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Hidden noise structure and random matrix models of stock correlations

Author

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  • Ivailo I. Dimov
  • Petter N. Kolm
  • Lee Maclin
  • Dan Y. C. Shiber

Abstract

We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and, moreover, indicates that the noise band is composed of multiple sub-bands that do not fully mix. Our findings allow us to construct effective generalized random matrix theory market models that are closely related to correlation and eigenvector clustering. We show how to use these models in a simulation that incorporates heavy tails. Finally, we demonstrate how a subtle purely stationary risk estimation bias can arise in the conventional cleaning prescription.

Suggested Citation

  • Ivailo I. Dimov & Petter N. Kolm & Lee Maclin & Dan Y. C. Shiber, 2012. "Hidden noise structure and random matrix models of stock correlations," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 567-572, November.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:4:p:567-572
    DOI: 10.1080/14697688.2012.664931
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    References listed on IDEAS

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    1. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
    2. Raj Kumar Pan & Sitabhra Sinha, 2007. "Collective behavior of stock price movements in an emerging market," Papers 0704.0773, arXiv.org, revised Nov 2007.
    3. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169.
    4. Parameswaran Gopikrishnan & Bernd Rosenow & Vasiliki Plerou & H. Eugene Stanley, 2000. "Identifying Business Sectors from Stock Price Fluctuations," Papers cond-mat/0011145, arXiv.org.
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    Cited by:

    1. Joongyeub Yeo & George Papanicolaou, 2016. "Random matrix approach to estimation of high-dimensional factor models," Papers 1611.05571, arXiv.org, revised Nov 2017.
    2. Sebastiano Michele Zema & Giorgio Fagiolo & Tiziano Squartini & Diego Garlaschelli, 2021. "Mesoscopic Structure of the Stock Market and Portfolio Optimization," Papers 2112.06544, arXiv.org.
    3. Yong Tang & Jason Jie Xiong & Zi-Yang Jia & Yi-Cheng Zhang, 2018. "Complexities in Financial Network Topological Dynamics: Modeling of Emerging and Developed Stock Markets," Complexity, Hindawi, vol. 2018, pages 1-31, November.
    4. Joel Bun & Jean-Philippe Bouchaud & Marc Potters, 2016. "Cleaning large correlation matrices: tools from random matrix theory," Papers 1610.08104, arXiv.org.

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