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Size matters: some stylized facts of the stock market revisited

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  • Z. Eisler
  • J. Kertész

Abstract

We reanalyze high resolution data from the New York Stock Exchange and find a monotonic (but not power law) variation of the mean value per trade, the mean number of trades per minute and the mean trading activity with company capitalization. We show that the second moment of the traded value distribution is finite. Consequently, the Hurst exponents for the corresponding time series can be calculated. These are, however, non-universal: The persistence grows with larger capitalization and this results in a logarithmically increasing Hurst exponent. A similar trend is displayed by intertrade time intervals. Finally, we demonstrate that the distribution of the intertrade times is better described by a multiscaling ansatz than by simple gap scaling. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

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  • 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.
    • Handle: RePEc:spr:eurphb:v:51:y:2006:i:1:p:145-154
    DOI: 10.1140/epjb/e2006-00189-6
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    References listed on IDEAS

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    Cited by:

    1. Johann Lussange & Ivan Lazarevich & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2021. "Modelling Stock Markets by Multi-agent Reinforcement Learning," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 113-147, January.
    2. Wei-Xing Zhou, 2012. "Universal price impact functions of individual trades in an order-driven market," Quantitative Finance, Taylor & Francis Journals, vol. 12(8), pages 1253-1263, June.
    3. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2009. "Detrended fluctuation analysis of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 433-440.
    4. Michelle B Graczyk & Sílvio M Duarte Queirós, 2017. "Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-23, July.
    5. 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.
    6. Ponta, Linda & Trinh, Mailan & Raberto, Marco & Scalas, Enrico & Cincotti, Silvano, 2019. "Modeling non-stationarities in high-frequency financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 173-196.
    7. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2010. "Complex stock trading network among investors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4929-4941.
    8. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2008. "Scaling in the distribution of intertrade durations of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5818-5825.
    9. Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2025-2034.
    10. Fabio Caccioli & Jean-Philippe Bouchaud & J. Doyne Farmer, 2012. "A proposal for impact-adjusted valuation: Critical leverage and execution risk," Papers 1204.0922, arXiv.org, revised Aug 2012.
    11. Luis Goncalves de Faria, 2022. "An Agent-Based Model With Realistic Financial Time Series: A Method for Agent-Based Models Validation," Papers 2206.09772, arXiv.org.
    12. Zoltan Eisler & Janos Kertesz & Fabrizio Lillo & Rosario Mantegna, 2009. "Diffusive behavior and the modeling of characteristic times in limit order executions," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 547-563.
    13. Plamen Ch Ivanov & Ainslie Yuen & Pandelis Perakakis, 2014. "Impact of Stock Market Structure on Intertrade Time and Price Dynamics," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-14, April.
    14. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    15. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
    16. Bertram, William K., 2008. "Measuring time dependent volatility and cross-sectional correlation in Australian equity returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3183-3191.
    17. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.
    18. Stanislao Gualdi & Giulio Cimini & Kevin Primicerio & Riccardo Di Clemente & Damien Challet, 2016. "Statistically validated network of portfolio overlaps and systemic risk," Post-Print hal-01705092, HAL.
    19. Vladimir Filimonov & Didier Sornette, 2013. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Papers 1308.6756, arXiv.org, revised Jul 2014.
    20. Qing Cai & Hai-Chuan Xu & Wei-Xing Zhou, 2016. "Taylor's Law of temporal fluctuation scaling in stock illiquidity," Papers 1610.01149, arXiv.org.
    21. Dimitrios Koutmos, 2023. "Investor sentiment and bitcoin prices," Review of Quantitative Finance and Accounting, Springer, vol. 60(1), pages 1-29, January.
    22. Bertram, William K., 2009. "Optimal trading strategies for Itô diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2865-2873.
    23. Kang, Bo Soo & Ryu, Doojin & Ryu, Doowon, 2014. "Phase-shifting behaviour revisited: An alternative measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 167-173.

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