Your FI has originated two loans, each having a $100 repayment obligation, 20% default probability, and 50% recovery rate. Defaults of the two loans, if ever, are independent. Discount rate is 5%. Suppose you proceed to CDO by pooling the two loans to create a senior tranche with promised repayment of $160 and a junior tranche with promised repayment of $40. By answering the following questions, show that the senior CDO has lower yield, and the junior CDO has higher yield, than that of the original loans.

a) Calculate the price and yield of the loan.

b) Derive the cash flow distribution of the pool by filling the following table.

Cash flow

Probability

c) (4 Points) Determine the yield on the senior tranche.

d) (3 Points) Determine the yield on the junior tranche.