Why Do Prices Change? Madhavan, Richardson and Roomans Take Apart the Tick

Watch a stock's price tick along, trade by trade, for an hour. It jitters constantly. Up an eighth, down an eighth, up again, flat, down.

Now ask a question that sounds naive but is not: what are all those little moves?

Some of them must be real: information arriving, the world learning something. Some of them must be pure mechanics: the price bouncing between the bid and the ask as buyers and sellers alternate. And some, less obviously, must be the market maker adjusting.

Madhavan, Richardson and Roomans built a model in 1997 that pulls the tick apart into its pieces, and along the way it fixed a subtle mistake that earlier decompositions had been quietly making.

The problem: the earlier models assumed order flow is a coin flip

Roll's estimator, and much of what followed, assumed that buys and sells arrive like flips of a fair coin: each trade independent of the last.

This is spectacularly false, and everyone who has looked at a tape knows it. Order flow is strongly autocorrelated: a buy is much more likely to be followed by another buy than by a sell. The reason is not mysterious. Big institutional orders are far too large to execute at once, so they are chopped into a long sequence of small child orders, all on the same side, executed over minutes or hours. That mechanical slicing makes order flow persistent.

Why does this matter for the price decomposition? Because it means the market maker can see you coming.

If a buy has just arrived, the market maker knows the next trade is more likely than not to be another buy. That expectation is already baked into their quote. So when the next buy does arrive, it is only partly a surprise. Only the unexpected part of the order flow can be genuinely new information. The predictable part was already priced.

Models that ignore this treat every buy as a fresh shock, and consequently overstate how much information trades carry. MRR's central methodological contribution is to fix that.

The key idea via analogy: the news and the toll booth

MRR's model says each observed price change is a sum of three ingredients, and the value of the paper is that these three are conceptually clean and separately estimable.

Ingredient one: public news. Sometimes the world simply learns something between two trades. A headline drops. The price moves. This has nothing to do with the trading process at all, and MRR explicitly let the model include it. Earlier decompositions often lumped this into "unexplained noise."

Ingredient two: what the market learned from the surprise in your order. This is the adverse selection piece, and it is where the autocorrelation fix bites. The market maker had an expectation of the next trade's direction. Your actual trade either confirms it or surprises it. Only the surprise moves the market's belief about fundamental value. If the market fully expected a buy and it got a buy, the belief barely budges. This is a permanent price change, because a belief revision does not un-revise.

Ingredient three: the toll. Regardless of information, the market maker charges a fee for taking the other side: to cover order processing, inventory risk, and their own margin. This produces the classic bid-ask bounce and it is transitory. The price hops to the ask when you buy, and hops back down when the next seller arrives. It reverts, so it is a cost, not news.

The clean punchline: the permanent part of the price move is what the market learned from the unexpected component of your trade, and the transitory part is what you paid for immediacy. Estimate the model on real transaction data, and you get numbers for both.

Why it mattered

• It got the accounting of information right. By explicitly modelling the predictability of order flow, MRR gave a much more honest estimate of how much information a trade carries. The lesson is deep and it echoes through modern execution: a predictable order is a cheap order in terms of information leakage, and a surprising one is expensive. This is one theoretical justification for why execution algorithms try to look like everybody else.
• It provided the workhorse spread decomposition for practitioners. The MRR model is one of the standard, widely implemented ways to compute the adverse selection component of the spread for a given stock. It sits alongside Glosten-Harris and Huang-Stoll in every microstructure toolkit, and it is used commercially in transaction cost analysis.
• It documented intraday structure. Applying the model across the trading day, the authors could show how the different components of the spread evolve from the open to the close, which is a genuinely useful practical fact for anyone deciding when to trade.
• It made "public information" a first-class citizen. Many microstructure models implicitly assume all price movement comes through trades. MRR allowed a channel for the price to move because the world simply changed, which is more honest and improves the estimation of everything else.

The honest limitations

• It is a structural model, so the answer depends on the structure. The decomposition is not a measurement, it is an inference conditional on a specific story about how trades and prices interact. Impose a different story, and you get different component estimates from the very same data. This is why Glosten-Harris, MRR and Huang-Stoll can disagree about the adverse selection share of the same stock's spread, and there is no neutral arbiter.
• Trade classification is upstream of everything. The model needs signed trades, which must be inferred. Errors propagate.
• Linear and stationary within the estimation window. The model assumes fixed parameters over the period estimated. Real markets change regime constantly, and the assumption of a constant order-flow autocorrelation and constant information content over a day is a simplification.
• The "market maker" is a single agent. The framing assumes one liquidity provider setting quotes. Modern markets have many competing providers on a public book, and the notion of a single dealer's expectation of the next trade needs reinterpreting.
• 1990s NYSE data. Discrete eighth-of-a-dollar ticks, a human specialist, one primary venue. The mechanism survives the translation to modern markets, but the estimated magnitudes are historical artifacts.

The one-line takeaway

Madhavan, Richardson and Roomans showed that a tick-by-tick price move is three things stacked together, public news, the market learning from the genuinely surprising part of your order, and the transitory toll you pay for immediacy, and that ignoring how predictable order flow is makes you badly overestimate how much information trades really carry.