Stock X has a 10% expected return, a beta coefficient of 0.9, and a 35% standard

Question

Stock X has a 10% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2 and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

(a) Calculate each stock's coefficiet 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 required returns, which stock would be more attractive to a diversified investor?

(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%, which of the two stocks would have the larger increase in its required return?

Explanation / Answer

(a) Calculate each stock's coefficiet of variation.

Stock X

coefficiet of variation = SD/Expected Return

coefficiet of variation = 35%/10%

coefficiet of variation = 3.50

Stock Y

coefficiet of variation = SD/Expected Return

coefficiet of variation = 25%/12.5%

coefficiet of variation = 2

(b) Which stock is riskier for a diversified investor?

Stock Y is riskier for a diversified investor as its beta is higher than stock x

(c) Calculate each stock's required rate of return.

Stock X

As per CAPM

Stock's required rate of return = risk-free rate + market risk premium*beta

Stock's required rate of return = 6 + 5*0.9

Stock's required rate of return = 10.5%

Stock Y

As per CAPM

Stock's required rate of return = risk-free rate + market risk premium*beta

Stock's required rate of return = 6 + 5*1.2

Stock's required rate of return = 12%

(d) On the basis of the two stock's expected and required returns, which stock would be more attractive to a diversified investor?

Stock X

Alpha= Expected Return - Stock's required rate of return

Alpha= 10% - 10.5%

Alpha= -0.5%

Stock Y

Alpha= Expected Return - Stock's required rate of return

Alpha= 12.5% - 12%

Alpha= 0.5%

On the basis of the two stock's expected and required returns , Stock Y would be more attractive to a diversified investor

(e) Calculate the required return of a portfolio that has $7,500 invested in Stock X and $2,500 invested in Stock Y.

Required return of a portfolio = Weight of stock x * Reuired return of stock x + Weight of stock Y * Reuired return of stock Y

Required return of a portfolio = 7500/(7500+2500) * 10.5 + 2500/(7500+2500) * 12.5

Required return of a portfolio = 11%

(f) If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

Stock Y as its beta is higher than stock x

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