The Whole Life of an Order: Bacry, Iuga, Lasnier and Lehalle on Impact at Every Scale

Most market impact research takes a photograph. It measures the price before a big order started and the price when it finished, computes the difference, and calls that the impact.

Emmanuel Bacry, Adrian Iuga, Matthieu Lasnier and Charles-Albert Lehalle decided to shoot a film instead. Using a large database of real institutional orders executed on European markets, they tracked the price from before the order began, through every stage of the execution, and onward through the following hours and days as the market digested it.

Doing this at every time scale on the same dataset, from trade-by-trade to daily, had not really been done, and it lets you see things a photograph cannot.

The problem: an order is a process, not an event

When a fund decides to buy a large position, that decision produces a metaorder: a parent instruction that gets chopped into thousands of small child orders and worked into the market over minutes, hours or days.

The life of that metaorder has several distinct phases, and each raises a different question.

• Before it starts. Does the price move before the first child order hits the tape? If it does, either information is leaking or the trader is deliberately timing their entry.
• While it is executing. How does impact accumulate as the order works? Does it build steadily, front-load, or taper?
• Immediately after it finishes. The trader stops pushing. How fast does the price relax back?
• Long after. Once the dust settles, how much of the price move survives? This residual is the permanent impact, and it is what the market has genuinely concluded from your trading.

A single before-and-after measurement collapses all four of these into one number and destroys the information in the process.

The key idea via analogy: watching the wave, not just the high-water mark

Think of dropping a heavy stone into a pond and only measuring the height of the water at one instant. You would learn very little. What you want is to watch the whole thing: the surface before the splash, the splash itself, the wave spreading, and the surface slowly returning to flat but perhaps at a very slightly different level than before.

The paper's findings, taken in order of the order's life:

During execution, impact follows the square root. The familiar concave relationship shows up again: impact grows as roughly the square root of the fraction of daily volume the order represents. This confirms, on a large and cleanly labelled European institutional dataset, the law that everyone else had been finding.

After execution, impact decays as a power law, and the speed depends on the order. Once the trader stops, the price relaxes back, but not exponentially and not all at once. It decays as a power law, and interestingly the exponent is not the same for every order. Short, quick metaorders show a decay exponent nearer 0.8, meaning a fairly rapid relaxation, while long, drawn-out metaorders decay more slowly, with an exponent closer to 0.5. The market forgets a hurried trader faster than a patient one. That makes intuitive sense: a long, persistent buyer looks more like someone who knows something, and the market is slower to discount them.

The decay has two speeds. The relaxation is not a single smooth curve. There appears to be a slow phase right after the order stops, followed by a faster phase later. The price does not immediately snap back the instant you stop buying, which is a real and useful fact for anyone trying to trade around their own footprint.

And the finding that surprised people most: the market does not anticipate the size of your order. You might expect that when a large buyer starts working an order, other participants would sniff out that a big one is coming and start front-running it, pushing the price up before the order really gets going. The data says no. The price before and at the very start of a metaorder does not know how big that metaorder is going to be. The market discovers the size only as the order reveals itself through its own trading.

That last result is quietly reassuring for institutional investors, and it is a meaningful piece of evidence in the long-running argument about how much information leaks out of the execution process.

Why it mattered

• It is a genuine multi-scale study, which is rare. Analysing impact from the individual trade all the way to the daily horizon on one consistent dataset removes a large source of confusion. Much of the apparent disagreement in the impact literature comes from different papers measuring different scales on different data and then arguing.
• The order-dependent decay is practically valuable. If you know that the price will relax faster after a short order than after a long one, that changes how you should think about the true cost of trading, and about whether it is worth waiting before you trade again in the same name.
• The lack of anticipation is a real empirical contribution to the leakage debate. It suggests that, at least in this market and period, the information leakage from a working order is less catastrophic than the folklore suggests.
• It confirms the square-root law on a fresh, independent, direction-labelled dataset. Independent replication on data nobody else has seen is exactly what a contested empirical law needs.

The honest limitations

• The data is a broker's flow, with all that implies. These are orders that arrived at one place. The clients who route there may differ systematically from the market as a whole, and clients do not send all their orders to one broker.
• Attributing price moves to the order is inherently ambiguous. During the hours your order was working, the price moved for a hundred reasons, most of them nothing to do with you. Separating your footprint from the market's own wandering requires assumptions, and different assumptions give different answers.
• Survivorship and cancellation bias. Orders that complete are not a random sample of orders that start. Traders pull orders that are going badly, which systematically flatters the measured impact.
• The decay exponents are estimates with real error bars. The distinction between an exponent of 0.5 and 0.8 is meaningful, but so is the uncertainty around each.
• European markets in one year. The venue structure, tick sizes and participant mix of European equity markets in that period are specific. Generalising is a leap.
• "No anticipation" may be a property of this sample. A market populated by more aggressive predatory algorithms might well anticipate order size, and the absence of the effect here does not prove its absence everywhere.

The one-line takeaway

Bacry, Iuga, Lasnier and Lehalle followed 400,000 real institutional orders across every time scale on one dataset and found that impact builds like a square root while you trade and then relaxes as a power law once you stop, that the market forgets a fast trader more quickly than a patient one, and, encouragingly, that the market does not appear to see the size of your order coming before you reveal it.