Below is the output from regressing daily excess return of ABC on daily excess return of S&P 500. Sample mean of daily excess return of ABC was 0.08% per day, and the sample mean of daily excess return of S&P 500 was 0.04% per day.
(Annualized) volatility of ABC is 29.63% and (annualized) volatility of S&P 500 is 16.71%.
For this problem, assume 250 trading days per year, and 0% risk-free rate.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.5971
R Square 0.3565
Adjusted R Square 0.3564
Standard Error 0.0150
Observations 6219
ANOVA
df SS MS F Significance F
Regression 1 0.7784 0.7784 3444.6028 0.0000
Residual 6217 1.4049 0.0002
Total 6218 2.1834
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.0004 0.0002 2.1569 0.0310 0.0000 0.0008
X Variable 1 1.0589 0.0180 58.6907 0.0000 1.0236 1.0943
a) Is the beta of ABC with respect to the S&P 500 statistically different from one?
A) Yes
B) No
C) Not sure, no clue, or no idea