Sequential Cross-Sectional Regression for Factor Return Analysis
Summary
This research note outlines a cross-sectional regression framework for studying historical returns of technical, expectation, and financial factors. It uses sequential single-factor regressions: each stage models the preceding stage’s residual, so later factor returns represent variation left after earlier factors have been accounted for. The factor order is chosen using the researchers’ judgment and is kept consistent because changing it alters the interpretation of the resulting returns.
The note also recommends combining conceptually similar, highly correlated exposures with equal weights when optimized weights are unavailable. It proposes comparing a factor’s sequential and single-step return series and their explanatory power to gauge overlap with earlier factors; a small remaining contribution may indicate substantial redundancy and a reason to exclude it. These are methodological recommendations, not empirical results in the provided text. The stated claim that this approach fully avoids multicollinearity is too strong: sequential residualization makes attribution order-dependent and does not remove all modeling or identification concerns.
Key ideas
- Sequential regressions use each stage’s residual as the response for the next factor.
- Factor ordering affects attribution and should remain consistent across follow-up analysis.
- Equal-weight composites are suggested for similar, correlated factor exposures when weights are not optimized.
- Comparing sequential and single-step estimates can help identify factors with little distinct explanatory contribution.
- Residualization does not eliminate every source of modeling uncertainty or make factor attribution order-independent.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.