Question

Consider two local banks. Bank A has 96 loans? outstanding, each for? $1.0 million, that it...

Consider two local banks. Bank A has

96 loans? outstanding, each for? $1.0 million, that it expects will be repaid today. Each loan has a

3%

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 $96

million? outstanding, which it also expects will be repaid today. It also has a 3%

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.

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Answer #1

Overall payoff of each banks = No of Loans Outstanding * Loan Value * (1-Probability of default )

a)Overall payoff of A = 96 * 1* ( 1-3%) = 93.12 million
Overall payoff of B = 1 * 96* ( 1-3%) = 93.12 million

b) Standard deviation = [Probability of recovery * ( Complete loan recovery - actual recovery)2 + Probability of default * ( Zero recovery - actual recovery)2]0.5
standard Deviation of each loan of A() = [0.97 * ( 1- 0.97)2 + 0.03 * (0 -0.97)2]0.5 = 0.17059
Standard deviation of each because there are 96 independent loans = /N0.5 = 0.17059/(96)0.5 = 0.0174
So overall standard deviation of all 96 loans of A = 1.6704

Standard Deviation of each loan of B() = [0.97 * ( 100- 97)2 + 0.03 * (0 - 97)2]0.5 = 17.0587

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