Question 1: Suppose the estimated linear probability model used by an FI to predict business loan applicant default probabilities is PD = 0.03X1 + 0.02X2 - 0.05X3 + error, where X1 is the borrower's debt/equity ratio, X2 is the volatility of borrower earnings, and X3 is the borrower's profit ratio. For a particular loan applicant, X1 = 0.75, X2 = 0.25, and X3 = 0.10.
A. What is the projected probability of default for the borrower?
B. What is the projected probability of repayment if the debt/equity ratio is 2.5?
Question 2: 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
|
|
Treasury strip
|
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?