Question

Consider two local banks. Bank A has 95 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 $95 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.

a. The expected overall payoff of each bank.

The expected overall payoff of Bank A is ________million. (Round to the nearest integer.)

The expected overall payoff of Bank B is ________million. (Round to the nearest integer.)

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

The standard deviation of the overall payoff of Bank A is _____ (Round to two decimal places.)

The standard deviation of the overall payoff of Bank B is ______ (Round to two decimal places.)

Answer 1

Answer a

Expected payoff is the same for both banks;

Bank A

Expected payoff = ($1 million x 0.94) x 95

                        = $89.3million

Bank B

Expected payoff = $95 million x 0.94

                        = $89.3 million

Answer b

Bank A

Variance of each loan = (1- 0.893)² x 0.893 + (0 - 0.893)² x 0.06

                                = 0.05807

Standard Deviation of each loan =

                                               = 0.24098

Now the bank has 95 loans that are all independent of each other so the standard deviation of the average loan is;

                                = 0.24098 /

                                = 0.0247

But the bank has 100 such loans so the standard deviation of the portfolio is,

                                = 95 x 0.0247

                                = 2.35

Bank B

               Variance = (100 - 89.3)² x 0.893 + (0 - 89.3)² x 0.06

                            = 580.71

Standard Deviation =

                          = 24.10