Trading costs

Market impact

∞structural

Reviewed 4 June 2026. As of 2026: a permanent feature of the market, not an edge that decays.

Trading moves the price against you. The square-root law says impact grows roughly with the square root of size relative to volume; temporary impact decays, permanent impact stays. It decides whether an edge survives costs.

See it move

The square-root impact lawdrag the sizeIX-IMPACT

Order size8% ADV

Total impact0.170

Permanent0.076

Temporary0.093

\Delta P \approx Y\,\sigma\,\sqrt{Q/V}

: concave, so doubling size raises impact by only ~41%, not 100%.

Order size (% of ADV)8%

Impact coefficient Y0.60

What to notice. Impact is concave in size, so the curve flattens. That is why slicing a big order into small children, each taking a tiny slice of volume, can cost far less than crossing it all at once. The permanent part stays; the temporary part decays after you stop.

What is market impact?

Market impact is the price change caused by your own order. When you buy, you consume the resting asks and you signal demand, so the price rises while and because you trade; selling does the reverse. It is the largest implicit cost for any sizeable order, and unlike the spread it grows with order size, which is precisely why it limits how much capital a strategy can deploy.

Start with the mechanics. The book is finite. A buy order eats the cheapest asks first, then the next, climbing the ladder: the same depth-consumption you can watch on the limit order book. That mechanical "walking" up the book is the visible part. The deeper part is that other participants infer information from your buying and adjust their own quotes up, so the price stays elevated even after you stop. Impact is mechanical depth consumption plus informational repricing.

This is the dominant term in implementation shortfall for any order large enough to matter, and the reason large orders are sliced over time by execution algorithms rather than fired at once. The crucial structural fact, which the rest of this page builds, is that impact is concave in size: doubling your order does not double your impact; it multiplies it by roughly $\sqrt{2}$ . That concavity is what makes large trades survivable at all.

Temporary vs permanent impact

Total impact during a trade splits into two pieces that behave completely differently. Temporary impact is the part of the price move that decays once you stop trading: you paid it to consume immediate liquidity, and the book refills as soon as your pressure is gone. Permanent impact is the part that persists, because the market has revised its view of fair value: your trade revealed information, and that revaluation stays. Only the permanent part survives.

Push a finger into water and the surface dimples; the dimple fills back when you remove the finger: that is temporary impact, the cost of immediacy. But if your finger told the market something (that an informed buyer is active) fair value itself shifts, and that shift stays. Most of what you pay while trading is temporary liquidity cost; what moves the consensus price is permanent, and is the cost the rest of the market keeps.

The standard two-part split (used verbatim by Almgren–Chriss): temporary impact tracks how fast you trade and recovers; permanent impact tracks your total signed volume and does not.

\underbrace{\eta\,\frac{n}{\tau}}_{\text{temporary (rate)}} \;+\; \underbrace{\gamma\,Q}_{\text{permanent (size)}}

Component	What it is	What it tracks	Does it survive?
Temporary	The cost of consuming immediate liquidity; the book refills once your pressure is gone	How fast you trade (the rate), $\eta\,n/\tau$	No, it decays once you stop trading
Permanent	The market revising its view of fair value once your trade has revealed information	Your total signed volume (the size), $\gamma\,Q$	Yes, the revaluation stays
Total	The full price move during the trade: temporary plus permanent	Both rate and size together	Only the permanent part; the temporary part relaxes away

This split is the central design lever for execution. Temporary impact pushes you to trade slowly (a low trading rate means low per-share liquidity cost) while timing risk and opportunity cost push you to trade fast. Permanent impact you pay regardless of speed. Trading temporary impact off against timing risk is exactly the Almgren–Chriss problem.

The modern, continuous refinement of this dichotomy is the propagator (transient-impact) model of Bouchaud and co-authors. Rather than a clean during/after split, each individual trade leaves a transient impact that decays over time according to a decay kernel $G(t)$ , and the observed price is the sum of all past trades' decaying contributions. Permanent impact is just the long-time tail of that kernel.

