Empirical Confirmation of the Square-Root Law of Market Impact in a U.S. Large-Cap Equity: A Reconstructed-Metaorder Study of AAPL Order Flow

Battle Count: 50

Directly relevant to algorithmic execution and market impact modeling. The square-root law is the foundational assumption in optimal execution frameworks (Almgren-Chriss, etc.). This paper provides the first confirmation on a U.S. equity using purely anonymous Level-3 data, validating that impact models can be calibrated from public tape without broker identifiers. The prefactor band [0.5, 1.0] (or [0.34, 0.69] corrected) is directly usable for sizing trades and estimating implementation shortfall. The structural tests (sign/chronology dependence) confirm the mechanism underlying impact, strengthening confidence in the model. The walk-forward stability across 32 weeks supports production use.

Requires processing ~0.5 billion Level-3 market-by-order events at nanosecond resolution. Book reconstruction, trade signing, metaorder identification (dominant-side runs), de-seasonalisation, and multi-setting calibration are computationally intensive. Access to Databento or equivalent Level-3 feed is a prerequisite. The statistical methods themselves (log-spaced regression, Hill estimator, bootstrap, permutation tests) are standard, but the data engineering pipeline for reconstructing the full limit order book and grouping anonymous trades into metaorders is non-trivial. The 9-setting robustness check and 32-week walk-forward add further computational burden.

Methods are described in detail (bin widths, thresholds, de-seasonalisation, walk-forward protocol). However, the Databento DBN Level-3 feed is a commercial data source requiring subscription. No code repository is provided. The reconstruction algorithm (dominant-side runs, 30s bins, 0.3 dominance threshold) is specified but not released as code. The bias correction factor of 2× is cited from Naviglio et al. (2025) working paper. Reproduction requires access to ~0.5 billion events of Nasdaq TotalView-ITCH data.