Chapter 2: Question 3B (page 258)
If prices are as likely to increase as decrease, why do investors earn positive returns from the market on average?
Over a long period, there is an expected upward drift in stock prices.
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Karen Kay, a portfolio manager at Collins Asset Management, is using the capital asset pricing model for making recommendations to her clients. Her research department has developed the information shown in the following exhibit.
a. Calculate expected return and alpha for each stock.
b. Identify and justify which stock would be more appropriate for an investor who wants to:
i. Add this stock to a well-diversified equity portfolio.
ii. Hold this stock as a single-stock portfolio.
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?
An analyst estimates that a stock has the following probabilities of return depending on the state of the economy. What is the expected return of the stock?
Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model:
a. What is the expected return on the market portfolio?
b. What would be the expected return on a zero-beta stock?
c. Suppose you consider buying a share of stock at a price of \(40. The stock is expected to pay a dividend of \)3 next year and to sell then for $41. The stock risk has been evaluated atβ= - .5. Is the stock overpriced or underpriced?
Suppose investors believe that the standard deviation of the market-index portfolio has increased by 50%. What does the CAPM imply about the effect of this change on the required rate of return on Google’s investment projects?
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