Empirical test on AAPL using reconstructed metaorders from full Nasdaq ITCH feed finds the square-root impact law with prefactor c_raw=0.69 consistent with global observations and preferred over linear or log forms by model comparison.
Diffusive in plain sight: An inconspicuous law of market impact
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abstract
Decomposing impact as the difference between realized and counterfactual returns and requiring both to be diffusive yields an identity that restricts admissible impact scaling at the level of individual participants. This constraint implies the square-root law in the information-neutral regime and a crossover to linear impact under strong informational coupling, consistent with empirical observations. In the weak-coupling regime, cumulative market impact is itself diffusive -- a diagnostic that many propagator and latent liquidity models fail to satisfy.
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Empirical Confirmation of the Square-Root Law of Market Impact in a U.S. Large-Cap Equity
Empirical test on AAPL using reconstructed metaorders from full Nasdaq ITCH feed finds the square-root impact law with prefactor c_raw=0.69 consistent with global observations and preferred over linear or log forms by model comparison.