Measuring Price Efficiency

If markets were perfectly efficient, a stock's price would jump instantly to its new fair value the moment relevant information arrived, and then sit there, doing nothing, until the next piece of information showed up. Real prices don't behave that cleanly. They overshoot and drift back, or they underreact and creep toward fair value over minutes rather than jumping there in an instant, or they wiggle around for no informational reason at all because of the mechanics of trading itself. Measuring price efficiency means putting a number on how far real prices deviate from that instant-and-permanent ideal.

The two failure modes

Overreaction / noise. Prices move more than the news justifies, then partially reverse. A large trade might push the price further than the trade's actual information content warrants, simply because it temporarily used up the liquidity sitting at the best price — that bounce-back has nothing to do with new information and everything to do with mechanics.

Underreaction / delay. Prices move less than the news justifies at first, then keep drifting in the same direction as more participants catch on or as the price gradually incorporates what a large order signaled. A stock that keeps grinding up for twenty minutes after a positive earnings surprise, rather than jumping there immediately, is displaying inefficient, delayed price discovery.

Both mean the same underlying thing: today's price is a worse predictor of tomorrow's "true" price than it should be if the market were doing its job perfectly.

A simple way to see it: the variance ratio

One of the most direct tools is comparing how much prices actually move over a long interval versus what you'd expect from the moves you observe over shorter ones. If a price is a pure random walk — which is what perfect efficiency implies, since only genuinely new information should move it — then the variance of a two-minute return should be exactly twice the variance of a one-minute return, four minutes should be four times, and so on, because random, independent steps add up in a specific, testable way.

Say five-second returns on a stock have a variance of 0.0004 (in some price-squared units), so ten seconds of independent five-second steps "should" have a variance of 0.0008. If the actual ten-second variance measured from the data comes out to 0.0006 instead, the ratio of actual to expected is 0.75 — prices are moving less over the longer horizon than independent five-second steps would predict, a signature of overreaction and partial reversal at the five-second scale (a trade pushes the price, and part of that push reverses within ten seconds). A ratio above 1 instead would point the other way: returns are positively autocorrelated, consistent with slow, drifting price discovery rather than a clean, one-time jump. This variance-ratio idea, applied at the scale of minutes within a single trading day, is exactly what Intraday Variance Ratios develops in full.

Where this shows up in practice

Exchanges and researchers use price-efficiency measures to evaluate market structure changes directly: does a new tick size, a new order type, or a new venue make prices more or less efficient? A narrower tick size might tighten the visible spread while making the price itself noisier at very short horizons, since a smaller minimum price increment lets small, uninformed order-flow imbalances move the last trade more easily. Two other tools extend the same idea in different directions — Hasbrouck's Pricing Error Variance separates a price into a permanent, information-driven component and a temporary, noise-driven one directly, and The Gonzalo-Granger Component Share asks, when a stock trades on several venues at once, which venue's quotes are actually leading price discovery rather than just following it.