Suppose you have $10,000 to invest. A broker phones you with some information you requested on certain junk bonds. If the company issuing the bonds posts a profit this year, it will pay you a 40 percent interest rate on the bond. If the company files for bankruptcy, you will lose all you invested. If the company breaks even, you will earn a 10 percent interest rate. Your broker tells you there is a 50 percent chance that they will break even and a 20 percent chance that the company will file for bankruptcy. Your other option is to in-vest in a risk- free government bond that will guarantee 8 percent interest for 1 year.
a. What is the expected interest rate for the junk bond investment?
b. Which investment will you choose if your utility function is given by U = M2?
c. Which investment will you choose if your utility function is given by U = √M?