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Chapter 8

Portfolio beta

1. A mutual fund manager has a $20 million portfolio with a beta of 0.95. The risk-free rate is 5.25%, and the market risk premium is 6.5%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund's required return to be 15%. What should be the average beta of the new stocks added to the portfolio? Round your answer to two decimal places.

** **

2. Required rate of return

Stock R has a beta of 1.7, Stock S has a beta of 0.4, the expected rate of return on an average stock is 9%, and the risk-free rate of return is 7%. By how much does the required return on the riskier stock exceed the required return on the less risky stock? Round your answer to two decimal places.

________%

** **

3. CAPM, portfolio risk, and return

Consider the following information for three stocks, Stocks X, Y, and Z. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)

Stock |
Expected Return |
Standard Deviation |
Beta |
||

X |
9.22 |
% |
16 |
% |
0.7 |

Y |
11.06 |
16 |
1.1 |
||

Z |
12.90 |
16 |
1.5 |

Fund Q has one-third of its funds invested in each of the three stocks. The risk-free rate is 6%, and the market is in equilibrium. (That is, required returns equal expected returns.)

** **

A. What is the market risk premium (r_{M} - r_{RF})? Round your answer to two decimal places.

__________%

B. What is the beta of Fund Q? Round your answer to two decimal places.__________

** **

C. What is the expected return of Fund Q? Round your answer to two decimal places.

_________%

- Would you expect the standard deviation of Fund Q to be less than 16%, equal to 16%, or greater than 16%?

a. less than 16%

b. greater than 16%

c. equal to 16%

** **

4. CAPM and required return

Calculate the required rate of return for Manning Enterprises assuming that investors expect a 4.2% rate of inflation in the future. The real risk-free rate is 1.25%, and the market risk premium is 7%. Manning has a beta of 2, and its realized rate of return has averaged 13.5% over the last 5 years. Round your answer to two decimal places. _________

** **

5. Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 1.52. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and to use these proceeds to buy another stock with a beta of 1.81. What would your portfolio's new beta be? Round your answer to two decimal places.

** **

6. Required rate of return

Suppose r_{RF} = 6%, r_{M} = 13%, and b_{i} = 2.

A. What is r_{i}, the required rate of return on Stock i? Round your answer to two decimal places. ___________%

B. Now suppose r_{RF} increases to 7%. The slope of the SML remains constant. How would this affect r_{M} and r_{i}?

I. r_{M} will increase by 1% and r_{i} will remain the same.

- Both r
_{M}and r_{i}will decrease by 1%. - Both r
_{M}and r_{i}will remain the same. - Both r
_{M}and r_{i}will increase by 1%. - r
_{M}will remain the same and r_{i}will increase by 1%.

** **

C. Now suppose r_{RF} decreases to 5%. The slope of the SML remains constant. How would this affect r_{M} and r_{i}?

I. Both r_{M} and r_{i} will increase by 1%.

II. Both r_{M} and r_{i} will remain the same.

III. Both r_{M} and r_{i} will decrease by 1%.

VI. r_{M} will decrease by 1% and r_{i} will remain the same.

VII. r_{M} will remain the same and r_{i} will decrease by 1%.

D. Now assume that r_{RF} remains at 6% but r_{M} increases to 14%. The slope of the SML does not remain constant. How would these changes affect r_{i}? Round your answer to two decimal places.The new r _{I }__________%

** **

E. Now assume that r_{RF} remains at 6% but r_{M} falls to 12%. The slope of the SML does not remain constant. How would these changes affect r_{i}? Round your answer to two decimal places. The new r_{i }____________%.

** **

7. Portfolio required return

Suppose you are the money manager of a $4.65 million investment fund. The fund consists of 4 stocks with the following investments and betas:

Stock |
Investment |
Beta |

A |
$ 380,000 |
1.50 |

B |
420,000 |
- 0.50 |

C |
1,100,000 |
1.25 |

D |
2,750,000 |
0.75 |

If the market's required rate of return is 12% and the risk-free rate is 7%, what is the fund's required rate of return? Round your answer to two decimal places.________%

8. Expected and required rates of return

Assume that the risk-free rate is 4% and the market risk premium is 5%.

A.What is the expected return for the overall stock market? Round your answer to two decimal places.____________%

B. What is the required rate of return on a stock with a beta of 0.8? Round your answer to two decimal places._________%

** **

9. CAPM and portfolio return

You have been managing a $5 million portfolio that has a beta of 1.70 and a required rate of return of 13%. The current risk-free rate is 5.25%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.90, what will be the required return on your $5.5 million portfolio? Round your answer to two decimal places.__________%

** **

10. Beta coefficient

Given the following information, determine the beta coefficient for Stock J that is consistent with equilibrium: r_{J} = 12%; r_{RF} = 6.6%; r_{M} = 12%. Round your answer to two decimal places.

Subject | Business |

Due By (Pacific Time) | 11/13/2013 04:00 pm |

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