“Risk” Factor vs Double Sorts

With regards to a cross-sectional asset pricing (stocks) study, I am testing if one variable can explain another. One common approach to do this, is to use the double-sorting portfolio technique (sort on variable a into portfolios, then dependent on a - sort b into portfolio). This approach seems to be adequate for such a problem, if you have a large sample so that you get reasonable amount of dispersion in your sort variables.

Another approach I have seen in the literature is to create factors of your preferred explanatory variables by using the Fama French factor methodology (HML,SML etc), then sort you portfolios on the first variable (the variable you would like to explain) and run time series regression of a Fama French three factor model (or CAPM) augmented with your new factor.

I am wonder if there are any arguments for performing the second over the first approach? Could these approaches complement each other,

Portfolio sorts and regression techniques are both very common in empirical research to examine the cross-sectional relation between two or more variables. Each have their own advantages and disadvantages. It would like to briefly highlight the most important ones.

Portfolio Sort

• It is a nonparametric technique, i.e. it does not make any assumptions about the nature of the cross-sectional relations between the variables under investigation. Therefore it can be helpful in uncovering nonlinear relations between variables

• It is difficult to control for a large number of variables when examining the cross-sectional relation of interest.

Regression techniques

• Applicable for controlling for a large set of other variables.

• Parametric technique, so one often assumes a linear relation between each control variable and the outcome variable.

I have used an approach to the second method to examine (or to orthonalize) a factor's "independence" vis-a-vis other factors. In addition to looking at R^2, also examining each factor's sensitivity and its t-stats.

If the intercept of the regression is statistically different from zero then it would indicate the "dependent" factor contributes more than the explanatory factors. If it is statistically zero (abs(t-stat) <= 2) then the dependent factor is subsumed by the explanatory factors.