Assignment #3: Portfolio Theory, CAPM, and Efficient Markets

1. There are two stocks in the market, stock A and stock B. The price of stock A today is $75. The price of stock A next year will be $63 if the economy is in a recession, $83 if the economy is normal, and $96 if the economy is expanding. The probabilities of recession, normal times, and expansion are .2, .6, and .2, respectively. S t o c k A pays no dividends and has a correlation of .8 with the market portfolio. Stock B has an expected return of 13 percent, a standard deviation of 34 percent, a correlation with the market portfolio of .25, and a correlation with stock A of .48. The market portfolio has a standard deviation of 18 percent. Assume the CAPM holds.

a. If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? Why?

b. What are the expected return and standard deviation of a portfolio consisting of 70 percent of stock A and 30 percent of stock B?

c. What is the beta of the portfolio in part (b)?

2. A portfolio that combines the risk-free asset and the market portfolio has an expected return of 9 percent and a standard deviation of 13 percent. The risk-free rate is 5 percent, and the expected return on the market portfolio is 12 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .45 correlation with the market portfolio and a standard deviation of 40 percent?

3. Suppose the market is semi-strong form efficient. Can you expect to earn excess returns if you make trades based on:

a. Your broker’s information about record earnings for a stock? Explain.

b. Rumors about a merger of a firm? Explain.

c. Yesterday’s announcement of a successful new product test? Explain.

4. A company has changed how it accounts for inventory. Taxes are unaffected, although the resulting earnings report released this quarter is 20% higher than what it would have been under the old accounting system. There is no other surprise in the earnings report, and the change in the accounting treatment was publicly announced earlier. Assume market efficiency. Will the stock price be higher when the firm releases the earnings report? Explain.

5. Which of the following statements are true about the efficient market hypothesis? Please explain your reasoning for each statement.

a. It implies perfect forecasting ability.

b. It implies that prices reflect some set of information.

c. It implies an irrational market.

d. It implies that prices do not fluctuate.

e. It results from keen competition among investors.

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