Stock X has a 10 percent expected return, a beta coefficient of0.9, and a 35 per

Question

Stock X has a 10 percent expected return, a beta coefficient of0.9, and a 35 percent standard deviation of expected returns. StockY has a 12.5 percent expected return, a beta coefficient of 1.2,and a 25 percent standard deviation. The risk-free rate is 6percent, and the market risk premium is 5 percent.
a) Calculate each stock's coefficient of variation. b) Which stock is riskier for a diversified investor? c) Calculate each stock's required rate of return. d) On the basis of the two stock's expected and requiredreturns, which stock would be more attractive to a diversifiedinvestor? e) Calculate the required return of a portfolio that has$7,500 invested in Stock X and $2,500 invested in Stock Y? f) If the market risk premium increased to 6 percent, which ofthe two stocks would have the larger increase in its requiredreturn?
a) Calculate each stock's coefficient of variation. b) Which stock is riskier for a diversified investor? c) Calculate each stock's required rate of return. d) On the basis of the two stock's expected and requiredreturns, which stock would be more attractive to a diversifiedinvestor? e) Calculate the required return of a portfolio that has$7,500 invested in Stock X and $2,500 invested in Stock Y? f) If the market risk premium increased to 6 percent, which ofthe two stocks would have the larger increase in its requiredreturn?

Explanation / Answer

Coefficient of Variation = Standard Deviation / ExpectedReturn

           The coefficient of variation allows you to determine how muchvolatility (risk) you are assuming in comparison to the amount ofreturn you can expect from your investment.

Stock X: Coefficient Variation = 0.35 / 0.10

                                                           

                 Stock X - CoefficientVariation = 3.5

Stock Y: Coefficient Variation = 0.25 / 0.125

( c) Calculating Required rate of return:

Required Return (Re) = Rf + ß * MRP(Market Risk Premium)

Stock X Required return = 0.06 + (0.9 * 0.05)

                                        =0.105 (or) 10.5%

Stock Y Required return = 0.06 + (1.2 * 0.05)

                                        = 0.12(or)12%          

    (d) Stock x – Expected Return =10%       Required Return = 10.5%

          Stock y– Expected Return = 12.5%     RequiredReturn = 12%

(e)Calculating Required return of aPortfolio:

      Required return (Re) =(7,500/10,000) 0.9 + (2,500/10,000) 1.2

                                       = 0.675 +0.30

                                       = 0.9750

       Requiredreturn       = 0.06 + (0.975)0.05

                                      = 10.875%

(f)     If the Market risk premium increasesto 6%, Required return is:

Stock X Required return = 0.06 + (0.9 * 0.06)

                                        = 0.114 (or) 11.4%

                       Stock X Required return = 11.4%

Stock Y Required return = 0.06 + (1.2 * 0.06)

                                        = 0.132 (or) 13.2%

                       Stock Y Required return = 13.2%

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