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Financial Applications of Random Matrix Theory: Old Laces and New Pieces

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  • M. Potters
  • J. P. Bouchaud
  • L. Laloux

Abstract

This contribution to the proceedings of the Cracow meeting on `Applications of Random Matrix Theory' summarizes a series of studies, some old and others more recent on financial applications of Random Matrix Theory (RMT). We first review some early results in that field, with particular emphasis on the applications of correlation cleaning to portfolio optimisation, and discuss the extension of the Marcenko-Pastur (MP) distribution to a non trivial `true' underlying correlation matrix. We then present new results concerning different problems that arise in a financial context: (a) the generalisation of the MP result to the case of an empirical correlation matrix (ECM) constructed using exponential moving averages, for which we give a new elegant derivation (b) the specific dynamics of the `market' eigenvalue and its associated eigenvector, which defines an interesting Ornstein-Uhlenbeck process on the unit sphere and (c) the problem of the dependence of ECM's on the observation frequency of the returns and its interpretation in terms of lagged cross-influences.

Suggested Citation

  • M. Potters & J. P. Bouchaud & L. Laloux, 2005. "Financial Applications of Random Matrix Theory: Old Laces and New Pieces," Papers physics/0507111, arXiv.org.
  • Handle: RePEc:arx:papers:physics/0507111
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    Cited by:

    1. Tianyu Cui & Francesco Caravelli & Cozmin Ududec, 2017. "Correlations and Clustering in Wholesale Electricity Markets," Papers 1710.11184, arXiv.org, revised Nov 2017.
    2. Gorban, Alexander N. & Smirnova, Elena V. & Tyukina, Tatiana A., 2010. "Correlations, risk and crisis: From physiology to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3193-3217.
    3. Varga-Haszonits, I. & Kondor, I., 2007. "Noise sensitivity of portfolio selection in constant conditional correlation GARCH models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 307-318.
    4. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    5. Gilles Zumbach, 2009. "The empirical properties of large covariance matrices," Papers 0903.1525, arXiv.org.
    6. Marsili, Matteo & Raffaelli, Giacomo & Ponsot, Benedicte, 2009. "Dynamic instability in generic model of multi-assets markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1170-1181, May.
    7. Reigneron, Pierre-Alain & Allez, Romain & Bouchaud, Jean-Philippe, 2011. "Principal regression analysis and the index leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(17), pages 3026-3035.
    8. Gautier Marti & Frank Nielsen & Philippe Donnat & S'ebastien Andler, 2016. "On clustering financial time series: a need for distances between dependent random variables," Papers 1603.07822, arXiv.org.
    9. Wang, Gang-Jin & Xie, Chi & Chen, Shou & Yang, Jiao-Jiao & Yang, Ming-Yan, 2013. "Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3715-3730.
    10. Tumminello, Michele & Lillo, Fabrizio & Mantegna, Rosario N., 2010. "Correlation, hierarchies, and networks in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(1), pages 40-58, July.
    11. Marya Bazzi & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2014. "Community detection in temporal multilayer networks, with an application to correlation networks," Papers 1501.00040, arXiv.org, revised Dec 2017.
    12. Paweł Oświęcimka & Stanisław Drożdż & Jarosław Kwapień & Rafał Rak, 2011. "Is It Possible to Predict Crash?," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 25.
    13. Sebastien Valeyre & Denis Grebenkov & Sofiane Aboura & Francois Bonnin, 2016. "Should employers pay their employees better? An asset pricing approach," Papers 1602.00931, arXiv.org, revised Oct 2016.
    14. Svensson, Jens, 2007. "The asymptotic spectrum of the EWMA covariance estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 621-630.
    15. Romain Allez & Jean-Philippe Bouchaud, 2012. "Eigenvector dynamics: general theory and some applications," Papers 1203.6228, arXiv.org, revised Jul 2012.
    16. Desislava Chetalova & Rudi Schafer & Thomas Guhr, 2014. "Zooming into market states," Papers 1406.5386, arXiv.org.
    17. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," Papers 1504.00590, arXiv.org.
    18. 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.

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