my Kidder Peabody days. And I thought, my gosh, we're doing incredibly well. We're helping the country. We're doing things in a colossal scale that nobody had ever done before. I think I may have not emphasized enough that Kidder Peabody came to dominate this market. We controlled over 20% of all the issuance. Remember, there were trillions of dollars of things being issued. So this little group of 20 year old kids basically, plus me the old guy in research. So them, the traders, they were issuing something on the scale of half a trillion to a trillion dollars of these CMOs. These kids in their mid 20s or late twenties. And the world seemed to be a better place for it. And I thought, my gosh this is an untold story that needs telling. And it's an incredible success story. Well, things suddenly changed and in 1994 there was a crash. So this is the first of three crashes I've lived through. There was a scandal at Kidder Peabody, the Joe Jet scandal, who was a trader, a government bond trader, who was accused of doctoring the books and faking his big profits. He had been Kidder Peabody man of the year in 1993. And then in 1994, they decided that all his profits were fictitious and that he doctored the books. And so he was fired. But he sued Kidder for discrimination. And it was a tremendous controversy that was in the front pages of the papers for months on end. And finally, General Electric, who owned Kidder Peabody, closed the firm. After hundred 135 five years, or I guess 129 years, they closed the firm. So I had to go back one day, from Yale, to Kidder Peabody, and I invited those 75 people in the research department into my office, and I said you're fired. And then I got up and I went to the office next door and somebody said to me, you're fired. And so we all fired each other and the entire 130-year-old company came to a close. So, the head trader of mortgages and bunch of his top lieutenants decided from a hedge fund. So Kidder Peabody got closed, actually sold, it wasn't closed, it was sold to Paine Webber. And Paine Webber dropped the name Kidder Peabody and hired many of the people from Kidder Peabody. And in fact, the second tier, or the more junior group of mortgage traders at Kidder Peabody, which was the leading mortgage company at the time, they took over the desk at Paine Webber. And then Paine Webber was bought by UBS. And those same guys took over the desk at UBS. So the junior crew at Kidder Peabody, some of whom were Yalies by the way, ended up running the UBS. Or a big part of the UBS mortgage desk. But in any case, our mortgage traders, the head guys, decided to from a hedge fund. Instead of selling, the CMOs, they would buy the CMOs. And we called it Ellington Capital Management. So I was one of six partners. I was a small partner, because again, I stayed at Yale. So this introduces the last player, the hedge funds. So what is a hedge fund? You heard the name, I'm sure a thousand times. It has a bad name now. But a hedge fund basically means four things. It means it's someone who hedges. You don't just buy and hold the thing and hope that the cash flows are good, you try to protect yourself against as many risks as possible. Just like I explained, we were doing at Kidder when we tried to get the same cash flows in every scenario. And we're going to mathematically study that in remaining lectures. But you try to hedge, that's where the name comes from. So you try to offset as many risks as you can. Of course, you still run some risks. But you're offsetting setting as many as you can. The second most important thing, is most of it's done, or a lot of a buying is done, not most, but a lot of the buying is done with borrowed money. That's called leverage. You don't just take your investor capital and buy something, you take your investor capital, you borrow some extra money, and then you buy some stuff. And the stuff you buy you use as collateral to guarantee that the lenders are going to get their money paid back. So a hedge fund is generally leveraged. The third definition of a hedge fund, third characteristic, is that they're very lightly regulated. So what does that mean? That means that a broker who sells something has to make sure that the client on behalf of whom he's buying, the broker, the stockbroker, has to make sure that the purchased item is appropriate for his client. We have no such obligations. We can buy and sell with anyone we choose on behalf of our clients. But our clients have to be sophisticated investors. We have to vouch that they're sophisticated. If they have enough money, like say $5 million to invest in the hedge fund, they are by definition sophisticated. And then they don't need to be protected by having a broker who's necessarily watching out to see whether investments are appropriate. We tell them what we're investing in and, of course, we're obliged to explain our strategy. But once they understand our strategy, we don't have to meet the same test that a simple broker meets on behalf of, let's say a poor retired individual. So there's less regulation and the fourth characteristic is hedge funds typically charge higher fees. So that's what a hedge fund is. Now, the first hedge fund was started in the 1940s, I believe, by someone named Jones. And he was a stock picker. And what he did, is instead of picking let's say the best car company, which he might have thought was Ford and leaving it at that, he would try to hedge his risk. So he'd buy Ford, and he'd short all the other car companies. So effectively, he wasn't just betting on Ford doing well. Because he could lose if the whole economy went badly, Ford and every other car company could go badly. Instead he was betting that Ford would do better than the other car companies. So he was concentrating his bet on something he understood more. You can't be an expert about everything. Presumably he was an expert about cars. And he knew Ford was better than General Motors. So that was a bet he wanted to take. But he didn't want to take a bet on the whole economy doing well or badly. So that was the beginning of the idea of the hedged fund. Now there's so many risks that a car company or any company runs. Does their president know what he's doing? Is Detroit going to be a good city? Is there going to change in government regulation? Is some foreign competitor going to appear on the scene? Is the price of oil suddenly going to change? There's so many things they can go wrong in a company, it really is very hard to hedge. So hedging really makes much more sense when you can make the problem mathematical. Well see, with mortgages it really is a mathematical problem to a much greater extent. So it makes much more sense to hedge. And I think it makes much more sense to be a hedge fund if you're trading in the mortgage market. Anyway, that's what I found out when I visited Wall Street in those days. So what did the hedge fund do? Instead of creating these CMOs, the hedge fund would buy them. And of course, buy the most complicated one. So in effect, the hedge funds would buy the most complicated, the residual piece we're talking about, and try to hedge that. So effectively, the hedge fund, by hedging it, was really carving out the cash flows of that last piece into complicated ways and selling them off to stabilize its profits. So really, the hedge fund actually was continuing the work of the investment bank of creating more and more pieces and trying to allocate the risk. And so the hedge fund is part of the entire operation, which was making this mortgage market behind the scenes make home ownership so much easier and reduce people's risk. Or so it seemed. We had a hard time raising money to begin with. Because after all, Kidder Peabody had just gone out of business. And not only had we gone out of business, but there was a general crisis at the time. It was not only the trading scandal of Joe Jett, but at the same time, there was a crisis in the derivatives market. Because all these complicated pieces that were being created where pieces went up and pieces went down, of course if you didn't know how to hedge your risk, you could end up losing a lot of money. So Orange County went bankrupt in 1994. And what did Orange County do? They bought a bunch of inverse floaters. So when the interest rates were going down in the early '90s, they were making a huge amount of money. And the fellow who ran Orange County's municipal investments, was twice municipal investor of the year. But in 1994, when everything turned around and interest rates skyrocketed for the year, his inverse floaters became almost worthless, and he bankrupted Orange County. So, it was some of our inverse floaters that were being bought, which helped bankrupt Orange County. Plus Kidder Peabody had just gone out of business because of Joe Jett. So it was very difficult for our hedge fund to raise money. Our motto was we created the mess, let us clean it up. Nonetheless, we did raise some money. We had an important starting investment from the Ziff Brothers and we had an incredible boom time. We made fantastic returns our first few years. 50% returns. And we grew into the biggest mortgage hedge fund in the country. And things were booming along. And then suddenly, there was another crash in 1998. So this was the second crash that I was exposed to. So, what happened in this crash? Well, as I told you, we were buying mortgages as the hedge fund, buying that residual piece, and buying it with borrowed money. So we would buy the piece, let's say for $100, by borrowing $80 dollars. So we'd use $20 dollars of investor capital, we'd borrow the other $80, we'd buy the piece for $100, and then we'd leave the piece with the lender as collateral. So if we didn't pay them back the $80, the guy could keep our piece. So his $100 piece was protecting his $80 dollar loan. So things were swimming along. We're going to talk a lot about leverage later. Well, in 1998, one of the big competitors, Long Term Capital, which was founded, as I think I mentioned earlier in the course, by Meriwether, who was the most important, famous, fixed income trader on Wall Street from Salomon. And two Nobel Prize winners, who I've mentioned many times, and you're going to hear about again, Merton and Scholes, creators, especially Scholes, of the Black-Scholes model, the most important tool on Wall Street for managing risk, as we'll discover in a few lectures. So these guys, the three of them, and nine other partners, 12 of them, created this wildly successful hedge fund. And in 1998, it suddenly went out of business. And in fact, the government had to step in with all the big investment banks, coordinating the big investment banks, to take it over so the whole market wouldn't crash down around it. We celebrated the crash of Long Term Capital, figuring that was one of our big competitors out of business and now we would have an easier time. But, I remember thinking at the time that was a mistake. But anyway, a few months later, we got a margin call. So suddenly, on a Friday morning in October of '98, one of our lenders called us up and said, we think the prices have gone down, it's not $100 anymore, it's less than that. We need X million dollars of extra margin to put for us to contribute. Because the $100 piece protecting the $80 loan, it was no longer $100 piece, it was a lower piece, so there was less cushion. We need extra cash to have a bigger cushion. So we said, oh this is crazy, the prices haven't gone down that far, that's not fair. And they said, you have until 4 o'clock Friday afternoon to pay us back. And if you don't pay us back, then on next business day, which happened to be Tuesday morning, because it was Columbus Day holiday on Monday, we'll just sell off all your pieces and pay ourselves back out of the proceeds the $80 and give you whatever is left over. Well, we figured what was left over wasn't going to be very much. Because they only needed their $80. So they didn't have an incentive to sell for the best possible price, although of course, they would tell us they'd sell for the best possible price. They wouldn't and it would be a fire sale. So we didn't know what to do. And we couldn't raise the money by 4 o'clock on Friday. So we called up Warren Buffett. We said, well this is so unfair, they're forcing us to sell, there's no reason why we should have to sell. This margin call is not proper. It's not right. There's no reason we have to sell. What's going to happen is on Tuesday we're going to be forced to sell all of our bonds at the same time. And they're going to all sell for like $80 or something. It's going to be a terrible blood bath, a fire sale. Prices will go for nothing. We'll be totally wiped out so unfairly. Why don't you buy our firm. We'll give you half our firm, some big percentage of our firm. You just make the margin call for us. And then you could have this firm with these great bonds. It's just a travesty. And it's going to be such a good investment for you. And you can save us and save the bonds and stop this travesty. And he said excuse me? And we said, well it's unfair, they're going to force us to sell on Tuesday. And the bonds will go for nothing when they are perfectly valuable bonds. And they are going to wipe us out. You can prevent that from happening and own our great firm. And he said, hell I think, I'll wait for Tuesday and buy the bonds myself. And so Warren Buffett didn't rescue us. And so that Tuesday it looked like we would go out of business. But over the weekend, we managed to hold an auction and sell the bonds ourselves. So in other classes in economics, you find out how to conduct auctions. I don't have time to describe this in great detail. But let me just say, that in a typical auction you have to worry about the winners curse. Everybody's thinking, I'd better not be the highest bidder, because that means I probably overpaid. Because those smart guys are bidding against me. So what we did over the weekend was, we called everybody up and we said, we've been forced by a margin call to sell these things. There's going to be a great deal for you. So why don't you come back from your vacation, one guy came back from Budapest, one big trader on Wall Street. We got a huge collection of traders there over the weekend. We showed them our bonds so they could think about it. And on Monday we held our auction. We didn't sell everything at the same time. At 12 o'clock, we sold the first third of our bonds. At 2 o'clock, the second third. And at 4 o'clock, the third third. Actually, we got a little behind schedule, but that was our plan. And so what happened was that at 12 o'clock, everybody basically bid $80. So we said, we're one of the bidders ourselves, of course. We told everybody, they all did it by email, we emailed everybody back, you've been outbid. Either by someone else or by us. You've been outbid. And all these guys, one from Budapest, from all over the world back there, thinking we're going out of business, bidding $80, they don't get to buy anything. So what would they do? What would they be thinking? So between 12:00 and 2:00, we're on the edge of our seats. Are they going to bid $80 again? Which means, of course, we get nothing. Because we just pay back the loan for $80 and we go out of business and our investors go out of business. Or are they going to realize that they have to bid more in order to beat other people. So we had no idea what was going to happen. But the price was basically $95 a 2 o'clock and $99 at 4 o'clock. So we celebrated saving our firm. And it turned out there was another complication after that, which I won't get into. Which is that the thing had happened over the holidays. And so the next morning, the buyers didn't get their bonds. Remember, we don't have the bonds to sell them. They're sitting with the person who lent us the money. So it was over a holiday, and the bonds didn't get transferred to the buyers. And so the prime broker who was supposed to vouch for all this, it was a holiday for him too. And so the whole thing was a mess. And it's actually quite an amazing story, which I don't have time to tell. But anyway, when the buyers didn't get their bonds, the next morning on Tuesday, they all got alarmed that maybe we didn't even have the bonds. And so everybody made a margin call against us. And we went from celebrating to suddenly thinking we're out of business again. But sometimes, when you're so badly off, people realize that they have to stop. And so there was a big conference call on Wednesday in which all of lenders, the sort of number two people at all the big investment banks got together in the conference call, and they agreed that if they all tried to get their money back at the same time, none of them would get it. And so they waited for us to gradually work ourselves out of the predicament. So we survived the crash of 1998. And then after that, we had another boom year. An incredible year in 1999. And things kept booming again for eight years or nine years until 2007. Before, I get to that, that experience was so seared in my mind, the second crisis, the 1998 crisis was so seared in my mind, that I wrote a paper called The Leverage Cycle. In which I said, what basically happens is people borrow a lot of money and they're very leveraged. Then something bad happens in the economy. And the lenders suddenly reduce the leverage. And so the big leveraged buyers, they go out of business. The leverage goes way down. Lenders will ask for more collateral. And there's also the bad news. And those three things together completely crush the market. And so lots of people are out of business and the whole thing's a mess. But then after things settle down, there's another boom. And then it's going to repeat itself over and over again. So that's The Leverage Cycle story I told in 2003. I wrote it right after the crisis of '98 and I said that this crisis, which in '98 seems to be so small, could be repeated on a much grander scale for the whole economy. So we had these boom years, right after the crisis of '98. And then in 2007,2008, there was another crash. This time on a grand scale. But it was exactly the same kind. And the last two lectures of this course are going to be about the most recent crisis. And so we're going to mathematically reexamine this entire story. And again, after the 2008 crash, when we almost went out of business again, our hedge fund. In 2009, we had the best year we've ever had. Better than all those other years, even in '95. So three times in a row. There's a crash, a boom, a crash, a boom, a crash, a boom. We made back more money in 2009 than we lost in the crisis of 2007,2008. So the course has to end with an explanation of why these cycles happened over and over again. It can't be an accident. It can't be all my fault that I've been in three of them. There's got to be something systematic going on. And that what I've been writing about it. And how I'll end course. And by the way, as you'll see, I spent a lot of time talking to the federal reserve, and Bernanke, and Summers, and also with the ECB, the European Central Bank about the leverage cycle. Which I think is generally becoming recognized as a central problem. But I want to end this lecture in the next 15 or so minutes, 20 minutes, by pointing out one change in the market. The next big change in the market. The next wave of securitization. So, this is the sub prime market, which we haven't mentioned yet. And which I will now describe. OK, so what is the sub prime mortgage market. So I already pointed out that securitization was a great idea. Now it was applied, remember, to prime mortgages. You had to be a very reliable homeowner to get one of those Fannie or Freddie loans. And because those people were so reliable, although they didn't behave perfectly rationally, you had cost and alertness issues, they still were very predictable. Well, a combination of things happened in the late '90s. Investors began to get the idea, this has worked out so well, and there's so many people who don't own homes in America because they're poor. Maybe we can extend home ownership to still more people. Of course, they're going to be riskier, because they're poorer, they have less resources. But we'll charge them a higher interest rate and that will compensate us for the extra risk. The government also saw this as a great opportunity to help the poor. So this combination of investors getting the idea and the government wanting to sponsor it, led to the creation of a new market, the sub prime market, which is what I'm going to describe now. And I'm going to talk about what went wrong, or begin to talk about what went wrong, but I'm going to leave most of it for the last two classes. So as I said, securitization is so important because, let me remind you, typically when a bank makes a loan, the bank finds out a lot about who it is lending to. But the bank is a bunch of managers and stuff. The shareholders of the bank are the people whose money is at risk. They aren't the ones looking at the loans. So if you're a shareholder, you own stock in a bank, two years later the bank is going to make a loan to somebody, risking your money. And you've got no idea who the guy is that the bank is lending to. Or what the characteristics are of the person who is getting a loan. Think of the securitization when you're buying a pool. When you get this pool, you could be told what are the characteristics of all the homeowners in the pool. It's something very concrete. A bank lends to homeowners, it lends to businesses. It's doing 6,000 things. Of course, it's risky to have bank capital. You know, equity, own shares of the bank. Because you don't know what they're doing. And they are doing so many different things. You should feel a lot more comfortable if where your money is going is very well delineated. That's the idea of a securitization. It's very well defined where the money is going. So it makes people more willing to lend. Corporate debt, that's another way of lending money. But if you own bonds in a firm, you're not the first person to get paid back. The people lending with collateral get their money first. And if the firm goes bankrupt, there is a big court case and it takes a long time to get your money back. Not in a securitization. So there are many ways that a securitization is more attractive than lending money through a bank. And that's the reason for the securitizations. Now here are the current numbers, the 2007 numbers. And there haven't been much securitizations since then. So the agencies are now up to $4 trillion, Fannie and Freddie. Now those jumbo loans I told you about, the big loans that the rich people take out, remember, which was $0.5 trillion in 2003, is now $0.8 trillion. But there are two more markets that have been created. There's the Alt-A. Those are people who don't have credit ratings good enough to get the Fannie Freddie loans. That's $0.8 trillion. But they are pretty good credit ratings. And then the sub prime population, of which there were $1 trillion loans issued by 2007. That's $1.8 trillion of lesser credit loans that didn't exist at all in 2002. So you add these numbers up, 4.8,0.8, and 1, that's $6.6 and $4 trillion of unsecuritized the banks are just holding loans. So over $10 trillion of loans as I said. OK, and then you add the commercials on top of that and you're getting very close to the value of the stock market. So all right so we've talked about this. The advantages of securitized loans. All right, so how did the sub prime market began? Well, you had to have a few legal hurdles. The first one, which some countries haven't managed to achieve and some people now are doubting we should've ever done, is it legal to charge a high interest rate to someone just because they're riskier. Is that usury? Or is that a reasonable return, because you're making a bigger risk? So, there are anti usury laws on the books. And so in order to make these loans, they had to become legalized. You had to get congress to pass a law to say that higher interest rate loans for riskier people is not usury. So then, you also had to figure out the tax treatment, which happened in 1986. And so the first pools were created in the late '80s, the early '90s, and Kidder Peabody, by the way, the firm I worked for at exactly that time, was one of the first creators of these sub prime like loans. So it was very small in the early days. And it worked pretty well in the early days. And, as I said, by 2007 it had grown to $1 trillion, 5 million people at an average loan of $200,000. Now, these are people who, as I said, have bad credit ratings. And so they pay a higher interest rate. Instead of say 6% at the time, or 5% at the time, they might pay 5% or 6% of the mortgage rate at that time. They might pay 8% for the first two years. And then at the end of the first two years, the rate jumps up by another 3%. Maybe to LIBOR plus 6%. LIBOR, remember, is the inter bank interest rate. So, it's already high, and then it jumps up after a couple of years. Now, many people have said this is the kind of predatory lending. That the homeowner is being lured into taking out a loan, not realizing that in a couple of years, the rate is going to go way up. But actually, there's some rationale to this. It turns out, that if you've made your payments for two or three consecutive years, the market thinks you're not such a subprime person anymore. After all, many subprime borrower are people who are young. They didn't pay their credit cards in college. Or they defaulted on something. And once they're married, have a house, have kids, and they pay for three consecutive years, the market figures, well these people are much better. So we'll give them another loan, they can refinance into a loan with a lower interest rate. Because they are no longer considered subprime. Maybe they moved to Alt-A or maybe even into prime. So you could count on 70%, by the end of the third year, of people refinancing their loan. During all those years from the 90s and the early 2000s. So you'd be left with 30% of the people who didn't refinance. Why didn't they refinance? Probably because there's something wrong with them, they were missing their loans [correction: payments]. They were much riskier than the original pool to begin with. So naturally, you're going to charge them a higher interest rate. So it's not such a crazy thing that the interest rate went up after two years. It isn't necessarily a sign of predatory lending. OK, now how do these loans get started? There's somebody called an originator. A broker would find a homeowner, a subprime homeowner, and then go to originator who would create the deal. Now what would the deal be? The pool would be a bunch of subprime homeowners and you'd have to get some data on the people. You'd have to figure out do they have a job? What's their debt? What's their income? Things like that. And all that would have to be reported to the potential buyers. So a buyer in the shares of these subprime pools would get a list. Not by name. You can't reveal the name of the homeowners. But what the zip code is of every house. And what the basic qualifications were of the homeowner. Do they have a job? What's the loan to value on the loan? What's their debt to income ratio? Stuff like that. Now, the servicer, who's often the originator. Let's say the originator is an investment bank. The servicer might be the same investment bank or a specialty servicer. What they do is just what the banks did in the Fannie Freddie story. They're the ones sending the letters, telling people they have to pay, collecting the money, and dividing it up to the bondholders, as we'll describe in a second. And they have one extra job. Because they're subprime loans, you can expect a bigger percentage of them to default. And when people default, sometimes they can't make the payments, they lose their job, something like that. The servicer is given the right to modify the loan. The servicer can say, OK I understand you can't pay, of course you can't pay, you're out of a job, you don't have any money. There's no point of us throwing you out of the house right away, maybe you'll get the job back. So we'll work out a deal where we delay your payments, or maybe reduce the payments, maybe even we reduce the principle that you owe, because in the end that's going to make our bondholders more money. So the all the bondholders have no right to talk to the homeowner. They don't know even though the homeowner's name. But the servicer who is sending the homeowner letters all the time and getting the money, of course the servicer knows the name and has the right to modify the loan. And if the homeowner doesn't pay and the loan is not modified, because the servicer doesn't think it's worth it, then the servicer can kick the homeowner out of his house. And take the house and sell it and pay the proceeds to the fund. But there's one extremely interesting provision that if the homeowner is not paying, during the time the homeowner doesn't pay, the servicer has to make the payments for the homeowner into the trust for the bond holders. That's supposed to give the servicer an incentive to hurry up and figure out what to do to change the loan or throw the homeowner out. And of course, when the house is finally sold, the servicer can recoup his advance payments out of the proceeds of the sale. And then later, the rest of the money goes to the bondholders. Now, the rating agencies played an important role in determining the ratings that I'm about to describe. So here's the thing would look. You have all the homeowners stuck into a pool, all those loans. I'm going to go for ten more minutes, by the way. You have all these loans stuck in a pool. So the money would be coming in, the homeowners, remember, are paying this high interest rate because they are subprime borrowers. So there's $100 of loans that went out. Let's say each loans is for $1.00. Where does the originator get the money to lend to the homeowners? Well, the originator is at the same time creating the bonds. So there'd be AA bonds, AA, A, BBB, with a bunch of minuses too, the over collateralization and the residual. So you'd create $81 of AAA bonds. These guys would pay that LIBOR, the inter bank rate, which let's say was 5% percent. Plus a tiny bit, 20 basis points, so 5.2%. The AA would pay a little bit more than that. And the single a little bit more than. That's probably misprint, that should be LIBOR plus 10. LIBOR plus 20, LIBOR plus 30, and then the BBBs, LIBOR plus 130. So you'd issue $81 worth of triple AAAs, $7 of AAs, $5 of As, $5 of BBBs. That adds up to $88, $93, $98. You're only getting $98. So you've got $98 worth of bonds that you used. So the originator has sold these bonds for $98. He's got to lend $100, so he's $2.00 short so far. But you notice that the interest rate all these bondholders are getting is 5% percent, or a little bit more. The homeowners are paying 8%. So there's extra money coming in that doesn't have to go to the bondholders. So there's this residual piece that gets the right to get the extra interest payments. So the originator either holds residual piece or finds some hedge fund and says, OK, you buy the residual piece. And maybe the residual piece is worth $5.00. So $98 plus $5.00 is $103. So the originator has gotten $103. The broker's fees, remember the broker had to find the homeowners, gets $2.00. So now he's only got $101. So he lends the $100 and pockets $1.00. So the originator would get 1% bear no risk for his work in creating the deal. Now, how can these AAA pieces be rated AAA? Now, to be rated AAA mean there's a one in a hundred chance, or something, that you're going to default. So how could that possibly be, when the loans are so risky? Well, what happens if somebody defaults? So this is the calculation. What happens if somebody defaults? Well, if you haven't paid for the first 30 days, that happens quite often. But if you go, 60 days without paying, nothing bad happens to you. After 60 days, you get a letter saying you're delinquent and a note is being made that's going to have an impact on your credit score. So being 60 days delinquent, seriously delinquent, is bad for the homeowner. After 90 days, you're considered likely to default. And so you get these very threatening letters from the servicer. And after 120 days, the servicer can start to try and throw you out of the house. But to throw you out of the house, maybe they have to go to court, they have to do a whole bunch of things. And so in those days, it took 18 months, 14 more months, after the four already, to throw somebody out. It now, has taken on average, a couple of years, or three years. It's getting more and more complicated to throw somebody out. Which we're going to get to in a minute. So you could be thrown out after say 18 months. Now what happens if you're thrown out of the house. Let's say, the house is sold for $0.80. When you originally had a $1.00 loan. Well, during the time the guy hasn't paid for that year and a half, if it was an 8% coupon, that means a year and a half is 12%. So $0.12 the guy hasn't paid. So the servicers had to pay up the $0.12. And then you have to hire a broker to resell the house. That costs six more cents. And the guy probably didn't pays taxes for the whole year and a half. So that's another three cents or so, that you've lost, depending on what the tax rate is. So you've lost $0.12 of servicer advances, $0.06 to the broker, that's $0.18 $0.03 cents for the taxes, that's $0.21. And the house only sold for $0.80 instead of 100. That's $0.41 cents you've already lost. That's a sort good scenario. You've already lost 40%. So the bondholders know that with this scenario they're going to lose 40% about of their loan. Where does that 40% is $0.40 cents, because remember there's only $1.00 loan to that guy, where does that come out of? Well, there was this over collateralization of $2.00. This is extra money pouring into the deal because everyone else is paying a higher coupon. So you take the money out of this extra cash flow that's coming in. If the default, the lost $0.40 is more than the extra cash flow coming in that year, then you reduce the over collateralization. There was $2.00 dollars. These bondholders were only owed $98 and there's $100 of loans outstanding. So you could lose $2.00 of loans and still have as much loans backing these bondholders. But once you get to the next dollar, you're going to take the $0.40 first out of the BBB piece. So as more and more houses go under, you go through the over collateralization, the extra interest. Then you start taking things out of the BBB piece. After you wipe that out, then you go to the A piece, and then the AA and finally go to the AAA. So how could you possibly think those pieces at the top were AAAs? Well because let's do a simple calculation. Actually, they look incredibly safe when you start to think about it. All this extra interest and the over collateralization and stuff like that it's sort of 8% protection. And on top of that, you've got the lower pieces bearing the original losses. OK, so even if you expected 40% percent of the homeowners to default, which is an astronomical figure. It was typically, in the past, less than a few percent. Even if you thought 40$ of the homeowners would be thrown out of their houses, and 40% of each homeowner was going to be lost in the scenario we just described of the 40% loss, 40% times 40% is only 16%. But the AAA pieces are protected by 8% and then are protected by another 19%, because they're only the top 81%. So 16% doesn't come anywhere close to the AAA guys. So that, in 2007, was a horrible scenario to imagine. That 40% of the homeowners, they are 5 million homeowners. That means 2 million people tossed on to the streets, losing 40% of each of the homes and you don't come close to touching the AAAs. That's why it seemed like they should be AAAs and so many people were willing to buy them. I've got one more thing to add to this background piece. The credit default swap. By the way, things are even rosier than that, at least looked at from the point of view of 2007 Because remember, 70% of the people were always prepaying. That means you got 70% of your money back for sure. So you only had 30% of the people left who could possibly default. So instead of having 40% default, you'd probably have 40% of the 30%. So you see, you could easily imagine that your AAAs were completely safe. And so I think the credit rating agencies didn't do such a horrible thing rating these things as people say. But I haven't finished the story. So watch what happens. So a new invention that happened in the end of 2005 was the credit default swap. CDS they are called, which you've heard a lot. So what is a credit default swap? It's just insurance on each of these bonds. So a credit default swap on the BBB would say, if there's a dollar of principal lost, because the homeowner's default, you take the loss out of the triple BBB, you can get insurance on the triple BBB. A CDS just is a promise to pay a dollar for every dollar that's lost in the triple BBB. And the CDS on the A is a promise to pay a dollar for every dollar that's lost on the A. So that was a huge market. It suddenly took off in 2005. And then there was an index that was created in 2006. So these are insurance on particular deals. But if you put all the insurance together, you can make an index of what the insurance is like. And so you can tell how valuable the bonds are. Because if you see that the insurance premium is changing you know that people realize there's a bigger chance of default of the BBB. So the insurance market, the index of it, is going to tell you a lot of information about what what's going on in the subprime world. OK, now, I don't have time to get to these legal issues. But I want to add the last fact. Things seemed to be going so well in the subprime world from the late 80s, early 90s, all through 2000, all through the middle 2000s that people got more ambitious still. So what did they do? They created CDOs. So what are CDOs now? Remember, we had these loans that got cut up into bonds. There was insurance in the bonds. So people said, let's take the BBB bonds. They're sort of at the bottom, they're protected a little bit, but near the bottom. Let's cut those up into different pieces. So we take BBB bonds from all different deals, we put those into another pool, and now we cut those into different pieces. And so you might have a pool that's from California, and a pool that's from Detroit, and a pool that's from Florida, that would just be a horrible combination, or a pool that's from Illinois and Ohio and stuff like that. You put them all together. And now, somehow the market decided that we could cut these into AAAs, AAs, and As with the same logic as before. But, this turned out to be catastrophic. In fact, the market went one step further, and not only took the BBBs that we said before and made them collateral for more AAA bonds and CDOs. But then took the As from this, which came from the BBBs and cut those up into more AAAs, CDO squareds. So that was the mortgage market, the subprime mortgage market. So you see, that there's a tremendous amount of synthetic stuff. By the way, these insurance pieces, if you're writing insurance, you're promising to pay basically what the BBBs pay, so it's like an artificial BBB. So they created the synthetic BBBs and used those to cut up too in the CDO market. OK, so I'm going to stop now with one final word. So the subprime market of $1 trillion, plus the Alt-A market, became the new frontier of mortgages. And as I said, everything went swimmingly in the 1990s and the early 2000s. And then in 2007, there was a tremendous crash. So in January of 2007, February of 2007, the BBB insurance index plummeted from 100 to 75. At that point, everyone declared, oh this is just the subprime market. It's small thing, don't worry about it. Bernanke said there's no problem. The stock market didn't blip at all. It continued on until October of 2007 when it hit its high. The world took notice of the subprime collapse, but everybody said it wouldn't amount to anything, because everybody underestimated the importance of the mortgage market. So we're going to see in the last two lectures, how this unraveling of the subprime market led to the unraveling of the entire economy. And we're going to show that everything that I've described, although it sounds very much more complicated with subprimes than it did with the prime mortgages earlier, is really when you get down to it, the same story of leverage and crashes and then booms. And we're going to begin the next class by talking about the mathematics of the prime mortgage market and prepayments and how to value those. And gradually we're going to get to the crisis and what caused it and what we should do to prevent future crises. Thanks.
