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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.

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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number physics/0507111.

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Date of creation: Jul 2005
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Handle: RePEc:arx:papers:physics/0507111

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Cited by:
  1. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Science & Finance (CFM) working paper archive 1102.1339, Science & Finance, Capital Fund Management, revised Mar 2011.
  2. Romain Allez & Jean-Philippe Bouchaud, 2012. "Eigenvector dynamics: general theory and some applications," Science & Finance (CFM) working paper archive 1203.6228, Science & Finance, Capital Fund Management, revised Jul 2012.
  3. 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.
  4. 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.
  5. 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.
  6. Gilles Zumbach, 2009. "The empirical properties of large covariance matrices," Science & Finance (CFM) working paper archive 0903.1525, Science & Finance, Capital Fund Management.
  7. Dalibor 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.
  8. 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.

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