Problem
Investor Corporation (IC) has $100 million to invest. It is considering two types of investments. One investment is perfectly safe and will yield a return of 5% after one year. The second investment is a one-year project which has an 80% chance of yielding a return of 20% but a 20% chance of being a total loss.
1. IC wants to maximize the expected return. How much will it invest in each of the two investments? Explain fully.
2. Suppose that IC discovers that the risky investment is covered by a government incentive program (which costs IC nothing) under which the government would repay IC's original investment if the project is a total loss. Now how much will IC invest in each type of investment? Explain.
3. Suppose instead that the government guarantee program pays only a fraction x of IC's original investment if the project fails. What is the minimum value of x necessary to induce IC to invest in the risky project?
4. Answer question (3) for the case where IC's management tries to maximize not the expected return, but the expected value of √w, where W is the amount of money (in millions of dollars) the bank has in its investment account at the end of one year.