The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called ``square-root impact law'', which states that impact grows as the square-root of traded volume, has nothing to do with price diffusion, i.e. that typical price changes grow as the square-root of time. We rationalise empirical findings on impact and volatility by introducing a simple scaling argument and confronting it to data.
@article{arxiv.1905.04569,
title = {Impact is not just volatility},
author = {Frédéric Bucci and Iacopo Mastromatteo and Michael Benzaquen and Jean-Philippe Bouchaud},
journal= {arXiv preprint arXiv:1905.04569},
year = {2019}
}