Use the following information to answer the problem(s)below.
Consider two banks.Bank A has 1000 loans outstanding each for $100,000,that it expects to be fully repaid today.Each of Bank A's loans have a 6% probability of default,in which case the bank will receive $0 for each of the defaulting loans.Bank B has 100 loans of $1 million outstanding,which it also expects to be fully repaid today.Each of Bank B's loans have a 5% probability of default,in which case the bank will receive $0 for each of the defaulting loans.The chance of default is independent across all the loans.
-The standard deviation of the overall payoff to Bank A is closest to:
A)$689,000.
B)$751,000.
C)$2,179,000.
D)$2,375,000.

Question

Quizplus · Accepted Answer

The expected payoff for Bank A is $100,000(1-0.06)=$94,000 per loan.
The expected payoff for Bank B is $1,000,000(1-0.05)=$950,000 per loan.
The overall expected payoff for Bank A is $94,000(1000)=$94,000,000.
The overall expected payoff for Bank B is $950,000(100)=$95,000,000.
The standard deviation of the overall payoff for Bank A is:
sqrt(1000) * sqrt(0.06*0.94*(100,000)^2)= $751,224.96.
Thus, the closest choice to the standard deviation of the overall payoff for Bank A is B) $751,000.

Use the Following Information to Answer the Problem(s)below