Beyond the Square Root: Evidence for Logarithmic Dependence of Market Impact on Size and Participation Rate

Abstract

We make an extensive empirical study of the market impact of large orders (metaorders) executed in the U.S. equity market between 2007 and 2009. We show that the square root market impact formula, which is widely used in the industry and supported by previous published research, provides a good fit only across about two orders of magnitude in order size. A logarithmic functional form fits the data better, providing a good fit across almost five orders of magnitude. We introduce the concept of an "impact surface" to model the impact as a function of both the duration and the participation rate of the metaorder, finding again a logarithmic dependence. We show that during the execution the price trajectory deviates from the market impact, a clear indication of non-VWAP executions. Surprisingly, we find that sometimes the price starts reverting well before the end of the execution. Finally we show that, although on average the impact relaxes to approximately 2/3 of the peak impact, the precise asymptotic value of the price depends on the participation rate and on the duration of the metaorder. We present evidence that this might be due to a herding phenomenon among metaorders.

A Million Metaorder Analysis of Market Impact on the Bitcoin

“…Usually, market participants have only access to their own proprietary data (Bershova and Rakhlin 2013, Brokmann et al 2014, Toth et al 2011a) which leads to an unavoidable conditioning to their trading strategies (even though in some cases many different strategies are collated together so part of the conditioning may average out). Two notable exceptions do however exist: In Moro et al (2009) hidden metaorders are directly inferred from brokerage codes, while Zarinelli et al (2014) have unprecedented access to the start times, end times and volumes of a huge amount of metaorders stemming from Ancerno's clients 3 . In this paper, we use a dataset which allows on the contrary to identify each trade with a unique trader, thereby leading to a complete picture of the market.…”

Market Impacts and the Life Cycle of Investors Orders

“…Note in [Zarinelli et al, 2015], authors underline the potential influence of the trading rate on the market impact components. It allows to avoid sudden accelerated trading rates having an hidden influence on the price moves.…”

Optimal execution with non-linear transient market impact

“…This strategy allows the trader to minimize costs whilst also minimizing the revelation of information to the rest of the market. The precise way in which it is optimal to split the large order (herein called metaorder ) [56] depends on the objective function and on the market impact model, i.e. the change in price conditioned on signed trade size.…”