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A unified econophysics explanation for the power-law exponents of stock market activity

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  • Gabaix, Xavier
  • Gopikrishnan, Parameswaran
  • Plerou, Vasiliki
  • Stanley, Eugene

Abstract

We survey a theory (first sketched in Nature in 2003, then fleshed out in the Quarterly Journal of Economics in 2006) of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volume. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively illiquid market. We show how the fat-tailed distribution of fund sizes can indeed generate extreme returns and volumes, even in the absence of fundamental news. Moreover, we are able to replicate the individually different empirical values of the power-law exponents for each distribution: 3 for returns, 3/2 for volumes, 1 for the assets under management of large investors. Large investors moderate their trades to reduce their price impact; coupled with a concave price impact function, this leads to volumes being more fat-tailed than returns but less fat-tailed than fund sizes. The trades of large institutions also offer a unified explanation for apparently disconnected empirical regularities that are otherwise a challenge for economic theory.

Suggested Citation

  • Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, Eugene, 2007. "A unified econophysics explanation for the power-law exponents of stock market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 81-88.
    • Handle: RePEc:eee:phsmap:v:382:y:2007:i:1:p:81-88
    DOI: 10.1016/j.physa.2007.02.030
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    References listed on IDEAS

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    7. Eric Kemp-Benedict, 2012. "Second-order Price Dynamics: Approach to Equilibrium with Perpetual Arbitrage," Papers 1202.5926, arXiv.org.
    8. Ren, F. & Zheng, B. & Chen, P., 2010. "Modeling interactions of trading volumes in financial dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2744-2750.
    9. Jovanovic, Franck & Schinckus, Christophe, 2016. "Breaking down the barriers between econophysics and financial economics," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 256-266.
    10. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.
    11. Emanuel Derman & Kun Soo Park & Ward Whitt, 2010. "A stochastic-difference-equation model for hedge-fund returns," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 701-733.
    12. Niu, Hongli & Wang, Weiqing & Zhang, Junhuan, 2019. "Recurrence duration statistics and time-dependent intrinsic correlation analysis of trading volumes: A study of Chinese stock indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 838-854.
    13. Coronel-Brizio, H.F. & Hernández-Montoya, A.R., 2010. "The Anderson–Darling test of fit for the power-law distribution from left-censored samples," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3508-3515.
    14. J. Tenreiro Machado & Fernando B. Duarte & Gonçalo Monteiro Duarte, 2012. "Power Law Analysis of Financial Index Dynamics," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-12, July.
    15. Yu Shi & Qixuan Luo & Handong Li, 2019. "An Agent-Based Model of a Pricing Process with Power Law, Volatility Clustering, and Jumps," Complexity, Hindawi, vol. 2019, pages 1-10, February.
    16. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
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