Learning Market Impact From Your Own Fills

The obvious way to measure market impact is to look at fills: for each trade, record the size and the price move that followed, then fit a curve. This is exactly what confounds a naive estimate. A desk doesn't trade randomly-sized orders at random times — it trades because it has a view, often precisely when it expects the price to move in its favour anyway. A buy order placed just before the price rises for reasons unrelated to the trade looks, in the raw data, exactly like a buy order that caused the price to rise. Separating "the trade moved the price" from "the price was already about to move, which is partly why the trade happened" is the entire difficulty of learning impact from your own fills.

Why this is a causal inference problem, not a regression problem

A naive regression of subsequent price change on trade size will pick up both the genuine mechanical impact of the trade (temporary displacement of the order book, permanent information content) and the selection effect of when and why the desk chose to trade that size. If the alpha model behind the trading correlates with near-term price moves — which is the entire point of having an alpha model — then trade size, timing, and subsequent returns are all entangled with the same underlying signal, and a regression coefficient on size cannot cleanly separate "impact of my trade" from "quality of my prediction."

Two ways researchers try to break this confound: use trades that are not driven by short-term alpha — index rebalance flow, forced liquidations, or randomised (or near-randomised) execution schedules — as a cleaner impact-estimation dataset, since these trades' timing is plausibly unrelated to near-term expected returns; or explicitly model and control for the concurrent alpha signal, so the impact estimate is conditioned on "holding the desk's own expected return constant." Neither is perfect, but both are attempts to isolate a causal effect rather than mistake correlation for it.

A worked example

A desk regresses post-trade 5-minute return on trade size (as a fraction of average volume) across a year of its own fills, and finds a strong positive relationship for buy orders: bigger buys precede bigger subsequent rises. Read naively, this looks like a square-root-shaped impact curve consistent with the literature.

The desk then isolates a subset of trades executed purely to rebalance index weights after an index reconstitution announcement — trades whose size and timing were dictated by the index change, not by the desk's own return forecast. Regressing post-trade return on size within this subset only produces a noticeably flatter relationship: some genuine impact, but much smaller than the full-sample estimate suggested. The difference between the two slopes is a rough measure of how much of the original "impact" estimate was actually the desk's alpha signal showing up as apparent price impact, because the desk tends to trade larger when its own conviction is higher.

Picture a mean-reverting path standing in for the residual price move after impact is removed — a trade's genuine impact should look more like a step that partially reverts (temporary impact bleeding off, permanent impact remaining), while a naive impact estimate contaminated by alpha will show a path that keeps drifting in the trade's direction, because it's capturing the forecast, not the footprint.

Where this goes wrong in practice

Even with a clean confound-free subset, sample size is usually small — genuinely alpha-free trades are a minority of any active desk's flow — so the resulting impact curve is noisier and harder to fit reliably than the full, biased dataset. Teams sometimes respond by blending the clean and biased estimates, which reintroduces exactly the bias the clean subset was meant to avoid unless the blending explicitly accounts for it.