Question

EVALUATING RISK AND RETURN Stock 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 30.0% 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. Do not round intermediate calculations. Cvx= ?Cvy=? C.Calculate each stock's required rate of return.Rx=? Ry=? Round your answers to two decimal places. D. On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor? E. Calculate the required return of a portfolio that has $9,500 invested in Stock X and $3,000 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places. F. If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

Answer 1

Coefficient of Variation

Coefficient of Variation is a measure of variability of return. It is mathematically represented as:

For Stock X, CV = (35%/10.5%) * 100 = 333.33% (or 3.33)

For Stock Y, CV = (30%/12.5%) * 100 = 240% (or 2.4)

b. Required Rate of Return

By CAPM, Required rate of return = Risk free rate + Beta * Market Risk Premium

For Stock X, Req rate of return = 6% + (1 * 5%) = 11%

For Stock Y, Req rate of return = 6% + (1.2 * 5%) = 12%

D. This question requires application of concept of Security Market line (SML), which is the line that reflects an investment's risk versus its return, or the return on a given investment in relation to risk. When the security is plotted on the SML chart, if it appears above the SML, it is considered undervalued because the position on the chart indicates that the security offers a greater return against its inherent risk. Conversely, if the security plots below the SML, it is considered overvalued in price because the expected return does not overcome the inherent risk. So, going by this concept, Expected rate of return for Stock X is less than its required rate of return, so it plots below the SML and hence is undervalued. By the same concept, Stock Y is overvalued. So Stock X is more attractive.

E. Required rate of return = (9500 * 11% + 3000 * 12%) = $1,405

$1,405 over a portfolio of 9500 + 3000 = 1405/(9500 + 3000) = 11.24%

F. By CAPM, Required rate of return = Risk free rate + Beta * Market Risk Premium

For Stock X, Req rate of return = 6% + (1 * 6%) = 12%

For Stock Y, Req rate of return = 6% + (1.2 * 6%) = 13.2%

Increase in required rate of return = (12% -11%)/11% = 9.09%

Increase in required rate of return = (13.2% -12%)/12% = 10%

(Intutively, since Beta for Stock Y is higher, in case of increase in market risk premium, change in required rate would be higher for Stock Y)