Consider two local banks. Bank A has 94 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 $94
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?
The expected payoffs are the same, but Bank A is less risky. I prefer Bank A.
The expected payoff is higher for Bank A, but is riskier. I prefer Bank B.
In both cases the expected loan payoff is the same:
$ 94 million times 0.96 equals $ 90.2 million$94 million×0.96=$90.2 million.
Consequently, I don’t care which bank I own.
The expected payoffs are the same, but Bank A is riskier. I prefer Bank B.