 0  0.2  0.4  0.6  0.8  1  1.2 -3 -2 -1  0  1  0  0.2  0.4  0.6  0.8  1  1.2 -3 -2.5 -2 -1.5 -1 -0.5  0  0.5  1 p log return partial distribution closed closed Figure 3: A distribution, appearing close to normal, as one might estimate from historic returns. There appears to be a mean above the risk-free rate (10%), which would traditionally be interpreted as a risk- premium for the uncertainty (variance or volatility). Figure 2: An example from physics illustrating how a common equilibrium is established due to interac- tion. Under the influence of gravity two columns of liquids interact. The flow of liquids is the analogue to the flow of assets through time ( e.g. being removed from the spot market and stored for later disposal) between the future and spot markets. A “flow against time” corresponds to short positions flowing forward in time (like the travelling of ‘holes’ in semiconduc- tors). If, for example, the left side corresponds to the spot market and the boundary between the liq- uids represents the asset price, then the arrow on top represents assets being carried to the future, and the arrow at the bottom represents borrowed cash positions to fund the arbitrage. The analogy could be taken further with friction and viscosity allowing slightly different levels on each side. We would argue in two ways: Firstly, uncertainty is not what warrants a premium as it is an insufficient description of risk. And secondly, the risk-premium is a misleading concept as it suggests that the premium is part of the distribution, but not the risk we receive it for. We believe risk is best defined as the probability of an adverse outcome as suitably defined for a cer- tain situation $^{8}$. Hence the risk should be part of the distribution describing our beliefs about all possible outcomes. If we are aware of possible negative out- comes we will demand compensating possible positive outcomes. Figure 3 shows a partial probability distribution which seems to have a significant “risk-premium” of about 15% above the risk-free rate of 10% (all log returns). Traditionally that would be seen as a com- pensation for the uncertainty (standard deviation) present. Figure 4 then shows the full distribution, which is actually a maximum-entropy distribution for a mean 8 Or through a probability distribution for adverse out- comes. 5