Market Impact Model

The irreversible price drift caused by a trade signaling private information to the market. This component is linear in signed order flow and represents the market's Bayesian update about an asset's fundamental value.

• Kyle's Lambda (λ): The slope coefficient linking net order flow to permanent price change.
• Mechanism: Market makers adjust quotes to reflect the probability that a trade originates from an informed counterparty.
• Key property: Does not decay; the price establishes a new equilibrium level.
• Example: A large buy program in a low-float stock causes the mid-price to drift upward permanently as the market infers positive news.

The transient price concession required to attract immediate counterparties. This component captures the cost of crossing the bid-ask spread and exhausting nearby limit orders.

• Concave function: Typically modeled as proportional to the square root of participation rate (σ * √(Q/V)).
• Decay characteristic: Dissipates as the limit order book replenishes, governed by the market resilience parameter.
• Mechanism: Compensates liquidity providers for inventory risk and adverse selection exposure.
• Example: A market order for 10,000 shares walks the book, executing against multiple price levels and temporarily depressing the last traded price.

An empirical regularity observed across global equity markets: market impact scales approximately with the square root of trade size relative to volume.

• Formula: ΔP ∝ σ * √(Q / V), where σ is volatility, Q is order size, and V is average daily volume.
• Universality: Holds across market capitalizations, time periods, and asset classes.
• Implication: Doubling order size increases impact by only ~41%, incentivizing larger but less frequent trades.
• Origin: Derives from the fractal nature of order book shape and the power-law distribution of limit order depths.

The speed at which the limit order book replenishes after being depleted by a trade. Resilience determines how quickly temporary impact dissipates and the price reverts to its permanent impact trajectory.

• Exponential decay model: h(t) = h₀ * e^(-ρt), where ρ is the resilience parameter.
• High resilience: Electronic markets with many market makers; impact decays in seconds.
• Low resilience: Illiquid securities or stressed markets; impact persists for minutes or hours.
• Strategic implication: Optimal execution schedules space child orders to allow resilience to partially heal the book between slices.

When an execution algorithm's participation rate exceeds ~10-15% of interval volume, the linear impact assumption breaks down. The model must account for super-linear cost escalation.

• Concavity shift: Temporary impact transitions from linear to a power-law function as the algo consumes a dominant share of available liquidity.
• Order book depletion: Walking deep into the book triggers cascading cancellations from liquidity providers who detect the aggressive demand.
• Gaming risk: High participation rates signal intention to predatory algorithms, which front-run the remaining order flow.
• Mitigation: Percentage of Volume (POV) algorithms dynamically cap participation to stay within the linear regime.

In multi-asset portfolios or ETF creation/redemption, trading in one instrument can propagate price pressure to correlated assets through arbitrage linkages.

• Arbitrage channel: Market makers hedge ETF trades by trading the underlying basket, transmitting impact across constituents.
• Correlation matrix: Cross-impact is proportional to the covariance between asset returns.
• Portfolio execution: Optimal liquidation of a basket must solve a multidimensional impact problem, not independent single-asset trajectories.
• Example: Selling a large technology ETF block depresses not only the ETF price but also the individual stock prices of Apple, Microsoft, and NVIDIA.