This study is the first to decipher market impact at all time scales on the same database, from a trade-by-trade scale to a daily one. Moreover, the very concentrated nature of the database (400,000 metaorders issued by investors, electronically traded, during one year—2010—, on European market all regulated by the same directive—MiFID—) ensures investors did not change their habits during the study. At the intraday scale, we confirm a square root temporary impact in the daily participation, and we shed light on a duration factor in [Formula: see text] with [Formula: see text]. Including this factor in the fits reinforces the square root shape of impact. We observe a power-law for the transient impact with an exponent between [Formula: see text] (for long metaorders) and [Formula: see text] (for shorter ones). Moreover, we show that the market does not anticipate the size of the metaorders. The intraday decay seems to exhibit two regimes (though hard to identify precisely): a “slow” regime right after the execution of the metaorder followed by a faster one. At the daily time scale, we show price moves after a metaorder can be split between realizations of expected returns that have triggered the investing decision and an idiosynchratic impact that slowly decays to zero. Moreover, we propose a class of toy models based on Hawkes processes (the Hawkes Impact Model, HIM) to illustrate our reasoning. We show how the Impulsive-HIM model, despite its simplicity, embeds appealing features like transience and decay of impact. The latter is parametrized by a parameter C having a macroscopic interpretation: the ratio of contrarian reaction (i.e., impact decay) and of the “herding” reaction (i.e., impact amplification).
Ubiquitous Power Law Scaling in Nonlinear Self-Excited Hawkes Processes