Quantitative_Finance_by_Yale_University	21_Dynamic_Hedging_and_Average_Life.txt	Prof: So time to start. So let me begin by reviewing a little bit of the dynamic hedging which I could have described a little bit more clearly last time. It's a very important idea and I made a little bit of a mess of it. I didn't make that big a mess of it, but a little bit of a mess of it. So let's be a little bit careful now about who knows what and what you're doing. So we said imagine somebody who knows that the probability the Yankees are going to win the World Series is 60 percent, and therefore each game of the World Series is 60 percent, and knows that the probability the Phillies win the game is 40 percent. So suppose that he finds somebody who is willing to bet with him on the Phillies. So he can win 100 dollars if the Yankees win. He has to pay 100 dollars if the Yankees lose. Now, his expected payoff is 20. He should take the bet because if the person's willing to bet at even odds, the Phillies fan's willing to bet at even odds and he knows the odds are 60/40, on expectation he's going to make 20. So it's clear what he should do, but the problem is he's subject to risk. Although he's right about the odds he could still, even though he's done the smart thing, he could still end up losing 100 dollars which could be a disaster for him. So what he would like to do is to hedge his bets. Now, what does it mean hedge his bet? Well, suppose there was another bookie who was willing to bet at 60/40 odds in either direction then what should he do? Well, if he can find another bookie who was willing to bet at 60/40 odds he should try and lock in 20 dollars no matter what. So he should do this bet. He should bet with the other bookie 80 dollars. He'd be willing to give up 80 dollars if the Yankees won in order to win 120 dollars if the Phillies win, and that's a fair bet according to the other bookie because it's 60/40 odds, 60 percent of this and 40 percent of that, this is 3 to 2 odds so it's a fair bet. So in other words, he makes money by taking advantage of the Philly fan to bet on the Yankees, but that subjects him to risk. So in order to minimize the risk he hedges his bet. That's where the expression came from. He hedges that bet by betting in the opposite direction, on--betting on the Phillies with his bookie, in the opposite direction, but standing to lose less than he, you know, he's betting in this proportion, in this amount so that he gets 20 no matter what. So he's locked in his 20-dollar profit. So that was where we began. Now, let's just think about it a little bit more carefully than I did before. Somebody, in fact, basically asked this question. Is he really making money because he understands better the odds of the Yankees winning the game? Is he making money because he knows the odds are 60/40 and the poor Philly fan thinks they're 50/50? The answer is no. That's not why he's making money. It doesn't matter what the odds are of the Yankees winning. He's winning because he's managed to arbitrage two different betters, namely the Philly fan and the other bookie, and the fact that they differ in their beliefs, the fact that he can trade with the bookie at 3 to 2 odds whatever bet he wants, and the Philly fan is trading at different odds with him. That's what enables him to make his profit. So how did he make the arbitrage--so what is an arbitrage? An arbitrage is, you find two bets which are more or less the same thing, which in fact are exactly the same thing, but trade at a different price. So what are the two bets? Well, there's the Philly bet, the Philly fan bet, and then there's the bookie bet plus borrowing 20 dollars. So he's going to make 20 for sure. So he could make the 20 at the beginning just by borrowing against his winnings. Then he'd have 20 at the very beginning and his payoffs from the Philly fan bet would be exactly--he'd owe the 20 so he'd have minus 100. So this bet is he'd be able to get 20 at the beginning, but he'd have to pay minus 100 and 100. He'd pay 100 dollars if the Yankees won, and get 100 dollars if the Phillies won. And so that way he'd cancel his bet at the end and end up with 20 dollars for sure. So just to say it again, he's made money apparently because he knows more than the Philly fan knows, but actually in order to guarantee that he doesn't run a risk he has to find another trader, and it's the presence of the other trader who's really giving him his profit opportunity, not his superior knowledge. And the fact that he has two different traders--and so why does that give him an opportunity? Because he can arrange a bet with the Philly fan and a bet with the other bookie, but combined with borrowing the money so that in the end he's going to just get 0 payoffs. Putting together the Philly fan bet, and the bookie fan bet, and borrowing 20 dollars he gets 20 dollars at the very beginning, and on net he has nothing at the end, so whatever losses he got from the Phillies he made up from the bookie bet. Whatever losses he had from the bookie bet he made up for it with the Philly fan bet. So arbitrage relies on replication. Somehow through some other bet--he was able to hedge his other bet. He was able to hedge his Phillies bet by replicating the bet with somebody else combined with borrowing to produce exactly the same payoffs in the end, or the negative of the payoffs in the end, and yet for a different price at the beginning. The Philly fan didn't demand any money upfront to make this (100, minus 100) bet with him. And with the bookie he's able to get 20 dollars upfront and make this the opposite bet, the (minus 100,100) bet. So by getting more money upfront and doing the opposite bet with the bookie he can end up completely canceling the Philly bet, Philly fan bet, and that's how he makes his profit. So that was the first idea. So what have I clarified? What I've clarified is that it wasn't his superior knowledge, it was the presence of two different traders that enabled him to make his profit, and I've clarified the method that he made the profit. The profit wasn't just kind of mixing in another bet, it was really cleverly arranging to undo totally the original bet. So he got actually 0 in the end and ended up with 20 dollars at the beginning. So let's just see now what you would do in a dynamic situation. Yes? Student: I apologize. I understand how this locks him into that $20 dollars, and how it makes sure he doesn't incur the losses that he might have occurred, but why would he do this if he has 20 dollars at the beginning and all this does is make sure no matter what he ends up with the 20 dollars at the end? Prof: Why would he do what at all? Student: This arbitrage at all, any of the bets. It seems like no matter what whether the Yankees or lose he ends up with 20 dollars. Why didn't he just keep his 20 dollars and not bet? Prof: He didn't have 20 dollars to begin with. He had no dollars. So he went and found the Philly fan and he made a bet against the Philly fan with no money. The Philly fan was willing to bet him 100 dollars on the Phillies. So he gets 100 if the Yankees win. He pays the fan 100 if the Phillies win. It didn't cost any money to do that. Then he goes out and makes another bet with the bookie. Again, it doesn't cost him any money. He gives up 80 dollars if the Yankees win, but he gets $120 if the Phillies win. So he's spent no money at all and his total profit is 20 dollars for sure. So what could he do since he knows he's going to make 20 dollars for sure in the future? He could just borrow it at the beginning if the interest rate's 0, have 20 dollars at the beginning, end up with 0 no matter what the uncertainty is and put the 20 dollars in his pocket. So that's another way of saying the same thing which is that he could, by combining the bets, put money in his pocket in at the beginning and no matter what happens in the future he doesn't have to give anybody any more money. So that's what he's done. That's what an arbitrage is. You put money in your pocket in the present and in the future you never have to face a problem. You've always got money that's going out in one hand you're getting from the other hand. Now, in a dynamic situation you can do the same thing. So I'm just reinterpreting what we did before a little bit. So in the dynamic situation what are you doing? The Philly fan now is betting on the whole World Series even though you know the odds are 60/40. So now that's an even worse bet by the Philly fan if you're right about the odds because the chances are even higher that the Yankees are going to win the series than one game. The odds, we know, are 71 percent. So by backward induction we did this calculation to say your expected payoff is 42 dollars. So let's suppose now--but now the key is that you're making money not just because you know better what the odds are, you're making money because there's another bookie standing there always ready to trade with you at 60/40 odds in any game. So the presence of the second bookie, even if you knew nothing, would enable you to make money in this case, lock in a profit for sure of 42 dollars. Now, how do you know that you can lock in a profit for sure of 42 dollars? Well, it's now done by dynamic hedging. You have to lay off part of your bet, a little part each day, each game and the amount that you lay off is going to depend on what happens, so that's why it's dynamic. It's a complicated calculation. So it seems almost hopeless to figure out what to do. I'm betting on the whole series. Many different things can happen. The Phillies could win the first game. The Yankees could win the first game. Lots of things could happen. By the end I want to make sure I've locked in my profit for sure. How can I do that? Well, the key is to think about marking to market. Just as we said, if you're assessing your position correctly, even though the World Series takes 7 games, if you were reporting to your investors, your hedge fund, you're reporting to your investors how you're doing, you should be telling them after the first game, you know, at the beginning you're telling them, "Look, I'm going to make 42 dollars. I expect to make 42 dollars." After the Yankees win the first game it looks like you're going to make 60, you know, now things are better, you expect to make 64 dollars on average, but if the Yankees lost the first game you'd only expect to make 9 dollars on average. So after the first game you go from thinking you're going to make 42 to being even more optimistic now, you're going to make 64 or you're going to make 9. So 60 percent times 64 40 percent of 9 is 42. So if you were telling your investors properly how you stood after the very first game you might have to tell them you've lost 33 of the 42 dollars that you told them before you were going to make. So you'd already be running a risk. You really only care, maybe, about getting money for sure by the end, but if you're doing proper accounting you should be worried all the way along whether you're making or losing money. And that's the key to how to have no risk by the end. You just run no risk at all the in between stages. So all you have to do is make a bet with the bookie who's standing by to make 33 dollars in case the Phillies win the first game. You're making a one game bet in exchange for losing 22 dollars if the Yankees win. This is still 3 to 2 odds, so the bookie's willing to do it. So the night before the first game you've bet with the Philly fan on the entire series, which is giving you a huge advantage, but you're willing to bet with the other bookie. The other bookie, we're assuming, is only standing by game by game. You're betting 33 to 22 on the Phillies. You're betting on the team you expect to lose. You're betting on that team with the other bookie, but in a smaller quantity. So this is going to mean that your profit after the first game, no matter what happens, is still going to be 42. So you can lock in 42 after every game. And so as I said last time the crucial thing is--so then one thing I didn't say. So one thing which I forgot to observe last time, which I think is interesting, is so is that what you should do? Should you do that after every game, always bet 33 to 22 against the Yankees with the other bookie? Well, the answer is no. What should you do if the Yankees win the first game? By winning the first game your expectation goes up to 64. Now it could be either 82--and the night after the first game you're much better off than you were before. Of course you laid off part of the bet with the other bookie, so you've had to pay off 22 so you're still only 42 ahead, but the Yankees have now won the first game. So it's now the night after the first game, before the second game. You're subject to more risk. What should you do now? You should go back to the bookie and make another bet on the second game, but should the other bet be 22 to 33? Absolutely not, because 64 up here goes to whatever that number is, which I forgot already, 82 and 1 half to 36 and 1 half. So what should you do? What should you do now? So I've done some rounding here which is going to screw everything up a little bit, but now what should you do here? After the first game you're here. Here you are after the first game. You've made your bet with the bookie. The first game you bet 33 against 22. Now what should you do the second game? What should your bet be with that bookie? He's still willing to give you 3 to 2 odds on the Yankees either direction. What should you do? You're not going to bet (33,22) again. You're going to make a different bet, and what should it be? Yes? Student: > Prof: Exactly. You should give up 18 if Yankees win and get 27 rounding up. She conveniently rounded a little bit because I had rounded a little bit. So you should do 18 and 27. Now notice that's still 3 to 2 odds. So the bookie's still willing to do that for you and you're locking in the 64 because it's going to be 64 again, and adding this is 64 again, right? So you've locked in whatever this number is. So in the first step you made a bet to lock this number in. In the second step you made a bet to lock this number in. You're always locking in where you were before. So that bet is changing each time, but you're always locking in what you were before, because after the Yankees have won a game now the next game is not quite as important. Time is running out on the Phillies so it's not as revealing the next game about what's going to happen. So you make a smaller bet up here than you did before. So why is that locking everything in? Because this average is now 64, what it was here, but don't forget you'd already made the initial bet to lose 22. So you've locked in 44 now here and also 44 here because you still owe the 22 from the first bet. So you just keep proceeding down the tree locking in where you were before and so by induction you've locked in 42. So that's what you're doing, and the bet is changing every time. So what do you think the bet is here, by the way? The bet here you could go from 9 to 36 or minus 32. So what should you do here? What should you do here? What's the bet that you're going to make with the bookie after the Phillies win the first game? So it's going to be minus 27 and plus 41, and that's 3 to 2 odds with some rounding, right, 13 and 1 half times 3 is 40 and 1 half. So it's still fair odds, so the bookie's willing to do that. You've locked in 9. So by induction you've always locked in where you were before and therefore you've locked in 42 all the way along. It sounds like we're locking in 9, but we're not locking in 9 because remember the first day you won 33 dollars from the bookie when the Phillies won the first game. So you've locked in the 9, but don't forget the 33 from before, so it's really you've locked in 42. So 42's locked in the whole way. So that's dynamic hedging. You have a complicated bet that depends on a lot of things along the way, but you bet each time along the way, maybe changing your bet each time depending on what's happened so far, and that way you can lock in whatever profit you had. So that's the thing that sports bookies have known for a long time. The expression "hedging your bets" comes from that and so that same logic can be applied to the market. But remember, the step that I didn't emphasize very much is that although you seem to be locking in where you were before, there's a slightly more abstract way of saying that, that at the end you're going to get 42 dollars for sure. So of course you could borrow all the way back from the beginning and get 42 dollars immediately and then never owe anything in the future, because whatever bet you were winning or losing with the Philly fan you were making up for with your myriad bets with the bookie. So it's a replication argument that by betting sequentially with the bookie different amounts, you're undoing the single long bet you had with the Philly fan. So now let's move from sports, as we did last time, to the market. So here we had the prepayment spreadsheet. And so we had, remember, this was a bond, a mortgage, a 30-year mortgage, 8 percent mortgage, and the interest rate started off at 6 percent and it had a 20 percent volatility. So the interest rates could follow this process. There you see it. They start at 6 percent, but they can go up or down by 20 percent, basically every period. So you assume that everybody knows this and knows that the probabilities are 50/50. That's like saying you know in advance there's a bookie out there, that is the market, that's willing to give you, no matter what day it is, 50/50 odds of the interest rate going up or down from then on. That's just like the bookie standing by. You now are going to take advantage of the fact that you can anticipate that the market will stand there ready to bet with you. Now, if the whole market freezes or something you can be totally screwed. You're doing your complicated dynamic betting with the market, one day you wake up and you can't bet anymore because nobody's willing to trade, something horrible has happened, 9/11 happened or something like that. You can be caught in a really bad situation and end up running a lot of risk. So you're relying on the market, so it's not surprising that when the market freezes up lots of people suddenly are exposed to more risk than they were before. So now in the market you're not going to be able to find these pure arbitrages. In the sports example it was a pure arbitrage. There was a Philly fan who is betting at even odds and a bookie who was betting at 3 to 2 odds. Now, you shouldn't expect that to happen. I mean, by what miracle did this fan come to you instead of to the other bookie? Why do you deserve to meet this fan and take advantage of him? What have you got that no other bookie has? It's a miracle he came to you and not to one of the other hundred bookies. Well, it's probably because you actually know something that the other bookies don't that you can take advantage of. So in the background here there's another thing that you knew. You knew the fan was going to pay off if he lost. Maybe the other bookies weren't willing to bet with him because they didn't think he was going to pay off if he lost. So that's the extra thing that you knew, you knew that he was going to pay off. Now it makes sense that he came to you and not to the other bookies because you actually knew something that they don't. And so that's how it really works in the market. You're relying on some piece of information you have that they don't. Of course you could be wrong about that information and then you get into a lot of trouble. So here in this mortgage what's the thing that you're relying on? I'm assuming that the rest of the market is standing by ready, as I said, to trade, to make interest rate bets with you, with everybody, at even odds whether the interest rate's going to go up or down. So no matter where you find yourself in the future, like here, someone is willing to bet at 50/50 odds that it will go up or down. Now, this is a year-long bet so you're going to have to take into account the interest rate. It's not just going to be 50/50. You have to discount all the cash flows by the interest rate, but it's basically a 50/50 bet discounted by the interest rate. So now what's new here? Well, you don't know what the cash flows are. So here's the extra piece of information you're adding. You know that the mortgage homeowner is rational and is going to prepay rationally. So you know what these cash flows are. Some of the time the mortgage homeowner is going to pay the 8 dollars he owes, some of the time he's just going to pay 8 dollars, in fact, here is what you know is going to happen. Down here where the 1s are he's going to pay his coupon of 8, pay off the remaining principal and that's the end of it. So in fact the very first day if interest rates went down the rational thing to do is to pay off the entire mortgage. So you know that's going to happen. Now, that's the extra information you have. You know what the cash flows are. If other people knew those cash flows they would figure out the price of the mortgage too. It's just they don't know those. You know the cash flows and you can now figure out that the price better be 98. Why--if there's someone else willing to trade with you to buy that mortgage for more than 98, like why might that happen? Because someone else might have the erroneous opinion that the homeowner will never call the mortgage, will never prepay because he's just going to be asleep all the time. So let's say the homeowner's a she. Let's say the homeowners are all shes. This other trader thinks they're all asleep and will never prepay. You know that these homeowners are all incredibly alert and on top of things, and so they're going to prepay, and the value's only 98. So because of that extra information you know the actual cash flows. Sorry, we're here. You know the cash flows. You know how to value the bond, and you know it's worth 98. So, and let's say the other guy's willing to pay you 120 for it. So you can sell it short. You can sell it to the guy short for 120. That means you owe whatever cash flows the mortgage pays, and you know what it's going to pay down there. So how can you lock in your profit? Well, because with 98 dollars at the very beginning you can replicate those cash flows. You can go out into the market and buy those cash flows, the very cash flows you know the mortgage is going to make. How can you do that? Well, because at the first step--remember what this says. The first step the price is 98. The interest rate could go up or down. If the interest rate goes up the payment is 8. That's the coupon plus 92 something; 92.6, and if it goes down the payment is 8. So what is this? The payment is actually 8. That's the cash flow that has to be made. The mortgage wasn't called here at the beginning so no matter what she does, the homeowner, she's got to pay the 8. So you know you're going to owe the guy 8 the first period. Now, down here she's actually going to prepay. So she's actually going to pay the guy the whole 99.1. Up here she's not going to prepay. She's going to hang onto the mortgage. So what is this 92.6? This is the present value, assuming those cash flows, of her future payments. So if you get 98 dollars you know that 1 half times this-- this by the way, is 102.6, so 1 half times this divided by 1.06 plus this thing, remember is 107.11 divided by 1.06 times 1 half. That's how we got the number 98,98.8 whatever it was. That's how you calculated 98.8 by backward induction. You took this value times 1 half discounted plus this value times 1 half discounted. That's how you got 98.8. So therefore, if people are willing to trade at these prices, in other words what's the price here? It's 1 half times 1 over 1.06 and this is 1 half times 1 over 1.06. You can buy 1 dollar here at a cost of 1 half times 1.06. You can buy 1 dollar here at a cost of 1 half divided by 1.06. Paying this amount at the beginning will buy you 1 dollar here. Paying this amount at the beginning will buy you 1 dollar here. So by paying this amount you can get this payoff, 102.6,100.6, sorry, 100.6. You can get this 100.6 and you can get 107.11 because precisely this is the cost that you have to pay for each dollar up here, and this is the cost that you have to pay here for each dollar down here. Why is that? Because we said the market is standing by recognizing that these are 50/50 odds that it has to discount. So that means the whole market is willing to trade you, will be willing to promise you 1 dollar here in exchange for this amount of dollars here. It'll be willing to promise you 1 dollar here in exchange for this amount of dollars here. So with this amount of dollars you can buy 8 dollars and have 92.6 leftover and you can also buy 8 dollars here with 99.11 leftover. So all this together is enough to make the prepayment because you know she's going to prepay here. That's what we found out. She's going to prepay at the first step down. Oh, what the hell does this say? She's prepaying just as we said. At the very first step she's prepaying. The first interest rate down she's going to prepay. So we know you're going to have to come up with all this money, but you've bought it over here. It cost you this amount. You bought all that. If things went up you'd have to pay 8, which you've also bought, but you've got 92.6 left over and that's going to be enough to buy everything that comes after that because the next day you're going to have to buy more stuff, and so you just keep buying going forward. So with 98.8 dollars you can buy all the future cash flows and you've sold the thing so you can make all your payments that you're obliged to by selling it short and you received 120 to begin with. So you locked in 21.2 dollars. So that's the gist of the whole thing. So I said it last time not very well. I said it a little bit better this time, still not brilliantly, but do you now get it? Someone ask me a question perhaps? Is it okay? So I'll say the punch line again. The punch line is that if you can find a favorable--so here what was different about the World Series and the mortgage example? In the World Series you took advantage of the fact that there was a bookie and a Philly fan willing to bet at different odds on the same thing, and so even though the Philly fan had a very complicated 7 day bet, and the other bookies were only willing to make day by day bets, you could take advantage of that disparity to lock in a profit for sure, and that's what you should try to do. In the market you're probably relying on something else. You're relying on the fact that you know more about the cash flows than the rest of the traders do, the rest of the market does, maybe because you understand prepayments better than they do. And so that's why I said it was so important to model prepayments. So let's say you understand prepayments better than they do so you know what the cash flows are going to be much better than the market does. You can take advantage of that. You need now this advantage. Just like in the World Series you might have needed the advantage of knowing the Philly fan would actually pay off if he lost. So there's that advantage that you have, and now you have to rely on the fact that the market or the bookie from then on day by day, year by year, is willing to make bets at these odds that you can anticipate. And so using that you can trade over and over again with the rest of the market and dynamically replicate what the payments you have to make by selling the bond short. So therefore you've locked in your profit because you can anticipate-- assuming the market stays there willing to trade at even odds you'll always be able to produce the cash flows with the 98 dollars you started with to exactly meet all your payment obligations you've incurred by selling the mortgage short. And since you sold it at the beginning for $120 you've made 21 dollars at the beginning and you'll never need those dollars. You just put them in your pocket. So that's how to dynamically hedge a winning position to eliminate the chance of loss. Of course you still bear a chance of loss. If you're wrong about the prepayments you're going to lose money, and if the rest of the market suddenly stops being there to make these year by year bets on which way interest rates are going to go you'll also be subject to a lot of risk. So you're relying on those two things, the whole market not collapsing and your being right about prepayments, but conditional on those two facts you've locked in your profit. So you got rid of a bunch of risk, the blind luck of (100, minus 100) from the roll of the dice of the Phillies. You got rid of that luck, but you still had to count on the bookie being there day after day after day, and in the mortgage case on the fact that you knew how to predict the prepayments. Yes? Student: So in the first example, what's the point of betting the second time since the maximum amount of money we can make is 42, and we already made it in first bet, so why should I come to you betting? Prof: I never made 42 on the first bet. Here at the beginning nothing's happened yet. The series hasn't been played yet. So I say to myself I've made this 100-dollar bet with the Philly fan for the whole series on who's going to win the series. That's going to happen 7 days later. So right now I can anticipate, on average I'll make 42 dollars. Some of the time I'll lose 100. Some of the time I'll win 100, but on average I'll come out 42 dollars ahead. So I've done a smart thing betting with the naive Philly fan, but I'm still potentially screwed. I could still lose 100 dollars. I'll still have to face my investors and tell them I've lost all your money. They're going to close me down, and so I don't want to run that risk. They don't want me to run that risk and I don't want to run the risk. I still want to take advantage of the Philly fans. So what I do is every game I make another bet against my inclination. I bet not on the Phillies, I bet, I mean, not on the Yankees who I think they're going to win, I'm betting on the Phillies because I'm undoing part of the gamble that I did with this guy. I'm hedging that gamble, but by doing that in a clever way, changing how much money I bet each game-- so the night before the first game I bet 33 dollars to 22 dollars on the Phillies winning. After the Yankees win the first game I bet 27 dollars to 18 dollars again on the Phillies winning. So I decrease my bet going up, I increase it going down. So by doing these clever game by game bets I lock in 42 dollars for sure. Yes? Student: Do you actually lock in for sure because say at the end of the last round you don't actually-- like that node is going to be the end, right? You don't actually have two branches coming out of it, > favorable outcome and > Prof: So you have locked it in. So how could that be? So it's a good question, but you've overlooked something. So her question is the game's going to end after 7 days. What if I ended with the minus 100? The Phillies won all four games. Doesn't it look like I've lost? So why didn't I lose? I bet 100 dollars with the original Phillies fan. I bet 100 dollars on the Yankees. If the Phillies win all first four games I've got to give the guy 100 dollars. Of course I made these side bets with all these bookies on the way. So what were the side bets? Student: Sorry. My question is the only nodes that are secured, that are locked in, are nodes with two branches coming out of it. There's going to be an end where there's no more branches coming out of the node and so what's the situation? Prof: The situation is you're up 42 dollars, but we're trying to understand why that is. That's your question, right? So you're going to be able to answer the question although you don't think so yet. So what happened the first time? The first time the Phillies won, that bet with the original Philly fan is looking worse. I had 42 dollars I expected to win. Now I only expect to win 9 dollars because the series is turning against me, but the bookie paid me 33 dollars. So I'm--33 dollars already in my pocket. This is 9. Now let's say I got to the end to the last game where this was a 0. Let's say this was the last game where I've lost. Well, this is minus 32. Let's say this is the last game. I lose 32 dollars here. Let's say it was only a two game series and I give up 32 dollars in case the Phillies win the first two games, right? So you're saying, "I'm down 32 dollars. That's the last node. How can I possibly be up 42?" Well, so what's the answer? Student: Because I hedged it with the bookies. Prof: What? Student: Because I hedged it with the bookies. Prof: Right, because I bet on the first game and the first bookie gave me 33 dollars. Then the second game I'm going to bet with the bookies and I'm going to bet minus 27 and 41. So although I now owe the Philly fan 33 dollars here, I made 41 dollars with the second bookie and 33 dollars with the first bookie. That's 74 dollars and I pay 32 to the original Philly fan so I'm still up 42 dollars. So it sounds like you have to do a lot of arithmetic. You don't have to do any arithmetic. I knew I was going to end up 42 dollars up. How is that? Because every bet I said let's look at the number here wherever we are on the tree like here. At this node after all the stuff that's happened before the bet I'm going to make with the bookie that one game is going to be enough to turn this random thing into 64/64. So I always take what happens further down the tree and turn it into what's happened at the beginning of the tree, but then I work it all the way back and it's 42. So that means, see this thing was 64 and 9, but I made a bet 22/33 with the bookie to turn it into 42/42. This thing was 64. I made a bet to turn this into 64/64, but with the 22 here that's also 42. So no matter how far I go on the tree I'm still exactly 42 ahead. Any other questions? Yes? Student: In the example that we just did for the mortgage, could you explain why we are gaining 8 dollars? I thought we'd be losing 8 dollars every branch. It's below the... Prof: Sorry, what am I doing? Student: In each branch we've said that we're gaining 8 dollars 92.6. Aren't we doing negative 8 92.6? Prof: So her question is in this case the mortgage--so now we're moving from the World Series to more real life. In this case I know the cash flows from this mortgage are worth 98.8, but somebody else not understanding the homeowner and how rational she is, someone else is willing to pay me 120 for that mortgage. So I sell the mortgage for 120 and I take 21 dollars and put it in my pocket. Now I've got 98.8 dollars left. So that's money now I have to do something active with. What do I have to do? I owe this guy a lot of payments. Every time she, let's say it's you, makes your payment, her payment, in the market I've sold the thing short. That means I owe--I've promised to deliver whatever that mortgage delivers. That's what it means to sell it short. So I've got to deliver the 8 here, say. I've got to deliver the 8 here, and here she's prepaying. I have to deliver the whole 107, right? So with 98.8 dollars I can afford to buy 100.6 dollars in this state and 107.11 in this state. How do I know that, because that's where the 98.8 came from. It said this total amount 100.6 times the price, which is the odds of it happening discounted, that's the price plus the 107.11 times its price, the odds it happens discounted, is exactly 98.8. That's where I got 98.8. So therefore with 98.8 dollars, remember the bookie's willing to go either way, with 98.8 dollars I can buy all these cash flows and all these cash flows. So what do I do? With the 107.1 down here I pay the 8, her coupon, and her 99.11 prepayment. I pay it all to that guy I sold the bond short to and I've kept my promise. That's the end of the mortgage. Up here the mortgage only delivered 8 so I only owe him 8, but I've got another 92.6 left. Why is that exactly what I need? Because from here on I have to use that money to buy the future cash flows because she's going to continue to pay her 8 and maybe eventually it will prepay. But by induction, by repeating this step over and over again I can always make the payment and have the present value left over to afford to buy the future payments plus the present value left over. So by induction I'm always making the coupon. Like in this first step I make the coupon payment plus I've got enough money left over to match the present value. So that means as I go forward, and forward, and forward I keep making the payment and matching the present value that's left over. By the time I get to the 30th year I've made the coupon payment. The present value left over is 0 because there isn't going to be any payments after that. So I've made all the payments. Student: Could you do this one year ahead as well? Prof: Yes, I could. So I was hoping you wouldn't ask me that because it's--so what happens in the next period. So here we know that she didn't pay. She didn't prepay. The present value is 92.6, so we're here, 92.6. Now, she didn't pay. Let's look at what she's doing, whether she's prepaying or not. So this is why I did the second graph. So if the interest rates go up the first time and then back down she's still not going to prepay. So we can now go up and see--oops. Here we are. So we can go up now and see what's happening here. It's 92.65. You go up to 83.95 or down to 97.2. 