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A Theory for Market Impact: How Order Flow Affects Stock Price

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  • Austin Gerig

Abstract

It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the market impact of hidden orders (orders that reflect the true intention of buying and selling) that matches the empirically measured result and that reproduces some of the non-trivial and universal properties of stock returns (returns are percent changes in stock price). The theory is based on a simple premise, that the stock market can be modeled in a mechanical way - as a device that translates order flow into an uncorrelated price stream. Given that order flow is highly autocorrelated, this premise requires that market impact (1) depends on past order flow and (2) is asymmetric for buying and selling. I derive the specific form for the dependence in (1) by assuming that current liquidity responds to information about all currently active hidden orders (liquidity is a measure of the price response to a transaction of a given size). This produces an equation that suggests market impact should scale logarithmically with total order size. Using data from the London Stock Exchange I empirically measure market impact and show that the result matches the theory. Also using empirical data, I qualitatively specify the asymmetry of (2). Putting all results together, I form a model for market impact that reproduces three universal properties of stock returns - that returns are uncorrelated, that returns are distributed with a power law tail, and that the magnitude of returns is highly autocorrelated (also known as clustered volatility).

Suggested Citation

  • Austin Gerig, 2008. "A Theory for Market Impact: How Order Flow Affects Stock Price," Papers 0804.3818, arXiv.org, revised Jul 2008.
  • Handle: RePEc:arx:papers:0804.3818
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    File URL: http://arxiv.org/pdf/0804.3818
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    References listed on IDEAS

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    1. Diamond, Douglas W. & Verrecchia, Robert E., 1987. "Constraints on short-selling and asset price adjustment to private information," Journal of Financial Economics, Elsevier, vol. 18(2), pages 277-311, June.
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    Cited by:

    1. B. Tóth & F. Lillo & J. D. Farmer, 2010. "Segmentation algorithm for non-stationary compound Poisson processes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 78(2), pages 235-243, November.
    2. Igor Skachkov, 2013. "Market Impact Paradoxes," Papers 1312.3349, arXiv.org.
    3. Fabrizio Pomponio & Frédéric Abergel, 2013. "Multiple-limit trades : empirical facts and application to lead-lag measures," Post-Print hal-00745317, HAL.
    4. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    5. 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.
    6. Bence Toth & Imon Palit & Fabrizio Lillo & J. Doyne Farmer, 2011. "Why is order flow so persistent?," Papers 1108.1632, arXiv.org, revised Nov 2014.
    7. repec:hal:wpaper:hal-00745317 is not listed on IDEAS
    8. Tóth, Bence & Palit, Imon & Lillo, Fabrizio & Farmer, J. Doyne, 2015. "Why is equity order flow so persistent?," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 218-239.
    9. Axioglou, Christos & Skouras, Spyros, 2011. "Markets change every day: Evidence from the memory of trade direction," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 423-446, June.
    10. Karol Wawrzyniak & Wojciech Wi'slicki, 2013. "Grand canonical minority game as a sign predictor," Papers 1309.3399, arXiv.org.
    11. Martin D. Gould & Mason A. Porter & Sam D. Howison, 2015. "The Long Memory of Order Flow in the Foreign Exchange Spot Market," Papers 1504.04354, arXiv.org, revised Oct 2015.

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