Question[1]. Walter Jasper currently manages a $5

[1]. Walter Jasper currently manages a $500,000 portfolio. He is expecting to receive an additional $250,000 from a new client. The existing portfolio has a required return of 10.75 percent. The risk-free rate is 4 percent and the return on the market is 9 percent. If Walter wants the required return on the new portfolio to be 11.5 percent, what should be the average beta for the new stocks added to the portfolio?

a. 1.50

b. 2.00

c. 1.67

d. 1.35

e. 1.80

[2]. A portfolio manager is holding the following investments in her portfolio:

StockAmount InvestedBeta

1 $300 million 0.7

2 200 million 1.0

3 500 million 1.6

The risk-free rate, k_RF, is 5 percent and the portfolio has a required return of 11.655 percent. The manager is thinking about selling all of her holdings of Stock 3, and instead investing the money in Stock 4, which has a beta of 0.9. If she were to do this, what would be the new portfolio’s required return?

a. 9.73%

b. 11.09%

c. 9.91%

d. 7.81%

e. 10.24%

[3]. A fund manager is holding the following stocks:

StockAmount InvestedBeta

1 $300 million 1.2

2 560 million 1.4

3 320 million 0.7

4 230 million 1.8

The risk-free rate is 5 percent and the market risk premium is also
5 percent. If the manager sells half of her investment in Stock 2 ($280 million) and puts the money in Stock 4, by how many percentage points will her portfolio’s required return increase?

a. 0.36%

b. 0.22%

c. 2.00%

d. 0.20%

e. 0.40%

[4]. A portfolio manager is managing a $10 million portfolio. Currently the portfolio is invested in the following manner:

Investment Dollar Amount Invested Beta

Stock 1 $2 million 0.6

Stock 2 3 million 0.8

Stock 3 3 million 1.2

Stock 4 2 million 1.4

Currently, the risk-free rate is 5 percent and the portfolio has an expected return of 10 percent. Assume that the market is in equilibrium so that expected returns equal required returns. The manager is willing to take on additional risk and wants to instead earn an expected return of 12 percent on the portfolio. Her plan is to sell Stock 1 and use the proceeds to buy another stock. In order to reach her goal, what should be the beta of the stock that the manager selects to replace Stock 1?

a. 1.40

b. 1.75

c. 2.05

d. 2.40

e. 2.60

[5]. Here are the expected returns on two stocks:

Returns

Probability X Y

0.1 -20% 10%

0.8 20 15

0.1 40 20

If you form a 50-50 portfolio of the two stocks, what is the portfolio’s standard deviation?

a. 8.1%

b. 10.5%

c. 13.4%

d. 16.5%

e. 20.0%

[6]. The CFO of Brady Boots has estimated the rates of return to Brady’s stock, depending on the state of the economy. He has also compiled analysts’ expectations for the economy.

Economy ProbabilityReturn

Recession 0.1 -23%

Below average 0.1 -8

Average 0.4 6

Above average 0.2 17

Boom 0.2 24

Given this data, what is the company’s coefficient of variation? (Use the population standard deviation, not the sample standard deviation when calculating the coefficient of variation.)

a. 1.94

b. 25.39

c. 2.26

d. 5.31

e. 1.84

[7]. Ripken Iron Works faces the following probability distribution:

Stock’s Expected

State of Probability of Return if this

the EconomyState Occurring State Occurs

Boom 0.25 25%

Normal 0.50 15

Recession 0.25 5

What is the coefficient of variation on the company’s stock?

a. 0.06

b. 0.47

c. 0.54

d. 0.67

e. 0.71

[8]. An analyst has estimated how a particular stock’s return will vary depending on what will happen to the economy:

Stock’s Expected

State of Probability of Return if this

the Economy State Occurring State Occurs

Recession 0.10 -60%

Below Average 0.20 -10

Average 0.40 15

Above Average 0.20 40

Boom 0.10 90

What is the coefficient of variation on the company’s stock?

a. 2.121

b. 2.201

c. 2.472

d. 3.334

e. 3.727

[9]. The following probability distributions of returns for two stocks have been estimated:

Returns

Probability Stock A Stock B

0.3 12% 5%

0.4 8 4

0.3 6 3

What is the coefficient of variation for the stock that is less risky, assuming you use the coefficient of variation to rank riskiness?

a. 3.62

b. 0.28

c. 0.19

d. 0.66

e. 5.16

[10]. A financial analyst is forecasting the expected return for the stock of Himalayan Motors. The analyst estimates the following probability distribution of returns:

