Conditioning on Cross-Sectional Dispersion

Cross-sectional dispersion is simply how spread out stocks are on some measure at a point in time — the standard deviation of, say, value scores or momentum scores across the universe on a given day. A factor signal ranks stocks relative to each other, so its ability to generate returns depends partly on there being meaningful differences to rank in the first place. When dispersion is high (stocks' valuations, say, are unusually spread apart), a value strategy has a wide gap between cheap and expensive names to exploit. When dispersion collapses (everything trades at a similar multiple), the same ranking-based bet has very little real difference to capture, even if the underlying factor logic is unchanged.

This matters for both sizing and interpretation. A researcher who measures a factor's historical information coefficient (IC) without separating high-dispersion periods from low-dispersion periods can badly misjudge current opportunity: the same factor with the same true skill produces a much larger IC when dispersion is wide than when it's compressed, purely as an arithmetic consequence of there being more spread to explain. Conditioning studies typically bucket history by trailing dispersion (e.g. terciles of cross-sectional standard deviation) and report factor IC separately within each bucket.

Worked illustration: suppose a value factor shows an average IC of 0.04 across all history, but splitting by trailing dispersion tercile shows IC of 0.07 in the high-dispersion tercile and only 0.01 in the low-dispersion tercile. A position sizing rule that ignores this would be roughly right on average but badly oversized in calm, compressed markets and undersized exactly when the factor has the most room to work.