Question: A five-year fixed-rate loan of $100 million carries a 7 percent annual interest rate. The borrower is rated BB. Based on hypothetical historical data, the

A five-year fixed-rate loan of $100 million carries a 7 percent annual interest rate. The borrower is rated BB. Based on hypothetical historical data, the probability distribution given below has been determined for various ratings upgrades, downgrades, status quo, and default possibilities over the next year. Information also is presented reflecting the forward rates of the current Treasury yield curve and the annual credit spreads of the various maturities of BBB bonds over Treasuries.

a. What is the present value of the loan at the end of the one-year risk horizon for the case where the borrower has been upgraded from BB to BBB?
b. What is the mean (expected) value of the loan at the end of year 1?
c. What is the volatility of the loan value at the end of year 1?
d. Calculate the 5 percent and 1 percent VARs for this loan assuming a normal distribution of values.
e. Estimate the approximate 5 percent and 1 percent VARs using the actual distribution of loan values and probabilities.
f. How do the capital requirements of the 1 percent VARs calculated in parts (d) and (e) above compare with the capital requirements of the BIS and Federal Reserve System?

New Loan Value plus Coupon S $114.82m 114.60m 114.03m Probability Distribution 0.01% 0.31 1.45 6.05 85.48 5.60 0.90 0.20 Forward Rate Spreads at Time t Rating 3.00% 3.40 3.75 4.00 0.72% 0.96 1.16 1.30 108.55m 98.43m 86.82m 54.12m Default

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