Question

The results of the estimated CAPM and Multifactor models for the returns of the GLCGX fund (Large Cap Growth) are given

below.

(a) What is the implication of intercept coefficient? What is the interpretation of each slope coefficient ?

(b) Which model better explains GLCGX fund returns: the CAPM or the Multifactor Model?

OUTPUT for Question 10:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.007049 0.002898 -2.432 0.0181 * rm 1.167201 0.058906 19.815 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.02243 on 58 degrees of freedom Multiple R-squared: 0.8713, Adjusted R-squared: 0.8691 F-statistic: 392.6 on 1 and 58 DF, p-value: < 2.2e-16

lm(r_glcgx~rm+hml+smb+mom) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.0009467 0.0024567 0.385 0.701

rm 1.0075831 0.0498170 20.226 < 2e-16 *** hml -0.4832266 0.0672459 -7.186 1.87e-09 *** smb -0.2584757 0.0522464 -4.947 7.47e-06 *** mom -0.0018580 0.0313426 -0.059 0.953 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.01643 on 55 degrees of freedom Multiple R-squared: 0.9345, Adjusted R-squared: 0.9297 F-statistic: 196.2 on 4 and 55 DF, p-value: < 2.2e-16

Answer 1

(a) Intercept is nothing but the mean value of the dependent variable, when all the predictors (independent variables are set to zero.It gives the average GLCGX fund when the predictors ( rm in CAPM and rm, hml, smb, and mom in the multifactor model) are equal to zero.

However, while testing the how change in one variable affects the other using regression, we might not be interested in studying a vitual scenario where the predictors are zero.Hence, intercept, here, might not have a significant interpretation.

Slope coefficient estimates are the figures in the output that appear under the column head 'Estimate'. It gives the mean change in the dependent variable for a unit increase in predictor variable. If the signs of the estimate are positive or negative, we say that it measures the mean increase or decrease in the GLCGX fund when the predictor increases by one unit respectively.

For CAPM, for a unit increase in 'rm', the GLCGX fund, on an average increases by 1.167201.

For Multifactor Model,

For a unit increase in 'rm', the GLCGX fund, on an average, increases by 1.0075831 units. For a unit increase in 'hml', the GLCGX fund, on an average, decreases by 0.4832266 units. For a unit increase in 'smb', the GLCGX fund, on an average, decreases by 0.2584757 units. For a unit increase in 'mom', the GLCGX fund, on an average, decreases by 0.001858 units.        

(b) A relative measure that measures the amount of variation in dependent variable that is explained by the independent variable is R square.The higher the explained variation, the better the model.

Hence, the model with higher R square would  explain GLCGX fund returns better. From the output, we find that the Multifactor Model (R square = 0.9297) explains GLCGX fund returns better than the CAPM model ( R square = 0.8691).

The  Multifactor Model explains almost 93% of the variation in  GLCGX fund returns.