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Random Matrix Theory and Fund of Funds Portfolio Optimisation

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  • Thomas Conlon
  • Heather J. Ruskin
  • Martin Crane
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    Abstract

    The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a Fund of Hedge Funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The Inverse Participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.

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    File URL: http://arxiv.org/pdf/1005.5021
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1005.5021.

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    Date of creation: May 2010
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    Publication status: Published in Physica A 382(2), (2007) 565-576
    Handle: RePEc:arx:papers:1005.5021

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    Web page: http://arxiv.org/

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    1. Burda, Zdzisław & Jurkiewicz, Jerzy, 2004. "Signal and noise in financial correlation matrices," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 344(1), pages 67-72.
    2. Burda, Z. & Görlich, A. & Jarosz, A. & Jurkiewicz, J., 2004. "Signal and noise in correlation matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 343(C), pages 295-310.
    3. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1999. "Random matrix theory and financial correlations," Science & Finance (CFM) working paper archive 500053, Science & Finance, Capital Fund Management.
    4. 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, Elsevier, vol. 335(3), pages 629-643.
    5. 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, Elsevier, vol. 368(2), pages 511-521.
    6. Wilcox, Diane & Gebbie, Tim, 2004. "On the analysis of cross-correlations in South African market data," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 344(1), pages 294-298.
    7. Zdzislaw Burda & Jerzy Jurkiewicz, 2003. "Signal and Noise in Financial Correlation Matrices," Papers cond-mat/0312496, arXiv.org, revised Feb 2004.
    8. Miceli, M.A. & Susinno, G., 2004. "Ultrametricity in fund of funds diversification," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 344(1), pages 95-99.
    9. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1998. "Noise dressing of financial correlation matrices," Science & Finance (CFM) working paper archive 500051, Science & Finance, Capital Fund Management.
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