Reading 64: Portfolio Concepts-LOS F习题精选 2010, face, security, between, market

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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) 0.0026.

C) 1.2163.

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

 

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The covariance of the market returns with the stock's returns is 0.005 and the standard deviation of the market’s returns is 0.05. What is the stock's beta?

A) 1.0.

B) 0.1.

C) 2.0.

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Beta_stock = Cov(stock,market) ÷ (σ_MKT)² = 0.005 ÷ (0.05)² = 2.0

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The covariance of the market returns with the stock's returns is 0.005 and the standard deviation of the market’s returns is 0.05. What is the stock's beta?

A) 1.0.

B) 0.1.

C) 2.0.

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Beta_stock = Cov(stock,market) ÷ (σ_MKT)² = 0.005 ÷ (0.05)² = 2.0

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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) 0.72.

C) 2.25.

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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.

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Jung Wu, CFA, uses the security market line to determine if stocks are undervalued or overvalued. Wu recently completed an analysis of Sang Tractor Supplies (STS) and derived the following forecasts for STS and for the broad market: 

• Forecasted return for STS: 10%
• Standard deviation forecasted for STS: 15%
• Expected return on the stock market index: 12%
• Standard deviation on the stock market index: 20%
• Correlation between STS and stock market index: 0.60
• Risk-free rate: 6%
  
  

To determine the fair value of STS, Wu should use the following risk value and should make the following valuation decision:

Risk value

Valuation

A) 0.45 Undervalued

B) 0.15 Overvalued

C) 0.45 Overvalued

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Wu uses the security market line as his framework of analysis. The appropriate risk measure for the security market line is the stock’s beta. The formula for beta equals:

where cov_im is the covariance between any asset i and the market index m, σ_i is the standard deviation of returns for asset i, σ_m is the standard deviation of returns for the market index, ρ_im is the correlation between asset i and the market index.

To determine the fair valuation for STS, Wu must compare his forecasted return against the equilibrium expected return using his security market line framework of analysis. The equation for the security market line is the capital asset pricing model:

E(R) = R_F + β[E(R_m) – R_F] = 0.06 + 0.45[0.12 – 0.06] = 0.087 = 8.7%.

Wu’s forecasted (10%) exceeds the equilibrium expected (or required) return for STS. Therefore, Wu should determine that STS is undervalued (should make a buy recommendation).

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

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

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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) systematic risk.

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

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