97.17. So what does that mean? So with 98.8 dollars I bought, I'm the guy selling the thing short, you're the smart rational pre-payer, so you paid 8 dollars here. That means because I've sold the mortgage short and you've made that 8-dollar payment I owe the guy the 8-dollar payment just as if he had the mortgage. So I've got to come up with the 8 dollars. Down here if things had moved here you would have paid 8 dollars plus the whole prepayment so you would have paid 107 dollars. But with 98.8 I can buy 8 92.6 up here and 8 99.11 down here. So I've bought all the cash flows I need to down here. I hand them over to the guy and I say, "You see, I kept my promise to deliver whatever that mortgage did, and I knew that she was going to prepay, I knew how smart she was and so I've kept my promise. You didn't think she'd prepay. I knew it. I've kept my promise." And then up here I've got the 8 dollars so I can make the payment, match it. I've got 92.6 left, now I don't give it to the guy because the payment's only been 8. I take the 92.6 and with the 92.6 that happens to equal this plus 8 times 1 half divided by 1.06, and it equals, also, this plus 8 times 1 half divided by 1.06. Not by 1.06, by the interest rate here which happens to be--you have to figure out what that interest rate was up there. So the interest rate went up to--it started at 6 percent and went up to 0732 percent. So this is .0732. How did this number 92.6 get calculated? It was exactly take the payment of 8, take the present value of what's left, multiply by 1 half and discount it at the interest rate here plus 1 half times this payment of 8 plus the value of what's left discounted by that interest rate. So this number 92.6 allows me to buy this and to buy that. So therefore, if things went up again I could make your 8-dollar payment that you make to the bank I have to make to the other guy because I sold the mortgage short. I've got the money to pay him. I've also got the money to pay him if things had gone down again 8 dollars. And I've got more cash in my pocket, this and this in the two cases. With this money I can continue to buy the future payments that you're going to make. So I always have enough money to make whatever payments it is that I have to, to keep my promise. Yep? Student: Is it sort of preferable from your point of view that the interest rate go up because your theory about prepayments isn't going to be put to the test? Prof: Well, don't forget, I'm locking in my 21 dollar profit for sure, so no matter what happens I'm going to just be able to make all the payments no matter what. Student: But now it seems that your theory about prepayments is... Prof: Correct, yes. Student: So it's like ambiguity, right? Not just the rest is like ambiguity, so it's sort of preferable... Prof: So good. So let me repeat his question, if he'll forgive me, in slightly different words. He's saying that I was able to take--this is what my hedge fund does, literally. We think we know better what the prepayments are going to be than the rest of the market, so we're willing to take on a commitment-- someone will pay us 120 dollars. We think 98 dollars are enough to buy all the promises that we've made by selling the thing short, say. We could be wrong. We have been wrong. The last two years we made a lot of mistakes. So you're saying, the question is, the reason why the guy is willing to pay so much is because down here he thinks he's going to get a lot of money. The interest rates are going down so, discounting at a lower rate, the mortgage is going to be worth a lot more. We don't think it's going to be more because we're expecting prepayments. Up here it's sort of obvious that there aren't going to be any prepayments. So if the world really goes, interest rates going up, then our theory of prepayments never gets put to the test and so we just make money. So our theory never gets put to the test. If interest rates go down then our theory's been really put to the test and we have to see whether she's really smart enough to prepay or not. So you're right. That's absolutely true, yep. But in any case we're going to assume our theory is correct and hedge in such a way so that if our theory is correct about prepayments we will exactly be in a position to keep our promises without ever running a risk of loss. Yes? Student: So with the World Series example. So let's say there are two situations where the Phillies win in 4 games or they win the series in 5 games. Either way you lose 100 dollars and you win 4 single game bets, but in one of the situations you've lost one single game bet because the Phillies won in 5 games rather than 4. How do the values reconcile? Prof: Because it couldn't have happened that there were four straight wins and then a loss. The series would have been over, right? So his question is I've asserted that no matter what way things go I'm going to end up 42 dollars ahead no matter what, and he's saying that's great, but he's a little skeptical it could be true because I'm always betting against this other bookie. I'm always betting on the Phillies with the other bookie, and so in one case the Yankees win 4 in a row. I lose 4 bets with the other bookie, with the bookie I'm betting on the Phillies, so I've had to take 4 losing bets with the other bookie. In the case where the Yankees win three lose one and then win in the end I've again lost 4 bets with the other bookie, but I've actually won a bet with the other bookie. So it seems like somehow things are better for me, so it seems unbelievable that I'm still at 42 in both cases. That's your question, right? So the reason is that my bets are changing. I don't make the same last bet. So the first three bets there's a Yankee win, Yankee win, Yankee win, each of those nights I'm making the same bet in the same scenario, but when the Phillies lose and then win again I've changed my bet, so I'm still going to end up--so the Yankees lost the, your scenario was the Yankees lost the 4th game, so that outcome is different from what it would have been in the first scenario because the Yankees lost instead of winning. So the bookie bet went the other way. But now the last bet I made is not the same bet as I would have made the night before. It's a different bet so that it just ends up with a different direction than the 4th bet plus this different 5th bet it adds back up to what would have happened had the Yankees won the fourth time. I don't know if that helps, but that's what happens. And the proof that it happens is just by induction. I gave a proof and you're saying the proof is amazingly good. Remember, the proof is very simple. You always make a bet so that no matter what happens your expectation is back to where it was the night before. And if you do that you have to end up--that's the proof that you've always locked in 42 from the beginning. And so you can ask a thousand questions like that and it's always going to be a complicated answer, but there has to be an answer because we've proved that there was one. Any other questions about this? Yes? Student: So with the mortgage example you're hedging against the interest rate going up. Prof: So with the mortgage example you're hedging against the interest rate going--no. When the interest rate goes up you actually pay less. You've made a promise. Remember, the price as the interest rate goes up--where's the mortgage, sorry. The value of the non-call, the value of the call, so as the interest rate goes up you owe less money because you're promising to deliver this stuff. So the interest rate's up, the mortgage you've sold short is less and less valuable, so that's the good scenario for you, but if the interest rate goes down that's the scenario where you could get into trouble. So you're trying to protect against the interest rate going down, and in order to do that you have to give money up in case the interest rate goes up. So now I want to--any other questions about this? It's quite an ingenious thing, I think. So we're going to have one more step of this, but this is the high watermark of the standard, you know, the finance guys who made finance such an important subject, and the rational expectations school of finance. This is kind of the most clever thing that they did. So this kind of reasoning, bookies maybe knew it for a long time, but Black-Scholes in 1973 started this kind of thinking and then lots of hedge funds started imitating it including my own. So I certainly didn't invent this idea of dynamic hedging. Now, let's take a step back. The crucial idea is marking to market. The crucial idea is that you want to hedge something through millions of scenarios and really the outcome you won't know until the end. What you should do is hedge at each step of the way your mark to market value. So you only have to do things a step at a time. There's an exponentially growing number of paths, but there are only two possibilities from today until tomorrow. So it's very simple to hedge two things. It seems incredibly complicated to hedge 2 to the 100 things, 2 to the 10th is a very big number, 2 is a very small number. You can hedge two things. It may be very complicated to hedge 2 to the 10 things, but you only have to hedge 2 things on every day. So once you've realized that, hedging is actually quite a simple operation. You don't have to do it by trading in the interest rate derivatives market. You could trade in a simpler market. Suppose, for example, that you knew that there were bonds being traded, let's say 30-year bonds. So let's just take a look at a 30-year bond here, callable bond, so this is exactly the same thing. This is the 30-year bond under the same circumstance. This is a 9 percent bond, coupon bond, and it's starting with the same 6 percent interest rates, exactly the same process as before. So the interest rates, those are the same interest rates as before. So here's the bond. Now, the bond starts at 140 dollars, can go to 121 dollars or to 159 dollars. Remember this thing that you're trying to hedge goes from 98.8 to 100.6 or to 107.11. So what you need to do now is--you've promised to make deliveries in the future, very complicated, but you know you can summarize that whole future. As long as you've got 100.6 dollars in the up state and 107.11 dollars in the down state after the very first step you will have hedged your mortgage obligation. But you could just buy the right percentage of bonds and be able to accomplish the same thing. So why is that? Well, there's a gap here and here. You owe less money here than you do down there. So the bond is worth less up here than down here. In fact this bond is worth 38 dollars more here than here. So the gap in the bond is 38. The gap in here is something like 6.5. So this is like 1 sixth. So as long as you held 1 sixth of the bond and something that paid the right constant amount in each case you would get the same payments here and here. So what is the right constant amount? 1 sixth of the bond, by the way, would cost you 22,24, 23, about 23 dollars, 1 sixth of the bond. So if you took the other 98.8 dollars and put it to the 1 year Treasury, I claim it's obvious--so take 1 sixth of the-- so 1 sixth of 30 year 9 percent bond. That's 1 sixth of this thing, which costs you what? It cost 23 dollars. The price of that is 23 dollars. Now, combine that with 75.8 dollars of 1 year Treasury, 1 year 6 percent Treasury. So hold those two things. I claim that'll pay you 100.6 here and 107.11 here. How do I know that without having to even calculate anything out? Well, the Treasury's going to pay the same amount here and here. It's going to be a constant. This thing, since its gap is 38 dollars and I only hold 1 sixth of it, it's going to pay me exactly 6 and 1 half more down here than it pays here because the gap instead of 38 will be 1 sixth of that, which will be 6 and 1 half. So the gap will exactly match that. So added that to the Treasury's constant payments I'm going to get something over here and 6 and 1 half dollars more than that down here. But since I've paid the same amount, 98.8, it's going to have to be that that constant was exactly right to make this be 100.6 and 107.11, because both the 1 year Treasury and the 30 year bond were calculated by discounting whatever their payments were here and here by the same prices, this and this. So there's a second way. Instead of trading in the derivatives market I could just hold a combination of two bonds, the 1 year Treasury and the 30 year 9 percent bond, and I'd still be perfectly hedged. But then when I got to here I'd want to change my mix. I'd want to hold a different 1-year bond at a different interest rate, so I have to buy a new 1-year bond and a different amount of the 30-year non-callable bond, 9 percent bond, but I could always reproduce these same two payments. So I don't have to hedge by holding derivatives, interest rate derivatives, I can hedge by holding standard bonds. And I can tell at a glance how much of the longer term bond to hold because I just have to match this gap in the prices since the 1 year bond is always going to pay the same thing up and down. Did that go too fast? Yeah? Student: I know it's just like> but how did you figure out how much of the 1-year bond to buy? Prof: So I want to hold 1 sixth of the 30 year bond, which cost me 140, so 1 sixth of that is going to cost me 23 dollars. All right, now I want to also hold a 1 year Treasury so that the payment 1 sixth of 121 at the top plus whatever the 1 year Treasury pays me is equal to 100.6 and such that 1 sixth times this value at the bottom, oh, sorry. It's 1 sixth this coupon is paying. Actually it wasn't 121.6. It's a 9 percent bond. I forgot its coupon, very bad of me. It won't change the numbers, but. So it's paying--I didn't write it down. So this thing is not paying 121. It's also paying the coupon. This is the present value of what's left. So it's paying 9 plus that. So it's 130 and here it's 168. The gap is still 38. So I want 1 sixth of 130. So 1 sixth of 130 costs--it's still the same number. It's 22. I did bad arithmetic to begin with so it's still 22. No, sorry, it's 1 sixth of this thing which is 140, so it's 23, right. Sorry. That didn't change. So the payment here is 130 and the payment here is 168. So 1 sixth of 130, that's the up payment, and this is 1 sixth of 168. Now, I want that plus whatever the 1 year Treasury gives me to equal 100.6 up here and 107.11 down here. That way I would have replicated things and hedged myself perfectly, right? But I don't have to figure out what that 1 year Treasury is. I think it's obvious. All I have to do is say subtract 23 from 98.8, so I just have to buy 75.8 dollars worth of the 1 year Treasury and that'll give me exactly the right payoff. Why is that? Because this number 140.93 divided by 6 is exactly this evaluated at this price, 1 half over 1.06 times this, this is the price 1 half times 1 over 1.06. All right, so that bond which cost 140.53 how did I get 140.53 there? I took the price of 1 dollar in the up state, which is it's 50 percent likely discounted, multiplying by its payoff 130, plus 1 half discounted multiplied by the payoff of 168. This is 168 because it's a 9 percent bond. So it's 1 sixth times 1 sixth--so if I get a sixth of the bond it'll cost me 140.43 divided by 6 which is 23. So what about the 1 year Treasury? That's going to give me some payment, an additional payment here and here, namely 1.06 times whatever I put in. So you notice that the gap between here and here since I've multiplied by 1 sixth is exactly this 6 and 1 half dollar gap. So the total I have to spend is 98.8 over here, so if I spend 23 dollars on the Treasury and the remaining amount-- 23 dollars on the 30 year 9 percent bond, the remaining amount of money which is 75.8 on the Treasury I will have spent this 98.8 dollars, but then I have to get the same payoffs. Why is that? Because they're all being priced at the same prices, so it's just the distributive law of arithmetic. If these payoffs times 1 sixth plus the Treasury payoffs equal 100.6 and 107.11 then it must be that the sum of the money I spent on the 30 year 9 percent bond, plus the sum of the money I spent on the Treasury has to equal 98.8. Therefore, I know that the amount of money of the 98.8 I spent on the 1 year Treasury was 98.8 minus the 23 I spent on the 30-year bond. So that's how you can--so to say it again just in a big picture look. There are two things that can happen. If you hold two bonds, a 1-year Treasury and a 30-year thing, you're obviously going to be able to match these two things by holding the right proportion of them. That is just obvious. And then less obvious is how quickly I'm figuring out how much of those two bonds to hold. And the way I'm figuring it out so quickly is because the 1-year Treasury is paying the same thing up and down, so I have to get all the variation out of the 30-year bond, so I have to hold the right proportion of the 30-year bond to get the same variation. So in the very big picture if you're trying to hedge some instrument with another instrument and a portfolio of stuff, much of which is certain, and only one thing that's risky, the amount of the risky thing you have to hold has to produce as much variation as the thing you're trying to hedge. So the key is being able to tell at a glance how much variation each thing has then you can tell in what proportion to hold them. And so the very last thing I want to tell you today, which is unfortunately going to take me a few minutes, is how traders look at variation and can guess it incredibly quickly. So a trader could look at this and guess without doing almost any calculations what the right hedge is. So just like we did the doubling rule I want to do the variation rule of thumb. And this is called duration and convexity, or average life. So I asked myself, suppose I have this 30-year bond, 30-year non-callable bond, that's this one, 9 percent bond. How could I guess, kind of, what the variation in price would be without having to do, you know, I've had to do this very complicated backward induction calculation. Now, remember once the interest rates go up here it's a random walk so on average they're pretty much, not pretty much, they're exactly what they were here. They start here. They go up and down, but on average they're still here. And over here they've gone down so the average is lower going forward. In fact, it's exactly equal to that. So if you're a trader and there was no uncertainty you would know that the present value with no uncertainty is going to be the coupon divided by (1 the interest rate) the coupon over (1 the interest rate) squared (in the last year) the coupon over (1 the interest rate) to the T 100 times [correction: over] (1 the interest rate) to the T. That's the value of the bond. Now, you sort of want to know how much is that price going to change when the interest rate changes. Well, at a glance, I mean, you just take the derivative. What is dPV/dr? It's going to be minus C over (1 r) squared - 2 C over (1 r) cubed - T times C over (1 r) to the (T 1) - T times 100 divided by (1 r) to the (T 1). That's the derivative. It looks like I'm making things even more complicated, you would think, but this turns out to be not so complicated, because this is a number--so let's put the minus on the outside, so I'll get rid of this. This is a number which you can sort of get in your head, so let's try writing it. Let's pull out one of the (1 r)s. So it's minus 1 over (1 r) times (C over (1 r) 2 C over (1 r) squared ... T times (C 100) (that's the last payment) over (1 r) to the T). Now, what is that? Can you interpret that? And the answer is yes you can interpret that because what is that? That's saying these are all the payments you're getting over the life of the bond. It's C, C and the last one's C 100. This number that keeps coming in front of them, though, is the year in which you're getting the payment. This is in the first year. I could put a 1 there. This is the payment in the second year. There's a 2 here. This is the payment in the Tth year. There's a T here. You got that T from taking the derivative of the denominator here. So it's like weighting the year in which the payments come by the value of those payments. So in the first year the value is C. The present value is C over (1 r). In the second year the payment is C, but discounted, C over (1 r) squared, and the last year the total payment is C 100, but you had to discount it by (1 r) to the Tth. So this is just like taking the average year in which the present value flows actually come. If I divided this now by the present value of-- the present value, these numbers down here, C over this C over this squared C 100 over this to the Tth, those are all weights multiplying the year in which the payments come. They add up to the present value. So basically I've just got a weighted average of what year the payments come in. This is called the average life. This thing in here is the average life because I've multiplied the year in which the payments come by the present value of the cash flows there and then I've made those multipliers add up to 1 by dividing by the PV. See, this in parenthesis, all these terms are the things multiplying the year in which the thing came. So if I add up all these coefficients here I'm just getting the present value. So now the coefficients add up to 1. So I'm just taking an average of the year in which the thing came and that's what the average life is, but that's equal to the derivative of the present value divided by the present value. So it's--the percentage change in the present value is the average year in which the payments come. So let's just think about it. Suppose you have a 10-year bond? It pays C, C, C, C, C, and then 100 at the very end. What do you think the average life is? Well, if there were no discounting the average life wouldn't be 5 because there's such a huge payment in the end. The average life would be 8 or 9, but there is discounting so this thing at the end won't count as much. So the average life is probably 7. If it's a 30 year bond, the average life, you're going to get C, C, C, C, and then all the way at the end you're going to get C 100. Well, if the payments were all equal and no discounting it would be 15, but there's a huge amount of discounting so that last payment is really pretty irrelevant, so probably--so it's not clear which way it goes, probably the average life will be less than 15. So you can see just by looking at the bond, and I'm ending with this thought, by looking at the bond itself you can figure out what the average life is. So a trader, just by a little experience and common sense, can figure out the average life. I mean, here are all the payments the way they're coming. They're coming evenly across the whole history of the bond with something at the end, so the average life is probably a little bit over the average, but if you go way off, you push the final payment too far to the end then it's becoming negligible, it's almost irrelevant, and so the average life by discounting will probably be before the average. So a 10-year bond probably has an average life of 7, a 30-year bond maybe has an average life of 12 or 13. Once you know the average life, you just have to hold bonds in proportion to their average lives. The dollar amount you put in each bond to hedge it is just proportional to its average life. So that's how a trader, without having to do any arithmetic, can kind of guess how much of the 30 year bond will it take to hedge a 10 year bond, and how much of a--so which has a higher average life? The longer the bond the higher the average life, the more sensitive it is to interest rate changes so the less of it you need to hedge your position, so if you hold the 30 year bond you don't have to hold that much of it, 1 sixth of it, in order to hedge this mortgage. The mortgage has a very short average life because it's prepaying so quickly. So it's not going to last very long. So this is an amazing connection between average life and sensitivity to interest rate. And average life is something you can guess. Sensitivity to interest rate is something you have to do huge calculations for, but the two are almost the same. So in the problem set we'll see if you can do it. I asked you a couple problems to do with average life, so.
Quantitative_Finance_by_Yale_University	9_Yield_Curve_Arbitrage.txt	All right, so last time we began, or maybe two times ago, we began a discussion of various vocabulary and facts you have to know about the markets if you want to think about finance. Today we're going to deal mostly with the most important one, the most basic one, the yield curve. And last time, we introduced this word, "yield." Now, yield is an extremely common expression in finance, and it turns out not to be that well defined, often, or that useful. But the word is so important and has been used so often that it still hangs around, even when probably we should use different concepts. So remember the yield was an attempt to look at an investment, and without paying any attention to the market or anything outside the investment, just looking at the investment itself, try to assess, give a number, quantifying how attractive the investment was. So we said you could apply that to a bond--it has cash flows. You could apply it to a hedge fund that's taking in money and paying out money, and the formula we came up with said that if the cash flows are given by C(1), C(2), the net cash flows, C(T) over the course of the period, and its price is some P(0), maybe it's a negative cash flow, so C(0). So some of these cash flows might be negative and some of them might be positive, then we should just look at the number Y, such that discounting all these things at rate Y gives you 0. The Y that did that was what we defined as the yield of the investment. So we saw that that had some advantages. For example, in a hedge fund, if you just look at the rate of return it makes on its money every year, that doesn't take into account that in some years, it's got a lot more money. So if those were the years that lost money, and the years when it hardly had any money were the years it made money, just taking the average, the multiplicative average, the geometric average of all those yearly rates of returns, would give a misleading figure. Well, the yield also gives a somewhat misleading figure, and I don't want to spend too much time on why it might be misleading, but I'll give you just an example. Suppose that the cash flows happen to be 1, -4, and 3. Now what's the yield to maturity? Well, there are two of them. You could have Y = 0, because 1 over (1 0), - 4 over (1 0), 3 over (1 0), is just 1 - 4 3. That equals 0, so the yield to maturity of 0 percent, the yield of 0 percent, makes this have present value 0. But also I could try Y = 200 percent, and then I'd have Y--I'd put a 2 and a 2 squared here, and I'd have 1 - 4 thirds 1 over 3 squared is 3 over 9, so it's 1 third. So it would be 1 minus 4 thirds, plus 1 third, which also equals 0. So is the yield to maturity, the internal rate of return 0 percent or 200 percent? It's ambiguous. So yield to maturity can't be the right way of doing things. To go back to the hedge fund example, you know, the hedge fund was taking in money, paying out money, taking in more money, paying out money, and we calculated the yield to maturity. Well suppose that there was some period, you know, here, at which point everyone had taken all their money out, so the hedge fund wasn't actually doing anything for a bunch of years, maybe for a long time, and then it started up and took money in and paid money out and stuff. Well, because the gap in time was very long with nothing happening, if you take a positive Y, the stuff that happens in the second incarnation of the fund is hardly going to be making any difference, because by that time, it will all be discounted a lot. So the yield will depend too sensitively on stuff early rather than stuff late. And so again, you get into troubles yielding just yield to maturity, so that can't be the right thing to do, even though people have done it for years. So the word, however, lives on, and there's no getting rid of the word because it's used in common vocabulary. Now what would Irving Fisher say you should do, if you had to summarize how good an investment was? What's his lesson? What do you do? An investment where there's no doubt about what the cash flows are going to be, what would he say you should do, to evaluate the attractiveness of it? What's our lesson, our main lesson from Irving Fisher? What would he say? Yes. Student: > like to check? Prof: Well, let's say they're cash flows, so it's money, money that you're going to get coming in and out, yeah, he'd say, deflate by inflation and turn them into real flows and then do what? So just continue your answer. So turn them into actual potatoes every time, apples each time. Deflate by inflation and then do what with the numbers? This is a simple question. You're thinking too hard. Yes? Student: Compare the present value. Prof: Okay, he'd say, "Just look at the present value of all these things." So of course, to do that, you'd have to know, what is the market rate of interest with which to compute the present value? So Fisher would say, "It's ridiculous to evaluate how good an investment opportunity is just by looking at the cash flows. You're throwing away too much information." You know what the market is doing, you know what the interest rates are. Use the market interest rates and figure out what the present value of all the cash flows is. So we're going to now do that a bunch of times, okay, for the rest of the class, and see what that means. So we have to begin, the two thirds of the class is going to be spent on the question, how do you know what the market rates of interest are? So how do you know what the market rates of interest are? How could you find out what the market rate of interest is? What would you do to find it out? Yeah. Student: You could go to a bank and see what they were estimating it to be. Prof: And if you looked in the newspaper, say, could you find it in the newspapers? What would you find in the newspapers? Yes? Student: You'd want to find a riskless investment, say like a T-bill. Prof: Okay, and so yes, you try and look at riskless investments like government bonds, where there can't be any default--at least, that's what they always used to say-- can't be any default on an American promise. America's government never broke a promise and they can always print the money, so presumably they don't have to break a promise-- so they're just promising money which they can print, so why should they ever break their promise-- so what would you find if you opened a newspaper? You would find, for different maturities-- it used to be up to 30 years--for different maturities, you would find the yield on the various bonds, okay? So why would you find the yield? Well, the yield of various government bonds, of gov. bonds. Why do they quote the yield? Well, that's just because, you know, a hundred years ago, people started using the idea of yield and so the vocabulary has been kept, even though it's not the best way of describing what's going on. So for instance, let's just look at some of the yield curves you might have seen over the last 9 years, almost 10 years, since December 2000. You would see that in December 2000, the yield on the 1-year bonds, you know, the short yields--this isn't a log scale, so this is 3,6, 12, okay. So the shortest bonds usually have lower yields than the highest bonds, but sometimes, like in December 2000, the yields are almost all the same. It's called the flat yield curve. Other times, like now, we're in this light blue one here, right now the short bonds have very small yields and the long bonds have much higher yields, so the last one is the 30-year bond. So you get the yield on every single bond. Now what do you notice about this picture, by the way? They can be very different at different time periods, so in December 2000, the interest rates were really high. The yields were 6 percent. I'm talking yields so far. We haven't talked about interest rates. We have to figure out what the interest rates are, but anyway, they're obviously going to be connected. So the yields were very high in December 2000, and they got much lower in December 2008, and they've stayed very low. So why are they so low now? What got them to be so low now? Yeah? Student: The Fed flooded the economy with money. Prof: The Fed flooded the economy with money. It wanted to drive the interest rates down to 0. So we're going to see very soon why the Fed might have wanted to do that, but these money rates don't move totally on their own. They have to do, and we said that Irving Fisher-- we haven't described Irving Fisher's theory of money and nominal interest rates-- but somehow, the Fed is controlling the nominal interest rates and it's changed the yield curve. So you notice that the yield curve now, December 2008, was this blue one. So the Fed, in the crisis of 2008, you know, was terrified, and it dropped the interest rate almost to 0, virtually 0, and it's kept it there, because from December 2008 till now, we're at October 2009, September 30^(th), 2009, a long time has passed from this dark blue to the light blue line, and the rate has been kept fixed there. But in the intervening time, the long rates have started to go way up. Now why might that be the case? What does that suggest to anybody? Does anybody know? Yeah? Student: > Prof: That could be one reason, and could there be another reason? Yeah? Student: Future expected inflation. Prof: Okay, so those are the two reasons. So they somehow know that, and some of you have no idea how they could possibly be thinking that. And so I'm going to explain, what information is there in the different yield curves. Okay, so the point is that every morning, every single financial analyst wakes up and sees these yield curves, you know, consults the market and sees where things are trading, and can produce a yield curve like that. Okay, so you've got a bunch of yields. Now what are the yields? Well, let's just do an example here. So I'm going to make up an example, which is very easy to compute. So let's try this one. Okay, so I'm reading here at the top, let's just say that you've got a bunch of different bonds. A 1-year bond, a 2-year bond, a 3-year bond, a 4-year bond and a 5-year bond. Now each of the bonds was issued--I'm assuming here that they were all issued on the same day. So they're issued with different coupons. Let's say they were all issued today. We'll come back at the end. Obviously the Treasury doesn't issue new bonds every single day, so how does this change when you arrive on a day when they haven't issued things? But let's just keep it simple and suppose that today, the Treasury has issued 5 different bonds over these 5 different years. Now the Treasury has to set what do they do? They decide how much of these bonds they're going to sell and they decide what coupon they're going to set. They set the coupon. So let's say the coupon they set was 1 dollar for the 1-year bond, 2 dollars for the 2-year bond, 3 dollars for 3 three-year bond, 4 for the 4-year bond, 5 for the 5-year bond. It's easy to remember, that's why I chose those numbers. And the face value, let's say, is always 100. So why did they set those coupons? Well, because given how much they want to sell, they're picking the coupon, hoping that the price turns out to be close to the face value. So let's say, when they actually market these, and supply equals demand in equilibrium, the prices turn out to be 100.1,100.2, 100.3,100.4, and 100.5. So 100.5 is the price the market's paying for the 5 year bond and if the coupon is 5, and they pay coupons once a year--they may pay twice a year, but let's say they pay once a year for simplicity, you're going to get 5,5, 5,5, and 105 the last year. If you bought the four-year coupon bond, you get 4,4, 4,104 the last year, right? So those are the bonds. Now the newspaper's not telling you any of that, so you're sort of losing that information, so you don't actually know that from reading the newspaper. So then, what do you know? You know that--you know the yields on all these things, okay? So here, this tells you the yield on each of these bonds. Going back to where I was. Okay, knowing the yield, you could figure out what the price of each of the bonds is, or in fact, the way that they calculated the yield that the newspapers reported. How did the newspapers get the yield? The newspapers said, well, for the 4 year bond, we're going to say that 100.4 = 4 divided by (1 the 4 year coupon bond yield), 4 over (1 Y (4)) squared, plus 4 over (1 Y (4)) cubed, plus 104 over (1 Y (4)) to the fourth. In this case, because these numbers are all positive, it's monotonic in Y (4), so there's a unique Y (4) which you can use to solve this equation, price = the discounted value at that yield of the payments. So that's how the newspapers, the reporter, that's how he got all the yields to show you that graph. He looked at the market, or could call the bank or something like that, had a computer screen, talked to his friends on Wall Street. He knew the price of all the bonds, he knew the coupons of all the bonds, and then he produced the yield for all the bonds. So the yield, as I say, that's the word that everybody uses, but really, the information that you want to deal with is the price, and what did the coupon actually pay? Okay, so that's what you know. Everybody knows this every day, the information I have given. Every morning, maybe every few hours, people will update it. They'll look at what are the coupon bonds paying and what are the prices? The thing that's changing from hour to hour are the prices, but we're taking a snapshot at the beginning of the day and looking at the prices. So now we've got prices of bonds, which I'm going to call capital Pis, Pi (1), Pi (2), Pi (3), Pi (4) and Pi (5). But now, what does Fisher say you should do? What's the most important thing to do? The most important thing to do is find the interest rates. So what has this got to do with interest rates? Well, if you modernize Fisher a little bit, the most important thing--he didn't put it this way, but this is really what he must have meant-- the most important thing to do is find the prices of the zeros. So [little] pi (1) is today's money price, today's money price for 1 dollar at time 1. pi (2) is today's money price for 1 dollar at time 2. pi (3), today's money price at time 3, and pi (5) is today's money price at time 5. Okay, now why do you want to find these things? Because once you know these things, you'd be able to value any investment. That original investment that we talked about, which maybe disappeared, this one. It disappeared. Anyway, once you have all the pis, if anybody tells you, if a hedge fund tells you, "This is the revenue I'm going to produce for you in the next five years," if a company says, "This is our business plan. We're going to build a factory today that's going come out a certain amount of money and we're going to get profits in the next five years, blah, blah, blah." If a new bond comes on the market and you don't know how to price it, and somebody offers a price for it, how do you figure out what it's worth? All you do is you take the cash flows, the Cs that I not very cleverly erased, you take the cash flows and multiply them by the pis. So the correct price P is just whatever the cash flows you're predicting times these pis that Fisher says is what you should really be finding. So nothing could be simpler. Now why is this the right price? Because if you can go in the market and buy 1 dollar at time 1 for pi of 1, and 1 dollar at time 2 for pi of 2, etc., you can buy all the cash flows from this investment project by spending this amount of money. So if the guy is offering you the investment opportunity at a higher price, it's crazy to do it. You could have bought those cash flows yourself by paying this price. If he offers it to you at a lower price than that, then definitely you should do it, because it's a bargain, because if you had to buy it yourself, it would be more expensive. In fact, you can make an arbitrage profit. If he's offering it to you at a lower price, you can buy it and how do you buy it? By selling these very promises, C(1), C(2), C(T) on the market, and if people believe you that you'll pay, you can sell it for this price. So you buy his project for a lower price. You sell it for a higher price. You make the difference, and when it comes time to keep your promises, the project is giving you the cash to keep your promises, so you lock in a profit for sure. So if you knew the pis, you would know for sure how to value any project where you knew for sure the cash flows, knowing the pis would tell you how to value it, and would tell you whether it was attractive or not attractive. You just look at how high the present value is. Okay, any questions about that? So we just need to figure out how to deduce what the little pis are from the data that we're going to be given, and that we are given every day by the market. Okay, so I said literally pi (1) is the price you would pay today to buy 1 dollar tomorrow. Now how could you go about buying 1 dollar tomorrow, given that the only things you can trade on the market are these Treasury bonds, these government bonds? And I've told you what they pay off and I've told you what their prices are. So how would you go and buy 1 dollar tomorrow and how much would it cost you, 1 dollar next year? How would you do that? You can trade, buy or sell any of these Treasury bonds. So in the background, I keep saying that we're going to have to worry about people defaulting. We're not quite doing it yet. So buying a Treasury bond, you need the cash to buy it. Selling a Treasury bond means you promise to deliver what the Treasury bond promises, and your promise is as good as the government's. So if you sell it to somebody, they'll pay you the same government price for it. So obviously in the background, you're going to have to do something to convince the guy you're making the promise to that you're going to keep your promise. So we're going to worry about that later. So for now, when I say that the market for those Treasury bonds clears at those levels, I mean that anybody who wants to can buy Treasury bonds at those levels, or can sell them, even if he doesn't have them, at those prices, by making the promise of what the Treasury bond does. Because we're assuming that the government and you, everybody is just as reliable, everybody is going to keep their promise. So whether it's the Treasury making the promise, or you making the promise, same thing. Okay, so how do you buy 1 dollar next year? What would you do in the market with the Treasury bonds to get 1 dollar next year? Yeah? Student: Can we just plug in 1 for our P in the bond prices and then figure out which bond you want to purchase? Prof: Well, you're supposed to be telling me. What do you want to do? I want to know exactly what to do. You can look at these numbers. By the way, are you all following these? Maybe this is mysterious. There's a 1-year Treasury bond that pays 101 dollars next year. The 2-year Treasury bond pays 2 dollars next year, then 102. The 3-year Treasury bond pays 3 dollars at the end of the first year, 3 at the end of the second year, 103 at the end of the third year, etc. And the 1 year Treasury bond happens to be selling at this price, the 2-year happens to be selling for that price. So what can I do with all these bonds to buy 1 dollar next year? All right, go ahead, you've started. Student: Buy a 2-year bond. Prof: A 2-year bond? It's next year, one year from now. Student: You could just divide the price of the 1-year bond by > Prof: You're a step ahead of me. I'm saying, what do you do--never mind how much does it cost? What do you do today to get 1 dollar next year? What transaction can you make today, what purchase can you make today to get yourself 1 dollar next year? Yes? Student: Just buy a 1-year bond. Prof: Buy a 1-year bond. Well, that will give me 101 dollars next year. I want 1 dollar next year. Student: Take that fraction > Prof: Okay, well, that's