Please solve the following problems:

__________________________________________________________________________________________________________________________________________________

1) If the rate on one-year Treasury strips currently is 6 percent, what is the repayment probability for each of the following two securities? Assume that if the loan is defaulted, no payments are expected. What is the market-determined risk premium for the corresponding probability of default for each security?

a. One-year AA-rated zero coupon bond yielding 9.5 percent.

b. One-year BB-rated zero coupon bond yielding 13.5 percent.

__________________________________________________________________________________________________________________________________________________

2) A bank has made a loan charging a base lending rate of 10 percent. It expects a probability of default of 5 percent. If the loan is defaulted, the bank expects to recover 50 percent of its money through the sale of its collateral. What is the expected return on this loan?

__________________________________________________________________________________________________________________________________________________

3) The bond equivalent yields for U.S. Treasury and A-rated corporate bonds with maturities of 93 and 175 days are given below:

93 Days 175 Days

U.S. Treasury 8.07% 8.11%

A-rated corporate 8.42% 8.66%

Spread 0.35% 0.55%

a. What are the implied forward rates for both an 82-day Treasury and an 82-day A-rated bond beginning in 93 days? Use daily compounding on a 365-day year basis.

b. What is the implied probability of default on A-rated bonds over the next 93 days? Over 175 days?

c. What is the implied default probability on an 82-day A-rated bond to be issued in 93 days?