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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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    1. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    2. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
    3. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, Oxford University Press, vol. 121(2), pages 461-504.
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    7. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
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    11. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2004. "On the Origin of Power-Law Fluctuations in Stock Prices," Papers cond-mat/0403067, arXiv.org.
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    Cited by:

    1. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
    2. Pirvu Daniela & Barbuceanu Mircea, 2016. "Recent Contributions Of The Statistical Physics In The Research Of Banking, Stock Exchange And Foreign Exchange Markets," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 2, pages 85-92, April.
    3. Tabak, B.M. & Takami, M.Y. & Cajueiro, D.O. & Petitinga, A., 2009. "Quantifying price fluctuations in the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(1), pages 59-62.
    4. Eric Kemp-Benedict, 2012. "Second-order Price Dynamics: Approach to Equilibrium with Perpetual Arbitrage," Papers 1202.5926, arXiv.org.
    5. 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.
    6. 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.
    7. de Mattos Neto, Paulo S.G. & Silva, David A. & Ferreira, Tiago A.E. & Cavalcanti, George D.C., 2011. "Market volatility modeling for short time window," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3444-3453.
    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. 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.
    10. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.

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