Suppose you have just inherited $\$ 10,500$ and are considering the following options for investing the money to maximize your return:
Option 1: Hold the money in cash and earn zero
return
Option
$\mathbf{2}:$ Loan the money to one of your friend's roommates, Mike, at an agreed-upon interest rate of $8 \%$, even though you believe there is a $7 \%$ chance that Mike will leave town without
repaying you.
Option 3: Invest the money in a corporate bond with a stated return of $5 \%$, although there is a $10 \%$ chance the company could go bankrupt.
Option 4: Put the money in an interest-bearing checking account that earns $2 \%$. The FDIC insures the account against bank failure.
a. If you are risk-neutral (that is, neither seek out nor shy away from risk $),$ which of the four options should you choose to maximize your expected return? (Hint: To calculate the expected return of an outcome, multiply the probability that an event will occur by the outcome of that event.)
b. Suppose Option 2 is your only possibility. If you could pay your friend $\$ 150$ to find out extra information about Mike that would indicate with
certainty whether he will leave town without paying, would you pay the $\$ 150 ?$ What does this say about the value of better information regarding risk?