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Part $1$

Consider two local banks. Bank A has

$8080$

loans$$ outstanding, each for

$$$$1\mathrm{.}11\mathrm{.}1$

$$million$,$ that it expects will be repaid today. Each loan has a

$4\%4\%$

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

$ $88$$$88$

million$$ outstanding, which it also expects will be repaid today. It also has a

$4\%4\%$

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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Part $1$

a$.$ The expected overall payoff of each bank.

The expected overall payoff of Bank A is

$$$$84\mathrm{.}4884\mathrm{.}48$

million. $($Round to two decimal$$ places.$)$

Part $2$

The expected overall payoff of Bank B is

$$$$84\mathrm{.}4884\mathrm{.}48$

million. $($Round to two decimal$$ places.$)$

Part $3$

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

The standard deviation of the overall payoff of Bank A is

$$$$1\mathrm{.}931\mathrm{.}93$

million. $($Round to four decimal$$ places.$)$

Part $4$

The standard deviation of the overall payoff of Bank B is

$$$$17\mathrm{.}2517\mathrm{.}25$

million. $($Round to four decimal$$ places.$)$