exactly the point. I take that fraction. That's what I wanted you to tell me. So little pi (1) is going to be (1 over 101) times the price of the one-year bond, because the 1-year bond is paying 101 dollars. So you take 1/101 of it, you'll get 1 dollar. And whatever the price of the 1-year bond is--actually, we know what that is. It's 100.1, that's how much it costs. To buy 1 of them cost 100.1. To get 1 over 101 of them costs pi (1). Okay, so this number, by the way, is some number which, actually, I of course worked out here. Happens to be .991, but we'll come back to that. So it happens to be point 991. So now we know pi (1). Well, how would you buy 1 dollar in year 2? So there's a way of directly buying 1 dollar in year 2, once you know how the Treasuries trade. So what I'm doing is I'm explaining the idea of replication, pricing. It's giving me pricing and it's going to lead to arbitrage. They're all basically similar ideas here. So what I want to do is directly buy 1 dollar in year 2. So I could probably go to a bank and they would actually make that trade for me. I could just call up the bank and say, "I want 1 dollar in year 2," and they'd tell me, pi (2), how much I have to pay for it. But how are they going to figure out what it's worth? They're going to see how--they're going to go out and have to buy the dollar for me. So they're going to go out and go to the Treasury market. And what are they going to do in the Treasury market to come up with my dollar in year 2? They're going to replicate my purchase of 1 dollar with a more complicated portfolio that they can actually trade, and that's how they're going to figure out how to price my request for 1 dollar in year 2. So what is this bank going to do in the Treasury market? What does it have to do to get 1 dollar for sure in year two, and nothing else? Okay? Student: Do they buy a 2-year bond and sell a 1-year bond? Prof: Okay, so what are they going to do? How much of the two-year bonds should they buy? Student: What they're going to sell is a... Prof: The 2 year bond. You're talking about the 2-year bond, so how much of the 2-year bond are they going to buy? Student: 1/102. Prof: 1/102, right. That's very good. Why is that? Because in year 2, we're talking about year 2 now, year 2, the 2-year bond pays 102. You get 1 over 102 of those, you've got 1 dollar in year 2, so that's Pi of 2. Which happens to be 100.2. That's how much that costs. Okay, but is that all you need to do? Is that it? Are you paying the right amount or are you paying too much, or what are you doing? You've got to do more than just that. Why is that? Yeah. Student: When you subtract 2 times the > Prof: Close, but not quite. Okay, so do your reasoning. You told me what else to do, which you slightly mis-said. So why do you have to do anything at all? Tell me the reason why you want to do something else. You're on the right track, you just slipped up a little bit. So why not just stop here? Student: Because you're also getting 2 dollars in year 1. Prof: Exactly, that's exactly right. By buying the 2-year Treasury, you got 102 in period-- by buying this fraction of the 2 year, you got just what you want in period 2, but you also purchased the coupon in period 1, which you don't need. So that's giving you more than you needed to buy. You've bought extra, so you're going to actually be able-- the cost of getting the dollar at the end of year 2 is a little bit less than what we've written so far, because you bought more. So far, this is buying too much. You bought the dollar in year 2. You also bought a little bit in year 1. You can now sell off the extra stuff you've gotten in year one to reduce your cost of buying that. So what should you do in year one? That's exactly what you were thinking. You just didn't quite say it right. So what should you do in year 1? Student: > Prof: I sell that. Okay, I sell. Okay, so I can get to sell 2 of little pi of 1, right? Because I know how much it costs me to buy 1 dollar at time 1 now. It's that number, so I'm getting-- so is that correct, what I've written here? That's what you said. That's not quite right. Yeah. Student: If you didn't actually buy 2 > Prof: Okay, so this is what he meant to say. So that's fine. Okay, so that's what you do, exactly. So everybody's following? You agree with me now, right? But, you know, we could plug in for this too, by the way. So pi of 1, we know what that is. Okay, so does everybody see what's going on here? To buy 1 dollar at time 2, you don't get the whole 2-year Treasury, you buy 1/102 of the 2 year Treasury, so it costs you that amount of money. But that gives you a little bit of extra at time 1. How much extra does it give you? Well, you've got 2 dollars extra for every 2-year Treasury, but you didn't buy a whole 2-year Treasury. You bought that fraction of it. So it gives you this much extra which you now get to sell off, so you're going to sell it off for this price, pi (1). And of course, we can plug in for pi (1), by putting 101 down here and putting 100.1 up here. Okay, so that was pretty clear, right? So now any questions about that? So that's going to be some number, which I calculated again, which happens to be 962, .962. So notice, of course, it's getting cheaper to buy--how much does it cost to buy 1 dollar in year one? It's that. To buy 1 dollar in year 2, is less. Now what about pi (3)? How would we get pi (3)? We'll stop at pi (3). How would we get pi (3)? Then we're going to find a very fast way of computing all these numbers. What's pi (3)? How would you get that? Student: Buy the 3-year bond, divided by > Prof: So the 3-year bond costs 100.3 but we don't need all of it. We need 1 over 103 units times that, okay. So that's our main cost. But then what else? Student: We need to get - 3 times > Prof: - 3 over 103, times little pi of 2. Right, because we got this extra stuff that we didn't need. Student: - 3 over 103 of little pi of 1, > Prof: Okay, so he's saying - 3 times 103 of pi of 1, okay, because we didn't need that. So is that the right answer? It's not the right answer. It's close. What did he overlook? So he said, you buy the three-year bond. So by buying the three-year bond, you're getting--if you bought the whole three-year bond, you'd get 3,3, 103. You only want 1 at the end, so you have to divide by 103. Now we get 3 over 103,3 over 103,1, and so he's saying we've got two extra payments. Let's sell them off. And so he sold them off like that. That's correct. So he sold them off, so this one he sold off at pi (2) and this one he sold off at pi (1), so he's making use of the fact that we've already found out this price and this price. But actually, that's slightly--okay, but we're talking about not what you would do talking to the banker. We're talking about what the banker would do, and he's got to trade in the Treasury market. So how's this guy going to do this? The banker and the Treasury market now, this Pi over 2 dollars, he's going to have to hold this complicated portfolio--what's he going to do to--? He's going to have to combine the 1 and the 2-year to do this thing and then the 1-year to undo that thing. So it's actually going to be--so in terms of trading, if you just had to trade Treasuries, what would you do? So this is the correct formula. That's correct and we can figure out what that is, okay. And so the correct formula is 91.68. That's .917. Okay, but you see what you've done is, these are the kind of fictitious things that Irving Fisher has told us to do. What you're really doing in the market is trading the Treasuries. So here, you've traded a Treasury. You've bought 1 over 103 units of a 3-year Treasury. Now what else should you do? You've got to trade Treasuries. How can you sell off this amount of money in year 2? You have to sell some Treasuries to do that, so what would you sell? Student: The 2-year coupon. Prof: The 2 year coupon bond, and so how much of that would you sell? Well, this is the amount of money you have to get. The 2-year coupon bond delivers how much money? It delivers 102, so if you did 1 over 102, you would get one, so you have to divide this by 102. Okay, and that you multiply by the price, which is 100.2. Okay, so there's that term, right? So what have we done here? We've had to sell off this amount of money. So how can you sell off this amount of money? Well, by selling 1 over 102 2 year Treasuries, you're selling off 1 dollar, but you don't want to sell off 1 dollar, you want to sell off something smaller than 1 dollar, so it's that amount. So you're selling that amount of 2 year Treasuries. But now what do you have to do? Now, you see, you've bought some 1-year dollars by getting the 3-year coupon bond. But by selling the 2-year coupon bond, you've made some promises in year one, so you've got to net out all those things and do the right thing on the one-year coupon bond, right? So that looks a little complicated, but you can obviously do it by algebra. So everybody following? You're not following what the right thing to do is, but let's just say in words what we've done. In words, what we've done is we've said, there are things you can actually trade on the market. Those are the Treasuries. Those are our benchmark securities. Let's call them benchmarks. Now what we're interested in is some other maybe fictitious securities or new securities. The price of the zeros, those are the basic building blocks that will help us evaluate the present value of any investment. So the reason why we know these prices is because we can replicate them by trading only the benchmarks, only the Treasuries. So to get the 1-year zero, we just buy us the correct fraction of 1 year Treasuries. To get the 2-year zero, we have to buy the correct fraction of 2 year Treasuries and sell the correct fraction of 1 year Treasuries, and that gets us that thing. So we've replicated the 2-year zero by a portfolio consisting of being long the 2 year Treasury and short the 1-year Treasury. Right? To get the 3-year zero coupon, we have to buy the 3-year Treasury, sell the 2-year Treasury and do something complicated that we haven't quite figured out yet with the 1-year Treasury, and that will duplicate the 3 year zero. And then we'll just add up the cost of that portfolio that replicates this, and that must be the price of that thing, okay? So that's what we're doing. Any questions about that? Are you following this? Yes? Student: Just to clarify, so pi of 1 is today's price for 1 dollar at time 2 or...? Prof: Time 1. Today is 0, so pi of 1 is what you pay at time 0 to get 1 dollar at time 1. pi of 2 is what you pay today at time 0 to get 1 dollar at time 2, okay? So knowing those little pis, you can evaluate the price of anything, just by multiplying the little pis by the cash flows in the future. And now the trick--this is the trick we're going to see over and over and over again-- the subtlety in finance is that they don't just tell you what the little pis are. You have to figure that out yourself, okay? And so how are you going to figure out the little pis? Well, you know the Treasuries. You can trade the Treasuries, and you know what those prices are. You can see it on the market. So by combining the Treasuries in a very clever way, you can end up getting the prices of all the zero coupon bonds, the things that pay just 1 dollar at the end. Why are they called zero coupon bonds? Because it's like--you just get principal at the end, of 1 dollar, without any coupons in the middle. So the little pis are called the zero coupon prices, because the payments are just 1 dollar--you know, pi (3) is the price of 1 dollar at time 3. It's as if there was a bond that paid no coupons and paid 1 dollar of principal at time 3. So the little pis are the prices of zero coupon bonds of various maturities, and those aren't really traded directly in the market. What's traded directly in the market, where pieces of paper change hands, are the Treasury bonds. But everybody, every day is calculating these zero coupon prices, because that's what they need to do to evaluate every single project that they might conceivably do that day, and decide whether it's a good project or a bad project. Is it worth the price or not worth the price? And it's done by the principle of replication, just as we said. So this formula is going to be slightly complicated. I don't know whether it's worth writing down. So we've got, buying the 3-year Treasury, the right amount of that. Then we have to sell a certain amount of the 2-year Treasury, because we accumulated extra coupons. But now we're also going to be able to sell a certain amount of the 1-year Treasuries, and so how much is that going to be? It's going to be some formula, okay. So it's going to keep track of everything we did and get a formula here. So I'm actually not going to bother, I think--I was going to write down the formula, but it'll take 3 minutes to work it out-- because there's a much faster way of getting all these numbers. But is everybody with me here? You all understand how I could get this number if I wanted to do the work to get it? I'd figure out I had to sell--I'd sell some of the 1 year and buy some of the 2 year--I'd do something complicated here, okay? Sorry, I would do something with the 1 year Treasury here to compensate for the fact that the 3-year thing I bought is paying me coupons here. The 2-year thing I sold is reducing some of those coupons, and so it's only the net coupon that I can sell, and I'm going to sell that by selling the 1 year Treasury, okay? So that's how I would get the number there, and I added the cost of doing all these things together, and I get .917. So you're silent, but are you following it? Who can I--okay. So it's too complicated to just figure this stuff out all the time. So instead, there's a very fast algorithm that you can do almost instantly, and that's why it's such a triviality to calculate these numbers ever day. So it's called the principle of duality. You go backwards, and you say to yourself, "What I want is pi (1), pi (2), pi (3), pi (4), and pi (5), and I've started to figure out what the replicating-- " so these are the prices of zeros. Prices of zero coupon bonds. That's what I want--want prices of zero coupon bonds. I have the prices of the Treasuries and the way I'm figuring out the prices of the zero coupon bonds is by replication. Now if somebody stupidly, as happened 50 and 60 years ago, fairly routinely, if somebody was willing to give me 1 dollar in year 3 and only ask 90 cents for it, then I would be able to lock in a profit. How could I lock in a profit? Because I would just--he's willing to give this to me for a low price of 90 cents instead of 91 cents. So what can I do? Let's say he's willing--he'd pay me, let's say more likely--let's say he'd pay me 93 cents. Say some guy came to me, I'm the banker, and he says, "I'll pay you 93 cents today to get 1 dollar in year 3," in other words, for a 3 year zero. Well, I'd say, "That's wonderful." I'll sell them this promise in year 3, of 1 dollar for 93 cents. Then with that 93 cents, I'll only use 91.7 of those cents and I'll go out and buy the 3-year Treasury. I'll sell some of the 2 year Treasury and I'll sell a little bit more of the 1 year Treasury. And that portfolio which I've done by doing that will pay me exactly 1 dollar in year 3, enabling me to keep my promise to him, but it will only have cost me 91.7 cents. So I'll have made a 1.3-cent profit for sure, with no chance--it's a pure arbitrage. I made a profit of 1.3 cents with no chance of losing any money, okay, because I've done all the transactions today, and the government's going to keep its promises. I don't have to worry about the government giving me the money, and so I'll be able to turn the money over to that guy in year 3. Meanwhile, he's given me his 93 cents. So if you want to do an arbitrage and make your profit, you have to figure out what the replicating portfolio is, and the replicating portfolio also tells you the price. But it takes a long time to figure out what all these arbitrage-replicating portfolios are. And maybe nobody's coming to you and offering a stupid deal like that. So you don't need to figure out--so the principle of duality is, you don't need to figure out the replicating portfolio to figure out what the pi (1), pi (2), pi (3), pi (4), and pi (5) are. I can find those numbers now just by clicking a button in Excel, trivially, without bothering to find the replicating portfolios. Then if some, you know, bad trader comes to me and offers me 93 cents for the 3 year zero coupon, then I'll figure out the replicating portfolio and take advantage of that offer to make a pure profit for sure. So what I want to show you know is how to get pi (1) through pi (5) without having to go through this complicated calculation. And it just reasons backwards, okay. So please interrupt if you're not following this logic. So you reason like this: we don't know what pi (1) through pi (5) are, but if you did know them, you'd be able to price the very bonds that the market is trading. So you'd know that 100.1 had to equal 101 times pi of (1). And you'd know that 100.2, the 2 year zero coupon [correction: Treasury] bond, whose price is 100.2, would have to be 2 times pi of 1 102 times pi of 2, right? Because pi of 1, remember, is the price you pay today for 1 dollar 1 year from now. 101 dollars, 1 year from now, costs 101--if you knew pi (1), this would be the price. If you knew pi (1) and pi (2), you could figure out the price of the zero coupon bond-- I mean, of the 2 year Treasury bond, because 2 dollars at time 1 cost 2 pi (1) and 102 dollars at time 2 cost 102 pi (2). And then the 3 year is 100.3 = 3 times pi (1) 3 times pi (2) plus 103 times pi of 3, etc. Then we can go down to the last--well, I'll just write them all. It doesn't take a second. Okay, and the last one is, 100.5 = 5 times pi (1) plus 5 pi (2) plus 5 pi (3) plus 5 pi (4) plus 105 pi (5), okay? So you don't know the little pis, but you do know these prices, because the market tells you, and you know the payoffs of all the bonds, because that's just written on them, literally, so you can just read what the payoffs are. You know the government's going to keep its promise. So rather than doing this complicated stuff, trying to figure out the pis, assume you had the pis. And then if you had the pis, it would tell you what the prices of everything were. So if you guessed the wrong pis, you'd get the wrong prices. But basically, you're solving 5 equations and 5 unknowns, and that's what Excel is so good at. It's going to start with a wild guess of the pis, and then it's going to move around the pis until you match all these prices. And since it's 5 equations and 5 unknowns, and they're all linearly independent, it'll be a unique set of pis that it will calculate. But that 1 set of pis has to be the replicating portfolio prices, because there's only 1 set of pis that are going to work and solve these equations, namely the ones you got by the replicating argument. So we can figure out the pis by solving 5 equations and 5 unknowns, so that's what I do. So if you guess the pis, 1,1, 1,1, 1, any questions about what I'm doing? If you write 1,1, 1,1, 1, you're going to get prices, you know. For the first one, it will just be 101, and for the 2 year, it will be 2 times 1 102 times 1, is 104. For the third one, with all the pis 1, which is obviously not the right thing, it would be 3 3 3. That's 109, so those are bad prices. We're trying to match what the market says the prices are. So all I do is, I subtract the market prices we're trying to match from the actual prices. I look at what the error is, which we're trying make 0, then I square the error. And then presumably this was adding the error, sum C16 to G16. I added the error, and so I now want to do my Excel thing. Hopefully--I haven't done this, but let's--it's got to work. Okay, so minimize, good, that. Such that by changing cells--which are the cells I want to change. I want to change the pis. Those are the ones that are wrong, so I do that. So I'm minimizing the squared error by changing the pis, B18, okay, and I solve. Okay, and I've done it. And there is the answer. So you notice that I got the same prices that I told you about before by replication, .991, .962, and .917, etc. So we got the pis. So that's step 1. All right, so that's what every single financial firm in the entire world does every single morning, and sometimes every single hour. So are there any questions about what we just did? You have to do this in the problem set. Is there anything puzzling you about this? Okay, now I'm going to start deducing all kinds of surprising things from this. I hope that you'll be surprised, but I want to make sure you've got the concept of what we've done now. Anybody puzzled by it? Okay, so somehow, Fisher's pi (1), pi (2), pi (3), pi (4), pi (5) are going to be deducible from what's going on in the markets, every day. All right, so let's ask one more thing that's deducible. Suppose I go to a bank and say, "I promise to give you 1 dollar in year 2. How many dollars will you give me in year 3?" What do you think the bank's going to tell me? Every bank will give me the same answer, if that yield curve--given this morning, and that was this morning's yield curve, if I ask every bank in the world, "I'll give you 1 dollar in year 2, you tell me how many dollars you'll be willing to give me-- " So what am I doing? I'm saying, "I promise today to hand over to you 1 dollar in year 2, and you know I'm going to keep my promise. And in exchange, I want a promise from you to give me a certain number of dollars in year 3." How many dollars is the bank going to offer to give me in year 3? Every bank will give the same answer, and what will that be? So the thing I'm asking, is, I'm asking for what's called the forward interest rate. So we've got these things, which are obviously very important numbers. Those are the most important things. Fisher would say those are the prices you use to get everything. But now I want to say something, I'm going to ask another important thing, almost as important. I want the forward rate. So 1 i_1-- Student: We can't see that. Prof: You can't see that. I'm glad you pointed that--can you see this? Student: Yes. Prof: Okay. The cameraman told me this board was great. But anyway, so how about, I'll write 1 i_1^(f), forward, is--by the way, am I calling that 1 i_0 or 1 i_1? Sorry, just want to get my notation straight. Okay, so let's call 1 i_0 is the--1 i_t is the number of dollars at t 1 in exchange for 1 dollar at t. So this is the number of dollars at t 1 agreed today. So we agreed today that you're going to pay this many dollars at time t 1 in exchange for 1 dollar at time t. So this is like the interest rate that you might pay at time t. You give up a dollar at time t, how much do you get at time t plus 1? The interest rate. But we're not there yet. We're agreeing to it today. So today we're agreeing to this interest rate. So what is the interest rate we'd agree to today, so we've locked in the rate? When it comes to time t, one guy's going to hand over the dollar, and when it comes to time t 1, the other guy is going to give back this many dollars. So what is the rate we would lock in today? It's called the period t interest rate forward, because we're locking it in today for a forward period of time, but it's really just the normal time t interest rate for one year, but we're locking it in today. So what would we lock in today? How do we compute that? We already know what that number is. What is it? Yes? Student: It's the ratio of pi (2) over pi (3). Prof: Well, I put t here, so something like that. Student: pi t over t 1. Prof: Okay, exactly. That's pi (t) over pi (t 1). That's it exactly. So why is that? Student: It's a tradeoff between the dollar t, t 1. Prof: Right, so all we're doing is this forward rate. We're exchanging time t dollars for time t 1 dollars at this ratio. But we're committing to do it today. But today we already know what the ratio is of time t dollars to time t 1 dollars. We know that pi (2)--in fact, we know what it is. pi (2) happens to be .962. That's a bigger number than pi (3). From today's point of view, 1 dollar at time 2 is worth more than 1 dollar at time 3. We already know how much more 1 dollar at time 2 is worth than 1 dollar at time 3. It's the ratio pi (2) over pi (3). So that ratio, as he says, pi (2) over pi (3), has to be exactly the exchange rate that the people are agreeing to today. That's what pi (2) and pi (3) mean. If you express it as an interest rate, it's 1 the forward interest rate. That ratio is 1 i^(f)_t. Okay, any questions about that? Yes? Student: What happens if your yield curve is downward sloping? Prof: If the yield curve is downward sloping, yes. Student: Do you agree to give them 1 dollar in year 2, they give you less than 1 dollar in year 3? Prof: Okay, so you've made a little mistake in your premise. Good question, but let me phrase your question a little differently, so you see the answer to it. The yield curve was almost flat in year 2000. So in the year 2000, the yield curve was almost flat. In fact, there are moments where the yield curve seems to go down. So if the yield curve goes down, what does that mean? Does that mean--between year 6 and year 7, the yield curve went down a little bit. Does that mean that pi (7) is less than pi (6)? Maybe, but it couldn't really be that way. Okay, so let me translate his question. He's saying, look, yield curves very often are flat. Mostly they go up, very often they're flat. Sometimes they even start to go down. He said, "That worries me that maybe pi (7) is less than pi (6)." But that could never happen. That would be crazy, because that would mean that there would be a negative interest rate in the future, and with money, that can never happen. You can store the money. No one's ever going to ask for a negative interest rate. He could just keep the dollar and keep it in his pocket. Why is that? Remember, pi (6) = 1 over (1 the 6 year yield) to the 6^(th) power. And pi (7) = 1 over (1 the 7 year yield) to the 7^(th) power. So it could be that Y(7) is less than Y(6) as it is there, and yet pi (7) is still small. Could be that Y(7) is less than Y(6), as it is over there, but because you're taking this to the 7^(th) power and this to the 6^(th) power, you still have pi (7) less than pi (6). So just because the yield curve is downward sloping, doesn't mean that the pis are going down. The pis could never go down. The pis are always going to go up. So excellent question. Any other questions? Okay, so we could get the i's. The i's will typically be going up. Suppose the yield curve is going up, by the way. Will the i's be going up faster or slower than the yields? Yeah, if this is the yield curve and I calculate the forwards, do you think the forwards will be going up faster or less fast than the yields? All right, well let's do it in the example. Let's just go back to our example that we were doing. Yield curve spreadsheet, okay. So maybe I did it here. Hopefully I solved it all. Okay, so here we got the actual pis. You see the pis are always declining. And if we now look at the yield curve, you can figure out the yield. How can you figure out the yield? Because you solve that formula we gave at the very beginning. You take the price of the--I guess I've erased it now. Okay, you know what the price is. To figure out the yield on the 3 year, we just plug in 1 Y of 3,1 Y of 3 squared, 1 over 1 Y of 3 squared, 1 over 1 Y of 3 cubed, and that gives us the yield. Remember, that's how the newspaper reporter figured out the yields. So I figured out the yields in the spreadsheet down here, and these are the yields. So this is what would appear in the newspaper. The 1-year yield is a little under 1 percent. The 2-year yield is a little under 2 percent. The 3-year is a little under 3 percent. The 4-year is a little under 4 percent, and the 5-year is a little under 5 percent. Those are the yields. So what if we did the forwards? The forwards, remember, are just the ratios of these pis. What are the forwards? They're down here. So what do they do? Sorry, I don't know how I did that, but here are the forwards, over here. So the forwards have gone up much faster than the yields. They went from .008 percent, which is the same as that one, to 2.9, which is bigger than 2.8, to 5, which is way more than 3.8, to 7.2, which is way more than that, to 9.6, which is way more than that. So the forwards went up much faster than the yields. So why is that obviously going to be the case whenever the yield curve is upward sloping? So if we go back to our picture here. We go back to our picture. If the yield curve were completely flat, what do you think the forward yields would be? This is just common sense to see if you have any idea what's going on. If you think about batting averages and how somebody's average changes each time he bats-- if the yield curve is flat, like in 2006, the forwards are going to basically be flat. But if the yield curve is upward sloping, then the forward yields are going to go up much faster. So why is that? Okay, well, remember, the yields, you know-- when you do a 5 year coupon bond, you're discounting all the cash flows, the previous 4 cash flows, using the same yield to discount them all. So if you go from year 4 to year 5, and you have to raise the yield a lot, it means, you know, like if you're a batter, and your average goes up. It means the last thing you did was better than the average of what you've done before, so it's going to be even higher. If your average was .300, and then you played a series against the Red Sox in which you did very well and your average went up to .320, in that series against the Red Sox, you obviously did even better than .320, because you have to average what you did then with what, your previous .300 to get .320. So if the average sort of is going up, remember the yield is the same thing over the whole history. If, when you take a longer history, the average has gone up, it must mean that the most recent thing went up really much more, okay? So the 4-year yield is sort of averaging the payoffs of the first 4 years. The 5-year yield's averaging it over 5 years. So if that yield, the 5-year yield, has gone up, what happened in the 5^(th) year must have gone up a lot to bring the long run average up, okay? So that's why the yield curve's going to go up much faster [correction: the forward rates, compared to the yield curve, are going to go up faster]. Okay, so we know now to summarize, everybody can look at these pictures every single day. From these pictures, they can deduce the pis. That's the crucial variable in the whole economy, the pis. But a second crucial variable is the forward yields, the 1 i^(f)s, which you can just get by the pis. Now why are the 1 i^(f)s so important? We know that the pis are critical, because they evaluate every project by multiplying the cash flows by the pis. Why are the forwards so important? The forwards are so important because, suppose you believed that--so the forwards, let's go back to what we got. Let's just look at the numbers here. Here are the forwards, remember, down here. Okay, suppose I said to you, "You tell me." You don't know anything about the economy, maybe, but you can read the newspapers and do mathematics like we've just been doing. What do you guess the interest rate's going to be in year 2? So this is the 0 year forward, the 1 year forward, the 2 year forward, the 3 year forward and the 4 year forward. If I say in year 2, "What do you think the interest rate-- guess what the interest rate's going to be," what would you guess? Yeah. Student: I have a question. Could you make this all real interest rates by doing this for TIPS? Prof: Yes. Right, I could do this real interest rate by doing it for TIPS. Fisher would say do that. Trouble is, that TIPS are not traded--they're becoming more and more freely traded in the market. They used to be traded very--people didn't want to trade them. So my classmate, Larry Summers, introduced TIPS, Treasury Inflation Protected Securities, and he, you know, announced this was a fantastic idea and was going to change radically the whole markets. And then nobody traded them, and they offered astronomical interest rates, real interest rates, to get anyone to buy them. And so they were nicknamed--it's really bad on camera--but their nickname became totally illiquid pieces of... and so the market has not used the TIPS to do most of its pricing. It uses the Treasury bonds, but yes, Fisher would say, if the TIPS were a reliable market, you would use the TIPS to get the real interest rate, and that's really what you should care about, is the real interest rate, not the nominal interest rate. But we're using the Treasuries here to get the nominal interest rate. However, you've now just dodged my question. My question was, if I asked you to predict, on the basis of the yield curve in this example, and what we've been able to deduce, what would you predict the interest rate was going to turn out to be 2 years from now, the 1-year interest rate? What would you predict? Yeah? Student: The market predicts > Prof: Which forward rate? Student: Sorry, which years were you >? Prof: Year 2. In year 2, what do you think the interest rate will be between year 2 and year 3? Student: Year 2 > Prof: It's today, and we're asking, what do you predict the market rate of interest will be in year 2, between year 2 and year 3? Student: The forward rate, it would be 1 i_2^(f). Prof: Okay, and I_2^(f) happens to be right here, 5 percent. Okay, so that's the forward. Student: > Prof: So 5 percent you'd predict. Student: > position, but not the best prediction. Prof: Okay, so let me refine that a little bit. If the world were one of total certainty, so everybody trading today had a perfect forecast of what was going to happen in the future, then of course, the forward rates in the market today would have to be exactly equal to the forward interest rate. Because suppose that you knew for sure the interest rate was going to be 4 percent in year 2. How could the market get to a 5 percent forward? That means that some guy is promising today, "You give me 1 dollar in year 2 and I'll give you 1 dollar 5 in year 3." And we're agreeing to that deal. But that's a ludicrous thing for him to do, because when he got to year 2, he could simply-- if he knew for sure what was going to happen in the future, and that the rate was going to be 4 percent, he would just--I said it backwards. What an idiot. Suppose he knew for sure the rate was going to be 6 percent, he would be--oh yeah, if he knew for sure the rate was only going to be 4 percent, he'd be a fool for promising to give the guy 5 percent today, because in the future, when he got the dollar, what would he do with it? Put it in the bank and get 1 dollar 4 next year? That wouldn't cover his promise. He'd be screwed, okay. So if he knows for sure that the rate 2 years from now is going to be 4 percent, the forward rate would also have to be 4 percent. So to say it backwards, if you assume everybody knows for sure what's going to happen in the future, then the forward rates would be exactly equal to what everyone is expecting to happen in the future. To say it slightly differently, if you happen to be the one ignoramus in the world who didn't know what was going to happen in the future, but you knew that everybody else who was trading in the market did know what was going to happen in the future, and you saw a forward rate of 5 percent, then you could deduce, even though you were an ignoramus, that actually 2 years from now, the interest rate was going to be 5 percent. Okay, so just what you said, but just said a little bit more precisely. We're assuming here perfect certainty about what's going-- we're assuming the traders who trade today all are completely convinced of what's going to happen in the future. Okay, so let's go back to our picture now. The picture of the zero yield curve. So what do you think this blue curve means? What are the traders convinced is going to happen in the future? The second half of the course is going to be dealing with uncertainty. We're now assuming, like Irving Fisher, that everybody trading today has no doubt about what's going to happen in the future. So what do you think these traders think about these prices, about the interest rates? We're now in the world today, this is September 30^(th), it's today. That's this curve. What does this curve mean? Making the assumption that traders today are convinced about what's going to happen next, you know, in the future 10 years and 30 years, what do we know that they are convinced of? Yes? Student: That interest rates are going to keep going up. Prof: That interest rates are going to go up and go up a lot. They're not just going to go up to 4 percent, because that's the 30-year yield. They're going to go up--the forward rates are going up much faster than that, so we could have computed what they think. So they think rates are going to go way up in the future, okay, much higher than that, because you're starting so low, staying low for a while. So the rates have to go up, the forward rates, really sharply to pull the average that high. So people are convinced that rates are going to go up in the future. That's what that tells you. And why would they be convinced of that? Well, for the two reasons that you gave at the beginning. One of you said, "The market is going to get more productive." Irving Fisher has already told us that when the market gets more productive, you know, you're more optimistic about what's going to happen later, the real interest rate goes up. And if inflation's constant, and the real interest rate goes up, the nominal interest rate goes up. The other possibility is that the real interest rate stays the same, but there's inflation in the future. The real interest rate the inflation is the nominal interest rate. That's another explanation for why people might expect the nominal interest rate to go up, okay? So you know that the market is predicting rates going up, and the two obvious explanations according to Fisher is that either inflation is going to go up or the real rate is going to go up. And why might the real rate go up? Well, there are a bunch of reasons, but most likely because productivity is going up. Okay, so I've got one more surprising conclusion to end this. So if you were certain about the future and you took the 5-year coupon bond, could you tell me what the price of the 5-year coupon bond was going to be next year? How would you figure that out? Assume that everybody is convinced that the 5 year coupon bond--that they know the future for sure. So therefore, from the zero curve--I erased my graph--this is the last question. I'll let you go as soon as you answer this. You need to answer this to do the problem set. Wrong graph, shit. Sorry. Okay, it'll only take 1 second to answer this. Okay, I'm telling you now that this is what everybody's looking at in the morning, okay, these numbers. They're getting all the forward rates and stuff like that. They're making all the deductions that we made. Now if you suppose that those people are convinced, they don't have any doubt about what's going to happen in the future. Because they don't have any doubt about what's going to happen in the future, you can infer from these prices what they think about the future. So the question is, can you infer what the price of the 5-year Treasury, which is now 100.5, that 5-year bond is 100.5, next year it will only be a 4-year bond. Do we know what its price is going to be next year? Yes. Student: Yes, you can stick the cash flows in > year 2,3, 4 and 5, and multiply them by the > Prof: By what pis? Student: The big pi, the price of the > Prof: Those pis. Those pis or something slightly different from those pis? It's going to be a year later, remember. Student: Oh, by the equivalent of those in year 2. Prof: How would you get that? Yeah? Student: Discount by forward rates, so it's like > 4 and 5, forward rate in 3,4, > year forward, add a discount > Each > would have one less forward in it. Prof: Okay, so what you both said is absolutely correct. Unfortunately, we're 2 minutes--we're ending now. So let me just end by saying, in the problem set, that's exactly the question. What is the 5-year coupon going to be priced next year? If there's a world of certainty, you're going to know what all the interest rates are in the future. And if you know what all the interest rates are in the future, obviously Fisher tells you, you can figure out the price is. However, to get the exact formula would take a few minutes and I unfortunately am a few minutes behind, so you're going to have to figure out what the right formula is, but it's what he said and what you were getting to.
