Question

An investor considers investing $10,000 in the stock market. He believes that the probability is 0.30 that the economy will improve, 0.40 that it will stay the same, and 0.30 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $15,000, but it can also go down to $8,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $10,000.a. What is the expected value of his investment?b. Should he invest the $10,000 in the stock market if he is risk neutral?c. Is the decision clear-cut if he is risk averse? Explain.

Answer 1

a. What is the expected value of his investment?

• $10,900

b. Should he invest the $10,000 in the stock market if he is risk neutral?

• If the investor is risk neutral, then he pays little attention to market risk, therefore, he/she should invest because the expected value is higher than the investment.

c. Is the decision clear-cut if he is risk averse?

• If the investor is risk averse, it means that he/she is afraid of market risk and likes to make decisions that involve the least possible risk. In this case, the possibility of losing money is not that large (in my opinion) and the expected value is relatively high, but a risk averse investor would probably prefer an investment that yields a lower rate but is more secure, e.g. US securities.

Step-by-step explanation:

total investment $10,000

• if economy improves = 0.30 x $15,000 = $4,500
• if economy remains the same = 0.40 x $10,000 = $4,000
• if economy deteriorates = 0.30 x $8,000 = $2,400

total expected value = $10,900