Suppose there are two ratings categories: A and B, along with default. The ratings-migration probabilities look like this for a B-rated loan:

The yield on A rated loans is 5%; the yield on B rated loans is 10%. All term structures are flat (i.e. forward rates equal spot rates). A loan in default pays off 50%.

a. You have two loans in your portfolio, both are B-rated, 3-year, 10% coupon bonds (paid annually), each with $100 face value. Compute the possible prices of the loans next year in each ratings bucket (just before the first coupon is paid). (6 points)

b. Compute next years mean value for each loan. (5 points)

c. Using the mean from part b as the benchmark, compute the 1-year VaR with 95% confidence interval for each loan (based on the actual distribution). (7 points)

d. Suppose the returns on the two B-rated loans in your portfolio have zero correlation (they are independent). This means, for example, that the probability that one loan remains B-rated and the other defaults equals the product of the marginal probabilities, or 0.90*0.05 = 0.045. Construct the probabilities and values for each possible outcome of your portfolio (there are 6 outcomes). (14 points)

e. Based on part d and using the mean of your portfolio as the benchmark, what is the 1-year VaR for the whole portfolio with 90.75% confidence interval? (8 points)