ProbabilityReturn

20% -5%

40 10

20 20

10 25

10 50

On the basis of this analyst’s forecast, what is the stock’s coefficient of variation?

a. 0.80

b. 0.91

c. 0.96

d. 1.04

e. 1.10

[11]. A stock market analyst estimates that there is a 25 percent chance the economy will be weak, a 50 percent chance the economy will be average, and a 25 percent chance the economy will be strong. The analyst estimates that Hartley Industries’ stock will have a 5 percent return if the economy is weak, a 15 percent return if the economy is average, and a 30 percent return if the economy is strong. On the basis of this estimate, what is the coefficient of variation for Hartley Industries’ stock?

a. 0.61644

b. 0.54934

c. 0.75498

d. 3.62306

e. 0.63432

[12]. An analyst has estimated Williamsport Equipment’s returns under the following economic states:

Economic StateProbabilityExpected Return

Recession 0.20 -24%

Below average 0.30 -3

Above average 0.30 +15

Boom 0.20 +50

What is Williamsport’s estimated coefficient of variation?

a. 0.36

b. 2.80

c. 2.86

d. 2.95

e. 3.30

[13]. Stock Z has had the following returns over the past five years:

Year Return

1998 10%

1999 12

2000 27

2001 -15

2002 30

What is the company’s coefficient of variation (CV)? (Use the population standard deviation to calculate CV.)

a. 99.91

b. 35.76

c. 9.88

d. 2.79

e. 1.25

[14]. An investor has $5,000 invested in a stock that has an estimated beta of 1.2, and another $15,000 invested in the stock of the company for which she works. The risk-free rate is 6 percent and the market risk premium is also 6 percent. The investor calculates that the required rate of return on her total ($20,000) portfolio is 15 percent. What is the beta of the company for which she works?

a. 1.6

b. 1.7

c. 1.8

d. 1.9

e. 2.0

[15]. Portfolio P has 30 percent invested in Stock X and 70 percent in Stock Y. The risk-free rate of interest is 6 percent and the market risk premium is 5 percent. Portfolio P has a required return of 12 percent and
Stock X has a beta of 0.75. What is the beta of Stock Y?

a. 0.21

b. 1.20

c. 0.96

d. 1.65

e. 1.39

[16]. A money manager is managing the account of a large investor. The investor holds the following stocks:

Stock Amount Invested Estimated Beta

A $2,000,000 0.80

B 5,000,000 1.10

C 3,000,000 1.40

D 5,000,000 ????

The portfolio’s required rate of return is 17 percent. The risk-free rate, k_RF, is 7 percent and the return on the market, k_M, is 14 percent. What is Stock D’s estimated beta?

a. 1.256

b. 1.389

c. 1.429

d. 2.026

e. 2.154

[17]. The returns of United Railroad Inc. (URI) are listed below, along with the returns on “the market”:

YearURIMarket

1 -14% -9%

2 16 11

3 22 15

4 7 5

5 -2 -1

If the risk-free rate is 9 percent and the required return on URI’s stock is 15 percent, what is the required return on the market? Assume the market is in equi­librium. (Hint: Think rise over run.)

a. 4%

b. 9%

c. 10%

d. 13%

e. 16%

Tough:

[18]. A money manager is holding the following portfolio:

Stock Amount Invested Beta

1 $300,000 0.6

2 300,000 1.0

3 500,000 1.4

4 500,000 1.8

The risk-free rate is 6 percent and the portfolio’s required rate of return is 12.5 percent. The manager would like to sell all of her holdings of Stock 1 and use the proceeds to purchase more shares of Stock 4. What would be the portfolio’s required rate of return following this change?

a. 13.63%

b. 10.29%

c. 11.05%

d. 12.52%

e. 14.33%

Multiple Part:

(The following information applies to the next two problems.)

A portfolio manager has a $10 million portfolio, which consists of $1 million invested in 10 separate stocks. The portfolio beta is 1.2. The risk-free rate is 5 percent and the market risk premium is 6 percent.

