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The amazing power of dimensional analysis: Quantifying market impact

Author

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  • Mathias Pohl
  • Alexander Ristig
  • Walter Schachermayer
  • Ludovic Tangpi

Abstract

This note complements the inspiring work on dimensional analysis and market microstructure by Kyle and Obizhaeva [18]. Following closely these authors, our main result shows by a similar argument as usually applied in physics the following remarkable fact. If the market impact of a meta-order only depends on four well-defined and financially meaningful variables, then -- up to a constant -- there is only one possible form of this dependence. In particular, the market impact is proportional to the square-root of the size of the meta-order. This theorem can be regarded as a special case of a more general result of Kyle and Obizhaeva. These authors consider five variables which might have an influence on the size of the market impact. In this case one finds a richer variety of possible functional relations which we precisely characterize. We also discuss the analogies to classical arguments from physics, such as the period of a pendulum.

Suggested Citation

  • Mathias Pohl & Alexander Ristig & Walter Schachermayer & Ludovic Tangpi, 2017. "The amazing power of dimensional analysis: Quantifying market impact," Papers 1702.05434, arXiv.org, revised Sep 2017.
    • Handle: RePEc:arx:papers:1702.05434
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    References listed on IDEAS

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    1. Albert S. Kyle & Anna Obizhaeva, 2016. "Market Microstructure Invariance: A Dynamic Equilibrium Model," Working Papers w0228, Center for Economic and Financial Research (CEFIR).
    2. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 461-504.
    3. 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.
    4. Albert S. Kyle & Anna Obizhaeva, 2016. "Market Microstructure Invariance: A Dynamic Equilibrium Model," Working Papers w0228, New Economic School (NES).
    5. Foucault, Thierry & Pagano, Marco & Roell, Ailsa, 2013. "Market Liquidity: Theory, Evidence, and Policy," OUP Catalogue, Oxford University Press, number 9780199936243.
    6. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    7. C. Gomes & H. Waelbroeck, 2015. "Is market impact a measure of the information value of trades? Market response to liquidity vs. informed metaorders," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 773-793, May.
    8. 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.
    9. Bence Toth & Yves Lemperiere & Cyril Deremble & Joachim de Lataillade & Julien Kockelkoren & Jean-Philippe Bouchaud, 2011. "Anomalous price impact and the critical nature of liquidity in financial markets," Papers 1105.1694, arXiv.org, revised Nov 2011.
    10. 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.
    11. Nicky J. Welton & Howard H. Z. Thom, 2015. "Value of Information," Medical Decision Making, , vol. 35(5), pages 564-566, July.
    12. J. Donier & J. Bonart & I. Mastromatteo & J.-P. Bouchaud, 2015. "A fully consistent, minimal model for non-linear market impact," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1109-1121, July.
    13. Jonathan Donier & Julius Bonart & Iacopo Mastromatteo & Jean-Philippe Bouchaud, 2014. "A fully consistent, minimal model for non-linear market impact," Papers 1412.0141, arXiv.org, revised Mar 2015.
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    Citations

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    Cited by:

    1. Sergey Nadtochiy, 2020. "A simple microstructural explanation of the concavity of price impact," Papers 2001.01860, arXiv.org, revised Dec 2020.
    2. Roncalli, Thierry & Cherief, Amina & Karray-Meziou, Fatma & Regnault, Margaux, 2021. "Liquidity Stress Testing in Asset Management - Part 2. Modeling the Asset Liquidity Risk," MPRA Paper 108295, University Library of Munich, Germany.
    3. Tathagata Banerjee & Zachary Feinstein, 2019. "Price mediated contagion through capital ratio requirements with VWAP liquidation prices," Papers 1910.12130, arXiv.org, revised Feb 2021.
    4. Dilip B. Madan & Wim Schoutens & King Wang, 2020. "Bilateral multiple gamma returns: Their risks and rewards," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-27, March.
    5. Banerjee, Tathagata & Feinstein, Zachary, 2021. "Price mediated contagion through capital ratio requirements with VWAP liquidation prices," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1147-1160.
    6. Paul Jusselin & Mathieu Rosenbaum, 2020. "No‐arbitrage implies power‐law market impact and rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1309-1336, October.
    7. Mathias Pohl & Alexander Ristig & Walter Schachermayer & Ludovic Tangpi, 2018. "Theoretical and empirical analysis of trading activity," Papers 1803.04892, arXiv.org, revised Oct 2018.
    8. Paul Jusselin & Mathieu Rosenbaum, 2018. "No-arbitrage implies power-law market impact and rough volatility," Papers 1805.07134, arXiv.org.
    9. Sergey Nadtochiy, 2022. "A simple microstructural explanation of the concavity of price impact," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 78-113, January.

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