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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:

₁

₀

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%.

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.

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.

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).

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?

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%.

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%?

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%.

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?

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%.

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?

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%

A)	all assets plot on the SML.

B)	all assets plot on the CML.

C)	investors own 100% of the market portfolio.

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.

A)	has a beta less than one.

B)	is overvalued.

C)	is below the efficient frontier.

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.

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%?

Mason Snow, CFA, is an analyst with Polari Investments. Snow's manager has instructed him to put only securities that are undervalued on the buy list. Today, Snow is to make a recommendation on the following two stocks: Bahre (with an expected return of 10% and a beta of 1.4) and Cubb (with an expected return of 15% and a beta of 2.0). The risk-free rate is at 7% and the market premium is 4%.

A)	only Cubb on the list.

B)	neither security on the list.

C)	only Bahre on the list.

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 flow or dividends) / beginning price. The required return uses the equation of the SML: risk free rate + Beta × (expected market rate - risk free rate).

For Bahre: ER = 10% (given), RR = 0.07 + (1.4)(0.11-0.07) = 12.6%. Stock is overpriced - do not put on buy list.
For Cubb: ER = 15%, (given) RR = 0.07 + (2.0)(0.11-0.07) = 15%. Stock is correctly priced - do not put on buy list (per Snow's manager).

If the risk-free rate of return is 3.5%, the expected market return is 9.5%, and the beta of a stock is 1.3, what is the required return on the stock?

Consider a stock selling for $23 that is expected to increase in price to $27 by the end of the year and pay a $0.50 dividend. If the risk-free rate is 4%, the expected return on the market is 8.5%, and the stock’s beta is 1.9, what is the current valuation of the stock? The stock:

The required return based on systematic risk is computed as: ER_stock = R_f + (ER_M – R_f) × Beta_stock, or 0.04 + (0.085 – 0.04) × 1.9 = 0.1255, or 12.6%. The expected return is computed as: (P₁ – P₀ + D₁) / P₀, or ($27 – $23 + $0.50) / $23 = 0.1957, or 19.6%. The stock is above the security market line ER > RR, so it is undervalued.

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:

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%.

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

A)	efficiently priced but the market is not.

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

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

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%?

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?

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.

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%?

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.”

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.

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:

A)	No, because it is undervalued.

B)	No, because it is overvalued.

C)	Yes, because it is undervalued.

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.