Mechanism underlying square-root impact of single market orders

Establish a rigorous mechanistic explanation for why the average impact of a single market order of size q—measured as the expected signed change in the mid-price after sufficient digestion/relaxation time—scales as the square root of q, and determine whether the hypothesized explanation based on a locally linear latent order book and subsequent “hot potato” dynamics among liquidity providers quantitatively accounts for this scaling.

Background

The paper shows that the well-known square-root market impact law for metaorders emerges from microstructural behavior: individual child orders already exhibit square-root impact in their volume, and the cumulative effect across a metaorder arises via an inverse square-root decay over time. This supports a largely mechanical origin of impact rather than an informational one.

In the conclusion, the authors identify a central unresolved question: why does a single market order’s impact scale as the square root of its volume? They suggest a plausible mechanism—local linearity of the latent order book combined with a ‘hot potato’ redistribution among market-makers until a final counterparty is reached—which would imply an average price displacement proportional to sqrt(q). They note that further empirical validation using the JPX dataset (or similar) would be needed to confirm or refute this explanation.