Question

Consider two local banks. Bank A has 100 loans​ outstanding, each for​ $1 million, that it...

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 that it also expects will be repaid today. It also has a

5 %

probability of not being repaid. Calculate the following.

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 a​ 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?

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