Question

Consider two local banks. Bank A has 76 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 $ 76 million outstanding, which it also expects will be repaid today. It also has a 4 % probability of not being repaid. Which bank faces less risk? Why?

(Select the best choice below.)

A. The expected payoffs are the same, but Bank A is riskier. I prefer Bank B.

B. In both cases the expected loan payoff is the same: $ 76 million times 0.96 equals $ 73.0 million$76 million×0.96=$73.0 million. Consequently, I don't care which bank I own.

C. The expected payoff is higher for Bank A, but is riskier. I prefer Bank B.

D. The expected payoffs are the same, but Bank A is less risky. I prefer Bank A.

Answer 1

Expected payoff is the same for both banks as it is probability weighted

However since bank A has same amount spread over various loan hence the variance will be much lesser.
The risk will be less because if one loan may default the others wont. This will reduce the variance.
However in case of bank B the variance comes out to be much higher because there is a single loan and if it defaults it may result in a much higher loss.

hence option D is applicable
D. The expected payoffs are the same, but Bank A is less risky. I prefer Bank A.