The Price of Being Late: What a Dislocation Is Worth a Microsecond, a Millisecond, and a Second After It Appears

A dislocation in a liquid futures market is worth a different amount to everyone who sees it, and the difference is mostly a matter of when. Suppose an index future, a rate future, or an energy contract moves several times its usual short-horizon variation in a single burst, so that its price no longer agrees with the price implied by the instruments that ordinarily anchor it: the cash index, the neighboring contract on the curve, the same exposure listed on another venue. Some participants observe this within a few microseconds; others within a few milliseconds; a person watching a screen notices in a second or two, if at all. The dislocation is the same event for all of them. What differs is how much of it remains by the time each can act.

This piece works through a stylized model of that decay. We are not interested in the arms race for its own sake, and we make no claim here about how fast any particular participant is. We are interested in the shape of the curve: how expected execution quality falls as reaction delay grows from a microsecond to a minute, why the fall is not smooth, and what the shape implies for a systematic investor deciding which part of the curve to occupy. The short answer is that delay has a price at every horizon, but the price is charged in three installments, and it is the installments, not the microseconds, that matter for the design of a trading process.

Three Populations, Three Clocks

Start with who corrects a dislocation. When a large aggressive order sweeps several levels of a futures order book, the price it leaves behind is temporarily wrong, in the narrow sense that other instruments say it should be somewhere else. Three groups of participants notice and act, and they act on three different clocks. Co-located market-making systems, which read the exchange's feed from inside the same building, reprice and refill within tens of microseconds; this is the population studied in the literature on latency races.^[1] Systematic firms connected over longer distances, or running heavier logic, reach the same conclusion within a few milliseconds to a few tens of milliseconds. Discretionary traders and slower cross-market strategies arrive over seconds.

Each population closes part of the gap, and the part each closes decays on its own timescale. A convenient way to write this is as a mixture: the fraction of the original move still open after a delay is a weighted sum of three exponentials, one per population. Figure 1 draws that curve on a logarithmic time axis from one microsecond to one minute, together with a second curve that matters more in practice: the expected capture net of two things a latecomer cannot avoid, the probability that there is any depth left to trade against, and the cost of crossing the spread to do it.

Two features of Figure 1 are worth dwelling on. The first is that the gross curve is not a slope but a staircase. Between the shelves, delay is expensive; on the shelves, it is nearly free. A participant who reacts in 300 microseconds and one who reacts in 3 milliseconds see nearly the same remaining opportunity in this model, because the population that would have taken it from them has already finished, and the next population has not started. The second feature is that the net curve is not monotone at the left edge. Below roughly a hundred microseconds the limiting factor is not the edge but the book: the sweep that created the dislocation also removed the depth one would need to trade it, so the earliest possible reactions meet an order book with little in it, and those arriving a few tens of microseconds later meet even less. Being first is not the same as being filled.

The Hole in the Book

The left edge of Figure 1 deserves its own picture, because it is where intuition about speed most often goes wrong. Immediately after a sweep, displayed depth near the touch on the depleted side is a fraction of what it was. It then falls further rather than recovering, as market makers whose quotes survived the sweep cancel them to reassess; the book bottoms out a few tens of microseconds in and stays thinner than the sweep itself left it for roughly the first hundred. Only then does refilling begin, first from the fastest systems reposting at new prices, then from everyone else, and depth returns to its prior level over a few milliseconds. Figure 2 stylizes this sequence for depth within two ticks of the mid and, for comparison, depth within ten ticks, which the sweep touched less and which recovers sooner.

The shape has a practical consequence. Any execution that arrives during the trough is competing for the least liquidity of the whole episode, and the market impact of taking it is correspondingly large; the prices available at that moment carry the edge in name only. Latency infrastructure that shaves a reaction from 80 microseconds to 20 buys an earlier arrival at a book that has less to offer, and in the model of Figure 1 a lower probability of being filled at all. The value of that purchase depends entirely on where the trough sits in the specific market, and the trough moves: it is shorter in contracts with many competing market makers and longer in contracts with few. We treat the recovery curve as something to be measured per contract and per session, not assumed.^[2]

Persistence Is Not One Number

The mixture in Figure 1 has a second reading. If each dislocation is closed at a random time drawn from one of the three populations, the gross curve is simply the probability that the dislocation is still open after a given delay. Turning that around gives the distribution of persistence: how long, across many episodes, a dislocation lasts before it is absorbed. Figure 3 bins that distribution into logarithmic buckets. It has three modes, not one. In the stylized model, about four episodes in ten are over within a hundred microseconds; about a third last between a millisecond and a hundred milliseconds; roughly one in six persists for a second or more. The buckets in between are nearly empty.

