The Pastor-Stambaugh Liquidity Measure

Some stocks bounce back sharply the day after a big price move on heavy volume, because dealers who absorbed the order flow need to be paid for the risk they took on, and that payment shows up as a price reversal once the pressure fades. Pastor and Stambaugh turned this into a measurable signal: for each stock each month, they regress next-day returns on today's signed dollar volume and today's return, and the size of the reversal coefficient becomes a proxy for how illiquid that stock was that month. Averaging across stocks produces a market-wide liquidity series that rises and falls with how easy it is to trade without moving prices.

The point of building this series is not the number itself but what it lets you do with it: stocks whose returns move more with aggregate market-wide liquidity — a "high liquidity beta" — have historically earned higher average returns, because investors want compensation for holding assets that get hurt worst exactly when liquidity dries up market-wide (a systematic risk, not something diversified away). This turns liquidity from a nuisance cost into a priced risk factor, alongside market, size, and value.

A quant desk building a multi-factor model can add a Pastor-Stambaugh liquidity factor the same way it adds a momentum or value factor: sort stocks by their historical sensitivity to the innovations in this liquidity series, and long the high-sensitivity, short the low-sensitivity portfolio. If that spread portfolio earns a positive average return over time, it supports the claim that liquidity risk is priced — investors demand extra return for exposure to market-wide liquidity shocks, separate from the up-front bid-ask cost of trading any single illiquid name.