bapswarrior

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&P500 is 0.20.
• Correlation between AAA and the S&P500 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 BBB Stock AAA

C) Stock AAA Stock BBB

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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.

bapswarrior

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.

bapswarrior

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.

AndyNZ

Janet Bellows, a portfolio manager, is attempting to explain asset valuation to a junior colleague, Bill Clay. Bellows explanation focuses on the capital asset pricing model (CAPM). Of particular interest is her discussion of the security market line (SML), and its use in security selection.
Bellows begins with a short review of the capital asset pricing model, including a discussion about its assumptions regarding transaction costs, taxes, holding periods, return requirements, and borrowing and lending at the risk-free rate.
Bellows then illustrates the SML, and explains how changes in the expected market return and the risk-free rate affect the line. In an effort to learn whether Clay understands the concepts she has explained to him, Bellows decides to test Clay’s knowledge of valuation using the CAPM.
Bellows provides the following information for Clay:

• The risk-free rate is 7%.
• The market risk premium during the previous year was 5.5%.
• The standard deviation of market returns is 35%.
• This year, the market risk premium is estimated to be 7%.
• Stock A has a beta of 1.30 and is expected to generate a 15.5% return.
• The covariance of Stock B with the market is 0.18.
• The standard deviation of Stock B’s returns is 41%.

Using this information, Clay must calculate expected stock returns and betas. Bellows especially wants to know Stock A’s required return, and whether or not the stock is a good buy.
Bellows then proposes a hypothetical situation to Clay: The stock market is expected to return 12.5% next year. Clay questions that return estimate in the context of the data listed above, and Bellows responds with four possible explanations for the estimate:

• The estimated risk premium is incorrect.
• Interest rates are likely to fall 1.5% over the next year.
• Given the data above, the return estimate is correct.
• The market beta is expected to rise over the next year.

Then Bellows provides Clay with the following information about Ohio Manufacturing, Texas Energy, and Montana Mining:

Stock	Ohio	Texas	Montana
Beta	0.50	XX%	1.50
Required Return	10.5%	11.0%	XX%
Expected Return	12.0%	10.0%	15.0%
Expected S&P 500 return	14.0%

Clay has been tasked with providing an investment recommendation on the three stocks.
Based on the stock and market data provided above, which of the following data regarding Stock A is most accurate?

Required 12-month return

Investment advice

A) 16.1% Buy

B) 14.15% Buy

C) 16.1% Sell

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ERstock = Rf + βstock (ERM − Rf). = 7% + 1.3 (14% − 7%) = 16.1%.The market risk premium for the upcoming year should be used in the calculation. Stock A’s required return is higher than its expected return, and as such the stock plots below the security market line. Stock A should be sold, not bought. (Study Session 18, LOS 60.f)

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The beta of Stock B is closest to:

A) 1.07.

B) 0.51.

C) 1.47.

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Beta = (covariance of stock B with the market) / (variance of the market portfolio)
= 0.18 / (0.35)2 = 1.47.
(Study Session 18, LOS 60.f)

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Which of the following represents the best investment advice?

A) Buy Montana and Texas because their required return is lower than their expected return.

B) Avoid Texas because its expected return is lower than its required return.

C) Buy Montana because it is expected to return more than Texas, Ohio, and the market portfolio.

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We can use the security market line (SML) to estimate the required return or beta on the various securities, and compare this with the expected returns.
The SML looks like this: E(r) = Rrf + β (RPM).
Since Montana’s beta is 1.50: 7.0 + 1.50(7.0) = 17.5% = the required return. Because Montana’s expected return is 15%, and the required return is 17.5%, Montana should not be purchased. Note that this is true even though Montana’s expected return is more than the other stocks and the market: it is not enough to compensate for the level of market risk assumed by holding the stock.
Texas’ required return = 11.0 = 7.0 + β(7.0), so β = (4/7) = 0.57. However, its expected return is less than the required return, so regardless of the beta value, Texas should not be purchased.
Ohio’s required return is given as 10.5, and the expected return is 12.0. Hence, Ohio is a buy. (Study Session 18, LOS 60.f)

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Assuming the market return estimate of 12.5% is accurate, which of the following statements is the best explanation for the estimate?

A) The estimated risk premium is incorrect.

B) Interest rates are likely to fall 1.5% over the next year.

C) Given the data above, the return estimate is correct.

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The expected return on the market during the upcoming year is 14% (7% risk-free rate plus the expected 7% market risk premium). As such, the 12.5% estimate does not match the data. The most rational justification for a lower expected return is an error in the estimated risk premium. Falling interest rates may boost expected stock returns, but the current rate is the most relevant to the projected market return for the upcoming year. (Study Session 18, LOS 60.f)

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With regard to the capital asset pricing model, relaxing assumptions about:

A) risk free borrowing and lending rates results in a lower intercept and steeper slope.

B) taxes will reduce differences between the capital market lines of different investors.

C) homogeneous expectations will result in the SML appearing more as a band instead of a line.

