Question

Suppose a bank has $100 million of assets to invest in either risky or safe investments. The first option is to put all assets in the safe investment, which will result in a 5% return and yield $105 one year from now. A second option is to put all the assets in the risky option, which will result in either a 50% return ($150 million) or a 40% loss ($60 million) with equal probability. A third option is to split the investments and put $50 million into each option. If we consider the possibility of bank losses being insured, which option maximizes the expected value of the bank’s investments? Group of answer choices

a. The safe option yields a higher expected value, but if losses are insured, the bank will maximize its expected value by choosing either the second or the third option.

b. Each option yields the same expected value, but if losses are insured, the bank will maximize its expected value by choosing either the second or the third option.

c. Each option yields the same expected value, but if losses are insured, the bank will maximize its expected value by putting all of its assets in the second (risky) option.

d. The third option maximizes the bank’s expected value whether bank losses are insured or not.

Answer 1

Option b (Each option yields the same expected value, but if losses are insured, the bank will maximize its expected value by choosing either the second or the third option.) is correct.

Reason: From all the options, the expected return is $105 but if losses are insured bank may choose second or third option.

Expected value of first option is $105.

Expected value of second option is as follows:

Expected value of third option is as follows: