1. 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 probability 0.7 and $180 with probability 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 probability 0.45 and $180 with probability 0.55. The prior belief of investors is that there is 0.70 probability that bank A has the higher-valued portfolio and 0.3 probability that bank B has the lower-valued portfolio. Suppose that bank A wishes to securitise 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 securitisation 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.
2. The market value of the assets of a corporation is currently $145 million but the owners wish to only use as collateral a value that will result in an interest rate of about 10%. The firm has on issue a debt outstanding that has a par value of $15 million and a due date of exactly five years. No intermediate interest payments are required. The risk-free (continuous) rate is 3.25% and the standard deviation of returns of the firm's assets is 60%. What is the value of the assets required by the debt holders to permit a fair interest rate of approximately10% (your answer should ensure that the fair interest rate is in the range of >9% and <11%)? State any simplifying assumptions made in your calculations.