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How the trading activity scales with the company sizes in the FTSE 100

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  • Gilles Zumbach

Abstract

This paper investigates the scaling dependencies between measures of "activity" and of "size" for companies included in the FTSE 100. The "size" of companies is measured by the total market capitalization. The "activity" is measured with several quantities related to trades (transaction value per trade, transaction value per hour, tick rate), to the order queue (total number of orders, total value), and to the price dynamic (spread, volatility). The outcome is that systematic scaling relations are observed: 1) the value exchanged by hour and value in the order queue have exponents lower than 1 respectively 0.90 and 0.75; 2) the tick rate and the value per transaction scale with the exponents 0.39 and 0.44; 3) the annualized volatility is independent of the size, and the tick-by-tick volatility decreases with the market capitalization with an exponent -0.23; 4) the spread increases with the volatility with an exponent 0.94. A theoretical random walk argument is given that relates the volatility exponents with the exponents in points 1 and 2.

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  • Gilles Zumbach, 2004. "How the trading activity scales with the company sizes in the FTSE 100," Papers cond-mat/0407769, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0407769
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    References listed on IDEAS

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    1. Marsili, Matteo, 2003. "Scale invariance and criticality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 17-24.
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    6. Vasiliki Plerou & Parameswaran Gopikrishnan & Luis. A. Nunes Amaral & Xavier Gabaix & H. Eugene Stanley, 1999. "Economic Fluctuations and Diffusion," Papers cond-mat/9912051, arXiv.org.
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    Cited by:

    1. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    2. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    3. Hsieh Fushing & Shu-Chun Chen & Chii-Ruey Hwang, 2012. "Discovering stock dynamics through multidimensional volatility phases," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 213-230, September.
    4. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    5. 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.
    6. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    7. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2006. "Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets," Papers physics/0603084, arXiv.org, revised Mar 2007.
    8. Rafael Velasco-Fuentes & Wing Lon Ng, 2011. "Nonlinearities in stochastic clocks: trades and volume as subordinators of electronic markets," Quantitative Finance, Taylor & Francis Journals, vol. 11(6), pages 863-881.
    9. 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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