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In Problems 21–23 below assume the risk-free rate is 8% and the expected rate of return on the market is 18% A share of stock is now selling for $100 It will pay a dividend of $9 per share at the

In Problems 21–23 below, assume the risk-free rate is 8% and the expected rate of return on the market is 18%.

  1. A share of stock is now selling for $100. It will pay a dividend of $9 per share at the end of the year. Its beta is 1. What do investors expect the stock to sell for at the end of the year? (LO 7-2)

  2. I am buying a firm with an expected perpetual cash flow of $1,000 but am unsure of its risk. If I think the beta of the firm is zero, when the beta is really 1, how much more will I offer for the firm than it is truly worth? (LO 7-2)

  3. A stock has an expected return of 6%. What is its beta? (LO 7-2)




  1. Two investment advisers are comparing performance. One averaged a 19% return and the other a 16% return. However, the beta of the first adviser was 1.5, while that of the second was 1. (LO 7-2)

    1. Can you tell which adviser was a better selector of individual stocks (aside from the

issue of general movements in the market)?

    1. If the T-bill rate were 6% and the market return during the period were 14%, which adviser would be the superior stock selector?

    2. What if the T-bill rate were 3% and the market return 15%?



  1. Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model: (LO 7-2)

    1. What is the expected return on the market portfolio?

    2. What would be the expected return on a zero-beta stock?

    3. Suppose you consider buying a share of stock at a price of $40. The stock is expected to pay a dividend of $3 next year and to sell then for $41. The stock risk has been evaluated at 5 2.5. Is the stock overpriced or underpriced?



  1. Based on current dividend yields and expected capital gains, the expected rates of return on portfolios and are 11% and 14%, respectively. The beta of is .8 while that of is 1.5. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 Index is 12%. The standard deviation of portfolio is 10% annually, while that of is 31%, and that of the index is 20%. (LO 7-2)

    1. If you currently hold a market-index portfolio, would you choose to add either of these portfolios to your holdings? Explain.

    2. If instead you could invest only in bills and one of these portfolios, which would you choose?



  1. Consider the following data for a one-factor economy. All portfolios are well diversified.













Suppose another portfolio is well diversified with a beta of 2/3 and expected return of 9%. Would an arbitrage opportunity exist? If so, what would the arbitrage strategy

be? (LO 7-4)






  1. Assume both portfolios and are well diversified, that ) 5 14% and

) 5 14.8%. If the economy has only one factor, and 5 1 while 5 1.1, what must be the risk-free rate? (LO 7-4)



  1. Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 30%.

Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3%, and one-half have an alpha of 23%. The analyst then buys $1 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1 million of an equally weighted portfolio of the negative-alpha stocks. (LO 7-4)

    1. What is the expected profit (in dollars), and what is the standard deviation of the

analyst’s profit?

    1. How does your answer change if the analyst examines 50 stocks instead of 20? 100 stocks?



  1. If the APT is to be a useful theory, the number of systematic factors in the economy must be small. Why? (LO 7-4)

  2. The APT itself does not provide information on the factors that one might expect to determine risk premiums. How should researchers decide which factors to investigate? Is industrial production a reasonable factor to test for a risk premium? Why or why not? (LO 7-3)



  1. Suppose two factors are identified for the U.S. economy: the growth rate of industrial production, IP, and the inflation rate, IR. IP is expected to be 4% and IR 6%. A stock with a beta of 1 on IP and .4 on IR currently is expected to provide a rate of return of 14%. If industrial production actually grows by 5%, while the inflation rate turns out to be 7%, what is your best guess for the rate of return on the stock? (LO 7-3)



  1. Suppose there are two independent economic factors, and . The risk-free rate is 7%, and all stocks have independent firm-specific components with a standard deviation of 50%. Portfolios and are both well diversified.



Beta on 1

Beta on 2

Expected Return (%)










What is the expected return–beta relationship in this economy? (LO 7-5)



  1. As a finance intern at Pork Products, Jennifer Wainwright’s assignment is to come up with fresh insights concerning the firm’s cost of capital. She decides that this would be a good opportunity to try out the new material on the APT that she learned last semester. As such, she decides that three promising factors would be (i) the return on a broad- based index such as the S&P 500; (ii) the level of interest rates, as represented by the yield to maturity on 10-year Treasury bonds; and (iii) the price of hogs, which are partic- ularly important to her firm. Her plan is to find the beta of Pork Products against each of these factors and to estimate the risk premium associated with exposure to each factor. Comment on Jennifer’s choice of factors. Which are most promising with respect to the likely impact on her firm’s cost of capital? Can you suggest improvements to her specifi- cation? (LO 7-3)



  1. Suppose the market can be described by the following three sources of systematic risk. Each factor in the following table has a mean value of zero (so factor values represent realized surprises relative to prior expectations), and the risk premiums associated with each source of systematic risk are given in the last column.

