Beyond the Square Root: Evidence for Logarithmic Dependence of Market Impact on Size and Participation Rate
By Elia Zarinelli, Michele Treccani, J. D. Farmer, Fabrizio Lillo, Piazzetta E. Cuccia. 2014
89 citations recorded by the source corpus.
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.
Subfields: Accounting, Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/5d9b3cf4ff6099018f294cb4139ddbeb6ff1eba8
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Citations in the corpus
- Deep learning for limit order books (2016, unknown): “Important related literature on limit order books includes Lillo et al. (2003), Farmer et al. (2004), Zarinelli et al. (2015), Curato † The theoretical models cannot be directly compared against the data-driven models in this paper due to the theoretical models’ lack of tractability for computing a…”
- Market Impacts and the Life Cycle of Investors Orders (2014, background): “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).”
- Universal scaling and nonlinearity of aggregate price impact in financial markets. (2017, unknown): “[10] Elia Zarinelli, Michele Treccani, J.”
- Optimal execution with non-linear transient market impact (2014, unknown): “The precise way in which it is optimal to split the large order (herein called metaorder) Zarinelli et al. (2015) depends on the objective function and on the market impact model, i.e. the change in price conditioned on signed trade size.”