▸ Show the propagator model optional

In the propagator framework the mid price is the sum of every past trade's decaying contribution, where $\varepsilon_s$ is the sign of the trade at time $s$ , $v_s$ its volume, $f(\cdot)$ an instantaneous (concave) impact function, and $G(\tau)$ a decay kernel.

p(t) = \sum_{s\lt t} G(t-s)\,\varepsilon_s\,f(v_s) \;+\; \text{noise}

The kernel falls from 1 toward a constant (the permanent fraction) as $\tau \to \infty$ . A power-law decay $G(\tau) \propto \tau^{-\beta}$ reproduces the empirically observed slow relaxation.

The no-dynamic-arbitrage condition (Gatheral 2010) constrains the joint shape of $f$ and $G$ so that a round-trip cannot be made costless. This is what forces the concave, square-root-like instantaneous form rather than a linear one.

The square-root law of market impact

The square-root law says the price impact of trading a quantity $Q$ over a session scales like the square root of the fraction of daily volume you represent. One line of intuition before the formula: trading a bigger slice of the day's volume costs more, but with sharply diminishing marginal damage: quadruple your size and you only double your impact.

Impact in basis points, with

\sigma

the instrument's volatility,

V

its daily volume,

Q

the order size, and

Y

a dimensionless constant of order one (calibrate it on your own data).

\mathcal{I}(Q) \;\approx\; Y\,\sigma\,\sqrt{\tfrac{Q}{V}}, \qquad \sigma \approx 1\text{–}2\%,\; Y \approx 0.5\text{–}1

Why a square root and not a straight line? A linear impact model would let you split a trade into pieces and arbitrage the difference, and it would make large trades impossibly expensive. The square-root form is what survives the no-dynamic-arbitrage constraint (Gatheral 2010) and what the data overwhelmingly shows, across equities, futures, FX and crypto, across decades. You will meet it named as the Gatheral square-root law or the Almgren et al. (2005) empirical form.

That concavity is the entire reason capacity exists at positive size. If impact were linear, net edge would fall off a cliff the moment you scaled. Because it is a square root, you can grow until the rising cost curve crosses your per-trade alpha, and that crossing point is your capacity.

One piece of shorthand you will meet is Kyle's lambda (Kyle 1985): a linear impact coefficient $\lambda$ where price moves by $\lambda$ times the signed order flow, used for small orders and for the informational, permanent component. The square-root law is the large-order, aggregate-trade regime; Kyle's $\lambda$ is the marginal, single-order linear regime. They are not contradictory; they describe different scales. Kyle's model is developed on adverse selection.

▸ Show the dimensional / informational sketch optional

Two complementary arguments land on the same exponent. Dimensional / latent-liquidity: if the visible book is only a thin slice of a much larger latent supply that reveals itself as price moves, and the latent density near the mid is roughly linear in price, then the shares needed to move the price by $\Delta$ integrate to a quadratic.

Q \propto \Delta^2 \;\;\Longrightarrow\;\; \Delta \propto \sqrt{Q}

Informational: a metaorder of size $Q$ carries information proportional to its surprise, and under fair pricing the permanent impact equals the information revealed. Under broad assumptions about the size distribution of metaorders this too yields a square-root-shaped permanent impact.

Both routes give an exponent of $\tfrac{1}{2}$ , which is why the law is so stable across markets and decades.

Why impact caps capacity

Capacity is the largest amount of capital a strategy can run before impact eats its edge. Because impact grows with size while per-trade alpha does not, there is a size at which the marginal trade's impact cost equals its gross alpha; beyond that, scaling up destroys money. The square-root law is the exact shape of that ceiling.

