Market impact & optimal execution

Definition

Market impact is the price movement your own trading causes — the execution cost beyond the quoted spread. It has two documented components: TEMPORARY impact (price pressure from demanding liquidity faster than it replenishes — reverts after you finish) and PERMANENT impact (the information your trading leaks into the price — doesn’t revert). Almgren-Chriss (2001) formalized the central trade-off: execute FAST and pay maximum impact, or execute SLOWLY and carry timing risk that the price moves away while you work — optimal execution schedules balance the two against risk aversion. The practitioner regularity layered on top is the SQUARE-ROOT LAW: impact scales roughly with the square root of order size relative to volume (documented empirically across markets; labeled empirical regularity, not theorem).

How it works / structure

• The cost anatomy: total cost ≈ spread cost + temporary impact (liquidity demand) + permanent impact (information leakage) + timing drift; inst-equity-market-makers inventory mechanics ARE the temporary component; anticipation by inst-hft-behavior converts sloppy footprints into extra permanent-looking cost.
• The square-root regularity (engine-relevant): impact ≈ constant × volatility × √(order size / daily volume) — the documented cross-market fit; practical reading: cost grows SLOWER than linearly (doubling size less than doubles per-share impact) but total dollar impact still compounds, and orders beyond low-single-digit percentages of average daily volume enter expensive territory fast.
• Almgren-Chriss scheduling: front-loaded trajectories for urgent/risk-averse execution, stretched trajectories for patient flow — the framework behind ms-execution-algos (VWAP/TWAP/ implementation-shortfall algos are its industrial implementations); the key input is the urgency-vs-impact preference, which is a THESIS property (fast-decaying alpha justifies paying up; slow theses shouldn’t).
• Retail scaling: below ~0.1% of daily volume, impact is mostly spread and timing — the framework still disciplines habits (limit orders, avoiding open/close chase, splitting entries) but the institutional machinery is overkill; the KB carries the size thresholds so the engine applies the right regime.

When it applies

Position sizing against liquidity (max position = what can be EXITED at acceptable impact in the thesis’s exit window — impact math belongs in sizing, not just execution); execution planning at size (schedule choice by alpha decay); strategy capacity estimation (backtests without impact costs overstate — quant-backtest-hygiene cost realism); stop-placement realism in thin names (ms-slippage-friction).

Risk profile & failure modes

• Ignoring it in sizing (the retail-to-serious transition failure): strategies that work at $10k die at $1M in thin names — capacity is a property the impact math predicts in advance.
• Model false precision: impact constants vary by name, regime, and venue mix — square-root estimates are planning numbers with ±50%-grade error, not billing rates.
• Stress nonlinearity: calm-market impact models break in dislocations (liquidity withdraws exactly when urgency peaks — the documented crisis pattern); liquidation plans need stressed-impact scenarios (risk-scenario-analysis).
• Leakage via predictability: deterministic schedules get anticipated (documented — the algo-detection arms race); randomization is part of the cost model, not a paranoia tax.

Evidence & limits

Almgren-Chriss (2001) anchors the optimization framework; the square-root law is documented across asset classes in the empirical microstructure literature (labeled regularity). Impact parameters are estimated from proprietary fill data at institutions — public models give magnitudes, not precision.

Falsifiable-thesis examples

Illustrations only, not signals:

• “Orders sized at 5% of ADV in mid-caps incur all-in costs within 2x the square-root-law estimate (model-calibration check)” — falsified by realized fill analysis.
• “Splitting a 2%-of-ADV order across 3 days reduces total impact vs single-day execution when no news intervenes (schedule thesis)” — falsified by paired execution records.

Cross-references

• The measurement layer: ms-implementation-shortfall
• The tools: ms-execution-algos; the priced surface: ms-liquidity, ms-slippage-friction
• The counterparties: inst-equity-market-makers, inst-hft-behavior