Allen must decide whether to invest $10,000 in the stock market or in a certificate of deposit (CD) at an interest rate of 9%. If the market is good , he believes that he could get a 14% return on his money. With a fair market, he expects to get an 8% return. If the market is bad, he will most likely get no return at all-in other words, the return would be 0%,. Allen estimates hat the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2, and he wishes to maximaize his long-run average return. (a) Develop a decision table for this problem. (b) What is the best decision?
(a) Decision table:
| Decision | Return (Good Market) | Return (Fair Market) | Return (Bad Market) |
|:----------------------:|:-------------------:|:--------------------:|:-------------------:|
| Invest in Stock | $1,400 | $800 | $0 |
| Invest in Certificate | $900 | $900 | $900 |
(b) To determine the best decision, we need to calculate the expected return for each option.
Expected Return for Investing in Stock:
E(stock) = (Return in Good Market x Probability of Good Market) + (Return in Fair Market x Probability of Fair Market) + (Return in Bad Market x Probability of Bad Market)
E(stock) = ($1,400 x 0.4) + ($800 x 0.4) + ($0 x 0.2)
E(stock) = $560 + $320 + $0
E(stock) = $880
Expected Return for Investing in Certificate of Deposit:
E(CD) = (Return in Good Market x Probability of Good Market) + (Return in Fair Market x Probability of Fair Market) + (Return in Bad Market x Probability of Bad Market)
E(CD) = ($900 x 0.4) + ($900 x 0.4) + ($900 x 0.2)
E(CD) = $360 + $360 + $180
E(CD) = $900
Comparing the two expected returns, we can see that investing in the Certificate of Deposit (CD) offers a higher expected return of $900, compared to $880 from investing in the stock market. Therefore, the best decision in order to maximize the long-run average return is to invest $10,000 in the Certificate of Deposit.
(a) To develop a decision table for this problem, we can consider the three possible market conditions: good, fair, and bad. We'll analyze the potential returns and calculate the expected returns for each decision.
Decision Table:
```
| Market Condition | Stock Market | Certificate of Deposit |
|------------------|--------------|-----------------------|
| Good | 14% | 9% |
| Fair | 8% | 9% |
| Bad | 0% | 9% |
```
(b) To determine the best decision, we need to calculate the expected return for each option.
Expected Return for Investing in the Stock Market:
Expected return = (Probability of good market * Return in good market) + (Probability of fair market * Return in fair market) + (Probability of bad market * Return in bad market)
Expected return = (0.4 * 14%) + (0.4 * 8%) + (0.2 * 0%)
Expected return = 5.6% + 3.2% + 0%
Expected return = 8.8%
Expected Return for Investing in the Certificate of Deposit:
Expected return = (Probability of good market * Return in good market) + (Probability of fair market * Return in fair market) + (Probability of bad market * Return in bad market)
Expected return = (0.4 * 9%) + (0.4 * 9%) + (0.2 * 9%)
Expected return = 3.6% + 3.6% + 1.8%
Expected return = 9%
Comparison:
- Expected return for investing in the stock market = 8.8%
- Expected return for investing in the certificate of deposit = 9%
Based on the comparison, the best decision is to invest in the certificate of deposit, as it offers a higher expected return of 9% compared to the stock market's expected return of 8.8%.