Stock X has a 10.0% expected return, a beta coefficient of 0.9, and a 35% standa

Question

Stock X has a 10.0% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.0% expected return, a beta coefficient of 1.1, and a 30.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

A. Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations.

CVx =

CVy =

B.Calculate each stock's required rate of return. Round your answers to two decimal places.
rx =
ry =

C.

Calculate the required return of a portfolio that has $5,000 invested in Stock X and $2,000 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places.
rp =

Explanation / Answer

For Stock X

Expected return = 10%

Standard deviation = 35%

Beta = 0.9

For Stock Y

Expected return = 12%

Standard deviation = 30%

Beta = 1.1

a.

Coefficient of variation is calculated by following formula:

Coefficient of variation = Expected return / Standard deviation

So by using above formula Coefficient of variation for stock X is calculated below:

Coefficient of variation = Expected return / Standard deviation

                                      = 10% / 35%

                                      = 0.28

Coefficient of variation of stock X is 0.28.

Similarly

By using above formula Coefficient of variation for stock Y is calculated below:

Coefficient of variation = Expected return / Standard deviation

                                      = 12% / 30%

                                      = 0.40

Coefficient of variation of stock Y is 0.40.

b.

Risk free rate = 6%

Market risk premium = 5%

For Stock X

Beta = 0.9

So required rate of return for stock X is calculated below using CAPM Model:

Required rate of return = Risk free rate + Risk Premium × Beta

                                     = 6% + 5% × 0.9

                                     = 6% + 4.5%

                                     = 10.50%

Required rate of return for stock X is 10.50%.

For Stock Y

Beta = 1.1

So required rate of return for stock Y is calculated below using CAPM Model:

Required rate of return = Risk free rate + Risk Premium × Beta

                                     = 6% + 5% × 1.1

                                     = 6% + 5.5%

                                     = 11.50%

Required rate of return for stock Y is 11.50%.

c.

Investment in stock X = 5,000

Investment in stock Y = 2,000

Required rate of return of portfolio is calculated below:

Required rate of return of portfolio = [($5,000 × 10.5%) + ($2,000 × 11.5%)] / ($5,000 + $2,000)

                                                                = ($525 + $230) / $7,000

                                                                = $755 / $7,000

                                                                 =10.79%

Required rate of return of portfolio is 10.79%.

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