Question

You are currently in debt $10,000 to your bank for getting a loan to pay for your house. The bank charges you 5% interest annually on the debt outstanding. You have $5000 of cash, which you are either going to invest in the stock market, or to pay to the bank to lower your debt. You esteem that if you invest in the stock market, the $5000 investment has 10% chance to drop to $4,000 60% chance to increase to $5400 30% chance to increase to $6000 What is the annual expected return for the investment in the stock market? If you are risk-neutral, would you be better off it you paid the bank to reduce your debt, or invested in the market?

Answer 1

The annual expected return for the investment of 5000 in the stock market:

E(X) =0.10(4000 - 5000)+0.60(5400 - 5000)+0.30(6000-5000) =0.10(-1000)+0.60(400)+0.30(1000) = -100 + 240 + 300 =$440​​​​​​

Annual reduction in interest for debt if 5000 is paid for debt:​​​​​​

0.05(10000 - 5000) =0.05(5000) =$250​​​​​​

Thus, as a risk neutral person, I would invest in the stock market because the expected return, E(X) > reduction in interest for debt (440 > 250).