Execution and Market Impact

A strategy's paper returns meet reality at execution: the act of trading moves the price against you, and for institutional size, impact — not fees — is the dominant cost. This lesson is how impact behaves and how execution manages it; it's also the practical sequel to the microstructure course.

Why your own order is your worst enemy

Buy aggressively and you consume the ask side of the book, walk prices upward, and signal — other participants (the informed-flow detectors of the Glosten–Milgrom lesson) read your buying and adjust quotes up before you finish. Impact splits into:

• Temporary impact: the liquidity you consume; the book refills, prices partially revert after you stop.
• Permanent impact: the information you leak; the market's fair-value update from observing your flow doesn't revert.

The empirical regularity — robust across markets, asset classes, and decades — is the square-root law:

$$\text{impact} \approx c\,\sigma\sqrt{\frac{Q}{V}}$$

for order size $Q$ against daily volume $V$, daily vol $\sigma$, constant $c \sim 1$. Trading 1% of a day's volume in a 2%-vol stock costs roughly $0.02 \times \sqrt{0.01} \approx 20$bps. Concavity is the interview-worthy surprise: the second million dollars costs less per dollar than the first — but total cost still grows like $Q^{3/2}$, which is what caps strategy capacity (sin #5 of the backtesting lesson, now with its formula).

The execution toolkit

Given a parent order, execution algorithms slice it to manage the impact/risk trade-off:

• TWAP: equal slices over time — simple, predictable (and exploitably predictable if unrandomized — the game-theory lesson's mixed-strategy point in production).
• VWAP: slices proportional to the market's typical volume curve (heavy at open/close); the industry benchmark, largely because it's easy to measure against.
• Implementation shortfall (Almgren–Chriss): the principled framing — total cost = impact (worse when trading fast) + timing risk (price drifts while you wait, worse when trading slow). Minimizing expected cost plus risk aversion × variance yields an optimal schedule: front-loaded for urgent/risky orders, stretched for patient ones. The exam-ready sentence: trade faster when volatility is high relative to impact, slower when impact dominates.
• Passive vs aggressive: resting limit orders earn the spread but face adverse selection (filled exactly when the market moves through you — the maker's dilemma from microstructure); crossing pays the spread but is certain. Every schedule is ultimately a mix of the two.

Implementation shortfall the metric — (execution price vs price when the decision was made) — is the honest scoreboard, capturing impact, timing, and opportunity cost; beating VWAP while shortfall bleeds means the benchmark, not the execution, was flattering.

The interview version

"You must buy \50M of a stock that trades \500M a day. How, and what does it cost?" — Square-root law: $\sqrt{0.1} \approx 0.32$, times ~2% vol → ~60bps of impact; schedule it over the day (or several) with a VWAP-ish profile, randomize the slicing, stay under ~10–20% of volume in any interval, and note the trade-off you're managing: stretching further cuts impact but adds timing risk. One formula, one trade-off, one anti-gaming caveat — that's a complete desk-grade answer. Follow-up they love: "your fill quality got worse after a month of trading this way" — your pattern got detected; re-randomize (the mixed strategy, again).