Portfolio Sorts and Factor Regressions for Cross-Sectional Research
Summary
The document compares two empirical approaches for studying whether one stock characteristic explains returns or another variable. Double sorts group stocks by one characteristic and then sort within those groups by a second. This nonparametric approach makes fewer assumptions about the shape of the relationship and can reveal nonlinear patterns, but it is harder to control for many characteristics at once.
A regression approach constructs a factor for the characteristic of interest, then tests it alongside established pricing factors in time-series regressions on portfolios sorted by the outcome variable. Regression can account for a larger set of controls, though it commonly imposes a linear relationship. One response also describes using factor exposure, fit, and the intercept’s statistical significance to assess whether a candidate factor adds information beyond other factors. These are methodological suggestions, not a reported empirical comparison; the document gives no dataset or results, and the interpretation depends on model specification and assumptions.
Key ideas
- Double sorts can expose nonlinear cross-sectional relationships without requiring a specific functional form.
- Portfolio sorts make it difficult to control for many characteristics simultaneously.
- Factor regressions can include more controls but commonly assume linear effects.
- Factor exposure, regression fit, and the intercept can help assess whether a factor adds information beyond existing factors.
- The document offers methodological discussion but no empirical results comparing the approaches.
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Full text
# "Risk" Factor vs Double Sorts # "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, ## Answer by skoestlmeier (score 4) https://quant.stackexchange.com/a/41614 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. ## Answer by Ashu (score 1) https://quant.stackexchange.com/a/34536 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.
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