Chapter 9 - The Capital Asset Pricing Model
9. d. [You need to know the risk-free rate]
10. Under the CAPM, the only risk that investors are compensated for bearing is the
risk that cannot be diversified away (systematic risk). Because systematic risk (measured by beta) is equal to 1.0 for both portfolios, an investor would expect the same rate of return from both portfolios A and B. Moreover, since both portfolios are well diversified, it doesn’t matter if the specific risk of the individual securities is high or low. The firm-specific risk has been diversified away for both portfolios.
11. a. McKay should borrow funds and invest those funds proportionately in
Murray’s existing portfolio (i.e., buy more risky assets on margin). In addition to increased expected return, the alternative portfolio on the capital market line will also have increased risk, which is caused by the higher proportion of risky assets in the total portfolio.
b. McKay should substitute low-beta stocks for high-beta stocks in order to
reduce the overall beta of York’s portfolio. By reducing the overall portfolio beta, McKay will reduce the systematic risk of the portfolio and, therefore, reduce its volatility relative to the market. The security market line (SML) suggests such action (i.e., moving down the SML), even though reducing beta may result in a slight loss of portfolio efficiency unless full diversification is maintained. York’s primary objective, however, is not to maintain efficiency but to reduce risk exposure; reducing portfolio beta meets that objective. Because York does not want to engage in borrowing or lending, McKay cannot reduce risk by selling equities and using the proceeds to buy risk-free assets (i.e., lending part of the portfolio).
12. a.
Expected Return Alpha Stock X 5% + 0.8 × (14% ? 5%) = 12.2% 14.0% ? 12.2% = 1.8% Stock Y 5% + 1.5 × (14% ? 5%) = 18.5% 17.0% ? 18.5% = ?1.5%
b. i. Kay should recommend Stock X because of its positive alpha, compared to
Stock Y, which has a negative alpha. In graphical terms, the expected return/risk profile for Stock X plots above the security market line (SML), while the profile for Stock Y plots below the SML. Also, depending on the individual risk preferences of Kay’s clients, the lower beta for Stock X may have a beneficial effect on overall portfolio risk.
ii. Kay should recommend Stock Y because it has higher forecasted return and lower standard deviation than Stock X. The respective Sharpe ratios for Stocks X and Y and the market index are:
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McGraw-Hill Education.
Chapter 9 - The Capital Asset Pricing Model
Stock X: Stock Y:
(14% ? 5%)/36% = 0.25 (17% ? 5%)/25% = 0.48
Market index: (14% ? 5%)/15% = 0.60
The market index has an even more attractive Sharpe ratio than either of the individual stocks, but, given the choice between Stock X and Stock Y, Stock Y is the superior alternative.
When a stock is held as a single stock portfolio, standard deviation is the
relevant risk measure. For such a portfolio, beta as a risk measure is irrelevant. Although holding a single asset is not a typically recommended investment strategy, some investors may hold what is essentially a single-asset portfolio when they hold the stock of their employer company. For such investors, the relevance of standard deviation versus beta is an important issue.
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Copyright ? 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.