Market Impact

For a retail order, the only cost that matters is the spread. For institutional size, the dominant cost is market impact: the price moves against you because you are trading. Buy aggressively and you push the price up, so each successive share costs more and the mark on what you already bought is inflated. Understanding impact, where it comes from, how it splits into components, and how it decays, is what separates a backtest that survives contact with reality from one that doesn't. It is the cost that Optimal Execution exists to manage.

Why impact exists at all

Two mechanisms, corresponding to the two great microstructure models:

1. Information (permanent impact). Trading conveys information. A buy tells the market someone might know something, so market makers rationally raise their quotes, the The Glosten-Milgrom Model and The Kyle Model mechanism. This part of the move is permanent: it reflects a genuine update to the consensus value and does not reverse.
2. Liquidity / inventory (temporary impact). To fill a large order now, you must consume standing liquidity and pay makers to take the other side of unwanted inventory. This part is temporary: once you stop trading and inventories rebalance, the price relaxes back. It is the cost of demanding immediacy, and it depends on how fast you trade, not just how much.

The clean decomposition: for a trade (or a metaorder) of size $Q$ executed over some interval, the observed price path is

$\underbrace{\text{permanent impact}}_{\text{information, does not revert}} \;+\; \underbrace{\text{temporary impact}}_{\text{liquidity, reverts after you stop}}.$

The linear-impact caricature (Almgren–Chriss form)

The workhorse parametrization treats the two components separately as functions of your trading rate $v = Q/T$ (shares per unit time):

$\text{permanent: } g(v) = \gamma\, v, \qquad \text{temporary: } h(v) = \eta\, v + \varepsilon\,\operatorname{sgn}(v).$

Permanent impact $\gamma v$ shifts the efficient price and is felt by all your shares; temporary impact $h(v)$ is the extra you pay on each slice for immediacy and vanishes when you stop. The constant $\varepsilon$ is the fixed half-spread cost per trade. Kyle's linear equilibrium is the microfoundation for the permanent term: $\gamma \leftrightarrow \lambda$, price impact per unit of net order flow. This linear form is what makes The Almgren-Chriss Model analytically solvable.

The propagator: impact with memory

Linear-permanent-plus-linear-temporary is a caricature because it has no memory, real impact decays gradually, not instantly. The propagator (transient impact) model of Bouchaud et al. captures this. Write the mid-price as a sum over all past trades, each signed $\epsilon_s = \pm 1$ with volume $v_s$, weighted by a decaying kernel $G$:

$m_t = m_{-\infty} + \sum_{s < t} G(t - s)\,\epsilon_s\, f(v_s) + \text{noise}.$

$G(\ell)$ is the propagator: the residual price impact of a trade $\ell$ steps ago. A key theoretical result is that because trade signs are strongly autocorrelated (big orders are split into long streams of same-signed child orders), $G$ must decay as a power law, $G(\ell) \sim \ell^{-\beta}$, for the price to remain (approximately) a martingale, a diffusive, unpredictable price. If impact were permanent and order flow persistent, prices would trend predictably and be arbitraged. The market resolves the tension by making impact transient: it decays just fast enough to cancel the predictability of persistent flow. This delicate balance is one of the deepest facts in microstructure and is what generates the empirical The Square-Root Impact Law for metaorders.

The response function

Empirically you measure impact through the response function $\mathcal{R}(\ell) = \mathbb{E}[(m_{t+\ell} - m_t)\cdot \epsilon_t]$, the average price change $\ell$ steps after a trade, signed by that trade's direction. It rises quickly, then flattens or slightly reverts: the fast rise is the immediate impact, the plateau is the permanent (information) component, and any decay from the peak is the temporary component relaxing. The permanent fraction is small for liquid names, most of the immediate move mean-reverts, which is exactly why patient execution is cheaper than aggressive execution.

Worked example

You must buy $Q = 100{,}000$ shares of a stock with daily volume $V = 2{,}000{,}000$ shares (5% of ADV) and daily volatility $\sigma = 2\%$ at a price of $50. Using a square-root impact estimate $\Delta P/P \approx Y\,\sigma\sqrt{Q/V}$ with $Y \approx 0.5$,

$\frac{\Delta P}{P} \approx 0.5 \times 0.02 \times \sqrt{0.05} = 0.5 \times 0.02 \times 0.2236 = 0.00224,$

about 22 basis points, or $0.112 per share at $50, roughly $11,200 of impact on the metaorder, dwarfing the one-cent spread. If you traded twice as fast over half the day, the temporary component would roughly double while the permanent stayed the same, the core reason you slow down. If you traded half as fast, impact falls but you hold the position longer and bear more price risk. That tension is the whole of The Almgren-Chriss Model.

Failure modes and caveats

• Impact is not a fixed number. It depends on rate, on the book's current liquidity, on volatility regime, and on whether other participants are trading the same way. A single "impact per share" is a convenient fiction.
• Cross-impact. Trading one asset moves correlated assets; in a portfolio liquidation the impact matrix is not diagonal, and ignoring cross-impact underestimates cost.
• Concavity breaks linear models. The linear Almgren–Chriss form overstates the impact of large trades relative to the empirical square-root law; use it for tractability, not for calibration of very large orders.
• Impact is partly your fault to measure. Distinguishing your impact from the price move that would have happened anyway (selection: you often trade because you expect a move) is genuinely hard and biases naive impact estimates upward.

In interviews

You should be able to explain the permanent/temporary split mechanistically, permanent = information (Kyle's $\lambda$, does not revert), temporary = liquidity/inventory (reverts when you stop, depends on rate). A strong answer connects the two: why must impact be transient given that order flow is highly persistent? Because permanent impact plus persistent flow would make prices predictable and arbitrageable; transient (power-law-decaying) impact is what keeps the price a martingale. Expect to estimate an order's cost with the square-root rule $\Delta P/P \approx Y\sigma\sqrt{Q/V}$ and to argue why impact, not spread or commission, is the binding cost for institutional size, motivating Optimal Execution.