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How efficiency shapes market impact

Author

Listed:
  • J. Doyne Farmer
  • Austin Gerig
  • Fabrizio Lillo
  • Henri Waelbroeck

Abstract

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e., the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of metaorder size, with average permanent impact relaxing to about two thirds of peak impact.

Suggested Citation

  • J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2011. "How efficiency shapes market impact," Papers 1102.5457, arXiv.org, revised Sep 2013.
  • Handle: RePEc:arx:papers:1102.5457
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    File URL: http://arxiv.org/pdf/1102.5457
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    Cited by:

    1. Paolo Barucca & Fabrizio Lillo, 2017. "Behind the price: on the role of agent's reflexivity in financial market microstructure," Papers 1708.07047, arXiv.org.
    2. Nataliya Bershova & Dmitry Rakhlin, 2013. "The non-linear market impact of large trades: evidence from buy-side order flow," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1759-1778, November.
    3. Thibault Jaisson, 2015. "Liquidity and Impact in Fair Markets," Papers 1506.02507, arXiv.org.
    4. Andre Cardoso Barato & Iacopo Mastromatteo & Marco Bardoscia & Matteo Marsili, 2011. "Impact of meta-order in the Minority Game," Papers 1112.3908, arXiv.org, revised Nov 2012.
    5. Thibault Jaisson, 2014. "Market impact as anticipation of the order flow imbalance," Papers 1402.1288, arXiv.org.
    6. Jonathan Donier & Julius Bonart, 2014. "A Million Metaorder Analysis of Market Impact on the Bitcoin," Papers 1412.4503, arXiv.org, revised Sep 2015.
    7. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    8. Emmanuel Bacry & Adrian Iuga & Matthieu Lasnier & Charles-Albert Lehalle, 2014. "Market impacts and the life cycle of investors orders," Papers 1412.0217, arXiv.org, revised Dec 2014.
    9. Damian Eduardo Taranto & Giacomo Bormetti & Fabrizio Lillo, 2014. "The adaptive nature of liquidity taking in limit order books," Papers 1403.0842, arXiv.org, revised Apr 2014.
    10. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," Post-Print hal-01277584, HAL.
    11. Kyle Bechler & Mike Ludkovski, 2014. "Optimal Execution with Dynamic Order Flow Imbalance," Papers 1409.2618, arXiv.org, revised Oct 2014.
    12. Elia Zarinelli & Michele Treccani & J. Doyne Farmer & Fabrizio Lillo, 2014. "Beyond the square root: Evidence for logarithmic dependence of market impact on size and participation rate," Papers 1412.2152, arXiv.org.
    13. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.
    14. Emilio Said & Ahmed Bel Hadj Ayed & Alexandre Husson & Frederic Abergel & Ahmed Bel & Hadj Ayed & Fr'ed'eric Abergel & Global Markets & Bnp Paribas, 2018. "Market Impact: A systematic study of limit orders," Papers 1802.08502, arXiv.org.
    15. Fabio Caccioli & Jean-Philippe Bouchaud & J. Doyne Farmer, 2012. "A proposal for impact-adjusted valuation: Critical leverage and execution risk," Papers 1204.0922, arXiv.org, revised Aug 2012.
    16. Bence Toth & Imon Palit & Fabrizio Lillo & J. Doyne Farmer, 2011. "Why is order flow so persistent?," Papers 1108.1632, arXiv.org, revised Nov 2014.
    17. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    18. repec:eee:ejores:v:264:y:2018:i:3:p:1159-1171 is not listed on IDEAS
    19. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    20. Iacopo Mastromatteo & Bence Toth & Jean-Philippe Bouchaud, 2013. "Agent-based models for latent liquidity and concave price impact," Papers 1311.6262, arXiv.org, revised Dec 2014.
    21. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2014. "$L_p$ regularized portfolio optimization," Papers 1404.4040, arXiv.org.
    22. Kyle Bechler & Michael Ludkovski, 2017. "Order Flows and Limit Order Book Resiliency on the Meso-Scale," Papers 1708.02715, arXiv.org.
    23. Emilio Said & Ahmed Bel Hadj Ayed & Alexandre Husson & Frédéric Abergel, 2018. "Market Impact: A systematic study of limit orders," Working Papers hal-01561128, HAL.
    24. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2016. "Liquidity Risk And Instabilities In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-28, August.

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