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Collective behavior of stock price movements—a random matrix theory approach

Author

Listed:
  • Plerou, V.
  • Gopikrishnan, P.
  • Rosenow, B.
  • Amaral, L.A.N.
  • Stanley, H.E.

Abstract

We review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory (RMT), developed in physics to describe the energy levels of complex systems. RMT makes predictions for “universal” properties that do not depend on the interactions between the elements comprising the system; deviations from RMT provide clues regarding system-specific properties. We compare the statistics of the cross-correlation matrix C—whose elements Cij are the correlation coefficients of price fluctuations of stock i and j—against a random matrix having the same symmetry properties. It is found that RMT methods can distinguish random and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine collective behavior among stocks.

Suggested Citation

  • Plerou, V. & Gopikrishnan, P. & Rosenow, B. & Amaral, L.A.N. & Stanley, H.E., 2001. "Collective behavior of stock price movements—a random matrix theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 175-180.
    • Handle: RePEc:eee:phsmap:v:299:y:2001:i:1:p:175-180
    DOI: 10.1016/S0378-4371(01)00293-X
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    Citations

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    Cited by:

    1. Zhaoyuan Li & Maozai Tian, 2017. "A New Method For Dynamic Stock Clustering Based On Spectral Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 50(3), pages 373-392, October.
    2. Sharifi, S. & Crane, M. & Shamaie, A. & Ruskin, H., 2004. "Random matrix theory for portfolio optimization: a stability approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 629-643.
    3. Charu Sharma & Amber Habib, 2019. "Uncovering networks amongst stocks returns by studying nonlinear interactions in high frequency data of the Indian Stock Market using mutual information," Papers 1903.03407, arXiv.org.
    4. Emmanuelle Jay & Thibault Soler & Jean-Philippe Ovarlez & Philippe De Peretti & Christophe Chorro, 2019. "Robust covariance matrix estimation and portfolio allocation: the case of non-homogeneous assets," Documents de travail du Centre d'Economie de la Sorbonne 19023, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Emmanuelle Jay & Thibault Soler & Eugénie Terreaux & Jean-Philippe Ovarlez & Frédéric Pascal & Philippe de Peretti & Christophe Chorro, 2019. "Improving portfolios global performance using a cleaned and robust covariance matrix estimate," Post-Print halshs-02354596, HAL.
    6. Bertrand M. Roehner, 2004. "Stock markets are not what we think they are: the key roles of cross-ownership and corporate treasury stock," Papers cond-mat/0406704, arXiv.org.
    7. Charu Sharma & Amber Habib, 2019. "Mutual information based stock networks and portfolio selection for intraday traders using high frequency data: An Indian market case study," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-19, August.
    8. Daly, J. & Crane, M. & Ruskin, H.J., 2008. "Random matrix theory filters in portfolio optimisation: A stability and risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4248-4260.
    9. M. Saeedian & T. Jamali & M. Z. Kamali & H. Bayani & T. Yasseri & G. R. Jafari, 2017. "Emergence of world-stock-market network," Papers 1703.08781, arXiv.org.
    10. Wang, Yan-Jun & Zhu, Yun-Feng & Zhu, Chen-Ping & Wu, Fan & Yang, Hui-Jie & Yan, Yong-Jie & Hu, Chin-Kun, 2019. "Indicator of serious flight delays with the approach of time-delay stability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 363-373.
    11. Dalibor Eterovic & Nicolas Eterovic, 2012. "Separating the Wheat from the Chaff: Understanding Portfolio Returns in an Emerging Market," Working Papers wp_025, Adolfo Ibáñez University, School of Government.
    12. Eterovic, Nicolas A. & Eterovic, Dalibor S., 2013. "Separating the wheat from the chaff: Understanding portfolio returns in an emerging market," Emerging Markets Review, Elsevier, vol. 16(C), pages 145-169.
    13. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Collective behavior of cryptocurrency price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 499-509.
    14. Hanie. Vahabi & Ali Namaki & Reza Raei, 2020. "Comparing the collective behavior of banking industry," Papers 2011.02026, arXiv.org.
    15. Sharkasi, Adel & Crane, Martin & Ruskin, Heather J. & Matos, Jose A., 2006. "The reaction of stock markets to crashes and events: A comparison study between emerging and mature markets using wavelet transforms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 511-521.
    16. Emmanuelle Jay & Thibault Soler & Eugénie Terreaux & Jean-Philippe Ovarlez & Frédéric Pascal & Philippe de Peretti & Christophe Chorro, 2019. "Improving portfolios global performance using a cleaned and robust covariance matrix estimate," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02354596, HAL.
    17. Emmanuelle Jay & Thibault Soler & Eugénie Terreaux & Jean-Philippe Ovarlez & Frédéric Pascal & Philippe De Peretti & Christophe Chorro, 2019. "Improving portfolios global performance using a cleaned and robust covariance matrix estimate," Documents de travail du Centre d'Economie de la Sorbonne 19022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    18. Roehner, Bertrand M., 2005. "Stock markets are not what we think they are: the key roles of cross-ownership and corporate treasury stock," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 613-625.
    19. Emmanuelle Jay & Thibault Soler & Jean-Philippe Ovarlez & Philippe de Peretti & Christophe Chorro, 2019. "Robust covariance matrix estimation and portfolio allocation: the case of non-homogeneous assets," Post-Print halshs-02372443, HAL.
    20. Emmanuelle Jay & Thibault Soler & Jean-Philippe Ovarlez & Philippe de Peretti & Christophe Chorro, 2019. "Robust covariance matrix estimation and portfolio allocation: the case of non-homogeneous assets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02372443, HAL.

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