Question[i]. Assume a new law is passed tha

[i]. Assume a new law is passed that restricts investors to holding only one asset. A risk-averse investor is considering two possible assets as the asset to be held in isolation. The assets’ possible returns and related probabilities (that is, the probability distributions) are as follows:

Asset X Asset Y

P k P k

0.10 -3% 0.05 -3%

0.10 2 0.10 2

0.25 5 0.30 5

0.25 8 0.30 8

0.30 10 0.25 10

Which asset should be preferred?

a. Asset X, since its expected return is higher.

b. Asset Y, since its beta is probably lower.

c. Either one, since the expected returns are the same.

d. Asset X, since its standard deviation is lower.

e. Asset Y, since its coefficient of variation is lower and its expected return is higher.

[ii]. Given the following probability distribution, what are the expected return and the standard deviation of returns for Security J?

State P_ik_J

1 0.2 10%

2 0.6 15

3 0.2 20

a. 15%; 6.50%

b. 12%; 5.18%

c. 15%; 3.16%

d. 15%; 10.00%

e. 20%; 5.00%

[iii]. You are holding a stock that has a beta of 2.0 and is currently in equilibrium. The required return on the stock is 15 percent, and the return on an average stock is 10 percent. What would be the percentage change in the return on the stock, if the return on an average stock increased by 30 percent while the risk-free rate remained unchanged?

a. +20%

b. +30%

c. +40%

d. +50%

e. +60%

[iv]. Oakdale Furniture Inc. has a beta coefficient of 0.7 and a required rate of return of 15 percent. The market risk premium is currently 5 percent. If the inflation premium increases by 2 percentage points, and Oakdale acquires new assets that increase its beta by 50 percent, what will be Oakdale’s new required rate of return?

a. 13.50%

b. 22.80%

c. 18.75%

d. 15.25%

e. 17.00%

[v]. Partridge Plastic’s stock has an estimated beta of 1.4, and its required rate of return is 13 percent. Cleaver Motors’ stock has a beta of 0.8, and the risk-free rate is 6 percent. What is the required rate of return on Cleaver Motors’ stock?

a. 7.0%

b. 10.4%

c. 12.0%

d. 11.0%

e. 10.0%

[vi]. The realized returns for the market and Stock J for the last four years are given below:

YearMarketStock J

1 10% 5%

2 15 0

3 -5 14

4 0 10

An average stock has an expected return of 12 percent and the market risk premium is 4 percent. If Stock J’s expected rate of return as viewed by a marginal investor is 8 percent, what is the difference between J’s expected and required rates of return?

a. 0.66%

b. 1.25%

c. 2.64%

d. 3.72%

e. 5.36%

[vii]. You have been scouring The Wall Street Journal looking for stocks that are “good values” and have calculated expected returns for five stocks. Assume the risk-free rate (k_RF) is 7 percent and the market risk premium (k_M – k_RF) is 2 percent. Which security would be the best investment? (Assume you must choose just one.)

Expected ReturnBeta

a. 9.01% 1.70

b. 7.06% 0.00

c. 5.04% -0.67

d. 8.74% 0.87

e. 11.50% 2.50

[viii]. HR Corporation has a beta of 2.0, while LR Corporation’s beta is 0.5. The risk-free rate is 10 percent, and the required rate of return on an average stock is 15 percent. Now the expected rate of inflation built into k_RF falls by 3 percentage points, the real risk-free rate remains constant, the required return on the market falls to 11 percent, and the betas remain constant. When all of these changes are made, what will be the difference in the required returns on HR’s and LR’s stocks?

a. 1.0%

b. 2.5%

c. 4.5%

d. 5.4%

e. 6.0%

Answer: a

[ix]. BradleyHotels has a beta of 1.3, while Douglas Farms has a beta of 0.7. The required return on an index fund that holds the entire stock market is 12 percent. The risk-free rate of interest is 7 percent. By how much does Bradley’s required return exceed Douglas’ required return?

