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 only repaid half ($0.5 million). 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 being repaid half ($50 million). The expected overall payoff of each bank is:
The standard deviation of the overall payoff of each bank is: