Beta- and Size-Adjusted Features
Beta- and size-adjusting a feature means stripping out the part of its value that is just explained by a stock's market sensitivity or market capitalization, leaving the part that might carry genuine, independent signal.
Prerequisites: Cross-Sectional Feature Standardisation
A raw momentum score often comes out high for small, high-beta stocks simply because they move more, not because momentum itself is doing anything special for them. Beta- and size-adjusted features correct for this by regressing the raw feature against beta and market capitalization each day, and keeping only the residual — the part of the feature's value that beta and size don't already explain.
Adjusting a feature for beta and size removes the part of its cross-sectional variation that is just a proxy for "high-beta" or "small-cap," so a model trained on the adjusted feature learns from the signal actually left over, not a repackaged size or beta bet.
Without this step, a model can end up making what looks like a sophisticated multi-factor bet that is actually just a disguised small-cap or high-beta tilt, which is a much simpler (and more crowded) trade than intended.
Worked example. Across 500 stocks, a raw feature's cross-sectional average is 0.20 among high-beta stocks and 0.05 among low-beta stocks. Regressing the feature on beta finds a slope showing beta alone explains most of that gap. After subtracting the fitted beta-driven component, a high-beta stock's adjusted feature value shrinks from 0.20 to roughly 0.03 — much closer to the low-beta stocks' residual, revealing that most of the original 0.20 was just beta exposure.
This adjustment is standard practice before feeding factors into cross-sectional models that are meant to isolate stock-specific signal from known systematic risk exposures.
Further reading
- Fama & French, 'The Cross-Section of Expected Stock Returns' (JF, 1992)