Question

c) A regression of stock A's returms on the market index Ms returns has produced the following output. Regression summary R Square Standard Error Observations 0.30667 0.02992 469 ANOVA df MS F Significance F 0.001 Regression Residual Total 0.1849 0.1849 206.5645 467 0.4180 0.0009 468 0.6028 Intercept ReturnM Coefficients Std. Error 0.00036 0.00138 0.70709 0.04920 i. What is the estimated equation that corresponds to these results? ii. What retum for stock A would be expected if M's retum was 5%? ili. What are the t-statistics for the intercept and M's return? iv. Give a 95% confidence interval for the coefficient of Return M v. Show how the regression's R-squared can be calculated from this output. vi. How can you tell from these results whether the market index M explains the retums of A?

Answer 1

i)

estimated return of stock's A = 0.00036 + 0.70709 * return M

ii)

return of M = 5%

estimated return of stock's A = 0.00036 + 0.70709 * 5% = 0.0357145 or 3..57%

iii)

t-stat for intercept =estimated intercept /std error = 0.000036/0.00138 =0.026086957

t-stat for slope (M's return ) =estimated slope / std error = 0.70709/0.0492 =14.37174797

iv)

n =   469
alpha,α =    0.05
estimated slope=   0.70709
std error =    0.0492

Df =    n - 2 =   467
critical t-value =    1.9651 [ excel function: =t.inv(α/2,df) ]

margin of error ,E =    t*Std error =   0.0967
      
confidence interval is      
lower bound = estimated  - E=   0.6104
upper bound = estimated slope  + E=   0.8038

v)

R² =SSr/SST =0.1849/0.6028 =0.3067

vi)

30.67% of variability in returns of A is explained by market index M