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?

Answer:

(a)   CalculatingCoefficient of Variation:

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

                  Stock Y –Coefficient Variation = 2

(b) A security risk is measured by Beta. Herestock Y has more beta. Thus, Stock Y is more risky then compared tostock X.

( c) Calculating Required rate of return:

Required Return (R_e) = R_f + ß * MRP(Market Risk Premium)

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

                                        =0.105 (or) 10.5%

Required return of Stock X = 10.5%

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

                                        = 0.12(or)12%          

Required return of Stock Y = 12%

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

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

           Stock Y is most attractive to a diversified investor, since stock yhaving its expected return is greater than the requiredreturn.          

(e)Calculating Required return of aPortfolio:

      Required return (R_e) =(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%

                 Required return = 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%