Problem 13-17 Using the SML [LO4]
Asset W has an expected return of 12.2 percent and a beta of 2.00. If the risk-free rate is 4.1 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Enter your expected returns as a percent rounded to 2 decimal places, e.g., 32.16, and your beta answers to 3 decimal places, e.g., 32.161.)
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If you plot the relationship between portfolio expected return and portfolio beta, what is the slope of the line that results? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
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Explanation:
First, we need to find the β of the portfolio. The β of the risk-free asset is zero, and the weight of the risk-free asset is one minus the weight of the stock, so the β of the portfolio is:
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| βP = wW(2.00) + (1 − wW)(0) = 2.00wW |
So, to find the β of the portfolio for any weight of the stock, we simply multiply the weight of the stock times its β.
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Even though we are solving for the β and expected return of a portfolio of one stock and the risk-free asset for different portfolio weights, we are really solving for the SML. Any combination of this stock and the risk-free asset will fall on the SML. For that matter, a portfolio of any stock and the risk-free asset, or any portfolio of stocks, will fall on the SML. We know the slope of the SML line is the market risk premium, so using the CAPM and the information concerning this stock, the market risk premium is:
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| E(RW) = .122 = .041 + MRP(2.00) |
| MRP = .081 / 2.00 |
| MRP = .0405, or 4.05% |
| So, now we know the CAPM equation for any stock is: |
The slope of the SML is equal to the market risk premium, which is .0405, or 4.05%
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