EVALUATING RISK AND RETURN Stock X has a 10% expected return, a beta coefficient

Question

   EVALUATING RISK AND RETURN   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 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 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 $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)

Coefficient of Variation (CV) = Standard Deviation / Expected Return

CVX = 35% / 10% = 3.5

CVY = 25% / 12.5% = 2.0

(b)

Since CV is a measure of standardized dispersion of two data sets or two series, a lower CV indicates lower risk.

Here, CVX < CVY, indicating X is a riskier stock.

(c)

Required Rates of Return = Risk Free Rate + Beta x (Market Risk Premium)

Stock X = 6% + (0.9 x 5%) = 10.5%

Stock Y = 6% + (1.2 x 5%) = 12%

(d)

If a stocks expected return (using CAPM) is more than required return, the stock is undervalues & the investor will buy the undervalued stock.

For Stock X: Expected Return (10%) < Required Return (10.5%)

For Stock Y: Expected Return (12.5%) > Required Return (12%)

So, stock Y is undervalued & attractive for buying.

(e)

Required return of Portfolio = Sum of (Proportion of stock in portfolio x Stock's required return)

Proportion of X = 7500 / (7500 + 2500) = 75%

Proportion of Y = 2500 / (7500 + 2500) = 25%

So, Portfolio required return = 75% x 10.5% + 25% x 12% = 10.875%

(f)

If market risk premium increases to 6%, then required return:

Stock X = 6% + (0.9 x 6%) = 11.4%

Stock Y = 6% + (1.2 x 6%) = 13.2%

So stock Y shows a larger increase.

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