Quantitative_Finance_by_Yale_University	5_Present_Value_Prices_and_the_Real_Rate_of_Interest.txt	Prof: I think I'm going to start. So this is really the beginning of the finance part of the course. So far we've reviewed general equilibrium, which I said Fisher invented or reinvented in order to do finance. And as you remember the main conclusions from general equilibrium are first that the market functioning by itself without interference from the outside, in other words a situation of laissez-faire, leads to allocations that are Pareto efficient. So they're in some sense good for the economy and good for the society. They don't maximize total welfare. That's not even a well-defined thing as we saw last time because how can you measure, how can you add one person's utility to another. It doesn't even make sense. So economists at first were wrong to think of that as the criterion for good allocations, but there's another better definition of efficiency that Pareto invented, called Pareto Efficiency, and the free market achieves Pareto Efficiency at least if there are no externalities and there's no monopoly. So that, lesson number one, was taken to mean that the government shouldn't interfere in the free market, especially shouldn't interfere in financial markets, and that's something we're going to come to examine. The second lesson we found was that the price is determined by marginal utility. It's not determined by total utility. So it may be that water is much more valuable than diamonds because it does a lot more good for everybody and for the world as a whole than diamonds do, but the last drop of water, really most people have as much water as they need, the last drop of water is not doing that much whereas the last diamond is a rare thing and not many people have them. So the last drop of water is worth less than the last equal weight of diamonds and therefore water is much cheaper than diamonds even though water's much more valuable as a whole than diamonds. The price of things depends on their marginal utility. A third implication of what we did is that there's no such thing as a just price. It depends on what peoples' utilities are and how much they like it. It depends on how much of the good there is. That's why diamonds are priced less than water [correction: that's why water is priced less than diamonds]. And it depends on how wealthy people are. If you transfer money from people who don't like apples compared to tomatoes, to people who like apples a lot compared to tomatoes, the price in the free market is going to reflect more the latter class of people than the former because they've got the money to spend, and so the price of apples is going to go up relative to the price of tomatoes. So those are the three basic lessons of general equilibrium. The first one about laissez-faire has a huge implication for whether there should be regulation, but the second pair of implications, what determines the price and how price changes as you redistribute wealth and so on, and no just price, that set of ideas, you'll see, is also going to be very important for finance. So those lessons seem clear. Some of those lessons were understood already by Aristotle as we said. So the ancients understood supply and demand, at least a little bit of supply and demand, and yet as soon as they moved from apples and oranges to finance, they all got hopelessly confused. So Aristotle said, "Interest is unnatural." I could go through a lot of people and what they said, but I'm going to just leave it at a few quotations. The Bible says interest is terrible. Judaism frowns on interest. Christianity frowns on interest. Islam frowns on interest. All the great religions of the world crystallizing, obviously, some of the most important thinking of the time, frowns on interest, so just to remind you of a few. So why do they frown on interest? Well, the idea is that you do nothing, the lender does nothing and he gets back more than he lent to begin with. He's making a profit without having exerted any effort whatsoever. So, Sulinay Middleton said, "In trade both parties are expected to gain, whereas in lending at usury only the usurer could profit." So in Deuteronomy in the Bible, so this is the Jewish Bible, is says, "Thou shalt not lend on usury," (that just means interest). "Thou shalt not lend on usury to thy brother. Usury of money, usury of victuals, usury of anything that is lent upon usury, "--that's all terrible. Of course, "unto a foreigner thou mayest lend upon usury, but unto a brother thou shalt not lend upon usury." So the Jews could lend to Christians but not to each other. So the Christian Church outlawed usury, called it a mortal sin. Luther, for example, says, "For who so lends that he wants it back better or more, that is open and damnable ocker. Those who do that are all daylight robbers, thieves and ockerers. Those are little Jewish arts and tricks." So there was this antipathy towards usury, and because Jewish moneylenders were able to lend to Christians there was an antipathy to Jewish moneylenders which we're going to come to when we talk about Shakespeare. So Muslims also forbid lending. In fact, even today it's illegal to charge interest in Islamic law. So in my hedge fund we tried to raise money, and there's lots of money in the Middle East, and most of it, by the way, ten years ago, almost all Middle Eastern money was invested in U.S. Government bonds and U.S. stocks, nothing else like in mortgages, for instance. So I went to Saudi Arabia and I met a bunch of brothers of the King, the eldest brothers of the King, and I suggested they invest in our hedge fund. And they actually became sort of interested, and so we had to write up a complicated contract. Now, you know a mortgage pays interest, so if you invest in the hedge fund and the mortgage is paying interest it looks like they're getting interest, and so that wasn't going to do. So we had to write a very elaborate contract which disguised the fact that interest was being paid, and it had to be overseen and blessed according to Sharia Law by a holy person who was going to verify that there was no interest. Now he charged a fee which was a percent a year which looked an awful lot like interest, but anyway so. So the point is all these religions have banished interest despite the fact that they themselves were involved in interest, and lending, and borrowing. A world can't function really without lending and borrowing and the charging of interest. So these religions that forbade it at the same time knew that it was going on and allowed it to go on and sometimes participated in it. But the point I'm trying to make is that there was vast confusion, and even today there's confusion because still today the Jewish law doesn't allow for interest between Jews, and--there's a charade that goes on there just like there is in Islamic law, and just like there is--still frowned upon by the Christian Church. So it's a hard subject to understand, and why is that? Why is it that it's so confusing, and how should we understand it? Well, Fisher cut through all this extremely simply, and the way he did it was he said, "Let's just think mathematically then we won't get so tied up in all these religious complexities. Just let's do something mathematical and concrete." So suppose that we consider a problem, which is the one I'm going to work with the rest of the class. Maybe I better do it over here. So let's say that there are two agents and two goods. So the two goods now are X_1 and X_2. So Fisher's first insight is that let's think of X_1 and X_2 as apples, but apples today and apples next year, Fisher said--although they're both apples, exactly alike, there's no difference between these apples, the apples this year are different goods from the apples next year. So let's move away from apples and tomatoes to apples this year and apples next year. So I'm not going to call them goods X and Y anymore. I'm going to subscript them by time. These are both X because it's the same good, but they're different goods because they occur at different time periods. So Fisher said we can incorporate time simply by having different goods. So of course people, he said, are going to have some utility of consuming today versus consuming tomorrow, and let's say this utility is (log X_1) (1 half log X_2) for Mr. A. So I'm going to come back to this in half an hour and explain why Fisher thought that this half made sense. You see, this Agent A likes good 1 a lot more than good 2. So Fisher would say that's because Agent A is inpatient. An apple is an apple, but if you get it now it's worth more to you, it gives you higher utility than getting an apple next year. "This is a law of human nature," he claimed, which I'm going to come back to later, and that's why when you write down the utility function there's a discount factor, which we're going to add--a discount factor-- which discounts, reduces, the utility you get from future consumption. So let's say (U^(B) of X_1 and X_2) = (log X_1 log X_2). So B is more patient than A is. B actually doesn't discount the future. A does discount the future. So A is impatient, relatively impatient, and B is patient. They have endowments, so E^(A) let's say the endowment is (1,0). Say it is (1,1) and E^(B) let's make that (1,0). But now Fisher wants to talk about finance and he wants to talk about stocks, and bonds, and interest and all kinds of things. So he says, "We've talked about good with no problem. We can talk about goods today and next year with no problem, let's talk about stocks." What is a stock? Let's say there are two stocks, stock alpha and stock beta. What are stocks? I mean, they're pieces of paper that you're trading, but they give you ownership of something like a factory or a company or something, and what good is the company? Well the good of the company is that it's going to produce something. So let's say that the stock is going to produce something in the future. So we'll call the production of the stock--so what is the future? There are only apples in the future. So let's say D^(alpha)_2 is 1 and D^(beta)_2 = 2. Fisher says, you can tell a lot of stories about what this stock does, and what its method of production is, and what kind of managers it has and a lot of stuff like that, but in the end people care about the stock because the stock is going to produce something, and the value of the stock is going to come from what it produces. So D^(alpha)_2 is what people expect the output of the stock to be next year which is the last year we're worrying about, and D^(beta)_2 which is 2 is what people expect the stock to produce next year. And we're going to assume that perfect foresight here. So Fisher says, "Well, in general people's expectations might be wrong," but let's start off with the case-- people anticipate something, surely they're looking ahead to the future when deciding whether to buy the stock. We've got to assume something about what they think. Let's suppose they actually get it right and they know what the price of the stock is next period. So what's going to happen? Well, we can define an economy and presumably the interest rate and the stock prices and all that are going to come out. Now I should mention, by the way, I forgot to say this, but as I write this down I suddenly realize I forgot to mention it. There are other theories of interest too. Another famous one was Marx's Theory of Interest. So this is to be contrasted with Fisher. What did Marx say? So in my youth when I was your age it was very fashionable to be a Marxist. You had to study Marxism basically. If you wanted to talk to women you had to know about Marx. So anyhow, I dutifully went off and read Marx. And so what's the idea of Marx? The idea was that he imagined an agricultural economy where you plant stuff today and then the output comes out tomorrow. So you put corn in today, corn comes out tomorrow. So it doesn't require much effort to plant the corn. You have to buy the corn. So the capitalists would buy the corn, but planting it didn't require much effort. However, harvesting it, picking the cotton, picking the chocolate, picking all that stuff takes a lot of effort. So in the end you'd get a lot of output. Now when you pick the output you'd have to pay workers in order to pick the output. So Marx imagined that there was a wage that was arrived at by the struggle, class struggle, between the capitalists and the workers over the subsistence wage. So the subsistence wage was something that resulted from this huge class struggle, and over time maybe it would rise as workers got stronger, but it was still always quite low and the subsistence wage was what the workers would get. And what's left over, which was the surplus--so the output being more than what was put in, was the surplus. Part of the surplus would go to the subsistence wage. The rest would go to profit. And so if you look at how much was put in to begin with, you get all the output back out, the same amount of corn you put in plus some extra you have to give to the workers, and extra that the capitalist gets back as his profit. The fact that the capitalist has done no work at all, he's just bought the corn, let someone else plant it, let someone else harvest, paid all those guys virtually nothing at the beginning and a lot at the end, he's gotten profit for doing nothing just like when you lend money, so the profit divided by the initial outlay, that was the rate of interest. And so Marx said that a capitalist, he could put his money in his bank or he could run this farm and make profit this way. So the money, interest in the bank would have to turn out to be the same as this rate of profit otherwise he'd put all the money in the bank. And if it was smaller the banks would have to give higher interest in order to attract depositors. So the capitalist's profit--rate of interest was determined by the rate of profit and the rate of profit was determined by the struggle between capital and labor. So we've got these religious figures and great philosophers saying interest is terrible. We've got this great philosopher-economist saying it's the result of a class struggle, and now we've got Fisher, actually Marx was pretty mathematical, but now we've got Fisher turning it into a simple math problem and saying, "Let's reason out the math problem and we'll have the answer to these questions, and it'll turn out to be quite different from what all these guys are saying." So here's his economy that I just described. The Fisher example, not literally an example he gave, but similar to one he gave. So he said, "All right, what happens in this economy? Let's just be very commonsensical. What we need to find out now is financial equilibrium," so financial equilibrium is much more complicated seeming than we had before, because we care about the prices. So now I'm going to use (q) for prices, a q for contemporary prices, q_contemporary, so the price you pay today to get the apple today. q_2 is the price you pay next year to get the apple next year. They're contemporary prices. And of course people are going to decide what they want to do, X^(A)_1, what they're going to end up consuming X^(A)_2, X^(B)_1, X^(B)_2, but now we've got a more complicated world. There's stocks to be traded and there's the price of stocks. So P--pi_alpha, I'm running out of letters. I'm going to switch to a Greek one. This is the price of stock A, stock alpha. And pi_beta is the price of stock beta. And then we have to know how many shares are they going to hold? Well, it's going be theta^(A), A's going to hold a certain number of shares of alpha, and theta^(A)_beta, A's going to hold a certain number of shares of stock beta, and B's going to hold a certain number of shares of alpha and a certain number of shares of beta. So we want to solve for all of that. Now, I should have said at the beginning if these are trees producing apples there was an initial stock. People owned a certain number of trees. So let's say theta-bar_alpha^(A), so this is the original ownership of alpha. Let's just say that's, I'll make up some number. I might as well use the same number I thought of before. Let's say that's 1, and let's say theta-bar^(B)_alpha is 0, and let's say theta-bar^(A) of beta is a half, and theta-bar^(B) of beta is a half. So the original economy is more complicated than before because we've added stocks. We characterized the stock. We said a stock is a very complicated thing. A company is very complicated, depends on managers and processes and there's all kinds of stuff you think about when you think about a stock, but really at heart all people are trying to do is forecast what are they going to produce. And so we're going to make it simple mathematically and say let's say we know what they're going to produce next period. So let's say it's a tree. Everybody knows the alpha tree's producing 1 apple. The beta tree's producing two apples. Alpha happens to own the only alpha tree. A owns the alpha tree, excuse me, and A and B own half each of the beta tree. So that's the original economy and the equilibrium is going to be, what are the prices going to turn out to be of X_1 and X_2, what are the prices of the trees going to turn out to be, how much will people consume and how many shares? Because alpha A began with all of tree maybe he'll sell his shares of tree and end up with not having a tree in the end. So we have to see where they began, the stock ownership to begin with and where they end up. So we have to solve all of that and it looks way more complicated than before, and so complicated that you can see why people might have gotten confused. But according to Fisher it's going to turn out to be a very simple problem in the end once we look at it the right way. So are there any questions about what the economy is and what are the variables that we're trying to explain? Yeah? Student: Sorry, I can't read what that says over theta alpha A. That's original ownership? Prof: Original ownership of stock alpha. And this is original ownership by B of stock alpha. This original ownership by A of stock beta, and this is the original ownership by B of stock beta, original ownership of alpha. Thanks. Yes? Student: Having defined all of these could you redefine what D stands for? Prof: D is the dividend. That's the output that we can all--thank you. I should just write this down. This is the anticipated dividend, which is the output since that's the end of the world of stock alpha in period 2. And D^(beta) of 2 is the anticipated dividend of stock beta in period 2. So it's 1 apple we're getting out of the alpha tree, 2 apples out of the beta tree, right? That's what the tree's good for. We can look at how beautiful it is. We could talk about how much the owner's actually watering the tree. We can talk about a lot of complicated stuff, but in the end all we care about is how many apples we expect to get out of it. All the other stuff goes into helping us think about how many apples we're going to get out of it in the end. So we cut to the bottom line. What are the apples we expect to get out of tree, 1 from the alpha tree, 2 from the beta tree. Someone else had their hand up. Student: I had it, but you answered it. Prof: Any other questions about this set up? So we're returning to first principles here, very simple example. When there's ever a big confusion about something important it's always good to go to first principles. There was a chess player when I was young named Mikhail Tal who was a world champion for a little while, and he said that every two or three years he'd go back and read his original introductory textbooks on chess. So we're going back to the first principles. How would you define equilibrium here for a financial equilibrium? Well, the first thing is just common sense. What are people doing? At time 1 what can they do? They can spend money, so I'm going to look at the budget set for Agent i, and i can be A or B so I don't have to write it twice. So he's going to say to himself, let's say A is he and B is she, i is he. He's going to say to himself--let's say i will say, "How much does it cost me to buy goods?" Well, the cost of apples is q_1 times X_1. That's how many apples I might end up with. Now, how much does it cost me to buy shares? It's going to be pi_alpha times how many shares I end up with, theta_alpha, plus (pi_beta times theta_beta). So I'm buying goods, I'm buying alpha shares and I'm buying beta shares and this is how much I have to spend to get the holdings I want of each. Now where did I get the money to do that? I got the money to do that because I started with my endowment of goods which was E^(i)_1, which in this case for A was 1 unit, for B was also 1 unit, and then I also had shares to begin with of these stocks. So I had ([pi_alpha times] theta-bar_alpha) (pi_beta theta-bar_beta). In period 1 that's what I had to do. I wanted to buy apples, shares and I had shares to sell and apples to sell. So that's what i did. So of course if X_1 is bigger than the number of apples i started with that means i has bought apples because he ends up with more than he started with, so that meant he must have been buying apples. If theta_alpha is more than theta-bar_alpha it means that alpha [correction: i] bought shares of stock alpha. Theta_alpha is less than theta-bar_alpha it means alpha [correction: i] sold shares of stock alpha. All right, now in the second period what happens? Well, in the second period we have q_2 times X_2. The shares are going to be worthless in period 2. So no one's going to buy them. Why are the shares worthless? Remember that when you buy a share of stock the dividend comes later. You don't get the dividend immediately. So someone buying stock in period 2, it's too late to get the dividend. It's already gone to the owner who bought the shares in period 1. So the buyer of a stock [doesn't] gets the dividend for a month or something. So next period's dividend is still going to go to the buyer in period 1, that's why it's valuable to buy shares in period 1 because you get next year's apple. So by next period you can buy the tree, but the world's coming to end. That tree's not going to do you any good. It doesn't produce any more apples. So nobody's going to bother buying shares. I don't have to bother with them. The prices are zero. And so what income do people have in period 2? Well, they've got the contemporaneous price times the apples that somehow they find on the ground or that their parents are going to leave them when they get old. So that's their endowment of apples, but what else do they have? They've got more apples than that. What else do they have? Student: The dividends. Prof: The dividends. So what are the dividends? Well, you bought theta_alpha to begin with so that's D^(alpha)_2. So if you bought the whole tree then you've got all the dividends, and similarly with beta. Theta_beta times D^(beta)_2 [correction: theta_beta times D^(beta)_2 times q_2. And, theta_alpha times D^(alpha)_2 should also be multiplied by q_2]. So that's it. So the budget set is a little more complicated. So that's the budget set. So it's got 2 equalities instead of 1 equality, so already things look a little more complicated. Now, so an equilibrium is going to have to be that i chooses (X^(i)_1, X^(i)_2), theta_alpha-- I can write, theta^(i)_alpha, theta^(i)_beta, that's all the choices he has to maximize U^(i) subject to this budget set. So A's going to pick what shares to hold, how much to consume today, then, of course, looking forward A's going to be able to figure out what he's going to end up consuming tomorrow. All right so, and now in equilibrium we have to have that (X^(A)_1 X^(B)_1) has to = (E^(A)_1 E^(B)_1). And then we do the shares, theta^(A)_alpha theta^(B)_alpha has to = theta-bar^(A)_alpha theta-bar^(B)_alpha, right? The stock market has to clear and theta^(A)_beta theta^(B)_beta has to = theta-bar^(A)_beta theta-bar^(B)_beta. So in period 1 the demand for apples has to equal the supply of all the agents, but now what's the last equation? This is a little trickier. What's the last equation? X^(A)_2 X^(B)_2 = E^(A)_2 E^(B)_2 .... Is that it? No. There's something else. Student: Plus dividends. Prof: The total consumption of apples is going to be the apples that they have on the ground, but also the ones that were picked off the trees, so these dividends. So it's going to be the total dividends which are [(theta-bar^(A)_alpha theta-bar^(B)_alpha) times that tree-- D^(alpha)_2] [(theta-bar^(A)_beta theta-bar^(B)_beta) times D^(beta)_2]. So just to say it in words, it's exactly what we had before except we have to take into account in addition to the goods market clearing, we have to take into account that the stock market has to clear. And in the end demand for goods has to equal the supply that people had in their endowments, but also what the companies are producing. These companies are producing output, apples. And so that's part of what the consumption is going to be in the economy. Are you with me here? It's a good time for questions, maybe. Yes? Student: Could you just explain again why we don't take stocks into consideration in period 2? Prof: So in period 2 you might wonder, pi_alpha is the price of the stock at period 1, stock alpha in period 1. Pi_beta's the price of the stock beta in period 1. How come I didn't write down the price of the stocks in period 2 and keep track of what they're holding in period 2? And the reason is that when you buy a stock you're buying it not for the dividends at this same moment in time. You don't get those dividends. The guy who already had it gets those dividends. When you buy the stock you're buying it for the future dividends you can get, and I've assumed the world's going to end after 2 periods because nobody's utility cares about period 3. So if you buy the stock in period 2 it's too late for you to get anything. There are no dividends because you can only get them in period 3, and there won't be any dividends in period 3, and if there were you wouldn't care about them anyway. So the stock's worthless to you. So the price of the stock in period 2, of both stocks, is going to be 0. So there's no point in putting down what people are buying of the stocks or selling or anything. It's just not worth anything. But in general you're right, and we're going to be more complicated later when you look at your income from having bought the stocks. You'll have as your income the dividend from the stocks plus the resale value of the stock, because you could sell the stock next period. But I just know the resale value's going to be zero because you're in the last period of the economy. And I just want to keep it very simple this first time. Step by step you'll be able to keep very complicated things in your head but not right at first, so any other questions? Yes? Student: Why are there endowments in period 1 and >? Prof: You mean why do people have endowments today and next year? Because you could think of the endowment, for example, as--here we've got apples, but usually the endowment is your labor, so you can work this year--your most important endowment is your energy and your labor. So you've got it this year. Next year if you're still alive that's new labor that you have. It's a different good so it's a second endowment that you have. So I don't want to get caught up in labor and all that and get involved with Marx again, so I'm just going to talk about apples. You have an endowment of apples when you're young and next year somehow you're going to have more apples. So you might have thought that the only apples next year come from what the firms are producing, but I allowed for the possibility that people have apples too just like their labor next year. Other questions? Yeah? Student: We then have to define E_2^(A) and E_2^(B) in terms of first period endowments, or is that something implied in the equation? Prof: I should have written this more carefully maybe. E^(A)_1 and E^(A)_2 is that, and this is E^(B)_1 and E^(B)_2 is that. So as he was suggesting back there I've assumed for person B that he's got an apple now. We aren't modeling what happened to get us here. The guys got an apple today. They both have an apple today. Somehow A's also going to have another apple tomorrow that he's going to find under his doorstep somehow that isn't being produced by the tree. And maybe you can think of it as labor that he's going to have next period. All right, so that's it. Fisher says as soon as you write down the economy mathematically all sorts of things are going to occur to you which if you're talking in words about justice and injustice you're going to be lost. So what can we get right away out of this? What can we get right away out of this? Well, the first thing is, how would we define inflation? What is inflation? What's inflation in this economy? Assuming we've got the equilibrium, which we're going to get soon, we're going to calculate it, but right now we don't what the numbers-- you know we've got a bunch of equations and stuff. We don't know what X^(A)_1 and q_1 and q_2 are going to turn out to be, but we're going to find out very soon. But before we find out, assuming we've gotten those, what will inflation be? What is inflation? Yeah? Student: Is it how much the ratio of the price of the dividend has changed? Prof: Well, we're talking about inflation. When you talk about the Consumer Price Index, inflation, what are they talking about? Yeah? Student: It's the rise of q_1 and q_2. Prof: So inflation is just q_2 over q_1, right? So that's the price of apples today. That's the price of apples next year. If the price of apples next year is bigger than this year we've got inflation. If it's lower we've got deflation. So already the model, you're talking about inflation. What else? What's the next most obvious? Well, I think I'm going to skip a bunch of stuff and get now to the key idea. The key idea is arbitrage. So Fisher says, "People have foresight." They're anticipating what the dividends are going to be. They understand that you can talk about how beautiful the tree is, and how much you like the owners, and how much they're watering it, and whether they have a good plan for irrigation, and whether they did well in college and stuff like that, but in the end all you care about the trees is how many apples they're going to produce. So knowing that, can we say something about pi_alpha pi alpha versus pi_beta? In equilibrium what's going to have to happen? There is going to be some connection, and what's the connection going to be? You've got two trees. Yeah? Student: The ratio between the prices would be the ratio between the >? Prof: Right, so pi_alpha is going to be pi_beta times D[^(alpha)_2 over D^(beta)_2]-- alpha will be better as long as the-- hopefully I've got that in the right order. And so in this case pi_alpha is going to equal a half pi_beta, because alpha's producing half the dividend that beta's producing. So obviously it's going to turn out to have half the price. That's the fundamental principle. We're doing it in the most trivial case, but it's the most fundamental principle of finance that if you've got two assets and they're basically the same up to scale then their prices have to be the same up to scale. Who's going to bother to buy alpha if it costs the same amount as beta when it only produces half as much? Yes? Student: Is that the same thing as saying that their yields will converge, that equation? Prof: Well, it is something like that, but that's a word that we haven't defined yet, so we're going to define it in the next class. So it's something like that, yep. Any other? So that is a very simple thing. Suppose after finding the equilibrium I added a third asset that paid 1 dollar in period 2 next year. Now, it would have a price of--added a third asset gamma, so pi_gamma--we'd have to solve for the equilibrium pi_gamma, and is there some word that I could use? So gamma is an asset that pays a dollar in period 2. It's like a bond promising a dollar in period two. The price of the bond would then have to be what? 1 over (1 i) where i is called the nominal interest rate, so we've got inflation is occurring in the model. If I added a bond, which I didn't bother to do because it's just yet another thing I'd have to write down, I could have had a third asset which pays a dollar. The others are paying off in apples. This one's paying a dollar and its price today, if you pay 80 cents today it's like saying I'm paying 80 cents today, I'm getting a whole dollar tomorrow. So it's like a 25 percent rate of interest, because another way of saying it is that 1 over pi_gamma is 1 i. I put only pi_gamma in today, I get 1 out tomorrow so I've gotten back not only the pi_gamma I put in but something extra, that's 1 the interest rate. So this world is going to have an interest rate in it. It's going to have inflation in it. With me so far? Let me add one more thing. I could come back to this. So I said that if you take theta_alpha less than theta-bar_alpha it means you're selling the stock. So I'm going to allow people to go even further, theta_alpha less than 0. So let me just write that again, theta_alpha less than theta-bar_alpha means selling alpha. Theta_alpha less than 0 is doing a lot more than selling. You don't have it to begin with, so what are you selling? Well, the mathematics is telling you that over there theta_alpha's going to be negative. Instead of getting extra dividends you're going to be giving up dividends because it's going to reduce your supply of money. So theta_alpha less than 0 is called selling short-- I don't know which one I've lost, but it's got to be bad-- if you can still hear me--you're selling short, this means. So you're selling something you don't even have. It's also called naked selling. It's also called making a promise without collateral. So I'm going to, for now, allow for that. So we're not taking into account that anybody's defaulting. If you take theta_alpha negative it means your income in the future is going to be reduced because you're going to have to deliver the dividend because you're going to have negative dividends, which means effectively you take out of your endowment those dividends and hand them over. So it's as if you always keep your promises. So this model so far, the Fisher model, assumes no default, no collateral. We're not worrying about any of that stuff, and of course that's going to be a critical thing. So you see something's happened that we never had happen before. In the past you traded money for a football ticket. You gave up something you wanted you got something that you also wanted. It was a trade of value for value. Everybody agreed the two things you traded were equally valuable. If you take theta_alpha negative, by taking theta_alpha negative that becomes a negative number here so it allows you to spend more. You can buy more goods by taking theta_alpha negative. That's negative. That means this can be more positive and still satisfy this constraint. So by selling a stock short you're promising to do something in the future. You get more money now you can eat more now, and then of course you have to consume less in the future because you have to pay back your promise. So you're exchanging something valuable, you're getting money, something valuable in exchange for a promise which is worth nothing until the future when you deliver on your promise. When you buy the stock you're buying part of the tree, but the tree's doing nothing for you now. You're doing it because it's going to be valuable next period. You're actually not physically owning the tree, you're owning a piece of paper that gives you a right to half the dividends of the tree. So you're getting something that's only good because it's a promise you think is being kept. So, so far for the next few lectures we're going to ignore the fact that people get very nervous when they give something up that's valuable in exchange for something that's just a promise. So a critical thing has happened here. So we've kept the same mathematics except we've surreptitiously added this huge assumption. Now Fisher said, "Having done that, what can you realize?" This is the most important insight. He said this model it looks so complicated. It looks like now we have vastly more equations. No wonder Marx and all those religious zealots were getting confused. We can simplify it all and be back to where we were before and yet talk about finance. So Fisher introduced the idea of present value prices. So he said look, when you buy a stock what are you really doing? This is the principle of arbitrage. He says when you buy a stock you're saying to yourself, I'm giving up money today. Now, money today is consumption because I would have used that money. If I didn't buy stocks I would have bought apples today and eaten them. So when I buy a stock I'm giving up apples today. I'm getting the stock which is then paying me dividends tomorrow, which whatever they are I'm selling off, I'm getting a profit out of the stock tomorrow and I'm ending up with apples tomorrow. Maybe I'm just eating the dividends straight off the tree. So when I buy a stock I'm really giving up apples today and getting apples tomorrow. And no matter how I do it, whether it's through stock alpha, or through stock beta, or through a nominal bond it's got to be the case that all three ways, or all 50 other ways you could imagine doing it have to give me the same tradeoff. This is your yield you were talking about, the same tradeoff. The amount of apples I effectively give up today in order to get apples tomorrow is going to be the same no matter which way I do it. If it weren't the same, if alpha's price was more than a half of beta's nobody would buy alpha. In fact they would start selling alpha. So that's why this assumption is so important. What would they do? Not only would nobody would buy alpha, but they start selling it. They'd say well, alpha is so expensive, let's say it's the same price as beta, I can sell alpha. With every alpha I sell I can buy stock beta, and so I haven't done anything today, but in the future I've got stock beta which is paying me 2. I owe, because I sold stock alpha short I owe 1, so I'll pay off the 1 I owe and I'll still be left with 1. I'm making an arbitrage profit, and so I'm not going to stop at selling 1 share of alpha. I'll sell 2 shares of alpha, then 3 shares of alpha, then a million shares of alpha, and everybody'll be selling alpha short to buy beta and the market for alpha will never clear. So that's why the prices will have to adjust. And so it has to be in equilibrium, the price of alpha's exactly half the price of beta, which is to say, in short, that if you solve for this equilibrium you can solve for an equilibrium where P_1 = q_1 is the price today of an apple today, and P_2 is the price today (that's why it's called present value price) of an apple next year. So if you've got this equilibrium by working your way through, by figuring out what the price of alpha is-- so the stock, for example, you want to figure out what the stock is. Suppose the stock of alpha, suppose the price turns out to be a half. Then by paying a half today you can buy stock alpha, which is going to pay you a whole dividend. So the price, therefore, of an entire--oh, let's do beta. Suppose the price of beta is a quarter. Suppose we happen to find out that the price of beta is a quarter. Then what's P_2? How much do you have to give up today in order to get an apple? Well, by paying a quarter today, that's the price, by paying a quarter today you're getting 2 dividends. So by paying a quarter today you're getting 2 dividends. If you paid to get 1 dividend you'd have to pay an eighth today. So the price P_2 would be an eighth in that case. So by piercing through the veil of the stock market you can always figure out what you're effectively paying today in order to get an apple next period. And that price which was just computed would be the same whether we looked at it from the point of view of going through stock beta, or through stock alpha, or through the nominal bond. It would always have to give us the same answer. So we know, from the financial equilibrium, we can deduce what P_1 and P_2 have to be, the present value prices. And so effectively, furthermore, stocks effectively just add to the endowments of goods. So we can now consider another economy. So let's consider the economy E-hat, so the hat economy. So U-hat-^(A) of X_1 and X_2 is the same as it was before, U^(A) of X_1, X_2, U-hat^(B )of X_1 and X_2 is the same as it was before, but endowments now E-hat^(A)_1 E-hat^(A)_2 is going to be what? Well, A over here began with 1 unit of each good, but A also owned all of stock alpha and half of stock beta. So all of stock alpha pays 1 dividend in the future, so really A effectively has claim on two apples in the future and another half of beta which is another apple in the future, so really A's initial endowment of goods is (1,3). How did I get that again? I said it was 1 apple to begin with he could anticipate having. He knew he owned all of stock alpha which pays 1 apple, so that's another one that's really his, and then in the future he's going to get half of the dividends of stock beta, and half of 2 is also 1. So he's got 3 apples in the future. And E-hat^(B)2, well his 1 doesn't change today, but what's his claim, effectively, on dividends in the future? Student: 1. Prof: 1, thank you. Somebody answered that. So we've now reduced the financial equilibrium to a general equilibrium, the same kind of economy we had before. It's just that we had to augment the endowments to take into account that people own stuff through the stocks. So what's the equilibrium of this economy? This has a simple general equilibrium. So what is it? How do we solve for equilibrium? Well, take P_1 = 1 and we'll solve for P_2. So let's just clear the first market. How do you clear it? You're with me here? It's a standard general equilibrium, the same kind we've done many times before. So see if I can do it. So person 1 is going to spend a third of his money [correction: will be two thirds], and how much money does he have? He has (1 P_2 times 3), that's A, right? His endowment is (1,3). This is his income, and he's spending a third of it on good 1. And the price of good 1, P_1, here is just 1. And then B is going to spend, he's a half, half Cobb-Douglas guy, so this is 1 and this is 1. He's spending half of his money and his income is [1 P_2 times 1] divided by 1, and that has to equal the total endowment which is 2,1 1. So did I go too fast? Yes? Student: Why is it a third? Prof: Well, it's probably wrong. So let's try it again. Maybe it's 2 thirds. Let's see what I was doing. I've taken the financial economy, which was very complicated, looks very hard to solve and Fisher says of course when we add uncertainty and things like that we're going to have to do other tricks. But without uncertainty, with perfect foresight and so on, and no uncertainty, Fisher says this is an easy problem to solve. You take the financial equilibrium with all its extra variables and you realize if people are rational they're going to see through all that complicated stuff. They're going to realize that alpha is just half as good as beta, and so they're going to realize that by holding stock they're making a certain tradeoff between alpha and beta. And we calculated the tradeoff. What was P_2? I forgot what P_2 was. Anyway, how much did you have to pay? If you pay pi_alpha divided by D^(alpha)_2, something like that, was P_2. So if it costs you a certain amount of money, if it costs you a quarter we said, so this is P_2, so through either stock, like beta's the one I solved it for. I said suppose beta, that's also equal to pi_alpha over D^(alpha)_2, we said if the price of beta turns out to be a quarter and you're getting two dividends then by paying a quarter you get two dividends. So it means to get one apple it only costs you an eighth, an eighth of a dollar. So P_2 we can figure out. So once we've got our financial equilibrium, it basically is determining a general equilibrium. So instead so let's go backwards. Instead of solving for the financial equilibrium that looks complicated let's solve for the general equilibrium. What is the effective general equilibrium? It's the same utilities as before, but we've augmented the endowments. By looking through the veil of the stocks we realized that A actually owns 3 apples in the future, 1 because he owns all of stock alpha and another one because he owns half of stock beta. So we've got this simple economy that we're used to solving that you did on the first problem set, so we can do it again and solve it. So I'm going to now solve for general equilibrium. I have to solve for P_1 and P_2 and all the X^(A)_1, X^(A)_2, X^(B)_1, X^(B)_2, but I can fix one of the prices to be one. So I'll fix P_1 to be 1. Then what does A do? So I made a mistake which is why you weren't following me. A, his Cobb-Douglas, 2 thirds of the weight is on good 1 and 1 third on good 2. So he's going to spend 2 thirds of his money on the first good. So that's why this should have been a 2 thirds as she pointed out, thank you. So 2 thirds of his money, what's his money? His endowment is (1,3), so it's [(P_1 times 1), which is 1 times 1, (3 times P_2)] divided by the price P_1. 