Reading 66: Portfolio Concepts-LOS f 习题精选 values, market, center, security, 2011

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Session 18: Portfolio Management: Capital Market Theory and the Portfolio Management Process
Reading 66: Portfolio Concepts

LOS f: Discuss the security market line (SML), the beta coefficient, the market risk premium, and the Sharpe ratio, and calculate the value of one of these variables given the values of the remaining variables.

 

 

The covariance between stock A and the market portfolio is 0.05634. The variance of the market is 0.04632. The beta of stock A is:

A) 0.8222.

B) 1.2163.

C) 0.0026.

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Beta = Cov(R_A,R_M) / Var(R_M) = 0.05634/0.04632 = 1.2163.

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Kaskin, Inc., stock has a beta of 1.2 and Quinn, Inc., stock has a beta of 0.6. Which of the following statements is most accurate?

A) The stock of Kaskin, Inc., has more total risk than Quinn, Inc.

B) The stock of Quinn, Inc., has more systematic risk than that of Kaskin, Inc.

C) The expected rate of return will be higher for the stock of Kaskin, Inc., than that of Quinn, Inc.

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Beta is a measure of systematic risk. Since only systematic risk is rewarded, it is safe to conclude that the expected return will be higher for Kaskin’s stock than for Quinn’s stock.

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Glimmer Glass has a correlation of 0.67 with the market portfolio, a variance of 23%, and an expected return of 14%. The market portfolio has an expected return of 11% and a variance of 13%. Glimmer stock is approximately:

A) 11% less volatile than the average stock.

B) 4% more volatile than the average stock.

C) 19% more volatile than the average stock.

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Beta is equal to the covariance divided by the market portfolio variance, or the product of the correlation and the ratio of the stock standard deviation to the market standard deviation. To derive the standard deviation, we take the square root of the variance. So beta = 0.67 × 0.479583 / 0.360555 = 0.891183. Glimmer shares are about 11% less volatile than the average stock.

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Which of the following statements about using the capital asset pricing model (CAPM) to value stocks is least accurate?

A) If the CAPM expected return is too low, then the asset’s price is too high.

B) The CAPM reflects unsystematic risk using standard deviation.

C) The model reflects how market forces restore investment prices to equilibrium levels.

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The capital asset pricing model assumes all investors hold the market portfolio, and as such unsystematic risk, or risk not related to the market, does not matter. Thus, the CAPM does not reflect unsystematic risk and does not rely on standard deviation as the measure of risk but instead uses beta as the measure of risk. The remaining statements are accurate.

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The capital market line:

A) helps determine asset allocation.

B) uses nondiversifiable risk.

C) has a slope equal to the market risk premium.

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The purpose of the CML is to determine the percentages allocated to the market portfolio and the risk-free asset. Both remaining answers reflect characteristics of the security market line.

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What is the expected rate of return for a stock that has a beta of 1.0 if the expected return on the market is 15%?

A) More than 15%.

B) Cannot be determined without the risk-free rate.

C) 15%.

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The expected return of a stock with a beta of 1.0 must, on average, be the same as the expected return of the market which also has a beta of 1.0.

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How are the capital market line (CML) and the security market line (SML) similar?

A) The CML and SML use the standard deviation as a risk measure.

B) The market portfolio will plot directly on the CML and the SML.

C) The CML and SML can be used to find the expected return of a portfolio.

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All portfolios will plot on the SML. The only portfolio that will plot on the CML is the market portfolio, because it is perfectly diversified.

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The security market line (SML) is a graphical representation of the relationship between return and:

A) unsystematic risk.

B) systematic risk.

C) total risk.

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The SML graphically represents the relationship between return and systematic risk as measured by beta.

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Rachel Stephens, CFA, examines data for two computer stocks, AAA and BBB, and derives the following results:

• Standard deviation for AAA is 0.50.
• Standard deviation for BBB is 0.50.
• Standard deviation for the S&500 is 0.20.
• Correlation between AAA and the S&500 is 0.60.
• Beta for BBB is 1.00.

Stephens is asked to identify the stock that has the highest systematic risk and the stock that has the highest unsystematic risk. Stephens should draw the following conclusions:

Highest Systematic Risk

Highest Unsystematic Risk

A) Stock AAA Stock AAA

B) Stock AAA Stock BBB

C) Stock BBB Stock AAA

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First, compare the betas for the two stocks. The beta for AAA can be derived with the formula:

Therefore, AAA has larger beta and greater systematic risk than stock BBB which has a beta equal to 1. To assess the unsystematic risk, note that total risk is measured by the standard deviation. Note that the standard deviations for AAA and BBB are identical. Therefore, AAA and BBB have identical total risk. Moreover, note that:

total risk = systematic risk + unsystematic risk.

We have already concluded that both stocks have identical total risk and that AAA has greater systematic risk. Therefore, BBB must have higher unsystematic risk.

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What is the beta of Hamburg Corp.’s stock if the covariance of the stock with the market portfolio is 0.23, and the standard deviation of the market returns is 32%?

A) 1.65.

B) 2.25.

C) 0.72.

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Beta_H = 0.23 / (0.32)² = 2.25

Hamburg stock is, on average, more than twice as volatile as the market.