Final answer:
The expected overall payoff of each bank is calculated by multiplying the loan amounts by the probability of repayment. The standard deviation of the overall payoff is determined by the variability in loan repayments, considering each loan's risk of default.
Step-by-step explanation:
The task is to calculate the expected overall payoff and the standard deviation of the overall payoff for each bank, given their respective loan and probability of non-payment. For Bank A, which has multiple small loans totaling $100 million, with an independent probability of 5% for each loan, the expected payoff would be the total loan amount multiplied by the probability each loan will be repaid (100 - 5%). The standard deviation would need to incorporate the varied outcomes of each independent loan. For Bank B, which has a single loan of $80 million with a 7% chance of non-payment, the calculation becomes more straightforward. The expected payoff would be the loan amount multiplied by the probability it will be repaid (100 - 7%). The standard deviation for a single loan would take into account only two possible outcomes: full repayment or no repayment at all.
Based on standard probability and statistics calculations, these figures allow us to best understand and compare the risk and expected returns between the two banks. It's important to keep in mind that in the real world, a bank's calculations are complex due to factors like changing interest rates and varying borrower repayment riskiness.