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Question - Consider two local banks. Bank A has 100 loans outstanding, each for $1 million, which will be expected to be repaid today. Each loan has a 10% probability of default. And out of the case of default, 80% of the portion can be recovered by half of the amount of the total loan and the remainder 20% has no recovery of the loan. The chance of default is independent across all the loans.
Bank B has only one loan of $100 million outstanding, which will be expected to be repaid today. This loan also has a 10% probability of default. And out of the case of default, 80% of the portion can be recovered by half of the amount of the total loan and the remainder 20% has no recovery of the loan.
Calculate the standard deviation of the loss amount of loan due to the default for bank A and for bank B.
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