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CAPM and Beta of Stocks

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 return by the widest margin. The risk-free rate is 6%, and the required return on an average stock (or "the market") is 10%. Your security analyst tells you that Stock S's expected rate of return, , is equal to 11%, while Stock R's expected rate of return, , is equal to 12%. 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:

Year Stock R Stock S Market
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.

Required: 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 ( - r)?

Solution Preview

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 return by the widest margin. The risk-free rate is 6%, and the required return on an average stock (or "the market") is 10%. Your security analyst tells you that Stock S's expected rate of return, , is equal to 11%, while Stock R's expected rate of return, , is equal to 12%. 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:

Year Stock R Stock S Market
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.

Required: 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 ...

Solution Summary

The solution uses CAPM analysis to choose between two Stocks the criterion being that the expected rate of return of the stock exceeds its required return by the widest margin. The beta for the two stocks is calculated first using the data given and then the beta valueas are input in the CAPM (Capital Asset Pricing Model) equation to calculate the required returns. These then are compared with the expected rate of return.

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