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Are trading invariants really invariant? Trading costs matter

Author

Listed:
  • Frédéric Bucci
  • Fabrizio Lillo
  • Jean-Philippe Bouchaud
  • Michael Benzaquen

    (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

We revisit the trading invariance hypothesis recently proposed by Kyle and Obizhaeva [1] by empirically investigating a large dataset of bets, or metaorders, provided by ANcerno. The hypothesis predicts that the quantity I := R/N 3/2 , where R is the exchanged risk (volatility × volume × price) and N is the number of bets, is invariant. We find that the 3/2 scaling between R and N works well and is robust against changes of year, market capitalisation and economic sector. However our analysis clearly shows that I is not invariant. We find a very high correlation R 2 > 0.8 between I and the total trading cost (spread and market impact) of the bet. We propose new invariants defined as a ratio of I and costs and find a large decrease in variance. We show that the small dispersion of the new invariants is mainly driven by (i) the scaling of the spread with the volatility per transaction, (ii) the near invariance of the distribution of metaorder size and of the volume and number fractions of bets across stocks.

Suggested Citation

  • Frédéric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Are trading invariants really invariant? Trading costs matter," Post-Print hal-02323318, HAL.
    • Handle: RePEc:hal:journl:hal-02323318
    Note: View the original document on HAL open archive server: https://hal.science/hal-02323318
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    References listed on IDEAS

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    1. Torben G. Andersen & Oleg Bondarenko & Albert S. Kyle & Anna Obizhaeva, 2016. "Intraday Trading Invariance in the E-mini S&P 500 Futures Market," Working Papers w0229, Center for Economic and Financial Research (CEFIR).
    2. Fr'ed'eric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2018. "Crossover from linear to square-Root market impact," Papers 1811.05230, arXiv.org.
    3. Albert S. Kyle & Anna Obizhaeva, 2017. "Dimensional Analysis and Market Microstructure Invariance," Working Papers w0234, New Economic School (NES).
    4. Michael Benzaquen & Jonathan Donier & Jean-Philippe Bouchaud, 2016. "Unravelling the trading invariance hypothesis," Papers 1602.03011, arXiv.org, revised Sep 2016.
    5. Mathias Pohl & Alexander Ristig & Walter Schachermayer & Ludovic Tangpi, 2018. "Theoretical and empirical analysis of trading activity," Papers 1803.04892, arXiv.org, revised Oct 2018.
    6. Anna, Petrenko, 2016. "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(1), March.
    7. Albert S. Kyle & Anna A. Obizhaeva, 2016. "Market Microstructure Invariance: Empirical Hypotheses," Econometrica, Econometric Society, vol. 84, pages 1345-1404, July.
    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. Albert S. Kyle & Anna Obizhaeva, 2017. "Dimensional Analysis and Market Microstructure Invariance," Working Papers w0234, Center for Economic and Financial Research (CEFIR).
    10. Albert S. Kyle & Anna A. Obizhaeva, 2016. "Market Microstructure Invariance: Empirical Hypotheses," Econometrica, Econometric Society, vol. 84(4), pages 1345-1404, July.
    11. Fr'ed'eric Bucci & Iacopo Mastromatteo & Zolt'an Eisler & Fabrizio Lillo & Jean-Philippe Bouchaud & Charles-Albert Lehalle, 2018. "Co-impact: Crowding effects in institutional trading activity," Papers 1804.09565, arXiv.org, revised Jul 2018.
    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.
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    Cited by:

    1. Alessandro Micheli & Eyal Neuman, 2020. "Evidence of Crowding on Russell 3000 Reconstitution Events," Papers 2006.07456, arXiv.org, revised Sep 2022.

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