The trimodal shape is the point, and it argues against a single-number summary of how fast a market corrects. A firm that measures the average persistence of dislocations in a contract and builds its process around that average will be too slow for the first mode and needlessly fast for the third. The question to ask of a market is not how long its dislocations last but which population absorbs which share, because that determines which mode a given reaction speed can reach. A participant whose reaction takes a few milliseconds cannot compete for the first mode at all, can capture most of the second, and can take the third at leisure; its process should be designed for the second and third rather than measured against the first.

Where the Time Goes

It is tempting to treat reaction delay as a single quantity to be minimized, but it is a chain, and the links are not equally movable. Figure 4 lays out a stylized reaction path from the moment an exchange publishes the trade that created the dislocation to the moment a responding order reaches the matching engine. Propagation across a data center floor is a matter of microseconds; propagation across a continent is a matter of milliseconds, fixed by distance and by the speed of light in fiber or air. Decoding, signal evaluation, and risk checks are engineering choices that trade thoroughness for time. Queueing at the exchange gateway and in the matching engine belongs to the venue and to everyone else who reacted at the same moment.

Seen this way, the question of how fast to be becomes a question of which link is worth shortening, and what would be given up to shorten it. Shortening the propagation links means co-location, which is available to anyone willing to pay for it and therefore confers little lasting advantage. Shortening the evaluation link means simpler logic, which is exactly what one does not want if the point of the signal is to be more right than the competition rather than earlier. Shortening the risk-check link is not a trade we are willing to make at any price. What remains is the plain position that some delay is chosen, some is bought, and some is imposed, and only the first kind is a design decision.

A Ledger of Delay

Figure 5 collects the model into a ledger. Each row is a reaction delay; the columns give, for the stylized parameters used throughout, the population that typically reacts at that delay, the share of the initial move still open, the probability of finding depth to trade against, and the expected capture net of the crossing cost. The numbers are illustrative and the parameters are stated in the note; what should survive a change of parameters is the ordering and the shelves.

Read down the third column and the price of being late is visible as three discrete charges rather than a running meter. The first charge, roughly half the move in this construction, is paid by anyone slower than the co-located population, which is almost everyone. The second is paid for arriving after the networked systems, over the interval from a few milliseconds to a few hundred. The third is paid over seconds, as the slowest population finishes the job. Between the charges the ledger is nearly flat, and a participant who has already paid the first charge gains little by shaving microseconds off a delay that already sits on the millisecond shelf. The last column adds the hole in the book from Figure 2: the earliest rows keep more of the move on paper but find less to trade against, and in this construction they capture no more of it net than a reaction on the millisecond shelf does.

What This Means for How We Work

Three practices follow. The first is to measure the curve rather than assume it. The decay of dislocations, the recovery of depth, and the distribution of persistence differ by contract, by time of day, and across regimes, and a process tuned to one contract's clocks is mistuned for another's. The microsecond staircase described here is the ordinary daytime texture of a liquid market, not its stress behavior: the 2010 flash crash unfolded over minutes and the dislocations of March 2020 over weeks, and neither is what the model above describes.^[3]

The second is to choose a shelf deliberately. A firm that competes for the first mode needs a different engineering organization, a different research process, and a different attitude to risk checks than one that competes for the second and third, and trying to occupy all three at once tends to mean occupying none of them well. The third is to price delay inside the research process itself. A backtest that assumes execution at the price observed at the moment of the signal is assuming a reaction delay of zero, and the model above says that is not a small approximation: it credits the strategy with the first charge of the ledger, which in live trading is paid by everyone except the fastest population in the building. We would rather know which shelf a strategy lives on before it is built than discover it afterward from the gap between the backtest and the fills.