Reading 51: An Introduction to Asset Pricing Models LOS e习题 2010, available, following, expected, properly

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LOS e: Calculate, using the SML, the expected return on a security and evaluate whether the security is overvalued, undervalued, or properly valued.

The following information is available for the stock of Park Street Holdings:

• The price today (P₀) equals $45.00.
• The expected price in one year (P₁) is $55.00.
• The stock's beta is 2.31.
• The firm typically pays no dividend.
• The 3-month Treasury bill is yielding 4.25%.
• The historical average S& 500 return is 12.5%.

Park Street Holdings stock is:

A) undervalued by 3.7%.

B) overvalued by 1.1%.

C) undervalued by 1.1%.

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To determine whether a stock is overvalued or undervalued, we need to compare the expected return (or holding period return) and the required return (from Capital Asset Pricing Model, or CAPM).

Step 1: Calculate Expected Return (Holding period return):

The formula for the (one-year) holding period return is:

HPR = (D₁ + S₁ – S₀) / S₀, where D = dividend and S = stock price.

Here, HPR = (0 + 55 – 45) / 45 = 22.2%

Step 2: Calculate Required Return:

The formula for the required return is from the CAPM:

RR = R_f + (ER_M – R_f) × Beta
RR = 4.25% + (12.5 – 4.25%) × 2.31 = 23.3%.

Step 3: Determine over/under valuation:

The required return is greater than the expected return, so the security is overvalued.
The amount = 23.3% ? 22.2% = 1.1%.

 

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Which of the following statements about portfolio management is most accurate?

A) The security market line (SML) measures systematic and unsystematic risk versus expected return; the CML measures total risk.

B) Combining the capital market line (CML) (risk-free rate and efficient frontier) with an investor's indifference curve map separates out the decision to invest from the decision of what to invest in.

C) As an investor diversifies away the unsystematic portion of risk, the correlation between his portfolio return and that of the market approaches negative one.

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Combining the CML (risk-free rate and efficient frontier) with an investor’s indifference curve map separates out the decision to invest from what to invest in and is called the separation theorem. The investment selection process is thus simplified from stock picking to efficient portfolio construction through diversification.

The other statements are false. As an investor diversifies away the unsystematic portion of risk, the correlation between his portfolio return and that of the market approaches positive one. (Remember that the market portfolio has no unsystematic risk). The SML measures systematic risk, or beta risk.

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The essence of the capital asset pricing model (CAPM) is embodied in which of the following equations?

A) The security market line (SML).

B) Both the security market line (SML) and the capital market line (CML) as they are both the same equation.

C) The capital market line (CML).

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The SML equation represents the essence of the CAPM.

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The expected market premium is 8%, with the risk-free rate at 7%. What is the expected rate of return on a stock with a beta of 1.3?

A) 17.4%.

B) 16.3%.

C) 10.4%.

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RR_Stock = R_f + (R_Market ? R_f) × Beta_Stock, where RR = required return, R = return, and R_f = risk-free rate, and (R_Market ? R_f) = market premium
Here, RR_Stock = 7 + (8 × 1.3) = 7 + 10.4 = 17.4%.

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What is the required rate of return for a stock with a beta of 1.2, when the risk-free rate is 6% and the market is offering 12%?

A) 7.2%.

B) 13.2%.

C) 6.0%.

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RR_Stock = R_f + (R_Market - R_f) × Beta_Stock, where RR= required return, R = return, and R_f = risk-free rate. 

Here, RR_Stock = 6 + (12 - 6) × 1.2 = 6 + 7.2 = 13.2%.

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The beta of Stock A is 1.3. If the expected return of the market is 12%, and the risk-free rate of return is 6%, what is the expected return of Stock A?

A) 13.8%.

B) 14.2%.

C) 15.6%.

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RR_Stock = R_f + (R_Market - R_f) × Beta_Stock, where RR= required return, R = return, and R_f = risk-free rate

Here, RR_Stock = 6 + (12 - 6) × 1.3  = 6 + 7.8 = 13.8%.

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The beta of stock D is -0.5. If the expected return of Stock D is 8%, and the risk-free rate of return is 5%, what is the expected return of the market?

A) -1.0%.

B) +3.0%.

C) +3.5%.

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RR_Stock = R_f + (R_Market ? R_f) × Beta_Stock, where RR = required return, R = return, and R_f = risk-free rate

A bit of algebraic manipulation results in:

R_Market = [RR_Stock ? R_f ? (Beta_Stock × R_f)] / Beta_Stock = [8 ? 5 ? (-0.5 × 5)] / -0.5 = 0.5 / -0.5 = -1%

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When the market is in equilibrium:

A) all assets plot on the SML.

B) all assets plot on the CML.

C) investors own 100% of the market portfolio.

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When the market is in equilibrium, expected returns equal required returns. Since this means that all assets are correctly priced, all assets plot on the SML.

By definition, all stocks and portfolios other than the market portfolio fall below the CML. (Only the market portfolio is efficient.

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A stock that plots below the Security Market Line most likely:

A) has a beta less than one.

B) is overvalued.

C) is below the efficient frontier.

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Since the equation of the SML is the capital asset pricing model, you can determine if a stock is over- or underpriced graphically or mathematically.  Your answers will always be the same.

Graphically: If you plot a stock’s expected return on the SML and it falls below the line, it indicates that the stock is currently overpriced, causing its expected return to be too low.  If the plot is above the line, it indicates that the stock is underpriced.  If the plot falls on the SML, it indicates the stock is properly priced. 

Mathematically: In the context of the SML, a security is underpriced if the required return is less than the holding period (or expected) return, is overpriced if the required return is greater the holding period (or expected) return, and is correctly priced if the required return equals the holding period (or expected) return.

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What is the expected rate of return on a stock that has a beta of 1.4 if the market risk premium is 9% and the risk-free rate is 4%?

A) 13.0%.

B) 11.0%.

C) 16.6%.

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Using the security market line (SML) equation:

4% + 1.4(9%) = 16.6%.