Who Started It? Lee and Ready's Rule for Telling Buys from Sells

Almost every important idea in market microstructure hinges on a single variable: signed order flow. Kyle's model is about how much informed buying pressure there is. Glosten and Milgrom is about what the market maker learns from a buy versus a sell. Price impact, adverse selection, PIN, information shares: all of them need to know, for each trade, who was the aggressor.

Here is the awkward part. The tape does not tell you.

A trade print says: 500 shares changed hands at 40.15 at 10:32:07.221. It does not say whether an impatient buyer reached up and took someone's offer, or an impatient seller reached down and hit someone's bid. Both parties are on the print. Neither is labelled.

Lee and Ready's 1991 paper is about how to guess, and their guess became a load-bearing wall of the entire empirical field.

The problem: every trade has a buyer and a seller

The distinction that matters is not "who bought and who sold," because every trade has one of each. The distinction is who was passive and who was aggressive.

Someone had already posted a resting order, patiently waiting. Someone else came along, decided they wanted to trade now, and crossed the spread to take it. The aggressor is the one demanding liquidity. The passive one is supplying it.

That distinction is everything. When we say "buying pressure moved the price up," we mean aggressive buyers, not the passive sellers they traded against. When Glosten and Milgrom say the market maker updates their beliefs after a buy, they mean an aggressive buy. Getting this backwards flips the sign on your entire analysis.

The key idea via analogy: which side of the counter did the deal happen on?

Picture a shop with a clearly posted price to buy from you (the bid) and a price to sell to you (the ask).

If a transaction happens at or near the shop's asking price, it is overwhelmingly likely that a customer walked in and bought. Nobody sells to the shop at the shop's high asking price, that would be leaving money on the table. Similarly, a transaction near the shop's bid almost certainly means a customer sold to the shop.

That is the quote rule, and it is Lee and Ready's primary test: compare the trade price to the midpoint of the prevailing quote. Above the midpoint, call it a buy. Below the midpoint, call it a sell.

Simple. But Lee and Ready identified two very real ways this breaks, and their solutions to those two problems are what made the paper canonical rather than obvious.

Problem one: trades inside the spread. Sometimes a trade prints exactly at the midpoint, or between the quotes. Maybe two customers were matched against each other, or someone got a price improvement. The quote rule has nothing to say: the trade is neither above nor below the midpoint. Lee and Ready's fallback is the tick rule: look at whether the trade price is higher or lower than the last different price. If the price ticked up, call it a buy. If it ticked down, call it a sell. The logic is that upticks tend to be buyer-initiated, which is the same bid-ask bounce intuition Roll used.

Problem two, and this is the sly one: the clocks lie. In the data systems of the era, trades and quotes were reported by different mechanisms with different delays. A quote update could be timestamped before the very trade that caused it, or, more damagingly, a trade could be stamped after the quote that a fast trader had already reacted to. If you naively match a trade against the quote with the nearest timestamp, you can systematically match trades to the wrong quotes and misclassify them.

Lee and Ready's fix was empirical and pragmatic: compare each trade against a quote from slightly earlier, deliberately lagging the quote by a few seconds to compensate for the reporting delay. Their specific recommendation, the famous five-second rule, is the single most quoted detail of the paper, and it is a wonderfully humble thing: not a theorem, but a calibration, chosen because it made classification work better on the data they had.

Why it mattered

• It unlocked the empirical field. You cannot test Kyle, Glosten and Milgrom, or any adverse selection model without signed trades. Lee and Ready made signed trades available to anyone with a TAQ dataset, and the wave of empirical microstructure research through the 1990s and 2000s rode on it.
• It is invisible infrastructure. Effective spread, realized spread, price impact, order imbalance, PIN, VPIN, order flow toxicity, Hasbrouck's trade informativeness: every one of these is computed on top of a trade classification, and for decades that classification was Lee and Ready's. The paper is cited thousands of times, and used silently even more often than that.
• It set the template of "principled rule of thumb." The paper is a model of a certain kind of honest empirical work: here is a measurement problem, here is a rule, here is exactly where the rule breaks, here is a fix, here is how well it does. It does not pretend to be exact. It makes a defensible guess and documents the guess.
• It made the industry take timestamps seriously. The observation that trade and quote clocks disagree, and that the disagreement biases everything downstream, was a genuinely important warning that echoes right into the modern latency literature.

The honest limitations

• It is a guess, and it is wrong a meaningful fraction of the time. Studies with access to actual order records, where the true aggressor is known, consistently find that Lee and Ready misclassifies a nontrivial share of trades. The errors are worst exactly where they hurt most: at the midpoint, in fast markets, and for small trades.
• The five-second rule is an artifact of 1991 plumbing. Modern exchange data is timestamped to nanoseconds with far tighter synchronisation. Applying a five-second lag to today's data is not conservative, it is catastrophic: five seconds is an eternity, and you would be comparing a trade against ancient quotes. Everyone knows this, most people adjust, but the number lives on in old code and occasionally in new papers, which is a real hazard.
• Errors are not random, they are biased. Misclassification does not just add noise. It tends to bias estimates of adverse selection and price impact in a particular direction, because midpoint trades and price-improved trades are not a random subset of trades. This means downstream results can be systematically off, not just noisy.
• The modern market has broken the premise. With hidden orders, midpoint dark pools, odd lots, retail internalization and sub-penny price improvement, an enormous share of volume now executes at or near the midpoint, precisely where the quote rule is useless and the tick rule is weak. In fragmented markets the "prevailing quote" is itself ambiguous, since you must decide which venue's quote counts.
• It was built for a single-venue, human-specialist world. Everything above compounds when the same stock trades on fifteen venues simultaneously.

Better methods exist now, and where actual order-level data is available you should use it. But for the vast body of research built on historical trade-and-quote data, Lee and Ready is what was under the floorboards.

The one-line takeaway

Lee and Ready gave the field a practical rule for a problem the data cannot answer directly, was this trade a buy or a sell?, by comparing the price to the quote midpoint, falling back on the direction of the last price move, and lagging the quote to fix the fact that trade and quote clocks do not agree.