You have regressed the excess returns for two stocks on the corresponding excess

Question

You have regressed the excess returns for two stocks on the corresponding excess returns for the market with the following results:

RA = 0.01 + 1.2(RM); R2 = 0.576; residual standard deviation = 0.103 RB = 0.02 + 0.8(RM); R2 = 0.436; residual standard deviation = 0.0.091

a. Which stock has more firm-specific risk?

b. Which firm has more market risk?

c. The market explains a greater percentage of the volatility of returns for which stock?

d. Assume the risk free rate is constant at 6%. Determine the regression intercept for stock A, if you had used total returns instead of excess returns.

Explanation / Answer

a. Firm-specific risk is measured by the residual standard deviation. Thus, stock A has more firm-specific risk: 10.3% > 9.1%

b. Market risk is measured by beta, the slope coefficient of the regression. A has a larger beta coefficient:

1.2 > 0.8

c. R2 measures the fraction of total variance of return explained by the market return. A’s R2 is larger than B’s: 0.576 > 0.436

d. The average rate of return in excess of that predicted by the CAPM is measured by alpha, the intercept of the SCL. A = 1% which is larger than B = –2%.

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