What is Kyle's lambda and how does it measure market impact?

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AcadiFi · Accepted Answer

Kyle's lambda (from Kyle 1985) measures the price impact per unit of signed order flow: delta_P = lambda * Q, where Q is net buy-minus-sell volume. Higher lambda means a less liquid market — the same order size moves prices more. Estimation typically regresses price changes on signed volume over short intervals: delta_P_t = alpha + lambda * signed_volume_t + epsilon_t. Lambda coefficient = market impact sensitivity. Example: Snowfield Medical Devices over 5-minute bars — signed volume of +$200,000 typically moves the midprice by $0.04 on a $50 stock. Lambda = 0.04/200,000 = 2.0e-7 per dollar, or equivalently 4 bps per $200k of imbalance. Interpretation: Kyle's model says informed traders extract rents equal to their informational advantage, and lambda equals the ratio of informed-trade variance to total order-flow variance scaled by asset volatility: lambda = sigma_v * sqrt(variance_informed / total_variance) / sigma_u. A market with high informed trading has high lambda. ```mermaid flowchart LR A[Order flow Q] --> B[Price change] B --> C[Slope = Kyle lambda] D[High lambda] --> E[Low liquidity/
high adverse selection] ``` Applications: lambda is a liquidity risk metric used for position-sizing in illiquid names, a benchmark for execution algos (expected impact for given size), and a proxy for information asymmetry in microstructure research. Time-series variation in lambda helps identify liquidity regime changes ahead of crises.

What is Kyle's lambda and how does it measure market impact?

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