Question

Consider two local banks. Bank A has 76 loans​ outstanding, each for​ $1.0 million, that it expects will be repaid today. Each loan has a 6 % 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 $ 76 million​ outstanding, which it also expects will be repaid today. It also has a 6 % probability of not being repaid. Calculate the​ following:

a. The expected overall payoff of each bank.

b. The standard deviation of the overall payoff of each bank.

Answer 1

Answer

a. Calculation of the expected payoff of Bank A :

Expected Payoff = Number of Loan * Loan Amount * (1 - Probability of Default)

= 76 * 1,000,000 * ( 1 - .06)

= 76,000,000 * 94%

= $ 71,440,000

Calculation of the expected payoff of Bank B :

Expected Payoff = Number of Loan * Loan Amount * (1 - Probability of Default)

= 1 * 76,000,000 * ( 1 - .06)

= 76,000,000 * 94%

= $ 71,440,000

b. Calculation of the SD (standard deviation) of the overall payoff of Bank A

Standard Deviation =

Standard Deviation =sqrt{((1-6%)*(1-(1-6%))^2)+(6%*(0-(1-6%))^2) /76

Standard Deviation = 0.0274

Hence, the SD of the overall payoff of Bank A is 0.0274 or 2.74 %.

Calculation of the SD (standard deviation) of the overall payoff of Bank B

Standard Deviation = sqrt{((1-6%)*(1-(1-6%))^2)+(6%*(0-(1-6%))^2) / 1

Standard Deviation = 0.2374

Hence, the SD of the overall payoff of Bank A is 0.2374 or 23.74 %.

Thank You...