2 thirds of the income divided by the price of the first good, that's how many of the first good he wants to eat. What does she want to do? She's patient. She's going to spend half her income on both goods, so half of her income which is [(1 P_2 times 1) divided by 1], that's how many apples today she wants and that's what we have to clear to clear the apple market at time 1. So does this make sense now? I'm looking at you in the front. Do you agree with this or is this confusing now? Do you follow this or is this confusing? I can say it again if it's confusing. Student: I've got a question. Prof: Yeah? Student: Our denominator represents what they want to have in the future? Prof: Remember how the Cobb-Douglas worked? This trick I'm going to use over and over again. With log utilities everybody will spend depending on the coefficient. So remember, this utility in the problem set, you know that this utility is just the same as if I put 2 thirds here and 1 third here, right? Because I'm just dividing this by 3, so instead of 1 and a half--so the original utility is this, right? It's (log X_1) (1 half log X_2), so the sum of this plus this is 3 halves. I can multiply by 2 thirds. So if I multiply this by 2 thirds I get 2 thirds here and 1 third here, right? And I haven't changed the utility function. And now I know this is a familiar pattern. A is always going to spend 2 thirds of his money on the first good. And B I can multiple this whole utility by a half and a half and B is going spend-- and now we recognize it as the common Cobb-Douglas thing and we could say that A's [correction: B's] going to spend half his money on the first good and half his money on the second good. So what have I done? Fisher said look, this model is so complicated. You're thinking in your heads, people are deciding in period 1 how much stock should I buy, how many bonds should I buy, how many apples should I eat, but really if they're smart they're not going to think that way. They're going to say to themselves how many apples should I buy today? How many apples do I want to consume tomorrow? All these financial assets are just methods for me getting apples tomorrow in exchange for apples today. And what's the tradeoff between the apples was this--P_1 and P_2 is the tradeoff between apples. You can look through the stocks and all that, but no matter which stock you think of buying there's going to be the same tradeoff between apples today and apples tomorrow because of the no arbitrage. The price of alpha is going to have to be exactly half the price of beta. So once I solve for this economy and get the price of alpha I'll know how many apples today I have to tradeoff in order to get apples tomorrow. So I might as well forget about all the stocks and just try to figure out what must that tradeoff between P_1 and P_2 be. So that's why you can forget about the stocks, forget about the bonds, everybody's thinking I'm trading off apples today for apples next year. I'm making all the trades today, because I'm trading apples today in exchange for promises for apples next period. So it's as if everything happens today. It's as if they're present value prices today. We trade today at prices P_1 and P_2 for apples today and apples next year. Of course the apples won't appear until next year, but I can sell an apple today at price P_1 and buy promises for apple next year at a price P_2, and that's the tradeoff I'm facing. If I face that tradeoff how much of my money am I going to spend on apples today? I'm going to spend 2 thirds of my money on apples today and the other third I'll spend on promises for apples next period. So this is a big insight Fisher had. It's not surprising it's a little puzzling. I'm so used to it that I've forgotten how puzzling it is. So ask me some more questions. This was not an obvious thought Fisher had. Yeah? Student: Do we typically expect the price in the 2nd period to be lower than the price in the 1st period? Prof: Often there'll be inflation, so q_2--the contemporaneous price next period might be higher than the contemporaneous price this period, but we don't care about that. What we care about is how many apples you have to give up today in order to get apples tomorrow. So P_2 is the present value price. What do you have to give up today to get the apple next period? So we expect P_2 to be less than P_1. Precisely because, well, we're going to come to that, that's the next thing I was going to talk about because everybody's putting more weight on consumption today than they are on consumption in the future. That's why the price P_1 is going to be bigger than the price P_2. Yep? Student: When we're solving it we're solving in real prices? Prof: So we're solving for P_1 and P_2 in present value prices. So the crucial thing is, he invented this term present value prices: the prices you pay today no matter when you're going to get the stuff. That's his big insight. You should look at present value prices. Holding stocks and all that complicated stuff is just giving you goods in the future. So when you buy the stocks today you should think, how much am I having to pay today to get an apple in the future? You can deduce that from the price of stocks and how many dividends they're paying. So everybody must have figured out a P_2. What does it cost today? How much money do I have to give up today to get an apple in the future? Well, I have to buy a stock and then sell the dividends and all that, but really what I should be thinking about is what's the price today I'm paying for one apple in the future, and that's P_2. And so when you think about it that way, although it's an intertemporal problem, it looks like a new model with time, Fisher said you can reduce it, think of it as if they're just the same problem we did before with two goods you're trading at the same time. That's not an obvious thing to have thought of. No one thought of it before him. Yeah? Student: The budget set, the second equation from the right-hand side. The second item shouldn't you have a q_2 as well, q_2 times >? Prof: Oh, absolutely. So this should have been a q_2 here because you'd sell the dividend and you get money by selling the dividend. Thank you. Ho, ho, ho, very good. Who said that? Who just asked that question? Where are you? I'll remember you. That was very good, exactly. So in the future you're getting the money. So what he pointed out is I made another mistake here. In the future the money you're spending on goods in the future you're going to get the dividends paid, of course you can sell the dividends for money and the price is q_2. So a q_2 has to appear over here just like there's a q_2 over there. So it's the goods times the price. That's the money you're getting in the future, and that's the money you're spending on the good X_2. Very good, too bad you didn't ask me that a while ago, but anyway. Any other questions? So we're back to this standard general equilibrium problem. We can take a financial equilibrium and turn it into a general equilibrium. And so when we solve this we're going to have (2 thirds P_2 1 half 1 half P_2) = 2. So it looks like 3 halves (I hope I haven't done this wrong) P_2 = 2 thirds 2P_2. Student: > Prof: Thank you, yeah, plus 2P_2. So we have 2P_2 a half a half P_2 so we have 5 halves P_2. That was lucky you caught that, 5 halves P_2. So 2 thirds is 4 sixths. And 3 sixths is 9 sixths. And 12 sixths - 9 sixths is... What is this? So what's 2 - 2 thirds - a half? Student: 5 sixths. Prof: 5 sixths. That's correct. So P_2 therefore equals 1 third. All right, so we've now solved for equilibrium. We know that P_1 has got to be 1. P_2 has got to be 1 third. We know that we can figure out what consumption's going to be, I mean X^(A)_1, for example, if we wanted to solve for that we just plug in a third here. So we'd have (2 thirds) times (1 3), which is 2 thirds times a 4, which is 8 thirds, I guess. And X^(B)_1, we could have solved for that too if we wanted to. X^(B)_1 is going to be a half times 4 thirds which is 2 thirds. No, that doesn't--a half plus what was this 1 third? No, it's 1 1 third which is 4 thirds times a half which is 2 thirds. Is that right? That doesn't look right, so maybe I did this wrong. 1 1 is 2 so this is 4 thirds. That looks better. X^(A)_1 is 4 thirds. X^(B)_1 is 2 thirds. So we have 4 thirds and 2 thirds, and so we could solve similarly for X^(A)_2 and X^(B)_2, which I won't bother to do. So we can figure out what the prices are, the present value prices and the present value consumption. But having done that, Fisher says, we took a hard problem we make it easy. Let's go back to the hard problem. So Fisher says the tradeoff between good 1 and good 2 is 1 to a third, so he defined--here's the nominal rate of interest. Fisher defined something called the real rate of interest. And he said that was a variable that you should pay a lot of attention to. So the real rate of interest he said is P_1 divided by P_2, so this is equal to 3 and so r is 200 percent. So how did I get that? Just as someone in the front said the good 2 is much less expensive. The present value of good 2 is much less than the present value of good 1. People think an apple today is much more valuable than an apple tomorrow. So if you give up an apple today you can get 3 apples next year. So if you put an apple in the bank it's like getting 200 percent interest on apples. So he called that the real rate--the apple rate of interest. You put an apple in the bank, you give up an apple today, buy stocks and when it comes out in the end you've got 200 percent more apples than you started with. So it's the real rate of interest. So that's his crucial variable. Now, let's go back to the original equilibrium. What is the stock price? Assume q_1 = 1. What is the stock price pi_alpha? Well, we can figure it out. How can we figure it out? What is pi_alpha? Well, stock alpha pays 1 good tomorrow so what is the price of pi_alpha? Student: > Prof: What? Somebody said it. I couldn't hear it--a third. How did I get a third? Because we figured out that once everybody looks through the veil, assuming the price P_1 is 1 and the price q_1 is 1, if they look through the veil they're going to say to themselves ah-ha, how much do I have to pay today to get an apple in the future? I have to pay a third to get one apple in the future. P_1 is 3 times P_2. So to get 1 apple in the future, it's only a third of an apple today. So the stock pays 1 apple in the future so therefore how much do I have to pay today? I have to pay 1 third of an apple today, and since I took the price of apples to be 1 it's going to be the price of 1 third. So what's the price beta? Student: 2 thirds. Prof: 2 thirds. So Fisher said look, we've solved now for all these financial things. So what you can't do, Fisher's theory does not explain how much of each stock, theta^(A), etcetera, the investors hold. Why is that? Well, because it doesn't matter. Not enough is happening in the economy yet. Alpha and beta are exactly the same. If you own twice as much of the alpha tree you get exactly the same as having the beta tree. So how can you possibly tell whether somebody's going to hold twice the alpha tree or just one beta tree? Either way he's going to get the same thing. So the theory can't possibly explain which one they're going to do. Somehow they'll work it out and divide up the tree so that everybody ends up with the right number of apples in the end. And it also does not explain inflation because you can't tell what q_2 is going to be. All right, because you see in this budget set, thanks to that inspired question, if you double q_2, q_2 appears everywhere; you're not going to change the second equation. So q_2 could be anything. You can double it or triple it, it won't matter, and the same with q_1. It's just like Walras said before, you can always normalize prices to be one. He had to add another theory of money and how many dollars were floating around in the economy to explain q_2. This theory won't explain it. So it does not explain inflation, and it does not explain who holds which stock, and so it does not explain the nominal rate of interest. It does not explain i, the nominal rate of interest, because 1 dollar, who knows what 1 dollar's going to be worth. It depends on how much inflation we have. But it does explain the real rate of interest. It does explain r, and that's the variable that Fisher said is the one economists should always pay attention to, the real rate of interest. So that's the crucial variable. So if you want to figure out what's the price today of a stock, so Fisher's famous equation's the price of the stock today, so pi_alpha divided by q_1, so the real price, as somebody said, the price in terms of goods of the stock today is always going to equal the dividend in the future divided by 1 r. Why is that? That's exactly what we already used. This is just a rewriting of the trick we did before. You take the dividend tomorrow, you multiply it by P_2 and then you realize that 1 r is just P_1 divided by P_2, so replacing the P_1s and P_2s by q_1 and 1 r, today's real stock price is just the dividends tomorrow discounted. This is what he called the Fundamental Theorem of Asset Pricing. If you knew the real rate of interest you'd be able to figure out what all the stocks were worth just like we did. Once we knew P_1 and P_2, the present value--the present value prices determine the interest rate because they're-- just as we said. P_1 over P_2, remember, is 1 r. So knowing P_1 and P_2 you're always normalizing P_1 to be 1, P_2's the same as 1 over 1 r. So if you know P_2 or you know 1 over 1 r, you know what the value of the stocks are. That's his critical insight. Now, just to finish... Yes? Student: That's q_2 or q_1? Prof: q_1, q_1 which is the same as P_1 because it's today's price. The contemporaneous price today is the present value of the price today. So let me just end on this one note. Fisher said we can take financial equilibrium without uncertainty, reduce it to general equilibrium. We know everything about general equilibrium, therefore we know everything about financial equilibrium, and we realize that the crucial variable in general equilibrium is relative prices. There is no just interest rate. The nominal interest rate, who the hell cares? The real interest rate is what we care about, and just in normal economics there's no just relative price, there's no just real interest rate. It depends on people's utilities. You make them more patient and that's going to affect the real interest rate. You make them less patient it's going to affect the real interest rate. You give them more endowments today versus tomorrow, that's going to affect the real interest rate. The relative price between today and tomorrow--that's the way you should think about finance. That's the way you should explain what's going on in the financial markets. So in the problem set you're just going to do a problem like that, and then I'm going to give more interpretations of this that Fisher gave. So I guess I'm out of time, so we'll stop here.
Quantitative_Finance_by_Yale_University	6_Irving_Fishers_Impatience_Theory_of_Interest.txt	Prof: All right, so we spent a long time reviewing general equilibrium and we've now switched to finance, and you're hopefully going to see that the principles of finance emerge very quickly from the principles of general equilibrium. So that although it seems it was a long interlude we've actually learned a lot about the financial economy. So I'm going to continue with the example that we started with the last time. So we have a financial economy. So in a financial economy--what is a financial economy? On this top board the financial economy is defined by lots of people in the economy and their utilities. So here we have for simplicity two kinds of people A and B with utilities given by the log X_1 1 half log X_2 etcetera. It's also people know today what their endowments are and they have some idea of what they're going to be tomorrow. They're labor powered today and they're going to be able to work again next year. So the labor endowments are given by (1,1) for A, and (1,0) for B. And then they also know that there are two stocks in the economy and they have to anticipate what the dividends are going to be. And as Fisher said, the main value of assets is that they give you something, they produce something. In this case they're going to be dividends and beta's producing dividends of 2, and alpha is producing a dividend of 1 next period, and then the ownership of shares. So that's the beginning of the economy and we want to define from that equilibrium which involves: what are the contemporaneous prices going to be, that's Q for contemporaneous, what are the prices of the stocks going to be, and who's going to hold which portfolio of assets of stocks, and who's going to consume what. And so Fisher said that's a very complicated problem. You can simplify it by looking at a general equilibrium problem which is much shorter to describe. And so the general equilibrium economy is going to be a much simpler one. It's going to consist of U^(A) and U^(B) the same as before, and E-hat^(A)_1, the endowments, E-hat^(A)_2 and (E-hat^(B)_1 E-hat^(B)_2). So we've left out half the variables up there and we define E-hat^(A)_1 = E^(A)_1 = 1 and E-hat^(B)_1 = E^(B)_1 = 1, but E-hat^(A)_2 (this is the Fisher insight) = E^(A)_2 what A owns of the payoffs of the future dividends, [theta-bar^(A)_alpha times D^(alpha)_2 plus theta-bar^(A)_beta times] D^(beta)_2. Since A owns half of the alpha stock, sorry, all of the alpha stock and half of the beta stock, his endowment is 1, his original thing, plus what the stock is going to produce, and after all he's the owner. So he's going to get all of 1 a half of 2 which is = 3. I took more space than I thought. And so similarly E-hat^(B)_2 is going to be 1 a half of 2 which = 2. So here endowments are this and also let's just write it here, E-hat^(A)_2 = 3, so this. So Fisher said we start with a financial equilibrium, we can switch to the economic equilibrium and solve this problem, and having solved that one go back and figure out how to solve this one. And you remember what the prices were. They turned out to be q_1--I might as well write it up there what the prices we had, we solved. We said first of all Fisher has no theory for the contemporaneous prices. It's all relative prices. I'm going to write that. Relative prices, is all we can ever figure out. Someone might always come along and change dollars to cents. When I was a little boy in France, on vacation, they suddenly announced that the franc was going to be divided-- everything that was a hundred francs would now be one franc. They just redefined the currency, so that might always happen. So you have to have some theory of money and whether the government's going to do that to figure out the nominal prices. So contemporaneous prices he says are 1,1. All right, but having realized that if there are many goods at time 1 he could figure out the relative prices, but with only 1 good at time one who's to say whether we're measuring dollars or francs or cents, we'll just call it 1, and the same thing's going to happen next year. Who knows whether it's dollars or cents or francs so we're going to call it 1 again. But after that he figured everything out. This turned out to be a price of a third, this turned out to be a price of 2 thirds and we figured out all the consumptions, which I've forgotten, of course. But anyway they were--who knows what they were, not that it's too important. All right, well I forgot what they were. Anyway, he figured out all the consumptions. I think they were--actually I sort of remember them. Well, let's say I don't. Anyway, he figured out all the consumptions. Does anyone remember what they were? All right, I will look them up, 4 thirds 2,2 thirds 2, so they were 4 thirds and 2, and 2 thirds and 2. He figured out in equilibrium, and how did he do it--because he solved over here first. We would have solved--he didn't do this exact problem, but he would have solved over here and we would have found with P_1 = 1, P_2 = a third, and sure enough X^(A)_1 = 4 thirds, X^(A)_2 = 2, and X^(B)_1 = 2 thirds, and X^(B)_2 = 2. So Fisher said start with the financial economy, figure out what the reduced general equilibrium is, solve for this equilibrium, and go back and figure out what the financial equilibrium should be. All right, so I want to now examine what we've done. And we did that the end of last class. You had to do it in a problem set. And you notice that the only difference between this and that is, the general equilibrium throws away a lot of irrelevant information because Fisher said people are rational. They look through the veil of all the gibberish of who owns the company and stuff like that, and they're just anticipating what the company is going to produce. They don't really care about whether there's a man running the company, or a woman running the company, or whether she's got an MBA from Harvard or from Yale. None of this is relevant, what the business plan is. All they care about is what's going to actually happen in the end. So if you think they're going to anticipate that correctly you don't need to worry about all the other stuff. So looking through the veil you can always reduce the financial equilibrium to a general equilibrium. Now, I want to go back and reexamine all that logic. So what's the first step in what Fisher did? And this is the idea of no arbitrage. So Fisher said people look through the veil of things. They understand stuff and you can count on their understanding to guide your understanding of the economy. So if you know that pi_alpha-- (this is a big pi)--pi_alpha = a third, so Fisher says well, you don't have to solve for the whole equilibrium to figure out what pi_beta is. What would pi_beta be? Well, Fisher would have said stock beta always pays off exactly what stock alpha pays off. So if these people are rational they're not going to allow for an arbitrage. So arbitrage means if there are two assets or two things that are identical, they have to sell for the same price--that's no arbitrage. If they sold for a different price there'd be an arbitrage. You'd sell the more expensive one and buy the cheaper one, and so you'd have accomplished a perfect tradeoff, but you'd have gotten the difference of money. So since pi_alpha is 1 third, pi_beta has to equal 2 thirds. That's the first, most important principle of finance that Fisher introduced; the idea of no arbitrage and making deductions for no arbitrage, so most of finance is actually being more and more clever about how to do no arbitrage. Over half of this course is going to be, let's look at situations where at first glance there doesn't seem to be any arbitrage. Then you realize if you're clever enough you'll recognize an arbitrage and be able to figure out all the prices without having to know all the utilities and everything else-- so one of the main goals of finance is to explain asset prices. You can see how no arbitrage is going to help do that, because if you knew what some of the asset prices were you could deduce what the rest might be. So that's the first thing Fisher did, and he's used this fact in connecting these two economies. So that's the first thing. Now, that principle can be used over and over again. Another application of it, let's suppose that we introduced a nominal bond with payoff 1 dollar in period 2. And suppose, as before, that q_1 = q_2 = 1, as we've already supposed. So then by definition the price of this bond is equal to 1 over 1 i, where i is the nominal interest rate. Why is that? Because you're going to get a dollar next year. If the price is less than a dollar this year you're turning something less than a dollar into something equal to a dollar. You're multiplying today's price by 1 i to get tomorrows price, so the rate of return is 1 i, taking whatever you put in today and getting 1 i tomorrow. So what is 1 i? So by no arbitrage we can figure out what 1 i must be. So 1 dollar today can go into 3 units of stock alpha, which goes into 3 units of X_2 as dividends, which equals 3 dollars. So you take 1 dollar today by buying stock alpha you can get 3 units of it since its price is a third, and since stock alpha pays one unit of output next period you know that 1 dollar today gives you 3 units of stock alpha, which gives you 3 units of good 2 as the output and at price 1 dollar tomorrow you've anticipated that's 3 dollars. So by buying stock alpha you can put in a dollar and get out 3 dollars. So it means that 1 i = 3, which means the interest rate is 200 percent. So that's a second thing you can deduce from that. So notice that by looking at part of the equilibrium here we can figure out a lot of the rest of the equilibrium. So what's another application? Well, Fisher said define the real interest rate as number of goods today goes into number of good tomorrow. So this will be, 1 r equals that. The number of goods today and how many good tomorrow do you get? So how can you do that? Well, 1 good today, 1 unit of X_1 is 1 dollar today, right? If you had one apple today you could sell it for q_1 times 1 apple, which is q_1 times 1, which is 1 times 1, which is 1 dollar today, which you can get 3 units, 3 shares, 3 units of stock alpha, which gives you 3 units of X_2. So 1 unit of X_1 today turns into 3 units of X_2, so therefore 1 r = 3 implies r = 200 percent. So that's the real rate of interest. So one of the tricks in going from here to here was to say that Fisher realized that people are going to look through all the gibberish of money and they're going to think about what apples are they giving up today and what apples are they getting tomorrow. They're not going to be confused by all the holding of assets in between. All right, so let's just make it a little bit more complicated. Suppose we started with q_1 = 1, q_2 = 2. Now, I told you that equilibrium--Fisher says there's always a normalization. Walras originally had the normalization in one period. There's a one period model in general equilibrium. In multi-period models there's a normalization every period. Every period there's a choice of whether you're dealing with dollars, or francs, or centimes, or how many, and so there's a free normalization. So let's take q_1 = 1 and q_2 = 2. Well, what does that mean? That means that inflation 1 (let's call it growth of money) g--i, I've already used for the nominal interest rate. So, 1 g is going to be 2 over 1 or just 2. So inflation = 100 percent. So what's pi_alpha going to be? I've done my work. Now the rest I'm going to just ask you for the rest of the numbers. What's pi_alpha? So if I re-solved equilibrium taking q_1 = 1 and q_2 = 2 all that's kind of money stuff so it's not going to change what happens over there. You're going to get the same equilibrium over there and you're going to go back to over here. So what's pi_alpha going to be? Ah-ha! Suppose we knew we were in the same real economy. There's nothing changed about utilities, endowments of goods, productivity of the stocks. All we know is that inflation's going to be higher now. So what do you think would happen in the new equilibrium? What's going to happen to the price of stocks today? Yes? Student: Is it just 2 dollars? Prof: Price of stock alpha. What was it before? Student: > Prof: So what was it before? Student: 1 third. Prof: Yeah, 1 third, so it's still 1 third. This is a big mystery in finance, a big question in finance. So you see why it's puzzling. You didn't get the answer right off, although she did. So you just have to think about it a second. If you really thought that people when they were buying and selling only bought a stock because they said to themselves, "How many apples am I going to get out of this stock? I don't care about dollars and centimes and francs. I'm not going to eat that. I'm going to eat the apples, and maybe I get the apples and sell them and eat pears instead, but I care about the goods I'm going to get. So I looked through all the veil." I should recognize that the stock, although it's now going to pay twice as many dollars as it did before, so it's going to pay 2 dollars. That's how someone guessed 2. Someone said 2. So how did he get 2? I didn't even realize how he came up with the number 2. He came up with the number 2 because he said, well the stock is paying 1 apple tomorrow, the price of apples is now 2, so it's paying 2 dollars tomorrow so maybe its price today should be 2. But no, that isn't how much the stock is worth. The stock is worth solving for this general equilibrium supply and demand. We already calculated before that the stock was a third, so the price of the stock is going to stay a third because the apples it pays tomorrow hasn't changed. It's still the same one apple. Now, how did we know the stock was priced at a third before? What was the stock in general? What's the price of the stock? The price of stock, remember, is how did we get it by going from here to here? We said it's going to equal the price of the stock divided by P_1. Now, the stock is only paying a certain number of goods. The price of the stock today is going to equal the present value 1 over (1 r) times its dividend. I'll write it this way. The price of the stock is P_2 times this. Let's just write this. What would Fisher say? How did we get the price of the stock from going from here to here? We got the price of the stock by saying the stock pays off one good tomorrow, but one good tomorrow is only worth a third of one good today, so therefore the value of the stock is only equal to a third times 1 = 1 third. So assuming P_1 = 1 that's what Fisher would say. Assuming P_1 is 1 you figure out how many units of today's good is it worth. Now, if P_1 isn't 1 then what do you do? Suppose P_1 were 5 and P_2 were--or P_1 is 6, let's say, and P_2 is 2 then what would you do? You'd have to say P_1 times pi_alpha = D^(alpha)_2. So if you multiplied all the prices by--am I putting the P_1 down at the bottom or the top? If you multiply out all the prices by 3, just leave it like this. We'll say if pi_alpha = P_2 times D^(alpha)_2. If you measure it in terms of goods, that's how you do it. So if you take this, this is also equal to 1 over P_1 divided by P_2 (if P_1 is 1, assuming P_1 is 1) times D^(alpha)_2, which is 1 over (1 r) times D^(alpha)_2. So Fisher said--so here's his famous equation. Fisher said the way to figure out the value of a stock, if you solve that problem over here, is to look at its dividends and discount them by the real rate of interest-- 1 unit of output tomorrow, since the value of an apple tomorrow is only a third of the value of an output today. Remember the interest rate 1 r, the real interest rate, is equal to the ratio of the two goods. So P_1 over P_2 is just 1 r, 1 r is P_1 over P_2. I'm making some things simple seem more complicated, sorry. So let's just say it again. When we solved that equilibrium over there we figured out that P_2 is only a third of P_1. When people think today how much would I give up of apples today to get an apple next year they don't think apples next year are worth nearly as much as apples this year. So they'd only give up a third of an apple this year to get an apple next year. P_2 is the amount you give up today to get an apple next year, so it's a third. Another way of saying that, if P_1 is 1, is that the real interest rate, the tradeoff between apples tomorrow and apples today which is P_1 over P_2, because 1 apple today can give you three apples tomorrow, so P_1 over P_2 is 3, so 1 r is three. So the apple tomorrow is worth P_2 times the dividend. That's just 1 over (1 r) times the dividend. So the value of a stock is the real dividends it's paying in the future discounted by the real rate of interest. You're turning tomorrow's next year's goods, finding the equivalent in terms of this year's goods, and the ratio of those two prices is the real rate of interest and so that's how you would get it. So another way of saying the same thing is you could turn cash next year into cash this year. So assuming q_1 is 1, another way of saying that is 1 over 1 i times D^(alpha)_2 times q_2. So you take the nominal rate of interest times the money that's being produced, because the nominal rate of interest says how do you trade off a dollar today for a dollar in the future? So a dollar in the future isn't worth, usually, as much as a dollar today so you have to discount it. So a certain number of dollars in the future are worth less dollars today. So you take the payoff of dollars in the future discounted by the nominal rate of interest and you get today's price, or you take the real dividends in the future discounted by the real rate of interest and you get today's price. So both those things are an application of the principle of no arbitrage, looking through the veil. So what would the nominal interest rate be in this case? In this case you see, how did I know that P^(alpha) was still a third? Because the real interest rate hasn't changed, it's still 200 percent. So D^(alpha)_2 is 1 and I'm still multiplying by 1 third, so I'm still getting a third for the price of alpha. So that's how she knew that the answer should stay a third because she knew nothing real had changed in the economy, therefore the real interest rate couldn't have changed, therefore the price of the stock still had to be the same. So how could we have used this [clarification: another formula] formula? We have to know what the nominal interest rate is. So what is the nominal interest rate? If you put in a dollar today how many dollars can you get out in the future in this new economy where there's 100 percent inflation? Yes? Student: 500 percent inflation. Prof: So that's right, now how did he do that? Because let's just do it. You take 1 dollar today at price q_1 = 1. You can buy 3 units of alpha still, because its price is still a third, and that tells you that you get 3 units of X_2, that's the dividend. Of 3 units of alpha each share of alpha pays 1, right, 1 apple, so now you get 3 apples, but that's equal to 3 times 2 because the price is 2, = 6 dollars tomorrow. So you've turned 1 dollar into 6 dollars. So 1 i = 6 over 1 implies i = 500 percent, just exactly what he said. So to say that just more simply the real rate of interest 1 r, this is the most famous equation Fisher ever wrote, is 1 i divided by 1 g. So this is called the Fisher Equation. His two famous equations are this, this is called the Fisher Equation and this which is called-- these two things which are the same are called the Fundamental Theorem of Asset Pricing. So why is this theorem true? The real rate of interest trades off apples today for apples tomorrow, the real rate of interest, apples today for apples tomorrow, so we had 1 apple giving you 3 apples. That's why r was 200 percent. Well, if inflation is 100 percent, so this is 2, 1 apple today gives you 3 apples in the future, but that means 1 apple today gives you 1 dollar, is one apple today gives you 3 apples or 6 dollars in the future. So 3 times 2, so if this is equal to 3 and inflation's 100 percent so this is equal to 2 then what's the fair rate of interest? What will the banks give you? Well, any banker can take a dollar, buy a stock, turn it into 3 units of dividends and then sell it for 2 dollars apiece and get 6 dollars. And so a banker can take a dollar and turn it to 6, so competition will force the bankers to give you 6 dollars for every 1 dollar you give it, next period. So the interest rate has to be 1 i = 3 times 2, or 6. So the real rate of interest is the nominal rate of interest divided by inflation. So that's one subtle, but once you realize it, obvious implication of thinking people are rational and make sort of simple calculations looking at the future. And a consequence of that is the price of assets, or you look at the cash that comes out in the future discounted by the nominal interest rate, or you look at the real goods that come out in the future and discount it by the real interest rate, and it's all the same thing. So does anybody know what the inflation is today, or what the nominal interest rates are today? So i is the nominal interest rate, the amount of interest you put in the bank and what they'll pay you at the end of a year. So we're going to--next class we're going to find out the exact numbers, but what do you think it is about? Does anyone have any idea? Take a wild guess. Is it 10 percent, 5 percent? Yep? Student: I think the inflation is usually around 3 percent. Prof: Usually, and do you think it's higher or lower than usual now-a-days? Student: It's probably lower. Prof: That's good. So let's say it's around 2 percent. So that means this is 1.02 and what do you think the nominal interest rate is now? Student: 1 percent. Prof: Who said that? That's a good--1 percent, that's about right. So what is the real rate of interest now? Student: > Prof: What? Student: > Prof: Well, 1 r is less than 1. So 1 r is around .99. So the real rate of interest is actually like negative 1 percent. How did that happen? Do you think it's standard to have the real interest rate be under 0? So why is it under 0? What's going on now that would make that happen? Yep? Student: The Federal Reserve wants to stimulate investment. Prof: Ah ha! The Federal Reserve has cut the interest rate, the nominal interest rate that it lends at to close to 0, let's say to 1 percent on the 1 year bond to 0 on the 3 month thing. So the reason they're saying they're doing that is to stimulate investment. That's what they teach you in macro, Keynesian, stimulate investment. We're going to find out that that's not the reason they're doing it at all. The reason the Federal Reserve is cutting the interest rate to almost zero is to just give money away to the banks, and why it that? Well, when you put your money and deposit it in the bank you're getting almost no interest, so the banks, the big banks have got all these deposits and people don't change what they do. They just leave their money in the banks getting no interest. So the banks have the money for free and they can make money with it. So normally they'd have to pay 3 percent interest or something and that would be expensive for them, and that expense is a big part of their expenses, they don't have it anymore. So we're going to come back to that what's really going on today, but that's what's going on. But anyway, the point is the nominal interest rate is somehow controlled by the Fed. That's why we don't have a theory of it. We're not going to do macro in this course. So Fisher doesn't have a theory of the nominal interest rate, of inflation, but he does tell you, given inflation and the nominal interest rate, that's determining a real interest rate, and people should look through that. So now they should say, this is sort of the Keynesian part, they should realize that actually an apple today if you just sort of put it in the bank you get less than an apple in the future so you should spend it and do something with it. That's the Keynesian idea, so people--why fritter away part of your apple, do something with it. That's why it's supposed to stimulate demand and activity today. So the point is, that's how you calculate the real rate of interest and shockingly it's negative and it's hardly ever negative, but it can be negative. Are there any questions about this no arbitrage business? All right, so let's do one more trick here, a Fisher thing. So let's go back to the equilibrium with q_1 = 1 and q_2 = 1. Suppose China offered to lend money, lend us dollars at a 0 percent interest? Would that be a great deal? Would people rush to do that? This is the equilibrium we solved over here already. So is that a great deal? Would that upset the equilibrium? Would anyone bother to take the Chinese deal if they lent at 0 percent interest, they were offering to do that? What? Student: No. Professor John Geanakoplos: They wouldn't take it? We're back here. What's the nominal interest rate in this economy?. Student: 200 percent. Professor John Geanakoplos: 200 percent interest, so if you want to borrow in this economy from another American you have to give the guy 200 percent interest. Here the Chinese are offering to lend you at 0 percent interest. So, yes, everyone would rush to take the thing and that would have a big effect on what the equilibrium was if the Chinese were willing to lend money at such a low rate of interest. Let's try another question. Suppose you invented a technology, new technology, new technology turns 1 unit, 1 apple today, into 2 apples tomorrow. Is this something people would rush to do or not? Suppose some inventor figured out how to do that, would he rush to do it? Could it be used to help the economy? So let's put it this way. Could this new technology be used to make a Pareto improvement, everybody better off? Yep? Student: That's no, because an apple tomorrow is worth less than half of an apple today. It's worth a third of an apple today, so no one would want to do that. Professor John Geanakoplos: So that's exactly the right answer. Actually you're answering two questions. I asked two questions. One is could it be used to help the economy, make everybody better off? If a social planner was in charge of things and the Chinese invented this new technology, or some American in Alaska invented this new technology should the government use the technology and could it use the technology to make everybody better off, and the answer to that is no. And then the answer to a second question is--suppose the guy in Alaska discovered it himself. He couldn't care less about the Pareto improvement and helping other guys or the American planners or anything, he just wanted to make a profit for himself. Would he make a profit? The answer is no, because the real prices, Fisher would say, are 1 and a third and no matter how you look at it the interest rate is 200-- he's losing money, because he's giving something up that's worth 1 and he's getting something that's only worth 2 thirds. So he'd be losing money to do it. He'd lose money. So we could prove that even. So the answer is no. That's the first question, and nobody would do it anyway. And fortunately nobody would choose to do it--choose to use it--because it loses money. So those are two separate questions. Could it be used and would any individual choose to do it? Would it be good for the society and would any individual choose to do it? The answers happen to agree here. So why can't it be used as a Pareto improvement? What's the proof of this that it can't be? The answer's no. What's the proof? Well, the proof is that if it did, if in the end it