Chapter 2: Q16I. (page 226)
If the simple CAPM is valid, which of the situations in Problems 13 – 19 below are possible? Explain. Consider each situation independently.
The correct answer would be: “Not Possible”
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If the APT is to be a useful theory, the number of systematic factors in the economy must be small. Why?
Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 30%.
Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3%, and one-half have an alpha of - 3%. The analyst then buys \(1 million of an equally weighted portfolio of the positive-alpha stocks and sells short \)1 million of an equally weighted portfolio of the negative-alpha stocks.
a. What is the expected profit (in dollars), and what is the standard deviation of the analyst’s profit?
b. How does your answer change if the analyst examines 50 stocks instead of 20? 100 stocks?
You are a consultant to a large manufacturing corporation considering a project with the following net after-tax cash flows (in millions of dollars):
| YEARS FROM NOW | After-Tax CF |
| 0 1-9 10 | -20 10 20 |
The project’s beta is 1.7. Assuming r f = 9% and E ( r M ) = 19%, what is the net present value of the project? What is the highest possible beta estimate for the project before its NPV becomes negative?
You know that firm XYZ is very poorly run. On a scale of 1 (worst) to 10 (best), you would give it a score of 3. The market consensus evaluation is that the management score is only 2. Should you buy or sell the stock?
You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest \(60,000 of her portfolio in your equity fund and \)40,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client’s portfolio?
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