Suppose that, as an owner of a federally insured S&L in the 1980s, the price of
ID: 2736305 • Letter: S
Question
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. 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.]
Explanation / Answer
Investment amount = $ 1 million
Option 1: invest in the stock market, which will pay $4 million with probability 0.5 and $2 million with probability 0.5
Expected value from option 1= payoff 1 * probability + payoff 2 * probability
= $ 4 million * 0.5 + $ 2 million * 0.5
= $ 2 million + $ 1 million = $ 3 million
Option 2: invest in junk bonds, which pay off $10 million with probability 0.1 and $0.5 million with probability 0.9
Expected value from option 2 = payoff 1 * probability + payoff 2 * probability
= $ 10 million * 0.1 + $ .5 million * 0.9
= $ 1 million + $ 0.45 million = $ 1.45 million
Expected value from option 1 is $ 3 million
Expected value from option 2 is $ 1.45 million
Therefore the investment in option 1 has the highest expected value to the S&L owner, which is $ 3 Million.
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