[19]. What is the portfolio’s required return?

a. 6.20%

b. 9.85%

c. 12.00%

d. 12.20%

e. 12.35%

[20]. The manager sells one of the stocks in her portfolio for $1 million. The stock she sold has a beta of 0.9. She takes the $1 million and uses the money to purchase a new stock that has a beta of 1.6. What is the required return of her portfolio after purchasing this new stock?

a. 10.75%

b. 12.35%

c. 12.62%

d. 13.35%

e. 14.60%

Web Appendix 5A

Multiple Choice: Conceptual

5A-[xxi]. Which of the following statements is most correct?

a. The CAPM is an ex ante model, which means that all of the variables should be historical values that can reasonably be projected into the future.

b. The beta coefficient used in the SML equation should reflect the expected volatility of a given stock’s return versus the return on the market during some future period.

c. The general equation: Y = a + bX + e, is the standard form of a simple linear regression where b = beta, and X equals the independent return on an individual security being compared to Y, the return on the market, which is the dependent variable.

d. The rise-over-run method is not a legitimate method of estimating beta because it measures changes in an individual security’s return regressed against time.

Multiple Choice: Problems

5A-[xxii]. Given the following returns on Stock J and “the market” during the last three years, what is the beta coefficient of Stock J? (Hint: Think rise over run.)

Year Stock J Market

1 -13.85% -8.63%

2 22.90 12.37

3 35.15 19.37

a. 0.92

b. 1.10

c. 1.75

d. 2.24

e. 1.45

5A-[xxiii]. Given the following returns on Stock Q and “the market” during the last three years, what is the difference in the calculated beta coefficient of Stock Q when Year 1-Year 2 data are used as compared to Year 2-Year 3 data? (Hint: Think rise over run.)

Year Stock Q Market

1 6.30% 6.10%

2 -3.70 12.90

3 21.71 16.20

a. 9.17

b. 1.06

c. 6.23

d. 0.81

e. 0.56

5A-[xxiv]. Stock X, and “the market” have had the following rates of returns over the past four years.

Year Stock X Market

1999 12% 14%

2000 5 2

2001 11 14

2002 -7 -3

60 percent of your portfolio is invested in Stock X, and the remaining 40 percent is invested in Stock Y. The risk-free rate is 6 percent and the market risk premium is also 6 percent. You estimate that 14 percent is the required rate of return on your portfolio. What is the beta of Stock Y?

a. 1.33

b. 1.91

c. 2.00

d. 2.15

e. 2.33

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.5A-[1]. Hanratty Inc.’s stock and the stock market have generated the following returns over the past five years:

Year Hanratty Market (k_M)

1 13% 9%

2 18 15

3 -5 -2

4 23 19

5 6 12

On the basis of these historical returns, what is the estimated beta of Hanratty Inc.’s stock?

a. 0.7839

b. 0.9988

c. 1.2757

d. 1.3452

e. 1.5000

5A-[2]. Below are the returns for the past five years for Stock S and for the overall market:

Year Stock S Market (k_M)

1998 12% 8%

1999 34 28

2000 -29 -20

2001 -11 -4

2002 45 30

What is Stock S’s estimated beta?

a. 1.43

b. 0.69

c. 0.91

d. 1.10

e. 1.50

Multiple Part:

(The following information applies to the next two problems.)

You have been asked to use a CAPM analysis to choose between Stocks R and S, with your choice being the one whose expected rate of return exceeds its required rate of return by the widest margin. The risk-free rate is 6 percent, and the required return on an average stock (or “the market”) is 10 percent. Your security analyst tells you that Stock S’s expected rate of return, , is equal to 11 percent, while Stock R’s expected rate of return, , is equal to 12 percent. The CAPM is assumed to be a valid method for selecting stocks, but the expected return for any given investor (such as you) can differ from the required rate of return for a given stock. The following past rates of return are to be used to calculate the two stocks’ beta coefficients, which are then to be used to determine the stocks’ required rates of return:

YearStock RStock SMarket

1 -15% 0% -5%

2 5 5 5

3 25 10 15

Note: The averages of the historical returns are not needed, and they are generally not equal to the expected future returns.

5A-[3]. Calculate both stocks’ betas.What is the difference between the betas? That is, what is the value of beta_R-beta_S?(Hint:The graphical method of calculating the rise over run, or (Y₂–Y₁)divided by (X₂–X₁) may aid you.)

a. 0.0

b. 1.0

c. 1.5

d. 2.0

e. 2.5

5A-[4]. Set up the SML equation and use it to calculate both stocks’ required rates of return, and compare those required returns with the expected returns given above. You should invest in the stock whose expected return exceeds its required return by the widest margin. What is the widest margin, or greatest excess return ( – k)?

a. 0.0%

b. 0.5%

c. 1.0%

d. 2.0%

e. 3.0%

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