Systematic Factor

Risk Premium

Industrial production, IP


Interest rates, INT


Credit risk, CRED



The excess return, , on a particular stock is described by the following equation that relates realized returns to surprises in the three systematic factors:

5 6% 1 1.0 IP 1 .5 INT 1 .75 CRED 1 e

Find the equilibrium expected excess return on this stock using the APT. Is the stock overpriced or underpriced? (LO 7-3)







  1. Which of the following statements about the security market line (SML) are

true? (LO 7-2)

    1. The SML provides a benchmark for evaluating expected investment performance.

    2. The SML leads all investors to invest in the same portfolio of risky assets.

    3. The SML is a graphic representation of the relationship between expected return and beta.

    4. Properly valued assets plot exactly on the SML.



  1. Karen Kay, a portfolio manager at Collins Asset Management, is using the capital asset pricing model for making recommendations to her clients. Her research department has developed the information shown in the following exhibit. (LO 7-2)



Forecasted Returns, Standard Deviations, and Betas

Forecasted Return

Standard Deviation


Stock X




Stock Y




Market index




Risk-free rate





    1. Calculate expected return and alpha for each stock.

    2. Identify and justify which stock would be more appropriate for an investor who wants to:

      1. Add this stock to a well-diversified equity portfolio.

      2. Hold this stock as a single-stock portfolio.



  1. Joan McKay is a portfolio manager for a bank trust department. McKay meets with two clients, Kevin Murray and Lisa York, to review their investment objectives. Each client expresses an interest in changing his or her individual investment objectives. Both clients currently hold well-diversified portfolios of risky assets. (LO 7-1)

    1. Murray wants to increase the expected return of his portfolio. State what action

McKay should take to achieve Murray’s objective. Justify your response in the context of the capital market line.

    1. York wants to reduce the risk exposure of her portfolio but does not want to engage in

borrowing or lending activities to do so. State what action McKay should take to achieve York’s objective. Justify your response in the context of the security market line.






  1. Jeffrey Bruner, CFA, uses the capital asset pricing model (CAPM) to help identify mispriced securities. A consultant suggests Bruner use arbitrage pricing theory (APT) instead. In comparing CAPM and APT, the consultant made the following arguments:

    1. Both the CAPM and APT require a mean-variance efficient market portfolio.

    2. The CAPM assumes that one specific factor explains security returns but APT does not.

State whether each of the consultant’s arguments is correct or incorrect. Indicate, for each incorrect argument, why the argument is incorrect. (LO 7-5)



  1. The security market line depicts: (LO 7-2)

    1. A security’s expected return as a function of its systematic risk.

    2. The market portfolio as the optimal portfolio of risky securities.

    3. The relationship between a security’s return and the return on an index.

    4. The complete portfolio as a combination of the market portfolio and the risk-free asset.



  1. According to CAPM, the expected rate of return of a portfolio with a beta of 1 and an alpha of 0 is: (LO 7-2)

    1. Between and .

    2. The risk-free rate, .

    3. ).

    4. The expected return on the market, .

The following table (for CFA Problems 7 and 8) shows risk and return measures for two portfolios.





  1. When plotting portfolio on the preceding table relative to the SML, portfolio R

lies: (LO 7-2)

    1. On the SML.

    2. Below the SML.

    3. Above the SML.

    4. Insufficient data given.

  1. When plotting portfolio relative to the capital market line, portfolio lies: (LO 7-2)

    1. On the CML.

    2. Below the CML.

    3. Above the CML.

    4. Insufficient data given.



  1. Briefly explain whether investors should expect a higher return from holding portfolio versus portfolio under capital asset pricing theory (CAPM). Assume that both portfo- lios are fully diversified. (LO 7-2)



Portfolio A

Portfolio B

Systematic risk (beta)

Specific risk for each individual security







  1. Assume that both and are well-diversified portfolios and the risk-free rate is 8%.


Expected Return









In this situation you could conclude that portfolios and Y: (LO 7-4)

  1. Are in equilibrium.

  2. Offer an arbitrage opportunity.

  3. Are both underpriced.

  4. Are both fairly priced.



  1. According to the theory of arbitrage: (LO 7-4)

    1. High-beta stocks are consistently overpriced.

    2. Low-beta stocks are consistently overpriced.

    3. Positive alpha investment opportunities will quickly disappear.

    4. Rational investors will pursue arbitrage consistent with their risk tolerance.



  1. A zero-investment well-diversified portfolio with a positive alpha could arise if: (LO 7-5)

    1. The expected return of the portfolio equals zero.

    2. The capital market line is tangent to the opportunity set.

    3. The law of one price remains unviolated.

    4. A risk-free arbitrage opportunity exists.



  1. An investor takes as large a position as possible when an equilibrium price relationship is violated. This is an example of: (LO 7-4)

    1. A dominance argument.

    2. The mean-variance efficient frontier.

    3. Arbitrage activity.

    4. The capital asset pricing model.



  1. In contrast to the capital asset pricing model, arbitrage pricing theory: (LO 7-4)

    1. Requires that markets be in equilibrium.

    2. Uses risk premiums based on micro variables.

    3. Specifies the number and identifies specific factors that determine expected returns.

    4. Does not require the restrictive assumptions concerning the market portfolio.



  1. A firm’s beta can be estimated from the slope of the characteristic line. The first step is to plot the return on the firm’s stock ( -axis) versus the return on a broad market index

-axis). Next, a regression line is estimated to find the slope.

    1. Go to, enter the symbol for Alcoa, and click on Get Quotes . On the left-side menu, click on Historical Prices; then enter starting and ending dates that cor- respond to the most recent two years. Select the Daily option. Save the data to a spreadsheet.

    2. Repeat the process to get comparable data for the S&P 500 Index (symbol ^GSPC). Download the data and copy it into the same spreadsheet as Alcoa with dates aligned.

    3. Sort the data from earliest to latest. Calculate the excess return on the stock and the return on the index for each day using the adjusted closing prices. (You can use four- week T-bill rates to calculate excess returns from the Federal Reserve website at www. )

    4. Prepare an xy scatter plot with no line inserted. Be sure that the firm’s excess returns represent the -variable and the market’s excess returns represent the -variable.

    5. Select one of the data points by pointing to it and clicking the left mouse button. While the point is selected, right-click to pull up a shortcut menu. Select Add

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