Your signal earns a roughly fixed edge per trade (say 4 bps) independent of how much capital you push through it. But the cost of pushing more capital grows as $\sqrt{Q}$ . Scale up and the rising cost curve climbs to meet the flat alpha line; where they cross, net edge is zero. Past that point you pay more in impact than the signal earns: the textbook over-capacity bleed.

Capacity is where the marginal impact cost equals the gross alpha per trade. Solving the square-root law for that crossing gives the capacity in terms of your edge.

Y\,\sigma\,\sqrt{\tfrac{Q^\star}{V}} \;=\; \alpha \quad\Longrightarrow\quad Q^\star \;=\; V\left(\frac{\alpha}{Y\,\sigma}\right)^{2}

This is the link from costs to performance. The capacity and alpha-decay curve bends over because of the square-root law. Impact is not one input to capacity; it is the mechanism of capacity. Crowding makes it worse: when many desks trade the same signal, aggregate impact rises and everyone's capacity falls.

It is also why execution is applied cost modelling. An execution algorithm exists to trade a given $Q$ while paying as little of this cost as possible, by spreading $Q$ over time to keep the instantaneous participation rate (and hence temporary impact) low, at the price of timing risk. Almgren–Chriss is the closed-form solution to that trade-off, and it takes this page's impact function as its input.

An honest 2026 note: the law's shape is structural and stable; the coefficient $Y$ is what separates desks. A better-calibrated, state-dependent impact model (conditioning on book depth, recent flow, time of day) lets you deploy more capital safely than a competitor using a flat textbook $Y$ . That calibration edge is durable and increasingly ML-driven; see estimating impact.

Worked example

A buy metaorder in a liquid US equity, illustrative and as of 2026. Reproduce it by changing inputs in the model above. Take a daily volume $V = 5{,}000{,}000$ shares, daily volatility $\sigma = 1.5\%$ (150 bps), price \$50, and impact constant $Y = 0.6$ (dimensionless; calibrate this on your own data).

A "small" order of $Q = 50{,}000$ shares is 1% of daily volume:

Small order (1% of daily volume) costs 9 bps, about \$2,250 in cash.

\mathcal{I} = 0.6 \times 150\,\text{bps} \times \sqrt{0.01} = 0.6 \times 150 \times 0.10 = 9.0\,\text{bps} \;\Rightarrow\; \$2{,}250

Now a "large" order of $Q = 200{,}000$ shares, 4% of daily volume, four times the size:

Large order (four times the size) costs only twice the impact. That is concavity made concrete: 18 bps, about \$18,000.

\mathcal{I} = 0.6 \times 150 \times \sqrt{0.04} = 0.6 \times 150 \times 0.20 = 18.0\,\text{bps} \;\Rightarrow\; \$18{,}000

On the temporary/permanent split: if roughly two-thirds of the during-trade impact is temporary and decays after you finish, the 18-bp large-order impact relaxes to a ~6 bp permanent shift. That 6 bps is the cost the rest of the market keeps, and what your next trade in the same name starts from.

And the capacity reading: if your signal's gross alpha is a flat 9 bps per trade, the small order is break-even on impact alone, while the large order is a 9-bp loser (18 bp impact against 9 bp alpha) before any other cost. Your capacity in this name is therefore near $Q \approx 50{,}000$ , exactly where the square-root cost meets the flat alpha line.

The numbers are synthetic and rounded; $Y$ , $\sigma$ and $V$ vary by instrument, regime and venue, and the temporary/permanent split must be measured, not assumed. The square-root shape is robust; the coefficient is yours to calibrate.

Where this fits

↑ Up · building block of Trading costs ↔ Across · composes with Estimating impact ↔ Across · composes with Almgren–Chriss optimal execution ↔ Across · composes with Capacity & alpha decay → Apply · makes money in VWAP, TWAP & POV → Apply · makes money in Statistical arbitrage → Apply · makes money in Equities & futures ⤓ Build / Buy · tool needed Datasets & tools