What Is a Millisecond Worth? Moallemi and Saglam Price Latency

Trading firms lay fibre optic cables in straight lines across continents. They build microwave towers. They pay enormous sums to place their servers a few metres closer to an exchange's matching engine. All of this is to reduce latency, the delay between deciding to trade and the trade actually happening.

Everybody agrees latency is bad and speed is good. But if you asked a trading firm exactly how many dollars a millisecond is worth, you would mostly get shrugs, hand-waving, and appeals to competitive necessity.

Ciamac Moallemi and Mehmet Saglam decided to answer the question properly, and the way they framed it is what makes the paper valuable.

The problem: speed is priced by arms race, not by analysis

The usual justification for spending on speed is that everybody else is doing it, and if you fall behind you will get picked off. That is a real argument, but it is not a valuation. It tells you that speed matters. It does not tell you what it is worth, which is the number you need to decide whether that microwave link is worth building.

The difficulty is that most stories about the value of latency involve a race: you and a competitor both see an opportunity and whoever gets there first takes it. Racing games are hard to model and the answer depends enormously on what your competitors are doing.

Moallemi and Saglam sidestep the race entirely, and this is the clever part.

The key idea via analogy: aiming at a moving target through a delay

Forget competitors. Imagine a single trader, alone, who simply needs to execute an order. She has no rivals, nobody is racing her, nobody is trying to pick her off.

Even in this friendly, solitary world, latency still costs her money. Why?

Because she is aiming at a target that keeps moving. When she looks at the market and decides to trade, she is looking at the price as it was a moment ago. By the time her order arrives, the price has moved. She is a hunter shooting at a bird, but the light reaching her eyes is delayed, so she is aiming at where the bird was, not where it is.

The longer the delay, the further the bird has flown by the time the shot arrives, and the worse her aim. And crucially, how much worse depends on how fast the bird is flying. In a volatile market, prices move a long way in a millisecond. In a calm one, they barely move at all.

So Moallemi and Saglam set up the problem as a pure execution problem with a delay. A trader is optimally executing an order, using dynamic programming exactly as in the classical execution literature, but every decision she makes is based on information that is stale by some fixed amount of time. Then they ask: how much worse is her outcome than it would have been with zero latency? That difference is the cost of latency.

The payoff is a closed-form expression for that cost, written in terms of quantities you can look up: the volatility of the asset, the size of the order, and the length of the delay. That is exactly what a firm needs to run a cost-benefit analysis on a technology spend.

The result has a clean and intuitive shape. Latency costs more when volatility is higher, because a fast-moving bird gets further away during the delay. And because the cost scales with the square root of the delay, in the way that random-walk price movements do, the first milliseconds you shave off are worth much more than the last ones. Going from one second to one hundred milliseconds is enormously valuable. Going from one hundred microseconds to ten is worth far less. There are steeply diminishing returns to the arms race.

When they take the model to real market data, they find that latency costs are of the same order of magnitude as other well-known trading costs, such as commissions and exchange fees. That is a genuinely useful calibration. It means latency is not a rounding error and it is not everything. It sits alongside the other frictions a desk already takes seriously, and it can now be traded off against them on the same terms.

Why it mattered

• It turned an arms race into a valuation. Before this, the value of speed was justified by competitive fear. Now it can be justified, or not justified, by arithmetic. That is exactly what a firm needs to decide whether the next increment of speed is worth its cost.
• It shows latency costs money even with no adversary. This is the paper's sharpest conceptual point. You do not need front-runners, predators, or races to make latency expensive. Volatility alone is enough. That is a far more general and more robust foundation than any race-based story.
• It quantifies diminishing returns, which is the practical question. Everyone knows more speed is better. What a firm actually needs to know is whether the next upgrade pays for itself, and the square-root scaling says that for most participants, past a certain point, it does not.
• It gives ordinary institutions a benchmark. Most funds are never going to win a latency race and should not try. This paper lets them estimate what their existing latency is actually costing them, which is the input to a rational decision about whether to care.
• It brought operations research tools properly to bear. Framing latency as a delay in a dynamic programming problem is exactly the right tool, and it is one the finance literature had not reached for.

The honest limitations

• The absence of competitors is a strength and a weakness. Ignoring the race gives clean, general results. But the race is also real. If a competitor is systematically faster, they will pick off your stale quotes, and that cost is a genuine one this framework does not capture. The paper gives you a lower bound on the cost of latency, not the whole of it.
• Latency is treated as a fixed, known constant. In practice, latency is a random variable with a nasty tail. The occasional hundred-millisecond spike may matter far more than the average, and a model built on a fixed delay cannot see that.
• It is a single-asset, single-venue setup. A great deal of the real value of speed in modern markets comes from cross-venue and cross-asset arbitrage, where being first to react to a move in one place and trade in another is the whole business. None of that is here.
• Adverse selection is absent. The deepest cost of being slow is that the trades you do get filled on are disproportionately the ones you should not have wanted. That selection effect is the heart of why market makers fear latency, and this model does not contain it.
• The calibration is data-dependent. The finding that latency costs are comparable to commissions comes from a particular dataset in a particular period, and the arms race has moved considerably since.

The one-line takeaway

Moallemi and Saglam priced latency by showing that even a trader with no competitors loses money from delay, because prices move while your information goes stale, and derived a closed-form cost in terms of volatility, order size and delay that reveals steeply diminishing returns to speed and puts latency costs on a par with commissions and fees.