Question

In an index model regression, if 1%+1.2(R _m −R_f​ )+2%+0.8(R_m −R_f) yields an R-square of 0.677 and a residual standard deviation σ(e) of 12%, what is the standard deviation of excess returns?

a) 20.8%
b) 23.3%
c) 28.3%
d) 31.6%

Answer 1

The standard deviation of excess returns is 23.3%.

Step-by-step explanation:

To find the standard deviation of excess returns, we need to calculate the residual standard deviation (σ(e)) and the standard deviation of the market risk premium (R_m - R_f). The equation provided, 1%+1.2(R _m −R_f​ )+2%+0.8(R_m −R_f), is a regression equation that relates excess returns to market risk premium. The coefficient of the term 1.2(R _m −R_f​ ) represents the beta of the stock.

Given that the R-square of the regression is 0.677 and the residual standard deviation σ(e) is 12%, we can calculate the standard deviation of excess returns.

The formula for the standard deviation of excess returns is σ(e) / sqrt(1 - R-square). Plugging in the values, we get 12% / sqrt(1 - 0.677) = 23.3%.