There should be 4 answers. Expected overall payoff for both banks and the standa

Question

There should be 4 answers. Expected overall payoff for both banks and the standard deviations for both banks.

Consider two local banks, Bank A has 80 loans outstanding, each for $1.0 million, that it expects will be repaid today. Each loan has a 4% 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 $80 million outstanding, which it also expects will be repaid today. It also has a 4% probability of not being repaid. Calculate the following: a. The expected overall payoff of each bank. b. The standard deviation of the overall payoff of each bank

Explanation / Answer

a) expected payoff of bank A : E(A) =(80*(1*0.96+0*0.04)) =76.8 million

expected payoff of bank B =E(B) =80*96 =76.8 million

b)

std deviation of bank A =(80*(E(A2)-(E(A))2)1/2 =(80*(0.96-0.962))1/2 =1.7527 million

std deviation of bank B =((E(A2)-(E(A))2)1/2 =(80*76.8-76.82)1/2 =15.6767 million

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