Impact-Decay Curves: Measuring How Long Market Impact Persists

When a large trade executes, it typically moves the market price immediately (temporary impact). But the price effect does not entirely reverse—some permanent price movement remains. Understanding and quantifying this dynamic is essential for execution algorithms and risk management. Impact-decay curves characterize how price impact evolves over time.

Temporary vs Permanent Impact

Almgren and Chriss provided foundational theory distinguishing temporary and permanent impact. A large market order causes immediate price movement. Part of this movement is "temporary" (the price bounces back as the order book rebalances), while part is "permanent" (the price permanently shifts).

Permanent impact reflects the information content of the trade. If a large seller exists, other market participants infer that someone with negative information is liquidating. They rationally adjust their willingness to hold that security, resulting in lower equilibrium prices. This permanently impacts the security's value.

Measuring Impact Empirically

Researchers estimate impact curves by examining transaction data. A typical methodology:

• Identify large trades (e.g., trades larger than normal order sizes)
• Record the price immediately before the trade (trade initiation price)
• Record prices at subsequent time intervals (e.g., 1 minute, 5 minutes, 1 hour after the trade)
• Compute the price change from initiation to each future time point
• Aggregate across many trades to estimate the average impact curve

This is the basis for empirical impact models. Research by Hasbrouck, Bouchaud, and others has documented that impact typically follows a power-law decay: impact = constant × (time^(-exponent)), where the exponent is often around 0.5 to 1.0.

Why Power-Law Decay?

The power-law structure emerges naturally from market-microstructure theory. When liquidity providers lose confidence after a large trade, they reduce their provision. But as time passes and no new negative information arrives, confidence recovers gradually. This gradual mean-reversion generates power-law decay rather than exponential decay.

The decay reflects the supply of new liquidity to the market. In highly liquid markets with many small traders providing liquidity, decay is faster. In illiquid markets with sparse participation, decay is slower.

Multi-Dimensional Impact Models

Simple impact curves that depend only on order size and time are incomplete. Real impact depends on:

• Asset liquidity and volatility
• Order aggressiveness (limit vs market order)
• Direction of trade relative to recent flow
• Information environment (news events, earnings announcements)
• Competitive environment (whether other traders are simultaneously trading)

Machine learning models can learn how impact varies with these dimensions. Random forests or gradient-boosted models predict impact given observed characteristics of a trade and its market context.

Time-Varying Impact in Different Regimes

Market impact is not constant. During volatile markets, impact is typically larger (prices shift more for a given trade size). During calm periods with ample liquidity, impact is smaller.

A sophisticated model includes regime variables: current volatility, bid-ask spread, recent order-flow intensity. The impact curve then conditionally depends on regime. Markov-switching models naturally capture this by maintaining separate impact curves for different market states and switching between them based on current conditions.

Forward vs Backward-Looking Models

Traditional impact curves measure average impact ex-post: given a trade of size X at time T, what was the subsequent price path? For execution optimization, we need forward-looking predictions: given that we are about to execute size X now, what impact should we expect?

These are not identical. Ex-post impact includes randomness: some trades happen to occur just before positive news (resulting in smaller measured impact), while others precede negative news (larger impact). Forward-looking models must estimate the conditional expectation, filtering out this randomness.

Implementation in Execution Algorithms

Execution algorithms use impact models to make optimal execution decisions. If total impact increases sublinearly with order size (e.g., impact proportional to quantity^0.7 rather than proportional to quantity), then breaking the order into smaller pieces increases total impact. Conversely, if impact increases super-linearly, breaking the order reduces impact.

Dynamic programming formulations allow algorithms to optimize execution time and ordering, contingent on evolving market conditions. As the algorithm observes actual impact from initial orders, it updates its beliefs about impact and adjusts the execution schedule for remaining orders.

Information vs Liquidity Impact

Recent research distinguishes information-driven impact (permanent) from liquidity-driven impact (temporary). Trading algorithms designed to minimize information leakage will behave differently than those optimizing pure execution cost.

Conclusion

Impact-decay curves quantify a fundamental market-microstructure phenomenon: how prices respond to trading and gradually revert. Understanding these dynamics is essential for optimal execution, risk management, and market design. Machine learning enhances the estimation and prediction of impact in multi-dimensional, time-varying market environments.