Reading 51: An Introduction to Asset Pricing Models - LOS percentage, determine, expressed, following, whether

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Q19. An analyst wants to determine whether Dover Holdings is overvalued or undervalued, and by how much (expressed as percentage return). The analyst gathers the following information on the stock:

• Market standard deviation = 0.70

• Covariance of Dover with the market = 0.85

• Dover’s current stock price (P₀) = $35.00

• The expected price in one year (P₁) is $39.00

• Expected annual dividend = $1.50

• 3-month Treasury bill yield = 4.50%.

• Historical average S& 500 return = 12.0%.

Dover Holdings stock is:

A)   undervalued by approximately 2.1%.

B)   overvalued by approximately 1.8%.

C)   undervalued by approximately 1.8%.

Q20. If a stock is located above the security market line (SML), an investor would consider the stock to be:

A)   undervalued, with less risk then expected for its expected return.

B)   efficiently priced but the market is not.

C)   overvalued, with too much risk for its expected return.

Q21. The expected rate of return is 2.5 times the 12% expected rate of return from the market. What is the beta if the risk-free rate is 6%?

A)   5.

B)   3.

C)   4.

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答案和详解如下：

Q19. An analyst wants to determine whether Dover Holdings is overvalued or undervalued, and by how much (expressed as percentage return). The analyst gathers the following information on the stock:

• Market standard deviation = 0.70

• Covariance of Dover with the market = 0.85

• Dover’s current stock price (P₀) = $35.00

• The expected price in one year (P₁) is $39.00

• Expected annual dividend = $1.50

• 3-month Treasury bill yield = 4.50%.

• Historical average S& 500 return = 12.0%.

Dover Holdings stock is:

A)   undervalued by approximately 2.1%.

B)   overvalued by approximately 1.8%.

C)   undervalued by approximately 1.8%.

Correct answer is B)         

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 = (1.50 + 39 – 35) / 35 = 15.71%

Step 2: Calculate Required Return

The formula for the required return is from the CAPM: RR = R_f + (ER_M – R_f) × Beta
Here, we are given the information we need except for Beta. Remember that Beta can be calculated with: Beta_stock = [cov_S,M] / [σ²_M]. Here we are given the numerator and the denominator, so the calculation is: 0.85 / 0.70² = 1.73. RR = 4.50% + (12.0 – 4.50%) × 1.73 = 17.48%.

Step 3: Determine over/under valuation

The required return is greater than the expected return, so the security is overvalued.
The amount = 17.48% − 15.71% = 1.77%.

Q20. If a stock is located above the security market line (SML), an investor would consider the stock to be:

A)   undervalued, with less risk then expected for its expected return.

B)   efficiently priced but the market is not.

C)   overvalued, with too much risk for its expected return.

Correct answer is A)

The SML plots required return for level of systematic risk (beta). A security priced above the SML has an expected return greater than that required by its level of systematic risk.

Q21. The expected rate of return is 2.5 times the 12% expected rate of return from the market. What is the beta if the risk-free rate is 6%?

A)   5.

B)   3.

C)   4.

Correct answer is C)

30 = 6 + β (12 - 6)
24 = 6β
β = 4

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