The standard deviation of the payoff of banks

Consider two local banks. Bank A has 100 loans outstanding, each for $1 million, that it expects will be repaid today. Each loan has a 5% probability of default, in which case the bank is not repaid anything. The chance of default is independent across all the loans. Bank B has only one loan of $100 million outstanding, which it also expects will be repaid today. It also has a 5% probability of not being repaid.

a. What is the expected payoff of each bank’s loans?

b. How risky are each bank’s loans? What is the standard deviation of the payoff of bank A’s portfolio of loans? (Hint: the risk of default is independent across loans, so the variance of the payoff of the 100-loan portfolio is simply 100 times the variance of the payoff of a single loan.)

What is the standard deviation of the payoff of bank B’s loan? Which bank faces less risk? Why?

Solution:

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