Suppose bank A has two loans, each of which is due to be repaid one period hence and whose cash flows are perfectly positively correlated and identically distributed random variables. Each loan will repay $365 to the bank with a probability of 0.7 and $180 with a probability of 0.3. However, while bank A knows this, prospective investors cannot distinguish the bank’s portfolio from that of bank B that the same number of loans, but each of its loans will repay $365 with a probability of 0.45 and $180 with a probability of 0.55. The prior belief of investors is that there is a 0.70 probability that bank A has the higher-valued portfolio and a 0.3 probability that bank B has the lower-valued portfolio. Suppose that bank A wishes to securitize these loans, and it knows that if it does so without credit enhancement, the cost of communicating the true value of loans to investors is 5.0 percent of its true value. Explore bank A’s securitization alternatives. Assuming that a credit enhancer is available and that the credit enhancer could (at negligible cost) determine the true value of the loan portfolio, what sort of credit enhancement should bank A purchase? Assume that everybody is risk-neutral and that the discount rate is zero.
