Market Impact Decay

Market impact decay is typically modeled as an exponential decay function, where the temporary price impact diminishes at a rate proportional to its current magnitude. The half-life of impact—the time required for 50% of the temporary dislocation to dissipate—varies by asset class and liquidity regime. For liquid large-cap equities, this half-life often ranges from seconds to a few minutes, while for illiquid small-caps or corporate bonds, it can extend to hours or days. The decay rate parameter is a critical input for optimal execution algorithms, as it determines how aggressively an algorithm should space child orders to avoid self-inflicted impact accumulation.

Resilience is the market microstructure property that governs the speed of impact decay. It measures how quickly the limit order book (LOB) replenishes after a liquidity-taking event. High-resilience markets exhibit rapid decay because new limit orders aggressively refill depleted price levels, restoring the bid-ask spread and order book depth. Factors influencing resilience include:

• Market maker competition: More market makers accelerate replenishment
• Tick size regime: Smaller tick sizes can slow replenishment at the touch
• Informed vs. uninformed flow: Trades perceived as uninformed attract faster liquidity replenishment
• Electronic vs. voice-brokered: Electronic limit order books generally exhibit faster resilience

Total market impact decomposes into two components with distinct decay profiles:

• Permanent Impact (Information Component): The price change that persists indefinitely, reflecting the market's inference that the trade conveys private information about the asset's fundamental value. This component does not decay and is proportional to the square root or linear function of trade size.
• Transient Impact (Liquidity Component): The temporary price concession paid to attract liquidity providers. This component decays fully over time as the order book replenishes, following the market's resilience dynamics.

Execution algorithms exploit this decomposition by trading more aggressively when transient impact dominates and more passively when permanent impact risk is elevated.

In the Almgren-Chriss framework and its extensions, impact decay directly shapes the optimal liquidation trajectory. When decay is fast relative to the trading horizon, the algorithm can trade more aggressively early on because temporary impacts dissipate before the next child order arrives, minimizing cumulative costs. When decay is slow, the algorithm must space orders more widely to avoid self-interaction, increasing timing risk exposure. Propagator models formalize this by modeling price impact as a convolution of past trades with a decay kernel, allowing the optimizer to compute the precise marginal cost of trading at each time step given the lingering effects of prior executions.

Practitioners estimate impact decay empirically using Vector Autoregression (VAR) models on tick-level trade and quote data. The methodology involves:

• Regressing subsequent price changes against lagged signed trade volumes
• Extracting the impulse response function, which traces the price path following a unit trade shock
• Fitting a parametric decay function (exponential, power-law, or hyperbolic) to the impulse response

Key empirical findings include that decay is often faster than exponential in the initial milliseconds (due to high-frequency market maker activity) and slower in the tail, suggesting a multi-timescale resilience structure. Accurate decay estimation is essential for calibrating realistic market simulators used in reinforcement learning-based execution agent training.

Impact decay is not symmetric across market conditions. Key regime dependencies include:

• Volatility regime: High-volatility periods accelerate apparent decay as noise dominates the price process, but this masks increased permanent impact risk
• Liquidity shocks: During liquidity crises, decay slows dramatically as market makers widen spreads and withdraw from the order book, causing transient impacts to persist and compound
• Trade direction: Sell orders often exhibit slower decay than buy orders in equity markets due to asymmetric risk-aversion among liquidity providers
• News events: Scheduled macroeconomic announcements create pre-announcement decay slowdowns as liquidity providers reduce inventory risk exposure

Adaptive execution algorithms incorporate real-time decay regime detection to dynamically adjust child order sizing and spacing.

The speed at which the limit order book replenishes after a liquidity-taking event. High resilience implies rapid Market Impact Decay, as new limit orders immediately refill the depleted price levels.

• Key Metric: Time for the spread to return to pre-trade levels.
• Drivers: High-frequency market makers and arbitrageurs.
• Contrast: Fragile markets exhibit slow decay and high execution costs.

A foundational optimal execution framework that mathematically decomposes impact into permanent and temporary components. The temporary component explicitly models the decay function.

• Permanent Impact: Linear function of volume, persists indefinitely.
• Temporary Impact: Decays according to a power-law or exponential kernel.
• Optimization: Balances impact cost against timing risk to find the optimal liquidation trajectory.

A real-time signal measuring the asymmetry between resting bid and ask liquidity. A sudden imbalance predicts directional price pressure and directly influences the decay rate.

• Calculation: (Bid Volume - Ask Volume) / (Bid Volume + Ask Volume).
• Decay Link: High imbalance slows decay as the dominant side absorbs liquidity faster.
• Usage: Execution algorithms pause or accelerate based on imbalance thresholds.

A measure of the permanent price impact of order flow, representing the slope of price changes against signed trade volume. It isolates the non-decaying, information-based component of impact.

• Interpretation: High lambda means trades convey significant private information.
• Decay Separation: Total impact minus Kyle's Lambda impact equals the transient, decaying component.
• Estimation: Derived from linear regression of mid-price returns on net order flow.

The comprehensive cost framework measuring the difference between the decision price and the final execution price. Market Impact Decay directly affects the realized shortfall.

• Components: Delay cost, explicit commissions, and realized market impact.
• Decay Role: Faster decay reduces the slippage on subsequent child orders.
• Benchmarking: Used to evaluate if an algorithm's scheduling effectively exploited resilience.

A machine learning forecast of the expected intraday volume distribution. Algorithms align execution schedules with high-volume periods to benefit from faster Market Impact Decay.

• Typical Shape: U-shape with high volume at open and close.
• Decay Correlation: High volume periods exhibit greater resilience and faster decay.
• Input Features: Historical volume buckets, auction imbalances, and news sentiment.