Problem:
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, which it also expects will be repaid today. It also has a 5% probability of not being repaid.
Requirement:
Question: Explain the difference between the type of risk each bank faces. Which bank faces less risk? Why?
Note: Please provide through step by step calculations.