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How efficiency shapes market impact

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  • 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, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
  • Handle: RePEc:taf:quantf:v:13:y:2013:i:11:p:1743-1758
    DOI: 10.1080/14697688.2013.848464
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    References listed on IDEAS

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    1. Martin D.D. Evans & Richard K. Lyons, 2017. "Order Flow and Exchange Rate Dynamics," World Scientific Book Chapters, in: Studies in Foreign Exchange Economics, chapter 6, pages 247-290, World Scientific Publishing Co. Pte. Ltd..
    2. Hasbrouck, Joel, 1991. "Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
    3. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
    4. Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, A. Craig, 1992. "An ordered probit analysis of transaction stock prices," Journal of Financial Economics, Elsevier, vol. 31(3), pages 319-379, June.
    5. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    6. Z. Eisler & J. Kertész, 2006. "Size matters: some stylized facts of the stock market revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(1), pages 145-154, May.
    7. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2004. "What really causes large price changes?," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 383-397.
    8. Kempf, Alexander & Korn, Olaf, 1999. "Market depth and order size1," Journal of Financial Markets, Elsevier, vol. 2(1), pages 29-48, February.
    9. F. Lillo & Szabolcs Mike & J. Doyne Farmer, 2004. "A theory for long-memory in supply and demand," Papers cond-mat/0412708, arXiv.org, revised Mar 2005.
    10. Philipp Weber & Bernd Rosenow, 2006. "Large stock price changes: volume or liquidity?," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 7-14.
    11. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2006. "Random walks, liquidity molasses and critical response in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 115-123.
    12. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    13. Laszlo Gillemot & J. Doyne Farmer & Fabrizio Lillo, 2006. "There's more to volatility than volume," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 371-384.
    14. Zoltan Eisler & Janos Kertesz, 2005. "Size matters: some stylized facts of the stock market revisited," Papers physics/0508156, arXiv.org, revised May 2006.
    15. Jonathan B. Berk & Richard C. Green, 2004. "Mutual Fund Flows and Performance in Rational Markets," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1269-1295, December.
    16. Keim, Donald B & Madhaven, Ananth, 1996. "The Upstairs Market for Large-Block Transactions: Analysis and Measurement of Price Effects," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 1-36.
    17. Glosten, Lawrence R, 1994. "Is the Electronic Open Limit Order Book Inevitable?," Journal of Finance, American Finance Association, vol. 49(4), pages 1127-1161, September.
    18. Challet, Damien, 2007. "The demise of constant price impact functions and single-time step models of speculation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 29-35.
    19. Carl Hopman, 2007. "Do supply and demand drive stock prices?," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 37-53.
    20. Esteban Moro & Javier Vicente & Luis G. Moyano & Austin Gerig & J. Doyne Farmer & Gabriella Vaglica & Fabrizio Lillo & Rosario N. Mantegna, 2009. "Market impact and trading profile of large trading orders in stock markets," Papers 0908.0202, arXiv.org.
    21. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
    22. J. Doyne Farmer & Paolo Patelli & Ilija I. Zovko, 2003. "The Predictive Power of Zero Intelligence in Financial Markets," Papers cond-mat/0309233, arXiv.org, revised Feb 2004.
    23. Kerry Back & Shmuel Baruch, 2007. "Working Orders in Limit Order Markets and Floor Exchanges," Journal of Finance, American Finance Association, vol. 62(4), pages 1589-1621, August.
    24. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    25. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Szabolcs Mike, 2006. "Market efficiency and the long-memory of supply and demand: is price impact variable and permanent or fixed and temporary?," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 107-112.
    26. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    27. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    28. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
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