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

Rating in 1 year Probability

A 0.05

B 0.9

Default 0.05

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%.

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). (12 points in total 2 points for each row below)