2009homework#6&7solution - Name: _ NetID: _ HADM 2222...

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Name: ___________________________________ NetID: _______________________ Prof. Q. Ma, HADM 2222 Fall 2009 1/3 HADM 2222 Fall 2008, Prof. Q. Ma Homework assignment #6, #7 combined [Due 10 a.m. Wednesday, November 18, 2008, Statler 435 drop box] 1. A stock has an expected return of 13 percent, the risk-free rate is 4.5 percent, and the market risk premium is 7 percent. What must the beta of this stock be? Solution: We are given the values for the CAPM except for the ! of the stock. We need to substitute these values into the CAPM, and solve for the ! of the stock. One important thing we need to realize is that we are given the market risk premium. The market risk premium is the expected return of the market minus the risk-free rate. We must be careful not to use this value as the expected return of the market. Using the CAPM, we find: E(R i ) = .13 = .045+ .07 ! i ; we solve for ! i = 1.21 2. A stock has an expected return of 15 percent, its beta is 1.45, and the expected return on the market is 12 percent. What must the risk-free rate be? Solution: Here we need to find the risk-free rate using the CAPM. Substituting the values given, and solving for the risk-free rate, we find: E(R i ) = .15 = R f + (.12 – R f )(1.45); solve we have .15 = R f + .174 – 1.45R f ; R f = .0533 or 5.33% 3. You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.65 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? Solution: The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the portfolio is as risky as the market it must have the same beta as the market. Since the beta of
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2009homework#6&7solution - Name: _ NetID: _ HADM 2222...

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