a) Consider two individual loans, L1 and L2: each will pay 100 with probability 0.9, but will default and pay 0 with probability 0.1. Whether the two individual loans will pay or default are independent events. Since each individual loan has identical payoff prospect (with independent default probability), they each value the same individually. Compute the expected payment and the variance of payment of each individual loan.

b) Consider a standard portfolio diversification product SD that is composed of 50% share of loan L1 and 50% share of loan L2, where L1 and L2 are as described in part a. Compute the expected payment and the variance of payment of SD.

c) Consider an SIV pooled from L1 and L2, where L1 and L2 are as described in part a, and sliced into a senior tranche (ST) and a junior tranche (JT) in the following manner: ST will receive 100 if either L1 or L2 pays, but will receive 0 if both L1 and L2 default; JT will receive 100 if both L1 and L2 pay, but will receive 0 if either L1 or L2 defaults. In any scenario, the SIV balances its cash flow and you can ignore any service fees. Compute the expected payment and the variance of payment of each of the two tranches.