Beta- and Size-Adjusted Features

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.

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.