led to an allocation X-hat^(A)_1, let's call it X-tilde ^(A)_1, X-tilde^(A)_2, and Xtilde^(B)_1, Xtilde^(B)_2 that made everyone better off. Then, well, we give their old proof. Then what? It means that P_1 Xtilde^(A)_1 P_2 Xtilde^(A)_2 is bigger than what? P_1^( )E-hat^(A)_1-- (all right, that's what you have in the Fisher economy) P_2 E-hat^(A)2 and similarly P_1 X-tilde^(B)_1 P_2 X-tilde^(B)_2 is bigger than P_1 E-hat^(B)_1 P_2 E-hat^(B)_2. So why is that? Because in this Fisher economy, the general equilibrium-- if this allocation really made A better off than what he's gotten, than 4 third and 2, he would have chosen it. And B, she would have chosen her thing if it was better than 2 thirds and 2. So clearly they must have been too expensive for those two to choose because they were rationally choosing the right thing given what they could afford. So then you just add the stuff up. You add and you find that total consumption value is bigger than total endowment value. That's in the Fisher economy, but we've changed the Fisher economy because now we've added this technology which took away some of the first good and made it into the second good, but that technology just lost money, which is bigger than total value in new technology economy, right? And so that's a contradiction because the consumption of this, however the new technology got used in the end the total consumption of the people had to be the total of what there was and what was produced in the economy. The value after the new technology is introduced in that new economy has only gone down compared to the Fisher economy, and the Fisher economy value of endowments must have been less than this brilliant new allocation, and that's a contradiction because this new allocation has to add up to the stuff that's there in the new technology economy. So that's how we know that no new technology could possibly make everybody better off, and we know trivially it makes everyone better off if and only if it makes a profit. So if and only if it makes a profit can it be used to make everybody better off, and amazingly, in a free market economy, people are going to use it if and only if it makes a profit. So they're going to use it if and only if it's a good thing for the economy. So that's the basic laissez-faire argument--that there are new discoveries all the time. Every other day somebody's thinking of something new. Are we going to use it? Should we use it? Is it something we need to read about in the papers and use? Well, there are a whole bunch of people, the discoverers themselves they're going to talk to their business friends, and they're going to say, "Do you want to lend me the money to get this thing going," and all of them are going to do this profit calculation. If they decide it loses money they're not going to do it, and thank god for that because it couldn't have helped everybody if they did use it. So that's the main lesson of laissez-faire. So let me just put this in perspective a little bit. In the old Russian economy of the 1930s and '40s there was no profit system, so the central planner had to figure out, should a new invention be used or not. So every time there's a new invention a committee had to get together, of central planners and decide whether to use it or not. And there's a famous guy named Kantorovich who was in charge of a lot of that. He won the Nobel Prize in economics. He shared it with a Yale economist named Koopmans and so Kantorovich told this very amusing story. He said that there were two central planning bureaus. One was in charge of allocations and one was in charge of prices. One had to set the prices. The other had to set the allocations. And of course the whole message here is that you have to combine these. You don't know whether it's worthwhile to change the allocation until you know whether the new technology's going to make a profit or not, and here they had the two things separated. They were telling people what to do before knowing whether they made a profit or not because they didn't have prices because there weren't free markets. So the bottom line of the Fisher story is that you take this complicated financial economy, you reduce it to something very simple that you learned how to do in your freshman year or your sophomore year, solve that, and you go back to this and you can understand a lot about this economy. That's something that most people didn't realize at the time and still don't realize now. So you ask a typical person if there's inflation, that means the dividends next year is going to be higher, is that going to raise the value of the stock today? Just like he said, "Yes of course because it makes the price of the dividends higher tomorrow." Fisher would say no, it doesn't change anything real in the economy. If there's more inflation there will be a higher nominal interest rate, so discounted by the higher interest rate payoffs of the stock will give you the same stock price as before. So we're going to do a thousand examples of this, but are there any questions about this? Yes? Student: Can you just review your arguments at the end? I'm just having a very hard time reading. Prof: Yeah, sorry. I don't know if this is in the way, by the way. So this is the argument we gave a few classes ago. I forgot when. We said, how do you know that a final allocation that emerges as a competitive equilibrium is Pareto efficient? And the argument was if you can do better-- that means, make everybody better off-- then each person, if you look at the value of what they're getting under the new regime it must be more than the value of their endowments otherwise they would have chosen the new regime and nobody chose it. That means everybody would have had to pay more for this new regime allocation than the value of their endowments. So this is more than that for person A, and person B's consumption is more than the value of this endowments, his extended endowments in the Fisher thing under this new regime, than the value of his endowments. You're following that? Student: Yeah. Prof: Then the next step was to add all this up. Now notice, however the new technology affects the world, obviously people can only eat what's being produced. Everything that's being produced is part of somebody's endowment. So if the new technology, if Mr. A invents the new technology, he gives up some of his good at time 1 to get more of the good at time 2, so his endowment has changed--but he's got a new endowment, but it's still his endowment. So whatever the new allocation is it has to add up to the new endowment. Now, I haven't even bothered to write down the new endowment, but I know the value of that new endowment. Whatever it is, it's going to be less than the value of the old endowment, because the new technology loses money. So the contradiction is the value of the new endowment after the technology is used, at the old equilibrium prices, is lower than the value of the old endowment at the old equilibrium prices. But that, since it's true for every person in the aggregate, that's less than the value of this new regime consumption. And that's a contradiction because the new regime consumption, that's all this stuff, has to equal exactly the total endowments in the economy to begin with, and that's the contradiction. So you can't make everybody better off. That simple argument, which as I said, my advisor Ken Arrow, another guy at Yale named Gerard Debreu-- both of them were working at the Cowles Foundation which is part of Yale-- that proof that they gave is the simplest and most important argument in all of economics. So we get as a conclusion that, putting it another way, that owners of firms should maximize the value of their firms, the stock market value of their firms, and thank God they do because if they find some new way of producing that's going to lose money it's going to make the stock market value go down. Remember the stock market value is just the same calculation, the value of all the output they're producing. If they find some way of losing money and they try to use it it'll make their stock market value go down. That's why they're not going to do it, and thank God for that because it'd be a bad thing for society if they did do it. Yes? Student: Well, it seems to me this proof is logically flawed because you're assuming that after the inception of a technology the prices are left unchanged, but that might not be true. Shouldn't you have some argument for the prices not changing after the inception of the technology? Prof: This is a very bold question, telling me that it's a flawed proof. I want to commend you for your courage. As it happens, however, you've asked the same question that somebody asked a class or two--which is a very good question. So the answer is no, I shouldn't have changed the prices and that's exactly the point of the proof. So, yes it's true that after the new technology is introduced the prices changes, everything changes, but we don't have to worry about all that complication. After all the changes there's going to be some final allocation of goods that supposedly makes everybody better off. So I can ask the hypothetical question. Would this new allocation to A at the old prices be something he could have afforded, and the answer must be no... Student: All right, I've got it. Prof: Well, let me just finish. You see the answer to your question, but I'm going to say it out because it's a very important question. The proof is clever precisely because of what you're asking. You have to do something that you wouldn't have thought of. You have this new economy, and new allocation, and new prices, but the proof says let's do the hypothetical thing of looking at the new allocation at the old prices. At the old prices A couldn't have afforded this new allocation because if he could have, he would have bought it because it makes him better off. So at the old prices A couldn't have afforded this new regime allocation. Similarly B, at the old prices, couldn't afford this new regime allocation. So at the old prices everybody would have to be spending more on the new regime allocation than the value of their endowment. That means at the old prices, the total in the whole society-- by adding it up--of the expenditures on the new regime consumptions must be bigger than the total value of the old endowments. Now that was the contradiction why at the old endowments without production you couldn't make everybody better off. We'd already have a contradiction. Now we add one more step. We've got this new technology that changed the old endowments. It changed the old endowments, but however it changed it we don't have to keep track of how it did it. It makes the value of the total endowments even less than it was before, so we actually get a worse contradiction than before. So it was a good question, so I thank you for the question. Any other questions? Yes? Student: Can you raise the board a little bit? Prof: Yes, I can raise which board, not this one? Student: Yes, that one. Prof: Yeah. Well, sorry. Student: Oh. Prof: So the bottom line here is that--let me just summarize. We've spent four classes on reviewing standard intermediate micro and macro. People never talk about that stuff when they do financial--finance courses, in typical courses. However, Irving Fisher, the inventor of half of finance, that's how he began. And it's going to turn out now, especially in light of this last crisis, that the best way to understand what's going on is to go back to the original underlying economy. So Fisher said you can always take--we haven't introduced risk, by the way. When that happens things are going to get more complicated. Fisher couldn't deal with risk. So without risk, where everybody's anticipating the dividends in the future, that means that you can always reduce a financial economy up there to a general equilibrium, which you've been taught before you got to this course, most of you, how to solve. And now that solution to that problem with marginal utility and Pareto efficiency that tells us an enormous amount about how the stock market and everything works. It tells us that the value of every stock is just the discounted real dividends, discounted at the real rate of interest, or the discounted nominal payoffs, cash flows, discounted at the nominal rate of interest. And it tells us that the real rate of interest is the nominal rate divided by the rate of inflation. And it tells us that it's a good thing all these owners of companies are maximizing profits or share value, which is the same thing, and that's helping society. So that's the lesson. A lot of that stuff is going to change a little bit, but that's the basic idea. So finally let's get to the point. For 2,000 years the public was confused about interest. They said--Aristotle, one of the greatest geniuses of all times, he thought interest was an unnatural act. It was horrible even though, of course, lots of people in Greece were charging interest. Delos, the Delphic oracle was charging interest, would lend money at interest, and Aristotle and everybody was talking about the Delphic oracle all the time. They weren't even paying attention. The Delphic oracle was charging interest and they were saying it's totally unnatural. So three religions all thought interest was a terrible thing. They all thought the just price was--the nominal rate of interest should be 0, but what Fisher says is the nominal rate of interest is irrelevant. Nobody cares about the nominal rate of interest. They look at apples today and apples next year. The money and stuff just gets in the way. It's the real rate of interest that you care about, and the real rate of interest doesn't have to be positive. It could be negative like it is today. The real rate of interest, what are the determinants usually of the real rate of interest if the Federal Reserve isn't mucking around with things, the real rate of interest is obtained by solving for P_1 and P_2 in this general equilibrium model. So what would change the real rate of interest? All you have are the utilities and the endowments. So here's the economy. What would change the real rate of interest? So the first thing Fisher says is impatience. So in fact one of his most famous articles is called an Impatience Theory of Interest, so let's call it that, Impatience Theory of Interest. So Fisher said that in his view people are impatient. Why? That means an apple today they thought was more valuable that an apple next year. Why? Because of the poor imagination, it was easy to think about eating the apple today. You can just hold it in your hand and it's so close, but to think about eating it in a year requires some imagination. They had poor imagination, and secondly, the second main reason is mortality. They might die between today and next year. So those are the two main reasons. He gives a bunch of others, which I'm going to mention shortly, but these are the two most interesting ones, poverty of imagination and the fact that you just might die in between. So what does it mean? An apple next year is not a sure thing. There is the Impatience Theory of Interest. So he said that's why it makes sense to have this guy A as impatient because he values the apple today more than a value tomorrow. He's got this discount rate, a half here. B's not impatient because the discount factor is one. So he put a discount factor--actually Fisher didn't quite have a discount factor, he had a more general thing, so Samuelson was the one who introduced the discount factor. It doesn't matter, but anyway so a discount factor to capture Fisher's idea that the good next year, the same apple next year is not worth as much to A as an apple this year. So suppose I change a half to a third? What will happen to the real rate of interest? So that makes people more impatient. Why does it make them more impatient, because now they care even less about the good next year. So when did this happen? In the Reagan years, the now generation, everybody talked about the now generation. People are getting more impatient. So what happens to the real rate of interest when people get more impatient? Does it go up or down? Student: It goes up. Prof: So why does it go up? That's correct. Student: Because there needs to be more of an incentive to save. Prof: Right, but now Fisher would say that a little bit more-- he would say it a little more formally, but that's exactly right. In order to get anybody to save, because they want the stuff now, you're going to have to give them a higher real rate of interest. That's exactly right. So how could you say it in this economy? [next slower] Remember in this economy, this Cobb-Douglas economy, you could prove it formally. You know that if P_2 (let's say) = 1 and we're solving for P_1 and here's the supply, this is X_1, and here's demand. So remember X^(A)_1 is going to be something like P_1 E^(A)_1 P_2 E^(A)_2 times 1 over 1 delta where delta-- what's called delta, the discount. Let's call this delta, so the discount. So to get these to add up to 1 I take 1 delta. So the weight on this thing is 1 over 1 delta times this divided by P_1. So if P_2 is 1 then this is just equal to 1 over 1 delta times (E^(A)_1 1 over P_1 times E^(A)_2). So clearly the demand goes down as P_1 goes-- as P_2--this is P_1, so P_2 = 1, so if I divide by P_1, P_1 over P_1 goes away. Then I have P_2 over P_1, and if P_2 is 1 that's just 1 over P_1. So obviously as P_1 goes up your demand goes down. That's just what you'd expect. So P_1 goes down the demand goes up, or P_1 goes up the demand goes down. So anyway, if you add up Cobb-Douglas people it always is like that. The demand for any good goes up as the price goes down, if its own price goes down. So if you change delta, if you make delta smaller, that's going to raise demand for A_1 at the old prices. Why? At old equilibrium prices, the same trick as before, at old equilibrium prices what's going to happen? Delta goes down like we just said, implies X^(A)_1 goes up. So the guy's demanding more now, but if he's demanding more at the old equilibrium prices-- so at the old equilibrium prices he's demanding more so the only way to clear the market is to raise P_1. Implies P_1 must go up to clear the market. So this is a formal proof of what he just said. So the common sense maybe is enough for you. If you care less about the future to get anybody to save you're going to have to raise the interest rate. To say it formally if we solve for equilibrium with a lower delta at the old equilibrium prices, this guy at the old prices, A would now shift and try to demand more of good 1. But if he demanded more of good 1 that would mean too much demand for good 1, and the only way to clear the price of good 1 is to raise the price P_1. But if you raise P_1 holding P_2 fixed that's just P_1 over P_2, so the interest rate, so the interest rate has to go up. So that's your argument made formal. So that's his Impatience Theory. That's the main determinant of interest according to Fisher. What's the second one? He says suppose people are more optimistic about E^(i)_2? Everybody thinks the world's going to be much better next year. We're going to have more endowments. What do you think is going to happen to the interest rate, the real interest rate, somebody else? Student: It'll decrease. Prof: It'll what? Student: Decrease. Prof: Decrease, why? Student: Because you're expecting things to be better > signifies people will save less. Prof: To save less or to save more? So let's think of good X_1. If people thought they were going to be richer at the old prices what would they do today for X_1 demand more or less today? Student: The rate would go up, right? Prof: Yeah, the right answer is up. He said down, but let's just figure out why. Student: They demand more > Prof: So the reason I gave the formal argument is because you can get confused here. So let's just do the intuitive one. So you had the idea back there of the intuitive one, you just got it backward, but you were on the right track. The point is there's going to be so much stuff around for people to eat tomorrow, you've got to get them to want to eat all that extra stuff tomorrow. So you have to give them an incentive to want to eat all that extra stuff tomorrow, so you have to raise the interest rate, not lower it. So you had the right idea, the wrong conclusion. Now, how can you actually give a formal proof of that so you know you're not confused? Again, like his question, at the old prices what's going to happen to the demand for X_1? At the old prices, since you're going to be so rich in the future, you think you're just incredibly rich now, so of course you're going to consume more today. So there's going to be more demand today and the endowment today hasn't changed. So there's going to be more demand today with the same endowment today, so therefore in order to clear the market today you're going to have to raise P_1 relative to P_2 so the interest rate's got to go up. So is that clear? It's a little surprising, so let me say that again. If you increase the endowments tomorrow the supply today of goods hasn't changed, but people are richer tomorrow. So clearly they're going to consume this fraction of their wealth. Their wealth is up. You tell anybody, "You're going to be rich next year. You're going to be worth a fortune," the normal person, Cobb-Douglas person, is going to consume more stuff today anticipating that he's going to be so rich tomorrow. He's going to borrow against tomorrow's wealth. And so therefore, in order to clear today's market where the supply hasn't changed, with all these people trying eat more today you have to raise today's price relative to tomorrow. That's, raise the real interest rate. So what's a third example? This is Fisher's most famous one. Suppose you transfer money, transfer wealth, from poor to rich. What would happen? We have to make an extra assumption here. Fisher felt that the people who were rich were rich because they were patient. They could charge interest and get lots of money. So if you change wealth you take away some money from the poor. That's what's happened in the American economy over the last 15 or 20 years. The rich have gotten richer and the poor are pretty much back where they were before. So suppose the rich get rich at the expense of the poor? What's that going to do to the real rate of interest? I'll--hang on a second. Yep? Student: That would make it lower. Prof: That's going to lower it. Why is that? Student: > Prof: So there's an intuitive way of saying it which is his which is that the rich, because they're patient, are probably the lenders. Now they're even more willing to lend and so the interest rate has to go down to get these other people to borrow. A formal way of saying it is that if you transfer money from the rich [correction: poor] to the poor [correction: rich] that means the poor guys-- the rich guys always consume a higher proportion in the future because they're more patient. So a more patient guy will consume more in the future. So if you take away wealth from an impatient guy and give it to a patient guy you're going to increase the-- the economy's going to be more in the hands of the patient people, and so the patient people--the mix is going to change. People on average are more patient than they were before so on average in the economy they're going to consume less than they were of today's good and so the shift is going to be in this direction, right? Because you've made people, a lot of them impatient, a lot of patient, you've increased the patient ones and decreased the impatient ones, so in balance you're going to decrease demand today because it was the impatient ones who wanted to eat today and the other guys were willing to wait. Now the guys who aren't willing to wait these guys don't have any money. They're the ones doing all the consuming today and now they can't afford to do much consuming, so you're going to reduce consumption today. So to get the market to clear again you have to lower the interest rate this time. So those are three famous conclusions of Fisher, more impatient people, higher interest rate, more optimistic about the future, higher interest rate, transfers from the poor to the rich lower interest rate. So what happens to the stock market in this case? Suppose people are more impatient. Does the stock market go up or down? Student: Down. Prof: Down, because the stock market price is just this, the real interest rate times the dividends. So I haven't told you the dividends changed, so if the dividends are the same and the real interest rate has gone up the stock market has gone down. Suppose people are more optimistic about the future, so not about the stocks producing more, but about whether there's more stuff in the world? Their own endowments will be bigger. The stock market is going to go down. That ones a little subtler because they could be optimistic about the stocks producing more, so that's ambiguous. So let's do the third. Suppose you transfer wealth from the poor to the rich, what's going to happen to the stock market? It's going to go up. So what happened in the last 20 years? The rich got richer, the poor got poorer, the interest rates got lower and lower and the stock market got higher and higher just as Fisher would have said. So I want to now end with just Fisher and Shakespeare, so I'm going to go over just a couple minutes. Maybe I'll have to start with Shakespeare. So Fisher's theory of interest, as I said, was making sense of thousands of years of confusion, so the idea is that interest is nothing other-- you shouldn't think of nominal interest. People look through all that. They look at the real rate of interest and the real rate of interest is just the ratio of two prices just like everything else in equilibrium, so therefore there is no such thing as-- it's an important price like anything else, but maybe I forgot to say it, there's no such thing as a just price. The price, in fact, that equilibrium finds is the best price because that's the price that's going to lead new firms and inventors to use technologies that help the economy as opposed to hurting the economy and wasting resources. So the price that the market finds is the just price and the real rate of interest is the right real rate of interest provided that people are rational and see through this veil. So, why is it that the real rate of interest is typically positive? Well, it's because, as I said, people are impatient and these different reasons. Now Fisher said one other reason that screws up the real rate of interest is people sometimes get confused by inflation. So this is an aside. He said that all contracts should be inflation indexed, and he forced his Yale secretary and his secretaries at his company to change their contracts-- I guess his Yale secretary is probably wrong, the secretaries at his business, Remington, he forced them to accept deals where their wage was indexed to inflation. And of course the Great Depression happened and all of the prices collapsed, and so all his secretaries got less money out of the deal so he wasn't too popular with them either. He says impatience is a fundamental attribute of human nature. As long as people like things today rather than tomorrow there's going to be interest. So interest is, as it were, impatience crystallized into a market rate, and the reasons for impatience are this foresight, lack of foresight, possibility of dying and then he talks about self control and stuff like that, the greater the foresight, etcetera. Now he has this racist view of the world, which I think is worth mentioning. So he compares the Scotch and the Irish, so the Scotch are patient, the Irish are totally impatient, no self-control and it gets worse and worse. I can't show you all of this. So Holland, Scotland, England, France these are all the places his family was probably from. They're incredibly patient. They're wonderful. They've got low rates of interest, incredibly thrifty people. Then you look at all these other dreadful people, Chinese, Indians, Blacks, Java Southerners, American Indians and then Greeks and Italians he mentions later, hopeless, high rates of interest, incredibly impatient. So anyway, the patient accumulate wealth and by waiting and lending they make production possible, because the people with all the good ideas where are they going to get the money to produce? They're going to get it out of the patient people who are willing to wait. If you can wait should I talk for five more minutes or do you need to go? I was going to do my--maybe I should let you go. Anyway, so what I was going to say last, I won't say it, is that Shakespeare anticipated all of Fisher's Impatience Theory of Interest and went a step further. He said, "Well, that's great but you should take into account that people won't keep their promises, and if they don't keep their promises you need collateral, and if you need collateral that's going to change a lot of stuff," and Shakespeare already had a lot of that figured out, and most of this course is going to be about, believe it or not, what Shakespeare had to say about the rate of interest and collateral. Okay, next time.
Quantitative_Finance_by_Yale_University	13_Demography_and_Asset_Pricing_Will_the_Stock_Market_Decline_when_the_Baby_Boomers_Retire.txt	Prof: All right, so I'm going to finish talking about overlapping generations today. I'm going to defer my plan to save Social Security till a couple of lectures from now, and I'm going to start to introduce uncertainty in this class. The exam will only cover the stuff up to basically the last problem set. There are a few things about overlapping generations I might say today, which will clarify what you already know, but you don't have to know anything beyond the problem you turned in on Thursday-- you're turning in today. So you I think are better informed now than you were yesterday. I think it's a big help to be doing the problems, so for those of you watching on screen at home, do the problems. So remember we had a situation where there were generations, each of whom was rich when young and poor when old, that looked like that. And it went on forever. That was the only difference from what we've had before. People's lives were shorter than the lifetime of the economy, and to go to the extreme, the economy goes on forever, even though people only live two periods. And then there was land, 1,1, 1,1. There's land, and then there's generation--because I forgot the generation--here's generation 0, generation 1, generation 2, generation 3... and time. This is time. And here's time 1, time 2, time 3, time 4, time 5, etc. Now this model, I've been told, is the hardest thing you do the entire class. Things are going to get much more complicated, but since they build up slowly, I think this model's the hardest thing you have to do the entire class. I realize it's a little bit confusing, but in the end, I don't think it's that complicated. And it reveals all the subtlety of Fisher's thinking, not that Fisher understood about overlapping generations, but his ideas, you can see here. So what are his ideas? You've got a complicated model in which you've got people trading apples when they're young, against land. So the objects in the economy are land, which you're supposed to think of as the stock market, okay, so we've got land and we've got apples. Now what's interesting is, the land is going to constantly change hands. So the young here are going to buy the land, but when they get old, they're going to sell the land. So the land is constantly changing hands. It's not that one person buys it at the beginning and holds it forever. So Fisher's formula, remember, was that the price of any asset was going to be equal to the discounted dividends. And the logic seemed to be at the time that the price, you know, if the person was going to buy the asset, that they could take the money now or they could wait and get all the dividends in the future, and they would compare what they would get out of the dividends in the future to what they have to give up today. But you see, in this example, it's a little more complicated. Nobody's going to hold the land and get all the dividends. Each person who buys the land knows that he's going to sell it long before getting all the dividends from that land. And yet the price of the land is still given by this formula, so we never use the fact, in Fisher's argument, that the same person had to hold the asset till the end. And so now we have a case, an extreme case, where people only hold the asset for one period. It's always turning over, turning over, turning over, but still the price of the asset is equal to the discounted dividends. So the secret to solving this problem, according to Fisher is, forget about the asset. That makes it too complicated. Fisher's argument again is, take financial equilibrium-- maybe I should write it on a different board-- Fisher's argument is, financial equilibrium, equilibrium, okay. Get rid of assets. Put dividends into endowments, and transform it into general equilibrium, the very thing you saw within the first couple days of class, okay, and then go backwards and figure out what the financial equilibrium is. So although it seemed very easy before, it's a little subtler this time, but it's the same principle. Whose endowment should you put the dividends into? The land is changing hands all the time. There's a new guy owning it, a new guy owning it every period, so whose endowments do we increase when we put the dividends of the land into someone's endowment? You put it into the endowment of the guy who owned it first. So put dividends into endowments of original owners, okay? So this old person who has the right to the first apple, his own endowment of an apple, and also the right to the first dividend, but he actually has a right to all the dividends. So his endowment, the endowment of Mr. 0 is going to be 2,1, 1,1, etc. Because he has his original apple, plus he's got--he has his endowment of an apple, because everyone when they're old has an apple. He's also, because he's owned the land before, gotten the right to this first dividend of the apple, that's 2, and because he's the original owner of land, he owns all the future dividend streams of the land. So we can forget about land after we've stuck the dividends into the right person's endowment, and now we just trade as if it's general equilibrium. We just look for supply and demand and the present value prices, which are p_1, p_2, p_3, etc., okay? And because it's symmetric, we know that this is going to equal 1-- p--we can always make one of them be-- one price can be 1, so the present value prices are going to look like this. The reason I can make this simplification is by symmetry. Every generation is the same, so it's obvious that I'll be able to keep repeating the same argument over and over again. Okay, and so what do I have--so remember, the land has disappeared here. Even though this generation is buying the land and selling the land, in Fisher's story, you don't have to pay attention to that. This guy bought the land, and then he sold the land, so it was a fair trade. So he started without it and ended without it. The fact that in between he used the land to save, you can already do that in a general equilibrium. You don't need to think about the land, because the only reason this guy is buying the land is to use it for a means of saving, which is already in Fisher's equation. So to solve for equilibrium is then quite simple. We just, in every generation, we look at-- remember, I forgot to write the utility functions, so we have U of consumption when young and old is 1 half log young [consumption] 1 half log old [consumption]. Okay, and so therefore, in equilibrium, we have to have that 1 half times the income of every generation-- every generation's going to have 3 when young 1 when old. Now from the point of view of any generation t, the prices are p, say, p_2 when young and p_3 when old. Now remember, any generation cares only about relative prices. So I can call them p_2 or p_3, or I can call them 1 and p, because the ratio's going to be p. So, much simpler to think of the prices as 1 and p. So the old guy, if I'm doing any t, like this period 4, the old guy here, you know, that's p_4 and p_3. He cares about p_3 and p_4. But he only cares about the ratio of p_3 and p_4, which is p. So from his point of view, he might as well have thought of them as 1 and p. So his income is 3 1p, and he's going to spend half his income on that good, which for him is a relative price of p. The young guy is going to spend half his income, which is also 3 1p. This is the relative price between t - 1 and t. This is the relative price between t and t 1. But he's now young, so his price when young is 1, and that has to = 3 1 1 =-- so I wrote it as 1 3 1 = 5, okay? And we solved that, and we found that p = .55. So are there any questions about how we did that? That's where we ended the last lecture. Is that clear to everyone? Yes. Student: > Prof: Okay. If I didn't have symmetry, I would have to say this is-- I would have to write this--in general, this would be 3p_t-1 1p_t over p_t, and this guy would be 3p_t 1 p_t 1, divided by p_t. Right? That would be, in general, if I had prices, the present value prices, this guy's income would be given by that, because he's the old at time t, and the young would be given by that, okay? And I'd have to do this, a new equation, for every t. Who asked? You asked the question, so does that make sense? Student: Yes. Prof: Okay, but I have to do that for every single t, so I have an infinite number of prices and an infinite number of equations. But then you say to yourself, "Well, hmm, if I take the ratio of p_t over p_t-1, to = p, then the ratio of these two prices is the same as this price," and so I'll have one equation and one unknown variable, and that same equation will get repeated every other generation. Because when I go to generation s, which is another generation, all that matters is the ratio between p_t-1 and p_t, and p_t and p_t 1. So if I assume those ratios are always the same, I'm going to be repeating the same equation over and over again. So if I can solve it once, I can solve it an infinite number of times. It's basically the same equation written infinitely often, and so as long as I stick in--keep these ratios constant, I'm just doing it over and over again, so I only have to do it once. So it doesn't have to work out that it's--it's just because every generation has the same endowments and every generation has the same utility. That's why it's such a simple thing to solve. Yeah? Student: With the regular p, before you erased it, is that a weight thrust that becomes the old > because we assume young age >? Prof: The p, this p, is just the ratio between--this is how I got p. p_t--okay, p is p_t over p_t-1, which also = p_t 1 over p_t. The ratio of all the prices is always p. The ratio between time t and time t 1, this good is more valuable than that good. This good is only worth p. p is .55. It's only worth 55 percent of this good. And then this good here is only worth 55 percent of that good. So the symmetry assumption, the symmetry of the problem suggests that I could guess that the prices are-- the present value prices are going to decline by the same percentage every period. Okay, any other questions? We'll keep going with questions. Yes? Student: Could you explain the e^(0) = 2,1, 1,1? Prof: Yeah, what is the endowment of the original old guy? He's the guy who owns the land. So what does he have? He has one apple, his endowment when he's old, like everybody else who's old. He has an apple, his own tree in his back yard gives him an apple when he's old, or when he's an old man or an old woman, he can barely scrape together one apple. Now he also has the land. The land is his for all time, so the land is paying an apple every year forever. So his own apple, at time 1, plus the land's apples is this 2, and the land produces an apple every time in the future. So that's his endowment. I stuck the dividends of the land into his endowment. Student: > like he lives forever, or >? Prof: Right, I'm not assuming he lives forever. He doesn't. In fact, he knows he's going to die in period 1. He wants to do all his consuming in period 1, but he hasn't--that's another subtle thing about this. You can own endowments that occur after you're dead. If you own a tree, the tree, the land is going to be producing stuff long after you're dead, so when you sell off the land, you're selling off those future dividends. Of course, you're not going to hold the land. If you don't care about your children, you're not going to hold the land beyond the time you live, because you want to just consume as much as you can. So you're going to sell off the land and consume, but you're selling off all these future dividends, okay? So another thing this model gives us is a new argument for the real interest rate, real r, being greater than 0. So why is it? Because from this formula--gosh, I was so clever. Where did I--oh, here. From the price of the asset, this discounted dividends, that's going to be 1 over (1 r), 1 over (1 r) squared, 1 over (1 r) cubed, ..., by the way, that's = to p p squared p cubed, you notice, okay? So the discounted value of the dividends is the price of land. So the price of land, of course, has to be finite, because if the old guy owned a thing worth an infinite amount of money, he'd sell it and he'd buy everything in the world. So if you're going to have equilibrium, there's no plot of land that sells for 10, for 100 trillion dollars. The price of every plot of land is some finite amount. So if the land is producing, I think it's sort of realistic. Land is probably going to produce forever. As long as the world lasts, if you've got land, you'll get something out of it. Someone will always want the land, and so if it's going to have a finite price, the whole future dividends have to be discounted to a finite number. If you put 0 in here for r, you get infinity. So this presence of land is forcing the discount rate above 0. So it's another argument that Fisher never would have thought of, because he never thought about infinities or anything like that-- another argument for the real interest rate being positive. Okay, any other questions about this? So we reduce it to one equation, and I'll put back the p here in just one unknown. Okay, = 5. And we saw that we get p = .55. And it's a quadratic equation, so you can all solve quadratic equations. Okay, what else do I want to say? So now you could analyze all sorts of things. You could do the same comparative statics Fisher does. Suppose we change the utility function and made this 1 third instead of 1 half. That would correspond to doing what? Making people more? More what? Impatient, okay. And what would you think would happen to the interest rate? Student: Go up. Prof: Go up, okay. So in the Excel file, we're going to do just that. We're going to see it's going to go up. Instead, we could do the Social Security thing, and we could have every young person give something to the previous old, which means everybody's endowment goes from say 3 to 2 and 1 to 2, so they get more in the future and less early on. So again, you could re-solve for equilibrium and Fisher's saying, if you've got more endowment in the future and less in the present, you're going to have a higher real interest rate. So you get a higher real interest rate. You could make the land more productive and change this to a 2 everywhere, and see what happened. So in this Excel file, I do that. Maybe I'll come back to that. So we're going to do those experiments in a second, but now I want to do two more things before I end this. The first is, I want to say, suppose we had growth in the economy. So what if you had growth? Where am I going to add growth? Over here. I shouldn't have erased that. So let's have growth. What happens? Well, Tobin, you know, Yale's greatest economist after Irving Fisher, he said something which was 90 percent right but not 100 percent right. He said, you know, I pointed out to him that I got these guys at Social Security. I worked with them. Anyway, these people at Social Security and the Social Security Administration calculated who were the biggest beneficiaries of Social Security, and it was Tobin's generation, the same generation as my father. And I said, "Look, it's your fault that Social Security is such a mess. You benefited and I'm going to have to pay for it." And just like you're feeling you're going to have to pay for it, so it's even worse for you. But even my generation's not getting a very good deal. Yours is getting a terrible deal, Tobin's got a great deal. And so he said to me, it's not his fault, it's my fault, because I didn't have enough children. So the question is, what happens if you--what does that mean? So what Tobin meant is that if, instead of having 1 child for every adult-- so every family has 2 children, in other words, instead of 1 child for every adult, so it goes 3,1, 3,1, 3,1, we start doubling-- the generations are growing through time. So since this is 30 years or something, we could think of the generations doubling. That wouldn't be such a fast growth rate. And so Tobin might have meant, if you double the generations, you're going to have 6 and 2 as the endowment. 