Empirical Confirmation of the Square-Root Law of Market Impact in a U.S. Large-Cap Equity (opens in new tab)

We test the square-root law (SRL) of market impact on a single U.S. large-capitalisation equity, Apple Inc. (AAPL), using the full Nasdaq TotalView-ITCH market-by-order feed over 178 trading days (2 December 2024 -- 19 August 2025; ~0.5 billion events). Without broker-tagged parent orders, we reconstruct metaorders from the anonymous tape and calibrate impact as $I/\sigma_D = c\,(Q/V_D)^{1/2}$ with the exponent fixed at the universal value $1/2$...