IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2606.07059.html

Diffusive in plain sight: An inconspicuous law of market impact

Author

Listed:
  • Julius F. Bonart

Abstract

Decomposing impact as the difference between realized and counterfactual returns and requiring both to be diffusive yields an identity that restricts admissible impact scaling at the level of individual participants. This constraint implies the square-root law in the information-neutral regime and a crossover to linear impact under strong informational coupling, consistent with empirical observations. In the weak-coupling regime, cumulative market impact is itself diffusive -- a diagnostic that many propagator and latent liquidity models fail to satisfy.

Suggested Citation

  • Julius F. Bonart, 2026. "Diffusive in plain sight: An inconspicuous law of market impact," Papers 2606.07059, arXiv.org.
    • Handle: RePEc:arx:papers:2606.07059
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2606.07059
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Guillaume Maitrier & Gr'egoire Loeper & Jean-Philippe Bouchaud, 2025. "The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator," Papers 2509.05065, arXiv.org.
    2. 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.
    3. 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.
    4. 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.
    5. Albert S. Kyle & Anna A. Obizhaeva, 2016. "Market Microstructure Invariance: Empirical Hypotheses," Econometrica, Econometric Society, vol. 84(4), pages 1345-1404, July.
    6. Guillaume Maitrier & Gr'egoire Loeper & Jean-Philippe Bouchaud, 2025. "Generating realistic metaorders from public data," Papers 2503.18199, arXiv.org, revised Apr 2025.
    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. George C. Chacko & Jakub W. Jurek & Erik Stafford, 2008. "The Price of Immediacy," Journal of Finance, American Finance Association, vol. 63(3), pages 1253-1290, June.
    9. Albert S. Kyle & Anna A. Obizhaeva, 2016. "Market Microstructure Invariance: Empirical Hypotheses," Econometrica, Econometric Society, vol. 84, pages 1345-1404, July.
    10. 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.
    11. Frédéric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Are trading invariants really invariant? Trading costs matter," Post-Print hal-02323318, HAL.
    12. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
    13. Yuki Sato & Kiyoshi Kanazawa, 2024. "Strict universality of the square-root law in price impact across stocks: a complete survey of the Tokyo stock exchange," Papers 2411.13965, arXiv.org, revised Dec 2025.
    14. 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.
    15. 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.
    16. Yuki Sato & Kiyoshi Kanazawa, 2025. "Why do financial prices exhibit Brownian motion despite predictable order flow?," Papers 2502.17906, arXiv.org, revised May 2025.
    17. Thibault Jaisson, 2015. "Market impact as anticipation of the order flow imbalance," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1123-1135, July.
    18. Frédéric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Are trading invariants really invariant? Trading costs matter," Quantitative Finance, Taylor & Francis Journals, vol. 20(7), pages 1059-1068, July.
    19. Fédéric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Crossover from Linear to Square-Root Market Impact," Post-Print hal-02323405, HAL.
    20. Madhavan, Ananth & Richardson, Matthew & Roomans, Mark, 1997. "Why Do Security Prices Change? A Transaction-Level Analysis of NYSE Stocks," The Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 1035-1064.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aniket Vasaikar, 2026. "Empirical Confirmation of the Square-Root Law of Market Impact in a U.S. Large-Cap Equity," Papers 2606.24019, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Johannes Muhle-Karbe & Youssef Ouazzani Chahdi & Mathieu Rosenbaum & Gr'egoire Szymanski, 2026. "A unified theory of order flow, market impact, and volatility," Papers 2601.23172, arXiv.org, revised Feb 2026.
    2. Guillaume Maitrier & Jean-Philippe Bouchaud, 2025. "The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility: A Unifying Framework," Papers 2506.07711, arXiv.org, revised Mar 2026.
    3. Thibault Jaisson, 2014. "Market impact as anticipation of the order flow imbalance," Papers 1402.1288, arXiv.org.
    4. Thibault Jaisson, 2015. "Liquidity and Impact in Fair Markets," Papers 1506.02507, arXiv.org.
    5. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    6. Guillaume Maitrier & Gr'egoire Loeper & Jean-Philippe Bouchaud, 2025. "Generating realistic metaorders from public data," Papers 2503.18199, arXiv.org, revised Apr 2025.
    7. 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.
    8. 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.
    9. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-11, October.
    10. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," Post-Print hal-01277584, HAL.
    11. 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.
    12. B. Tóth & Z. Eisler & F. Lillo & J. Kockelkoren & J.-P. Bouchaud & J.D. Farmer, 2012. "How does the market react to your order flow?," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1015-1024, May.
    13. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    14. Emilio Said, 2022. "Market Impact: Empirical Evidence, Theory and Practice," Working Papers hal-03668669, HAL.
    15. Yang Zhou & Jianwen Chen & Ruipeng Wei, 2026. "Order Splitting and Liquidity Replenishment Are Jointly Necessary for the Square-Root Law of Market Impact:," Papers 2607.04280, arXiv.org.
    16. Bonart, Julius & Lillo, Fabrizio, 2018. "A continuous and efficient fundamental price on the discrete order book grid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 698-713.
    17. Johannes Muhle-Karbe & Zexin Wang & Kevin Webster, 2024. "Stochastic Liquidity as a Proxy for Nonlinear Price Impact," Operations Research, INFORMS, vol. 72(2), pages 444-458, March.
    18. Jean-Philippe Bouchaud, 2021. "The Inelastic Market Hypothesis: A Microstructural Interpretation," Papers 2108.00242, arXiv.org, revised Jan 2022.
    19. Bence Toth & Imon Palit & Fabrizio Lillo & J. Doyne Farmer, 2011. "Why is order flow so persistent?," Papers 1108.1632, arXiv.org, revised Nov 2014.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2606.07059. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.