Problem. 03: A bank has made a loan charging a base lending rate of 10 per cent. It expects a probability of default of 5 per cent. If the loan is defaulted, it expects to recover 50 per cent of its money through sale of its collateral. What is the expected return on this loan? Solution: E(r) = p(1 + k) + (1 p)(1 + k)(a) where a is the percentage generated when the loan is defaulted. E(r) = 0.95(1 + 0.10) + 0.05(1 + 0.10)(0.50) = 1.0450 + 0.0275 = 1.0725 1.0 = 7.25%

Problem. 04: Assume a one-year Treasury strip is currently yielding 5.5 per cent and an AAA-rated discount bond with similar maturity is yielding 8.5 per cent. If the expected recovery from collateral in the event of default is 50 per cent of principal and interest, what is the probability of repayment of the AAA-rated bond? What is the probability of default? Solution: