Permanent Impact

Permanent impact occurs when the market interprets a trade as conveying private information about an asset's true value. Market makers and other participants adjust their quotes not because of inventory imbalances, but because they infer that the trader possesses superior knowledge. This is the core of Kyle's (1985) model, where the market maker sets prices to be regret-free in expectation, given the observed net order flow. The price adjustment is a direct function of the informed component of the trade.

The magnitude of permanent impact is quantified by Kyle's Lambda (λ), a coefficient representing the market's depth and adverse selection risk. It defines the linear relationship between net order flow imbalance and the permanent price change.

• High λ: Indicates an illiquid market with high adverse selection; a small trade causes a large permanent price shift.
• Low λ: Indicates a deep, liquid market where large trades can be absorbed without being interpreted as strongly informed.
• Mathematically, the permanent price change ΔP = λ * Q, where Q is the signed trade size.

It is critical to decompose total market impact into its permanent and temporary components. Temporary impact is the transitory price concession paid to attract liquidity; it reverses as the order book replenishes. Permanent impact is the non-reverting price change that persists long after the trade is complete. The Almgren-Chriss model formalizes this split, modeling permanent impact as a linear function of the trading rate and temporary impact as a function of the instantaneous speed of execution.

Empirical studies across global equity markets reveal that permanent impact does not scale linearly with trade size but follows a concave function, most famously the Square Root Impact Law. The expected price change ΔP is proportional to σ * √(Q / V), where σ is volatility, Q is trade size, and V is average daily volume. This implies that doubling a trade's size increases its permanent impact by a factor of roughly 1.4, not 2, reflecting the market's adaptive resilience to large informed trades.

Permanent impact is the realized cost of adverse selection for liquidity providers. When a market maker trades with a counterparty who has a high probability of being informed, the subsequent price movement is permanently adverse. Metrics like VPIN (Volume-Synchronized Probability of Informed Trading) attempt to measure this toxicity in real-time. A high VPIN reading signals that order flow is dominated by informed traders, leading to a higher expected permanent impact and causing market makers to widen spreads preemptively.

In the Almgren-Chriss execution framework, the permanent impact component is treated as an unavoidable cost of trading that is independent of the strategy's speed. Since it is a linear function of the total shares traded, a trader cannot reduce the total permanent impact by slicing the order—it is a sunk cost of the decision to trade. The optimization therefore focuses on balancing the temporary impact and timing risk (volatility) of the execution schedule, accepting the permanent impact as a fixed penalty for accessing the market.

The transient price concession required to attract liquidity for a trade, which fully reverses after the order completes. Unlike permanent impact, temporary impact reflects inventory risk compensation rather than information revelation.

• Reverses as limit orders replenish the book
• Proportional to trade size and urgency
• Dominant in liquid, high-volume names
• Modeled as a resilient price process in Almgren-Chriss frameworks

A foundational measure of market illiquidity from Kyle's 1985 model, representing the linear coefficient between order flow imbalance and permanent price change. A higher lambda indicates that trades convey more information.

• Estimated via regression: ΔP = λ · Q + ε
• Inversely related to market depth
• Used to calibrate optimal execution schedules
• Captures the information content of order flow

The cost incurred when trading against counterparties with superior information, causing post-trade prices to move unfavorably. This is the mechanism through which permanent impact manifests in dealer markets.

• Measured via realized spread decomposition
• Higher for illiquid or opaque securities
• Drives the bid-ask spread width
• VPIN metrics estimate real-time toxicity

The unintended signaling of a large trading intention to the market, allowing predatory participants to front-run and accelerate permanent impact. Leakage transforms temporary price pressure into lasting adverse moves.

• Occurs via order book patterns and venue selection
• Mitigated by iceberg orders and dark pools
• Primary driver of alpha decay in large executions
• Detected through correlation breakdowns in child order fills

An empirical regularity stating that expected price impact scales with the square root of trade size relative to volume. This non-linear relationship implies that slicing large orders reduces total impact.

• Impact ∝ √(Q / V) where Q is size, V is volume
• Validated across equities, futures, and FX markets
• Foundation for optimal execution slicing
• Deviations signal regime changes or information events

The seminal optimal execution framework that formalizes the trade-off between market impact costs and timing risk. Permanent impact enters as a linear function of shares traded, while temporary impact depends on trading speed.

• Objective: minimize expected shortfall + risk penalty
• Produces optimal trading trajectories (VWAP, TWAP variants)
• Permanent impact treated as information leakage cost
• Extended to include stochastic liquidity and alpha decay