Because each transaction has a significant level of subordination, credit events would typically have to occur with respect  to numerous entities in a collateral pool before we would have a claim payment obligation in respect of any particular  transaction, meaning that our risk adjusted exposure to each corporate entity in a CDO pool is significantly less than our  notional par exposure. In the unlikely event that all of our five lar gest corporate obligors were to have defaulted at  December 31, 2012, absent any other defaults in the CDOs in which these obligors were included, we would not have incurred  any losses due to the significant subordination remaining in each transaction in which these entities were included. TruPs CDOs. In our TruPs transactions, we provide credit protection for the timely payment of interest and principal  when due on a bond (a “TruPs bond”), representing a senior tranche of a CDO comprised mainly of  TruPs. The collateral for  TruPs CDOs generally consists of subordinated debt obligations or preferred equity issued by banks, insurance companies, real  estate investment trusts and other financial institutions.  TruPs are subordinated securities generally issued by financial services  institutions to supplement their regulatory capital needs. Generally , TruPs are subordinated to substantially all of an issuing  institution’s debt obligations, but are senior to payments on equity securities of such issuer (including equity securities  purchased by the U.S. government under the  Troubled Asset Relief Program).  As of December 31, 2012, the collateral underlying our insured TruPs bonds consisted of securities issued by 503  separate issuers, including 441 banking institutions (comprising 77.2% of the total  TruPs collateral based on notional amount)  and 61 insurance companies (comprising 22.4% of the total  TruPs collateral based on notional amount). In addition, the  TruPs  collateral included a small percentage of securities issued by real estate investment trusts.  The collateral underlying our insured TruPs bonds consists of between 21 and 106 issuers per  TruPs bond, with the  concentration of each issuer averaging 1.9% per  TruPs bond. As of December 31, 2012, our exposure to any one issuer in our  insured TruPs bonds ranges from $0.2 million to $42.0 million per bond, with an average exposure of $9.6 million per issuer  per bond. No issuer represented more than 11.1% of the total collateral underlying any one  TruPs bond. Many of the issuers in our insured  TruPs bonds were negatively affected by the recent U.S. economic challenges. Certain  of these issuers have defaulted on their obligation to pay interest on their  TruPs or have voluntarily chosen to defer interest  payments, which is permissible for up to five years. Since we believe there is a strong correlation between interest deferrals and  ultimate defaults, we closely monitor deferrals as well as defaults in assessing the subordination remaining beneath our insured  TruPs bonds. In 2012, the cures of previous deferrals of interest payments on the  TruPs collateral have outpaced initial defaults  and deferrals, suggesting that the general financial position of the collateral pool has been improving.  Based on our most recent projections, we do not expect ultimate net credit losses on any of our insured  TruPs bonds. It  should be noted, however, that even relatively small changes in TruPs default rates or economic conditions from current  projections could have a material impact on the timing and amount of cash available to make interest and principal payments on  the underlying TruPs bonds. Therefore, the occurrence, timing and duration of any event of default and the amount of any  ultimate principal or interest shortfall payments are uncertain and dif ficult to predict. In addition to credit risk, we also potentially face liquidity risk with respect to certain of our  TruPs CDOs. See  “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Liquidity and Capital Resources”  for additional information. CDOs of CMBS. In our CDOs of CMBS transactions, we provide credit protection for the timely payment of interest  (limited to the amount of future premium payable to us) and principal when due on these pools of securities.  We have directly insured four CDOs of CMBS transactions, containing 127 CMBS tranches that were issued as part of 88  securitizations. While there has been some deterioration in the underlying CMBS transactions, we have a high level of  subordination for these transactions and we do not currently project principal losses for our insured tranches in these four  transactions.  While Radian Asset Assurance insures all principal shortfalls for our CDOs of CMBS transactions, the terms of our credit  protection limits claims for interest shortfalls to the amount of premiums we would otherwise be entitled to receive from the  applicable transaction. As of December 31, 2012, the remaining aggregate contractual premiums that we expect to earn for  these transactions is $5.2 million in the aggregate. 29