a. 3.0%

b. 6.5%

c. 5.0%

d. 6.0%

e. 7.0%

[x]. Company X has a beta of 1.6, while Company Y’s beta is 0.7. The risk-free rate is 7 percent, and the required rate of return on an average stock is 12 percent. Now the expected rate of inflation built into k_RF rises by 1 percentage point, the real risk-free rate remains constant, the required return on the market rises to 14 percent, and betas remain constant. After all of these changes have been reflected in the data, by how much will the required return on Stock X exceed that on Stock Y?

a. 3.75%

b. 4.20%

c. 4.82%

d. 5.40%

e. 5.75%

[xi]. Historical rates of return for the market and for Stock A are given below:

YearMarketStock A

1 6.0% 8.0%

2 -8.0 3.0

3 -8.0 -2.0

4 18.0 12.0

If the required return on the market is 11 percent and the risk-free rate is 6 percent, what is the required return on Stock A, according to CAPM/SML theory?

a. 6.00%

b. 6.57%

c. 7.25%

d. 7.79%

e. 8.27%

[xii]. Some returns data for the market and for Countercyclical Corp. are given below:

YearMarketCountercyclical

1999 -2.0% 8.0%

2000 12.0 3.0

2001 -8.0 18.0

2002 21.0 -7.0

The required return on the market is 14 percent and the risk-free rate is 8 percent. What is the required return on Countercyclical Corp. according to CAPM/SML theory?

a. 3.42%

b. 4.58%

c. 8.00%

d. 11.76%

e. 14.00%

[xiii]. Stock X, Stock Y, and the market have had the following returns over the past four years.

YearMarket X Y

1999 11% 10% 12%

2000 7 4 -3

2001 17 12 21

2002 -3 -2 -5

The risk-free rate is 7 percent. The market risk premium is 5 percent. What is the required rate of return for a portfolio that consists of $14,000 invested in Stock X and $6,000 invested in Stock Y?

a. 9.94%

b. 10.68%

c. 11.58%

d. 12.41%

e. 13.67%

[xiv]. The risk-free rate, k_RF, is 6 percent and the market risk premium,
(k_M – k_RF), is 5 percent. Assume that required returns are based on the CAPM. Your $1 million portfolio consists of $700,000 invested in a stock that has a beta of 1.2 and $300,000 invested in a stock that has a beta of 0.8. Which of the following statements is most correct?

a. The portfolio’s required return is less than 11 percent.

b. If the risk-free rate remains unchanged but the market risk premium increases by 2 percentage points, the required return on your portfolio will increase by more than 2 percentage points.

c. If the market risk premium remains unchanged but expected inflation increases by 2 percentage points, the required return on your portfolio will increase by more than 2 percentage points.

d. If the stock market is efficient, your portfolio’s expected return should equal the expected return on the market, which is 11 percent.

e. None of the statements above is correct.

[xv]. A portfolio manager is holding the following investments:

StockAmount InvestedBeta

X $10 million 1.4

Y 20 million 1.0

Z 40 million 0.8

The manager plans to sell his holdings of Stock Y. The money from the sale will be used to purchase another $15 million of Stock X and another $5 million of Stock Z. The risk-free rate is 5 percent and the market risk premium is 5.5 percent. How many percentage points higher will the required return on the portfolio be after he completes this transaction?

a. 0.07%

b. 0.18%

c. 0.39%

d. 0.67%

e. 1.34%

[xvi]. Assume that the risk-free rate is 5.5 percent and the market risk premium is 6 percent. A money manager has $10 million invested in a portfolio that has a required return of 12 percent. The manager plans to sell $3 million of stock with a beta of 1.6 that is part of the portfolio. She plans to reinvest this $3 million into another stock that has a beta of 0.7. If she goes ahead with this planned transaction, what will be the required return of her new portfolio?

a. 10.52%

b. 10.38%

c. 11.31%

d. 10.90%

e. 8.28%

[xvii]. The current risk-free rate is 6 percent and the market risk premium is
5 percent. Erika is preparing to invest $30,000 in the market and she wants her portfolio to have an expected return of 12.5 percent. Erika is concerned about bearing too much stand-alone risk; therefore, she will diversify her portfolio by investing in three different assets (two mutual funds and a risk-free security). The three assets she will be investing in are an aggressive growth mutual fund that has a beta of 1.6, an S&P 500 index fund with a beta of 1, and a risk-free security that has a beta of 0. She has already decided that she will invest 10 percent of her money in the risk-free asset. In order to achieve the desired expected return of 12.5 percent, what proportion of Erika’s portfolio must be invested in the S&P 500 index fund?

