“Qualitative” Regression On KLCI

Common linear regression is quantitative in nature.  However, it could be used as a qualitative measure under certain condition.  For example, suppose we want to examine the seasonality of stocks returns, we could estimate the regression model using “dummy” variables as independent variables.  A “dummy” variable takes on a value of 1 if a particular condition is true and 0 if that condition is false.

Using the KLCI monthly closing return data from November 2011 to November 2018, we can estimate a regression including an intercept and 11 dummy variables, one for each of the first 11 months of the year.  The equation that we estimate is

Return_t = b₀ + b₁Jan_t + b₂Feb_t + … + b₁₁Nov_t + e_t

where each monthly dummy variable has a value of 1 when the month occurs and a value of 0 for other months.  The intercept b₀, measures the average return for KLCI in December because there is no dummy variable for December.

The following table shows the results of the regression.

The low R² suggests that a month-of-the-year effect in KLCI returns may not be very important for explaining KLCI returns.  However, the significance of F-Test is that it is below the conventional level of 5%, which indicates that we cannot reject the null hypothesis that all of the coefficients jointly are equal to 0.  This means that we could look at the seasonality effect on certain months that are statistically significant such as December (Intercept), May, June, August, September and November.  Amongst those months, only December has positive average return while other months have negative average returns.  Will the history repeat itself in December 2018, perhaps window dressing for this holiday season?

Reference:

CFA Program Level II Reading Assignment by Sanjiv R. Das, PhD, Richard A. DeFusco, PhD, CFA, Dennis W. Mcleavey, CFA, Jerald E. Pinto, PhD, CFA, and David E. Runkle, PhD, CFA