1. Temporary impact is the tell
A large buy order lifts the price. Some of that move is permanent — the trade carried information, and the market repriced. But some of it is just the cost of demanding immediacy from a market that had to be paid to supply it, and that part decays: the price drifts back once the pressure is off. The more illiquid the asset, the larger the temporary component, and the bigger the subsequent reversal. Liquid names absorb the same order flow with barely a wobble; illiquid ones lurch and then snap back. That reversal — order flow today, a return in the opposite direction tomorrow — is a signal you can measure from price and volume alone, no book required.
2. The Pástor-Stambaugh regression
Lubos Pástor and Robert Stambaugh (2003), in "Liquidity Risk and Expected Stock Returns," made the idea precise. Regress an asset's next-period excess return on its current return and its current signed volume — volume carrying the sign of that period's return, a proxy for the direction of order flow:
rᵉₜ₊₁ = θ + φ·rₜ + γ·sign(rᵉₜ)·vₜ + εₜ₊₁
Here rᵉ is the excess return, r the raw return, and v the dollar volume. The coefficient that matters is γ. It answers a sharp question: after a day of buying pressure (positive signed volume), does the next day's return tend to be negative — a reversal? If so, γ is negative, and the more negative it is, the stronger the bounce-back per unit of volume, and the less liquid the asset. In a deep, liquid market order flow moves the price and it stays: no reversal, γ near zero.
3. Reading gamma
γ is a liquidity gauge with a built-in sign convention: more negative = less liquid. It is expressed per unit of (signed) volume, so it scales with how much flow it takes to move the price — exactly the quantity a trader cares about when sizing an order. Read against its own history, a γ that drifts more negative is liquidity draining out of a name; a γ pinned near zero is a market that shrugs off size. Because it is estimated over a window — typically a month of daily observations — a single γ is noisy for one stock, but the signal is real and it aggregates: average it across a market and you get a clean read on systematic liquidity.
4. From a number to a priced risk factor
The reason Pástor-Stambaugh is a landmark is not the per-stock number — it is what the aggregate does. Averaging γ across stocks gives a market-wide liquidity series, and its month-to-month innovations form a traded liquidity factor. Pástor & Stambaugh showed that stocks whose returns move most with that factor — the ones that suffer most when market-wide liquidity dries up — earn higher average returns. Liquidity, in other words, is a priced risk: investors demand compensation for holding assets that turn illiquid precisely in the states of the world where liquidity is most precious. A measure built from nothing but daily prices and volume turns out to explain a slice of the cross-section of returns.
5. Where it sits next to the order book
This is a low-frequency, price-based lens, and that is its strength and its limit. Its strength: it needs only returns and volume, so it works on any asset with a price history — no order-book feed, no tick data. Its limit: it is a coarse, after-the-fact read, not a real-time one. It complements the microstructure tools rather than replacing them. Where order-book depth and slope measure liquidity ex ante from resting size, and Amihud illiquidity measures realized price impact per unit of volume, the Pástor-Stambaugh γ isolates the reversing part of that impact — the temporary component that a deep book would have absorbed. Three angles on the same thing: how much does it cost to trade, and how much of that cost comes back.
6. Caveats worth keeping
A per-stock, per-month γ is a noisy estimate — a handful of daily observations fitting three coefficients — so treat a single value with humility and lean on aggregation and history. The sign proxy (return sign standing in for order-flow direction) is exactly that, a proxy; on days when returns and true order-flow direction diverge it adds noise. And the measure presumes that reversals are liquidity, when some short-horizon reversal is also just mean reversion or overreaction — which is why it is read as part of a suite, not in isolation. Used with those caveats in mind, it is one of the most durable liquidity signals in the literature.
7. Computing it
Our open-source orderflow-metrics library ships it, dependency-free, in TypeScript and Python — the ordinary-least-squares fit included, no linear-algebra library required:
import { pastorStambaughGamma } from "orderflow-metrics";
// aligned daily series (typically one month per estimate)
const returns = [
0.012, -0.008, 0.005, -0.02, 0.015, 0.004, -0.011, 0.02, -0.006, 0.009, 0.001,
-0.014, 0.017, -0.003, 0.006, 0.011, -0.019, 0.007, 0.002, -0.01, 0.013, -0.004,
];
const excessReturns = [
0.01, -0.01, 0.004, -0.022, 0.013, 0.003, -0.013, 0.018, -0.008, 0.007, 0.0,
-0.016, 0.015, -0.005, 0.004, 0.009, -0.021, 0.006, 0.001, -0.012, 0.011, -0.006,
];
const volumes = [
1.2, 0.9, 1.5, 2.1, 1.1, 0.8, 1.7, 1.3, 0.95, 1.05, 1.4, 2.0, 1.15, 0.85, 1.6,
1.25, 2.2, 1.0, 0.9, 1.8, 1.35, 1.1,
];
pastorStambaughGamma(returns, excessReturns, volumes);
// { gamma: -0.00801, phi: 0.26788, intercept: -0.00079 }
// γ < 0 → order flow reverses → the illiquid direction
The negative γ says that on this series, buying pressure is followed by a reversal — the signature of temporary price impact. The Python distribution exposes the same function (pastor_stambaugh_gamma), returning the same three coefficients. It sits beside order-book liquidity, Amihud illiquidity, and the execution-cost tools inside the wider market-microstructure toolkit we build in the open — install it from our open-source page (npm and PyPI, MIT-licensed).
8. Conclusion
Liquidity hides in plain sight, in the way prices give back part of what order flow takes. The Pástor-Stambaugh measure reads that reversal off returns and volume alone, turns it into a single number with an honest sign, and — aggregated — into one of the few liquidity signals the market actually prices. It will not replace a live order book, and it was never meant to; it answers a different, cheaper question, on any asset with a price. Explore the rest of the toolkit in our quantitative research library, or read the implementation in our open-source metrics.