a. 23.33%

b. 33.33%

c. 53.33%

d. 66.66%

e. 76.66%

[xviii]. Your portfolio consists of $100,000 invested in a stock that has a beta = 0.8, $150,000 invested in a stock that has a beta = 1.2, and $50,000 invested in a stock that has a beta = 1.8. The risk-free rate is
7 percent. Last year this portfolio had a required rate of return of 13 percent. This year nothing has changed except for the fact that the market risk premium has increased by 2 percent (two percentage points). What is the portfolio’s current required rate of return?

a. 5.14%

b. 7.14%

c. 11.45%

d. 15.33%

e. 16.25%

[xix]. Currently, the risk-free rate is 5 percent and the market risk premium is 6 percent. You have your money invested in three assets: an index fund that has a beta of 1.0, a risk-free security that has a beta of 0, and an international fund that has a beta of 1.5. You want to have 20 percent of your portfolio invested in the risk-free asset, and you want your overall portfolio to have an expected return of 11 percent. What portion of your overall portfolio should you invest in the inter-national fund?

a. 0%

b. 40%

c. 50%

d. 60%

e. 80%

[xx]. A money manager is holding a $10 million portfolio that consists of the following five stocks:

StockAmount InvestedBeta

A $4 million 1.2

B 2 million 1.1

C 2 million 1.0

D 1 million 0.7

E 1 million 0.5

The portfolio has a required return of 11 percent, and the market risk premium, k_M – k_RF, is 5 percent. What is the required return on Stock C?

a. 7.2%

b. 10.0%

c. 10.9%

d. 11.0%

e. 11.5%

[xxi]. You have been managing a $1 million portfolio. The portfolio has a beta of 1.6 and a required rate of return of 14 percent. The current risk-free rate is 6 percent. Assume that you receive another $200,000. If you invest the money in a stock that has a beta of 0.6, what will be the required return on your $1.2 million portfolio?

a. 12.00%

b. 12.25%

c. 13.17%

d. 14.12%

e. 13.67%

[xxii]. Currently, the risk-free rate, k_RF, is 5 percent and the required return on the market, k_M, is 11 percent. Your portfolio has a required rate of return of 9 percent. Your sister has a portfolio with a beta that is twice the beta of your portfolio. What is the required rate of return on your sister’s portfolio?

a. 12.0%

b. 12.5%

c. 13.0%

d. 17.0%

e. 18.0%

[xxiii]. Stock A has an expected return of 10 percent and a beta of 1.0. Stock B has a beta of 2.0. Portfolio P is a two-stock portfolio, where part of the portfolio is invested in Stock A and the other part is invested in Stock B. Assume that the risk-free rate is 5 percent, that required returns are determined by the CAPM, and that the market is in equilibrium so that expected returns equal required returns. Portfolio P has an expected return of 12 percent. What proportion of Portfolio P consists of Stock B?

a. 20%

b. 40%

c. 50%

d. 60%

e. 80%

[xxiv]. You hold a diversified portfolio consisting of a $5,000 investment in each of 20 different common stocks. The portfolio beta is equal to 1.15. You have decided to sell one of your stocks, a lead mining stock whose b is equal to 1.0, for $5,000 net and to use the proceeds to buy $5,000 of stock in a steel company whose b is equal to 2.0. What will be the new beta of the portfolio?

a. 1.12

b. 1.20

c. 1.22

d. 1.10

e. 1.15

[xxv]. A mutual fund manager has a $200,000,000 portfolio with a beta = 1.2. Assume that the risk-free rate is 6 percent and that the market risk premium is also 6 percent. The manager expects to receive an additional $50,000,000 in funds soon. She wants to invest these funds in a variety of stocks. After making these additional investments she wants the fund’s expected return to be 13.5 percent. What should be the average beta of the new stocks added to the portfolio?

a. 1.10

b. 1.33

c. 1.45

d. 1.64

e. 1.87

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