A five-year fixed-rate loan of $100 million carries a 7 perc…

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.    Rating   Probability Distribution (%) New Loan Value AAA 0.01% $114.82m AA 0.31 114.60m A 1.45 114.03m BBB 6.05   BB 85.48 108.55m B 5.60 98.43m CCC 0.90 86.82m Default 0.20 54.12m   Information also is presented reflecting the forward rates of the various maturities of BBB bonds over Treasuries. One Year Forward Curves Plus Credit Spread for BBB-rated bonds t   Rate 1 3.72% 2 4.36% 3 4.91% 4 5.30%     a) What is the present value of the loan at the end of one year for the case where the borrower has been upgraded from BB to BBB? (5) [PV] b) What is the mean (expected) value of the loan at the end of year 1? (5) [Mean] c) What is the standard deviation of the loan value at the end of year 1? (15) [SD] d) Calculate the 5 percent and 1 percent VARs for this loan assuming a normal distribution of values. (5) 5% VAR =[VAR5] 1% VAR = [VAR1]   e) Estimate the approximate 5 percent and 1 percent VARs using the actual distribution of loan values and probabilities. (10) 5% VAR =[VAR5a] 1% VAR = [VAR1a]

The following spot rates from the Treasury strip and corpora…

The following spot rates from the Treasury strip and corporate bond yield curves are given to you.   Spot 1 Year  Spot 2 Year Treasury strips 5.0 6.1 BBB-rated bonds 7.0 8.2   a) Calculate the marginal probability of default and repayment on the BBB-rated bond in year 1 (5) Repayment Probability = [P1] Default Probability = [D1]   b) Calculate the marginal probability of default and repayment on the BBB-rated bond in year 2  (10)  Repayment Probability = [P2] Default Probability = [D2]   c) Calculate the cumulative probability of default on the corporate bond over the next two years.  (5) [CP]