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

honeycfa

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%.

---

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%.

 

aarongreen

奥奥

honeycfa

Charlie Smith holds two portfolios, Portfolio X and Portfolio Y. They are both liquid, well-diversified portfolios with approximately equal market values. He expects Portfolio X to return 13% and Portfolio Y to return 14% over the upcoming year. Because of an unexpected need for cash, Smith is forced to sell at least one of the portfolios. He uses the security market line to determine whether his portfolios are undervalued or overvalued. Portfolio X’s beta is 0.9 and Portfolio Y’s beta is 1.1. The expected return on the market is 12% and the risk-free rate is 5%. Smith should sell:

A) both portfolios X and Y because they are both overvalued.

B) either portfolio X or Y because they are both properly valued.

C) portfolio Y only.

---

Portfolio X’s required return is 0.05 + 0.9 × (0.12-0.05) = 11.3%. It is expected to return 13%. The portfolio has an expected excess return of 1.7%

Portfolio Y’s required return is 0.05 + 1.1 × (0.12-0.05) = 12.7%. It is expected to return 14%. The portfolio has an expected excess return of 1.3%.

Since both portfolios are undervalued, the investor should sell the portfolio that offers less excess return. Sell Portfolio Y because its excess return is less than that of Portfolio X.

honeycfa

An investor believes Stock M will rise from a current price of $20 per share to a price of $26 per share over the next year. The company is not expected to pay a dividend. The following information pertains:

• R_F = 8%
• ER_M = 16%
• Beta = 1.7

Should the investor purchase the stock?

A) No, because it is undervalued.

B) No, because it is overvalued.

C) Yes, because it is undervalued.

---

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.

Here, the holding period (or expected) return is calculated as: (ending price – beginning price + any cash flows/dividends) / beginning price. The required return uses the equation of the SML: risk free rate + Beta * (expected market rate - risk free rate).

ER = (26 ? 20) / 20 = 0.30 or 30%, RR = 8 + (16 ? 8) × 1.7 = 21.6%. The stock is underpriced therefore purchase.

honeycfa

Luis Green is an investor who uses the security market line to determine whether securities are properly valued. He is evaluating the stocks of two companies, Mia Shoes and Video Systems. The stock of Mia Shoes is currently trading at $15 per share, and the stock of Video Systems is currently trading at $18 per share. Green expects the prices of both stocks to increase by $2 in a year. Neither company pays dividends. Mia Shoes has a beta of 0.9 and Video Systems has a beta of (-0.30). If the market return is 15% and the risk-free rate is 8%, which trading strategy will Green employ?

Mia Shoes

Video Systems

A) Buy Sell

B) Buy Buy

C) Sell Buy

---

The required return for Mia Shoes is 0.08 + 0.9 × (0.15-0.08) = 14.3%. The forecast return is $2/$15 = 13.3%. The stock is overvalued and the investor should sell it. The required return for Video Systems is 0.08 - 0.3 × (0.15-0.08) = 5.9%. The forecast return is $2/$18 = 11.1%. The stock is undervalued and the investor should buy it.

honeycfa

The expected rate of return is 1.5 times the 16% expected rate of return from the market. What is the beta if the risk free rate is 8%?

A) 3.

B) 4.

C) 2.

---

24 = 8 + β (16 ? 8)
24 = 8 + 8β
16 = 8β
16 / 8 = β
β = 2

honeycfa

Consider the following graph of the Security Market Line (SML). The letters X, Y, and Z represent risky asset portfolios. The SML crosses the y-axis at the point 0.07. The expected market return equals 13.0%. Note: The graph is NOT drawn to scale.

Using the graph above and the information provided, which of the following statements is most accurate?

A) Portfolio Y is undervalued.

B) The expected return (or holding period return) for Portfolio Z equals 14.8%.

C) Portfolio X's required return is greater than the market expected return.

---

At first, it appears that we are not given the information needed to calculate the holding period, or expected return (beginning price, ending price, or annual dividend). However, we are given the information required to calculate the required return (CAPM) and since Portfolio Z is on the SML, we know that the required return (RR) equals the expected return (ER). So, ER = RR = R_f + (ER_M – R_f) × Beta = 7.0% + (13.0% ? 7.0%) × 1.3 = 14.8%.

The SML plots beta (or systematic risk) versus expected return, the CML plots total risk (systematic plus unsystematic risk) versus expected return. Portfolio Y is overvalued – any portfolio located below the SML has an RR > ER and is thus overpriced. Since Portfolio X plots above the SML, it is undervalued and the statement should read, “Portfolio X’s required return is less than the market expected return.”

honeycfa

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) 4.

B) 5.

C) 3.

---

30 = 6 + β (12 - 6)
24 = 6β
β = 4

honeycfa

Luis Green is an investor who uses the security market line to determine whether securities are properly valued. He is evaluating the stocks of two companies, Mia Shoes and Video Systems. The stock of Mia Shoes is currently trading at $15 per share, and the stock of Video Systems is currently trading at $18 per share. Green expects the prices of both stocks to increase by $2 in a year. Neither company pays dividends. Mia Shoes has a beta of 0.9 and Video Systems has a beta of (-0.30). If the market return is 15% and the risk-free rate is 8%, which trading strategy will Green employ?

Mia Shoes

Video Systems

A) Buy Sell

B) Buy Buy

C) Sell Buy

---

The required return for Mia Shoes is 0.08 + 0.9 × (0.15-0.08) = 14.3%. The forecast return is $2/$15 = 13.3%. The stock is overvalued and the investor should sell it. The required return for Video Systems is 0.08 - 0.3 × (0.15-0.08) = 5.9%. The forecast return is $2/$18 = 11.1%. The stock is undervalued and the investor should buy it.

honeycfa

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) undervalued by approximately 1.8%.

C) overvalued by approximately 1.8%.

---

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%.