2 guys at 3 and 1, which means 6 and 2. Then you're going to have 12 and 4. It's going to be a gigantic growth, and so each generation, when it's old, the young guys, if there's 6 and 2 here now-- I should use a different color. If I wrote 6 and 2 here, then each guy would have to-- or 2 guys at 3 and 1, each (3,1) guy would only have to give up half a unit, because there'd be 2 of them each giving half a unit to the old guy. And each one, when he gets old, getting a full unit. So this guy would get a full unit. The next generation would only give up half a unit, and because there were 4 times as many people in the next generation, each of them would still give 1 half, making these 2 old guys get their full 1. And when they got old, they'd similarly get a full 1 each of them. So it would seem that if you had a faster growing population, then Social Security would be a much better deal, because the young would have to give up less to the old and still get fully paid back when they were old, and so Social Security wouldn't have been a problem. Ok, so why wasn't it our fault, my fault--and your generation is probably not going to have any more children than my generation. Is that true, Tobin's argument? Is it true that if we just had enough children, no one would have to lose out in Social Security? We could make the original generation better off and also every other generation after that better off? Yeah? Student: > even giving up half to get 1 wouldn't > Prof: Right, exactly. And so you can't know that until you actually solve the model. So the point is, that if the generations keep growing like that, the interest rate is going to go up, and so it's still going to be a loss, because although you're going to be trading off - 1 half to get 1, as opposed to - 1 to get 1--so this looks like a much better scenario. Once you get to this scenario, there's going to be a bigger interest rate. So remember, the present value of that trade is - 1 (1 over (1 r)). That's why it's negative, because r is positive. Here it's - 1 half (1 over (1 r)), but that's a different r. That's an r, I'll put it at the top, that's in a new economy, a growing economy, and that r is going to be a bigger r. So even though it's - 1 half instead of 1, this thing's going to be small enough, so you still end up losing money. But you'd never know that unless you solved it. And in fact, it's still going to depend on a little delicate assumption. So Tobin, by the way, never bothered to work this out. I claim that if you're going to be doubling the population like this, there are going to be a lot more people working on the land, and so the dividends of the land are probably going to grow at the same rate. So I would add a 2 here. I'd make the dividends of the land also double, if the population doubled. So the land dividends are going to grow. Now you can see why the interest rate has to go up, because the present value of the land still has to be a finite number, the present discounted value of the dividends. And if the dividends are growing, then the interest rate had better be growing even faster if you're going to make that a finite number. So sure enough, when you solve it, you're going to get a higher interest rate. So how would you solve it? Let's say the growth rate is g, so every generation is 1 g times bigger the previous generation. So you could just change this equation very simply. What would you do? Well, for any generation, it's the same equation, except that you've got 1 g times as many old guys as you have--these are young guys. The number of young guys is 1 g times the number of old guys. So if it's generation t, time t, this would be (1 g) to the (t - 1), and this would get multiplied by (1 g) to the t. And the dividend, 5, so everybody's endowment is also going up, so it would be--actually I screwed up. It would be, the old guy's 1 times (1 g) to the (t-1) the young guys times (1 g) to the t, the dividend times (1 g) to the t, or t - 1, whichever. Okay, so that's the new equation. You can divide through by (1 g) to the (t - 1). So this is period t's market clearing equation, but you can see I haven't--because the number of old guys, for each one of them that's behaving like that, but there are now this many of them, and the young guys are behaving just as before, but there are this many of them, more of them. And then the endowments of the old have been grown that far, you know, the old generation has this many endowments. The young has this much endowments when young, and then the land we also assumed grew. Okay, so now you can just divide through by (1 g) to the (t - 1), and that goes away, and that just leaves that, and that goes away, and that goes away, and that goes away. So you'd have that equation. Student: Can you do that again? Prof: Oh no, yes. I was afraid someone was going to do that. So let's just see where I got this equation from. So I took my original equation, which didn't have any 1 gs in it, and I just said, if I had growth in the economy, it's no big deal to take that into account. I'm still going to have 1 equation, so I can still solve it. It's just that at every time t, how many old guys do I have? I have each old guy behaving the same way as before, except that now there's been a growth of 1 g. This is a generation before this one, so this generation is of size (1 g) to the (t - 1). The young generation, which was 1 generation ahead, has grown by a factor of 1 g. So there's (1 g) to the t of these guys. So I take their old demand, you know, the same for each guy, but different number of guys, and the young generation's demand, and I have to set it = to the supply. But that's just the old guy's endowment, so 1 for each old guy, and there are that many old guys, the young guys' endowment, same as before, and there are that many of them, the land, which I've also assumed has been doubling, 1 g is 2. So the land is also doubling. And I'm not sure whether I called this t or t - 1, but either one, it's not going to make a big difference, okay? Who asked the question? You follow that, right? I've got 1 gs everywhere, so I can cancel a lot of them out. That's all I did. So if I divide by (1 g) to the (t - 1), I just get rid of the (1 g) to the (t - 1)s. I change (1 g) to the t divided by (1 g) to the (t - 1). That's just to the first power. I got rid of this one. I made this to the first power, and this to the first power, okay? So I can solve that perfectly easily and I'll do that in Excel in a second. And then we can see what happens to everybody's utility. So any questions about what I did here? Yes. Student: > Prof: Yeah, it's going to change the answer, but it's going to qualitatively be the same. Student: > Prof: Well, it depends whether when I do this I want to say this is 2, 4,8, 16 or whether I want to call it 1,2, 4,8, 16. So I don't know which is the right thing. Probably I should have done 1,2, 4,8. Probably the way I have it here which is t - 1. Okay, any other questions about this? So the last thing to do is to just do it numerically, because it's a pain to have to solve these, you know, these quadratic things. It's only 1 equation, but it's still a pain to solve, and I happen to have written a file that you can use to solve these all automatically. This doesn't look too good. So the first one, the first case I did, suppose A, that's the exponent for how patient you are. That's half, that's the first exponent, half, half. So I always can make the log utilities, the 2 coefficients, so it's A log B. So I'm assuming utility here, U of young and old is A log young (1 - A) log old, old consumption, okay? So A I took to be 1 half. That's just what we were figuring out. I took the endowments when young to be 3 and when old to be 1 and the land output to be 1 forever. Then the price is what I'm going to try and solve for, and so I solved the market clearing equation and cleared it and did Excel solver and got the consumption, which we figured out was 1.775 when young and when old was 3.225, which adds up, the two of them add up to 5 together, just as we thought. And so I even calculated the utility of each of the people. I didn't do log utility, actually, I wrote a monotonic transformation. I put Y to the A, Z to the (1 - A). It's easier for me, you get positive numbers. That's e to the U. So I might as well describe utility as the exponent of U. Take e to it, so it's a positive number. When you do logs of small numbers, you get negatives, so that's easier to look at. So that's the utility. Okay, now we can do Social Security. What happens with Social Security? The only effect of Social Security, remember, it's the same model. You just take stuff away from the young and give it to the old. So nothing changes, except the young's endowment goes down to 2 and the old's endowment goes up to 2. And then the rest of the model's exactly the same. And so, of course, it's going to give you a different price. p_A is different. So p_A is smaller. That means today's price of next year's good is smaller. There must be more discounting. So I did the interest rate, 1 over 1 r = p, so the inverse of p is this thing. So the forward rate is 161 percent, and if you think of that as 30 years, that's an annualized 3.2 percent interest rate. Before, it was only a 2 percent interest rate annualized, right? Remember we got the 1 r to be 181 percent, 1.81, so r is 81 percent. So this Social Security doubled the interest rate from 81 percent to 161 percent. Huge increase in the interest rate, so Social Security has raised the interest rate. And so you re-solve the whole equilibrium and it didn't crush everybody, but everybody's utility went down except for the very first generation. We know they won for free. But now I could do the same thing with growth. I could just solve that equation on the left, and so I plug in now the growth rate from generation to generation, 1 growth, and here I've got 2. So it doubles every period, just the example I did, and so I solve it and you see that of course from the generations growing and land is being more productive and there are more apples and stuff like that, there's just more for everybody to consume. It's actually made everybody better off. But now we see that Tobin and the interest rate is higher, way higher, 247 percent instead of 161 percent. If I do now Social Security in the growing economy, every generation when young only has to give up half an apple and get 1 whole apple when old, so that raises the interest rate from 247 percent to 300 percent, annualized from 4 percent to 4.7 percent. So the rate of growth is faster now than the growth of the economy, right? This interest rate, 300 percent is faster than the rate of growth, which is 100 percent. So again, everybody is going to lose. They're going to go from 3.06--they're still going to lose by Social Security, to go down to 3. But Tobin, I would say, is 90 percent right, although more children doesn't solve the Social Security problem, because it's going to increase the rate of interest. So you're still going to have losers. Nonetheless, the loss is now much smaller with lots of children than it was before. So Tobin, I would say, is 90 percent right. If only every generation would have more children, we still would have had a crisis in Social Security. We still would have had this every generation complaining it was getting a bad deal, but it would be a lot less bad than it was before. And then I did this variant, depending on what we said, whether the growth was--whether I had a g to the t or a g to the (t - 1) there. It doesn't really change that much. Okay, so that's it. So you see, just by a very simple modification of the problem, you can resolve--it's just understanding is, at least in my mind, so much clearer now about what role growth plays. Having more children doesn't make the problem go away. It makes it better, but you can never make it go away, because the interest rate is always going to be higher than the rate of growth of the economy. So let's do one last experiment on this stuff. Another problem to resolve. I wrote a paper, the newspapers were saying the same sorts of things and I'll tell you what they were saying. Oh no, I did a mistake. Sorry. Okay, so remember those pictures that we showed before of the stock market. If you take out inflation, the stock market seems to go in these waves where prices go up and then they come down, then prices go up, then they come down and prices go up, then they come down. We've had 5 big waves of stock markets going up and coming down. We're now in a period where they've been coming down. The stock market is lower now than it was 10 years ago, correcting for inflation. In fact, even not correcting for inflation. So why would you expect that to happen? Is there any logic to that? So here's an old picture of the stock market. I wrote this paper in 2005. Remember at the first class, we had a picture like that. You can see the stock market going up and down, up and down, up and down, up and down, five waves. It's now come down further. This is like 2001 or '02, so it's come down way further than that. So is there any explanation for why that would happen? So here's an explanation I gave in a paper, which a lot of people in the newspapers were giving. I said, the baby boomers. I said all these baby boomers like me, we're getting old. We're going to start selling our stocks and so the stock market's going to go down. And so that's what newspapers were saying too. The difference is, that the economists criticized the newspapers and me and they say, "Oh you're crazy," they said. "The stock market, it can't be that the stock market is going to go down, and everybody knows it's going to go down, because if we knew it was going to go down in the future, it would have already gone down now." Okay, so you have to give an argument. So what I pointed out was that if you look at the history of live births, you get the same cycle. Look, it went up and down, up and down. I don't know if you can read that. I can hardly read it myself. What years are these? Why is it so unreadable? Let's just see if I blow it up a little bit. Now I can see it. This is 1910, '20, '30, '40, '50, '60, '70, '80, '90,2000. You can see these were live births. So births, there a baby boom and then a plummet, then another huge baby boom. That's the famous baby boom, my baby boom, and then a plummet. And then there was another baby boom. I forget what they call it, the X generation or whatever it is, some other baby boom that happened. Basically my baby boomers, me having children, another big baby boom and then birth rates are going to go down. So I think that you are--the number of 18 year olds in the country is at its all time high, or is going to be in two years when my poor son tries to get into college. And so then it's going to go down again. So this is a cyclical thing that keeps happening over and over again with baby booms and busts. And everybody knows about the baby boom after the war, my generation, the '50s and '60s when I was born. Everybody knows about that, but they don't realize that there's been baby boom after baby boom after baby boom, and this is a cyclical phenomenon. And then the thing that they really don't know is that it's exactly the same as the stock market, that those 5 patterns in the stock market were the same patterns of the baby boom. Okay, so I'm going to end with that picture. Okay, so a picture is worth a thousand words, but it's not that compelling an argument. You need a little bit of analytics. Suppose everybody knew that generations were going to get bigger and then smaller and then bigger and then smaller. Would the stock market go up and then down and then up and then down, as I was saying, and as all these newspaper columnists were saying? Or would it just stay the same, as these less imaginative economist critiquers were saying, that it couldn't have anything to do with demography? Because by rationality, people would look forward and they'd anticipate it going down, so they'd all sell before it went down, so it would never go down. So it turns out that it does go up and down, and that argument the economists gave doesn't make any sense, because they were implicitly assuming that the rate of interest stayed the same the whole time. And if the rate of interest doesn't stay the same, then there's no reason why the stock market has to stay the same. So let's go back to where we were before and change the model a little bit. Let's suppose that the model is an alternation between big generations and small generations. So let's suppose that you have (6,2), (3,1), and (6,2). I think I kept--so it's a good question. What should I do with land? I think I kept it at 1 every period. God, I hope that wasn't the key to the result. So in the paper, of course, I had, you know, people living 80 years and I had their income reflecting the sort of trend in income over the lifetime. But anyway, for the purposes of this class, let's say there's a small generation where it goes young 3, old 1. Then the next generation, which is just 2 guys, so they're both (3,1) guys, so in aggregate, they're going to be (6,2). The next generation's (3,1), the next generation's (6,2), the next generation's (3,1) and it keeps alternating like that forever. Now, how would you solve for equilibrium? Does the whole thing just get much more complicated? I mean, what happens, after all? Any questions here about what we're doing? So it looks way more complicated, but it's not. It's a little bit more complicated, but not much. You can still solve for this. So I'm going to not spend too much time on this, but I'm just going to show you what you would do. So what would you do? Well, by symmetry, I claim, you can guess that there are going to be two prices. So you notice that every generation only cares about the relative price when it's young and when it's old. So there's this relative price. That relative price between consumption at time 1 and time 2, that's going to affect the generation born at time 1. It actually has no effect on any other generation. These generations are born after that, so this interest rate, this relative price between these two periods affects only 1 generation. So this generation is affected by the interest rate between time 2 and time 3. This generation is affected by the interest rate at time 3 and time 4. Every generation is responding to the interest rates during its life, not during another generation's life. So by symmetry, I think, you can guess-- and it turns out to be true--that there's going to be a price, a relative price--I should call them small-- for the small generation, and a relative price for the big generation. The same thing is going to happen. So this relative price will be p_small, this will be p_big. Then we'll get p_small again here, and p_big connecting these guys. And it's just going to keep repeating itself over and over again. And by symmetry, you could guess that the equilibrium would look like that. Is this making sense? It's not making sense. Is it making sense? So what would I have to check to see that there's equilibrium? Let's do it over here. Let's do a small generation. Okay, so we never did the first. So the first generation, it depends whether we start with a small one or a big one. But remember, if we can clear all the markets for all time, except the first market, that one has to automatically clear. That was Walras' insight. So we know that if we can clear all these, the first one's going to look very different, but it's going to clear anyway, so I don't really have to worry about it. So we'll see why that works. So I'm going to now talk about market clearing at any time, except the first one, which is more complicated. The first one seems really complicated because there's this guy 0 who owns these dividends that go on forever. But of course, they're just worth the price of land, which he's going to sell off. But anyway, we'll come back to that in a second. So in every generation, every time period, when small generation is young, what do you get? What's the market clearing equation going to be? Well, the small generation is going to be young, so that means the old generation is big. Sorry, it's a half-year, so the big old guys, their endowment is going to be 6. There's 2 of them, so I can put the 2 out here. 3 1 p_big, divided by p_big, that's the big old generation and the young generation, they're the usual 3 1 p_young, divided by 1. A has to = now, how many endowments do we have? We've got 2 old guys each owning 1, so that's 2 times 1. That's their endowment, 3, that's the young guys, the land dividend. So that's 6. Student: If you divide the second > small? Prof: So this should be p_small, not p_young. p_small. No, I don't, because the old guys--the big generation is old. The small generation is young. So the young generation, they're consuming in their youth now, so they're looking at their endowment. The price when they're young is 1. So their young endowment is 3, their old endowment-- their income's 3 times the price to them of 1 when they're young, plus the endowment of 1 when they're old times p_small, divided by the price when they're young, which they're thinking of as 1, right? They only care about the relative price between young and old. That relative price is determined by p_small. So I could call it p_t and p_t 1, but I know that ratio is going to be p_small. So really, it only depends on the ratio, so I might as well just use the ratio, p_small. This is a crucial idea that I've used 100 times and I think-- I've used it now 3 or 4 times anyway-- so, but I think some of you don't quite know what the hell I'm talking about. So somebody ask me a question if they don't know why this is right. Whoever just asked it, maybe you still don't know why it's right. Who asked this question a minute ago? Yes. Do you understand how I got this? You do. Okay, but when the old guys--see, the old guys, which is the big generation, we're clearing time--we're looking at this time. So the total endowment is 3 for the young generation. Their endowment is 2, and the 1 unit of land. That's where I got the total supply of 6. So this generation when it's young, they care about the p_small, the relative price between here and here, and so they're looking at p_small, the relative price of 1 to p_small. The old generation at the same time is looking over their lifetime at the ratio of consumption here to here, which is given by p_big. So they've got a p_big here, and they're consuming when old, so they're dividing by p_big, okay? But now we've got a second equation, which is when the big generation is young. So why don't you tell me what that equation's going to be? How much is the endowment when the big generation is young? That's, maybe, clearing it this time. Here the big generation is young, so what's the endowment? It's going to be the young--so the old, there's only going to be 1 old guy. There are going to be 2 young guys, each have endowment of 3,1 unit of land, so that's 8. You can see that adds up to 6 1 1 is 8. Okay, and what's their demand? What's the demand for the 2--so there's the old. What are the old going to be doing here? It's in this generation we're doing the market clearing. Somebody knows how to answer this. Yeah. Student: > Prof: : Over here, the young, the small generation only has 1 when it's old. Student: Big generation. Prof: : But big generation, that's over here. We're clearing at this time period, so there's a bunch of young guys and just a few old guys. So the endowments are 6 1 1. The time is going that way, so that's why that's an 8 over here. So if this is the 1 old guy's endowment, 2 young guys who have 3 each, that's endowment of 6, the land is 1, so you get 8. That's how I got an 8 over there. That's the supply. So what's the demand? Who's trying to buy the stuff? What's the demand of the old guys? Student: > Prof: And that's going to be what? They're planning to spend when they're old. We're doing this one. They make their plans when they're young. They anticipate what the prices are going to be and so how much do they plan to spend when they're old? Student: 1 half times 3 1p-- Prof: 3 1p what? p what? What p? Student: p_small. Prof: p_small, exactly. Over p_small, plus Student: > Prof: What are the young guys doing? We're over here. So 2. There are 2 of them. What's this? p what? Divided by? Oh, there's 1 half here. Student: > Prof: 1. Okay, exactly. So that's it. So there are 2 equations and 2 unknowns, p_big and p_small, and 2 equations. So to solve this whole model, you could get 2 equations--you just have to solve these two simultaneous equations, which I did. And then you can find the effect. So the economist critiquers would say, "Well, p_big should equal--" What would be the price of land, by the way? So what's the price of land going to be in the end? What's going to be the price of land, according to Fisher, at time 1? At time 1, let's say. So right here, what's the price of land? Remember, it's the price after the dividend is paid, so what's the price of land? Student: > Prof: Let's do the present value of the discounted dividends. What would it be? Maybe I'd better write it over here. Remember, the dividends are just 1 1--you know, 1 --so there's going to be 1 1 1 1, but I'm going to be multiplying by something. So what is the price of land? p_small, incidentally, =-- I could always write that as 1 over 1 r_small and I could write p_big as 1 over 1 r_big. Okay, so what's the price of land going to be? So it's the price of land starting here just after the dividend is paid. So it's hard to think about this, but if you can figure this out, then you've totally understood everything in the course, because this is so much more--it uses all the ideas in a just way more complicated way. Yes? Student: > Prof: Well, start telling me the formula. So if I want--when I do the first terms, what is this first term? Student: > Prof: So you would put 1 r_small here? Okay, and now what would you put over here? Student: 1 r_big. Prof: You'd put 1 r_big here? Student: > Prof: Okay, very good. So now you guys really know what's going on. What would you put over here? Student: > Prof: Okay, exactly. 1 r_small time 1 r_big, times 1 r_small. Okay, that's that one. I'm going to stop with that. Too much. dot, dot, dot. So you have the idea now. What's the idea? You're taking the present value of all the dividends. So this dividend, you have to discount it by 1 r_small. This one, you have to discount it twice. First to bring it back here, that's 1 r_big, then to bring it back here, that's another 1 r_small. So 1 r_big, 1 r_small. The third dividend, you discount first at the small discount, then at the big discount, then at the small discount, just like that. You keep adding them. So why should the prices--what if you look at the price of land at time 2? Is it the same number as that? Is it the same formula? Student: > Prof: It's not the same formula, because at time 2 you're starting here, and the first discount is p_big. So it's going to be 1 over 1 r_big 1 over 1 r_big times 1 r_small 1 over 1 r_big times 1 r_small times 1 r_big dot, dot, dot. So this isn't the same as that. It would only be the same as that if r_big was = to r_small, if p_small was equal to p_big. So which one do you think is bigger? Do you think p_small is = to p_big, or one of them is bigger than the other, and why? That's the answer to the critics' puzzle. So you see, you've taken something that appeared in the newspapers. It sounds like common sense. If there are all these middle-aged people like me, bidding up--you know, there are so many of us who want to hold stocks. We're at the peak of our earning power. We've got tremendous amounts of money. What are we going to do with it except put it into stocks. You'd think common sense would be the price of stocks would have to go up. When we get old and we're selling all our stocks, you'd think the price of stocks would have to go down, okay? So that would tell you that the interest rate was going to be bigger or smaller. So that would suggest that the price at time 1, when the small generation was young, would be low, and the price at time 2 would be high. And that could happen if this interest rate was low, and this interest rate was high. But does that happen or doesn't that happen? You can't know until you solve in the model. The critics said, "Oh, that can't be right, because somehow the price should even out and everybody should be looking ahead and buying or selling at the right time." You can't buy and sell at the right time, because you're going to be dead. So you don't have much choice, except when you're young here to save, and when you're old here to dis-save. They seem to have overlooked that small problem. So the point is that, to know the answer, you can't just reason it out verbally. You have to write down a model, solve for the model and see what happens. And sure enough, it happens--so we go back to the paper now. Okay, are there any questions about this? Okay, so all I did in this spreadsheet is I wrote down these 2 equations. So you see that I've got the young and the old are the same half, half log utilities. The small generation is 3,1, the big generation is 6,2. Land is always producing 1 every period and we get 2 different prices. The price is called p_A. That's the A generation, which is the small generation and the B generation, which is the big generation. So you can see that p_A is a very small number when the generation is small, and that means the discount rate is very high. So a high interest rate when the generation is small, and a low interest rate when the generations are big. So in the money making peak of the big generation, the real interest rate is small, and so that means you're not discounting very much, and so the prices are very high of land. And so sure enough, the price when the small generation is young is 1.29, and when the big generation is young, it's 2.08, vastly higher. So it really is the case that as the generations rise and fall, the interest rates rise and fall and the price of land rises and falls, and everybody's rational, anticipating everything. So it really could be--I'm not saying it's true, because it could be a coincidence that these things all matched up, but the fact is, demography can have a big effect on economic equilibrium in the stock market. And you can be an economist and believe in demography. You don't have to be a Marxist or something to think demography and fertility and all that stuff is going to affect the economy. For a long time, economics tried to wall itself off from other social sciences and say, "Oh, those fertility people and, you know, all those touchy-feely people, it's got nothing to do with the real markets." Well, it has a lot to do with the real markets. Okay, so one last thing, would you rather be in the small generation or the big generation? Student: > Prof: Of course, the answer's there, but tell me why. Yeah? Student: Small. Prof: Okay, that's correct. So I'm screwed. And so why is that? Student: > Prof: It turned out to be the utility of the--this is the utility of the big generation per person. Of course, adding the two people together, it's bigger, so per person it was this, a lot less than the generation of the utility of the small. So why did that happen? Why exactly is that happening? So remember, I'm distinguishing your peak. I'm calling young your peak earning years and old I'm calling the stuff when you're retired, I'm not earning very much. So why is it that a high interest rate is good? Yes. Student: It encourages consumption today for the younger generation. Prof: Well, I think the point is, if you're making money when you're young, and you've got a high interest rate, that means a high return. So you can make a big return through your life, whereas my generation had a very low return. The return I'm getting now is terrible. It's negative. The return I'm getting now is just hideous. But when my parents were young, they were making an astronomical return, incredible rates of return. And they were earning money in their younger years and investing it to save when they were old and they were getting incredibly high return. There was nothing to do with my money. There are so many people like me pouring money into the stock market, we're getting a very bad return, and that's why it's not so good to be part of a big generation. So other people had said the same thing. They said big generations have to squeeze into the same houses, so there's less housing stock, or we build more houses, the next generation comes along, there are all these houses built for them and there are less of them, so they get better houses. Everything's better when you're the small generation. You're screwed as the big generation and here's an example of it. Okay, so that's it for Social Security. All the things I wanted to say about Social Security. Now the exam, as I say, you won't have to do the two generations and all that stuff on the exam. But the first part about solving for the .55, that one you might have to do something like that. But anyway, the lesson that you can have a controversy in the newspapers with arguments on both sides, you never can figure out the right answer till you write down a model. And the model can be very simple, the kind of thing you could do as an undergraduate. That's the lesson I'm trying to communicate. All right, so from now on though, we have to change gears and I think the course gets a lot more interesting, okay. But we needed all this background basics to have the logic of finance. But finance is really nothing without uncertainty. If you don't know what's going to happen tomorrow, that's when the thing gets interesting, that's when you have to think harder, that's when people make mistakes, that's when a hedge fund can make a profit, that's when everything gets more exciting, when there's uncertainty, and we have to start adding uncertainty to our thinking about the world. So since I only have a few minutes, I'm going to spend the last few minutes just reminding you of what you're supposed to know about uncertainty, which is this slide, okay? So it's not a very complicated thing. Where's the--I see PowerPoint. Okay so there are two kinds of uncertainty, one of which we're never going to get to. So the uncertainty that we're going to work with in this course is everybody understands what could possibly happen. So this was a brilliant states of the world model, it's called. So Leibniz is supposed--see, it says states of the world right there. Leibniz was the one who first invented the idea of states of the world. He said, "We live in the best of all possible worlds." So if you don't know what's going to happen in the future, we're going to represent that as many potential states of the world. Now there are other ways you could model uncertainty, and it's a big subject in epistemology and philosophy. I'm going to stay--hew closely to the states of the world thing. So if there's something about the world we don't know tomorrow, I'm not going to assume that it's just vague in our minds and we can't quite make it out. I'm going to assume you actually can make it out. It's just you don't know which of the possibilities are going to happen. So it's many states of the world. So an example of that, of course, is spinning a dice, or spinning two dice, so you don't know which of 36 possibilities is going to happen. Each of those would be one state of the world. Okay, so those are all the possible sums, so there are more states of the world than there are outcomes, notice. You can get 2 through 12, is the sum of the dice, but there's still 36 possible states of the world. And so that random variable, the sum of the two dice, is expressed as a function. It says, in every state of the world, what is the random variable's value? So our state of the world, by that I mean something that's so detailed that it tells you the value of every random variable. So that's how I'm going to be thinking of uncertainty, that we're here today and a bunch of different things could happen tomorrow, and this is an exhaustive list of everything that can happen tomorrow. We're going to have to come back and criticize this assumption, but it introduces uncertainty in a way which is still quantifiable and not vague. So you can talk about the histograms of outcomes of the dice, you know, how many ways, what are the chances of getting a 7,6 out of 36, etc. So this is stuff I'm sure you all know, okay. The most famous histogram of mathematics is the normal distribution, which I don't have time to explain. And so a normal distribution, remember, is this exponential thing. The dice example, you know, sort of looks like it. In fact, if you had enough dice, and you kept averaging their outcome, it would be normally distributed. So lots of things turn out to be normal. One of the properties of normal is that the tail gets small very quickly, and so you're not going to get very many outliers. The normal distribution is a very common distribution. There're lots of reasons why it should occur all the time, and it's also mathematically very easy to work with. So economists for a long time assumed that everything was normally distributed, but an implication, as I say, of normal distribution is that it's very unlikely something extreme is going to happen, because this thing goes down exponentially fast to 0, so you're almost never going to see something way out here. Yet we get these crashes fairly frequently. Every 10,20, 30 years or something, there's some gigantic outlier. So clearly things can't be normally distributed, and that's called fat tails. I'm sure you've heard about that in the newspaper. We're going to come back to that. Now there are a couple of things that you need to-- so you can represent the payoff of any random variable as a picture, and every state, what is its payoff? So a riskless random variable, riskless investment, will pay the same amount in every state. I still have a few minutes here. Okay, so now two incredibly important concepts, which I'm sure you know--or at least the mean you know--just the average, what's the expected payoff? So the expected payoff is, you multiply the outcome in every state by the probability of the state and you add it up. Okay, so there are how many different ways? So if you have 1 dice, you can figure out the expectation of 1 dice. It's equally likely to get 1,2, 3,4, 5 or 6, and so if you add all those up, multiplied by a sixth, you get 3 and 1 half. So the expectation of 1 dice is 3 and 1 half. The expectation of two dice is therefore--okay, that's 1 dice. Okay, now the expectation of adding 2 dice together is of course going to be 7, because the expectation of 1 dice is 3 and 1 half and the other dice is 3 and 1 half, and so the expectation of the sum is the sum of the expectation, so it's 7. Okay, so you know that. Now one more thing that you have to know is the variance. So how do you measure how uncertain you are about what's going to happen? Well, the simplest number to do, like with the dice, is to say, the expectation is 3 and 1 half. When we don't get 3 and 1 half, it means there is some error. Expectation wasn't confirmed. So you could just measure the error as the distance between 3 and 1 half and what you actually got. So if you got a 4 you could say you were off by 1 half. But people don't do that. They measure the square of the distance and they take the average square of the distance, and that's called the variance. So if you got 4 when you were expecting 3 and 1 half, the error is 1 half squared, so you take 1 sixth times 1 half squared, 1 sixth times 1 and 1 half squared, 1 sixth times 2 and 1 half squared. That's for the high mistakes. And the low mistakes, you'd take 1 half times 1 half squared, 1 half times 1 and 1 half squared, plus 1 half time 2 and 1 half squared [correction: 1 sixth times each error, not 1 half]. Now why do they use the expected squared error instead of just the expected error? Well, for this simple reason, which you may not have thought of: if you had to guess-- if you looked at the error as the penalty for making a wrong guess, and you were forced at the beginning to say, "What guess would you like to make for how the dice is going to turn out-- how the dice is going to turn out and if you're wrong, we'll penalize you by this measure of error?" Well, if you were just taking the absolute error, your best guess would be any number between 3 and 4. You could say 3 and 1 half, but you could also say 3 and 1 quarter, because if you said 3 and 1 quarter, you'd become closer on all the low rolls of the dice, and be a little further off on all the high rolls, and you'd get exactly the same error. So you could say any number between 3 and 4. But if you make the error the square of the mistake, your best guess is always to say the expectation. 3 and 1 half is the only thing you can say to minimize your expected penalty, if the penalty is the squared error. So because of that--so that's connected to a mathematical thing and orthogonal vectors and all that. Because of that, the error we talk about always is the squared error. And so that's whenever we're measuring uncertainty, we're going to talk about the squared error, the average of the squared errors--or the square root of that, which is called the standard deviation. Okay, I've one more minute to just finish this. I'm assuming you all know that or can learn that. One more thing, I'm going to assume you know, the last thing is the covariance. What does it mean to say that random variables X and Y move in the same direction? So this was quite a brilliant thought. So what it means is that to move in the same direction, means if X surprises you by being above what you would have expected, so if the expectation of X is X bar, and the expectation of Y is Y bar, if you multiply the 2 and they're both higher than you expected, you'll get a positive number. If they're both lower than expected, you'll also get a positive number. So by taking this sum, the expected deviation from the expectation, multiplied, you get a number which, when it's very positive, it means they're either both positive together or both negative together. So they're going in the same direction. If one of them is above the average while the other one's below the average, then you'll get a negative number. So big covariance means they move in the same direction. Big negative covariance means they move in the negative direction. Okay, so I'm going to take it for granted you know this, and we're going to take this up, starting right after the exam, which is on Tuesday.

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