Suppose that, as an owner of a federally insured S&L in the 1980s, the price of real estate falls, and most of your loans go into default. In fact, so many loans go into default that the net worth of the S&L is negative ($5 million). Federal regulators haven’t realized this yet, but they will shortly. As a last-ditch attempt to save the bank, you attract $1 million in new deposits with very generous interest rates to depositors. You have two possible investments you can make with the $1 million. You can invest in the stock market, which will pay $4 million with probability 0.5 and $2 million with probability 0.5. Alternatively, you can invest in junk bonds, which pay off $10 million with probability 0.1 and $0.5 million with probability 0.9.
a. Which investment has the highest expected value to an ordinary investor? Show your calculations
b. Which investment has the highest expected value to you, the S&L owner? Show your calculations. [Hint: Federal deposit insurance limits an S&L's losses to zero.]