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Taxes change investors’ return expectations. Considering different marginal tax rates will result in a vast array of different after-tax requirements, leading to a vast array of CMLs and SMLs for different investors. The assumption of no transaction costs allows investors to make a profit even if a stock is just slightly off the SML. If risk-free borrowing and lending does not exist, then a portfolio of risky securities must be created such that the portfolio beta equals zero. The zero-beta portfolio is similar to the risk-free asset in that both have zero betas, but they differ in that the zero-beta portfolio has a non-zero standard deviation. The expected return on the zero-beta portfolio exceeds the risk-free rate therefore the SML will now have a higher intercept and a flatter slope. (Study Session 18, LOS 60.f)

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If the market risk premium decreases by 1%, while the risk-free rate remains the same, the security market line:

A) becomes steeper.

B) parallel-shifts downward.

C) becomes flatter.

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Since the security market line runs from the risk-free rate (RFR) through the market return, holding the RFR constant and decreasing the market risk premium will cause the SML to become flatter. (Study Session 18, LOS 60.f)

AndyNZ

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 covim is the covariance between any asset i and the market index m, σi is the standard deviation of returns for asset i, σm is the standard deviation of returns for the market index, ρim 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) = RF + β[E(Rm) – RF] = 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).

AndyNZ

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) 2.25.

B) 1.65.

C) 0.72.

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BetaH = 0.23 / (0.32)2 = 2.25
Hamburg stock is, on average, more than twice as volatile as the market.

AndyNZ

Which of the following statements regarding beta is least accurate?

A) The market portfolio has a beta of 1.

B) A stock with a beta of zero will tend to move with the market.

C) Beta is a measure of systematic risk.

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A stock with a beta of 1 will tend to move with the market. A stock with a beta of 0 will tend to move independently of the market.

AndyNZ

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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Betastock = Cov(stock,market) ÷ (σMKT)2 = 0.005 ÷ (0.05)2 = 2.0

AndyNZ

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) 1.2163.

B) 0.8222.

C) 0.0026.

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Beta = Cov(RA,RM) / Var(RM) = 0.05634/0.04632 = 1.2163.

AndyNZ

Answer the following three questions based on the information in the table shown below for the risk-free security, market portfolio, and stocks A, B, and C. Their respective betas and forecasted returns based on fundamental analysis of the economy, industry, and specific company analysis are also provided.

Stock	Beta	F(R)
A	0.5	0.065
B	1.0	0.095
C	1.5	0.115
Risk-free	0.0	0.030
Market	1.0	0.090

Based on the information in the above table, the expected returns for stocks A, B, and C for a risk-averse investor are:

A

B

C

A) 4.5% 9.0% 13.5%

B) 6.0% 9.0% 12.0%

C) 6.5% 9.5% 11.5%

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The expected rate of return for any individual security or portfolio can be calculated using the capital asset pricing model (CAPM):

E(R) = rf + Bi(RM – rf)

Expected rate of return for A = 0.03 + 0.5(0.09 – 0.03) = 0.03 + 0.03 = 0.06 or 6.0%.
Expected rate of return for B = 0.03 + 1.0(0.09 – 0.03) = 0.03 + 0.06 = 0.09 or 9.0%.
Expected rate of return for C = 0.03 + 1.5(0.09 – 0.03) = 0.03 + 0.09 = 0.12 or 12.0%.

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Based on the information in the above table, which of the stocks should be held long in a well-diversified portfolio?

A) A, B, and C.

B) Both A and B.

C) A only.

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The first step is to calculate the expected rate of return for each security using the capital asset pricing model (CAPM):

E(R) = rf + Bi(RM – rf).

Expected rate of return for A = 0.03 + 0.5(0.09 – 0.03) = 0.03 + 0.03 = 0.06 or 6.0%.
Expected rate of return for B = 0.03 + 1.0(0.09 – 0.03) = 0.03 + 0.06 = 0.09 or 9.0%.
Expected rate of return for C = 0.03 + 1.5(0.09 – 0.03) = 0.03 + 0.09 = 0.12 or 12.0%.The next step is to compare the forecasted return (FR) for each security with the expected return.

• If the forecasted return is greater than the expected return, then the stock is under-priced and should be included in the portfolio.
• If the FR is less than the expected return, then the security is over-priced and should not be included in the portfolio.

The forecasted returns for stocks A and B are greater than their expected returns. Therefore, both A and B should be included in the portfolio and not stock C.

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Based on the information in the above table, which stocks are currently in equilibrium?

A) Stocks A and B are in equilibrium.

B) None of the stocks are in equilibrium.

C) All of the stocks are in equilibrium.

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Stocks in equilibrium are properly priced and will lie on the security market line. The forecasted return for the individual security will equal the expected return based on the CAPM. The first step is to calculate the expected rate of return for each security using the CAPM:

E(R) = rf + Bi(RM − rf).

Expected rate of return for A = 0.03 + 0.5(0.09 − 0.03) = 0.03 + 0.03 = 0.06 or 6.0%.
Expected rate of return for B = 0.03 + 1.0(0.09 − 0.03) = 0.03 + 0.06 = 0.09 or 9.0%.
Expected rate of return for C = 0.03 + 1.5(0.09 − 0.03) = 0.03 + 0.09 = 0.12 or 12.0%.
Based on the expected returns given in Table 1 and the calculated required returns for stocks A, B, and C, none of the stocks are in equilibrium.