Question

Evaluating risk and returnStock X has a 10.5% expected return, a beta coefficient of 1.0, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.Calculate each stock's coefficient of variation. Round your answers to two decimal places.CVx = ________CVy = ________Calculate each stock's required rate of return. Round your answers to two decimal places.rx = _____%ry = _____%Calculate the required return of a portfolio that has $9,000 invested in Stock X and $3,500 invested in Stock Y. Round your answer to two decimal places.rp = _____ %

Answer 1

Answer and Explanation:

The computation is shown below:

a. For coefficient of variation

CVx is

= Standard deviation ÷ expected return

= 35% ÷ 10.5%

= 3.33

CVy is

= Standard deviation ÷ expected return

= 25% ÷ 12.5%

= 2

b. For required rate of return using the Capital Asset Pricing model , the formula is shown below:

= Risk free rate of return + Beta × market risk premium

For rx, it is

= 6% + 1 × 5%

= 6% + 5%

= 11%

For ry, it is

= 6% + 1.2 × 5%

= 6% + 6%

= 12%

c. For required rate of return of a portfolio, first we have to find out the beta which is shown below

Beta = (Invested amount in Stock X ÷ Total investment amount) × (Beta of stock X) + (Invested amount in Stock Y ÷ Total investment amount) × (Beta of stock Y)

= ($9,000 ÷ $12,500) × (1) + ($3,500 ÷ $12,500) × 1.2)

= 0.72 + 0.336

= 1.056

The total investment amount is

= $9,000 + $3,500

= $12,500

Now the required rate of return of a portfolio is

= Risk free rate of return + Beta × market risk premium

= 6% + 1.056 × 5%

= 6% + 5.28%

= 11.28%

Therefore we applied the above formulas