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Random matrix theory for portfolio optimization: a stability approach

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  • Sharifi, S.
  • Crane, M.
  • Shamaie, A.
  • Ruskin, H.
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    Abstract

    We apply random matrix theory (RMT) to an empirically measured financial correlation matrix, C, and show that this matrix contains a large amount of noise. In order to determine the sensitivity of the spectral properties of a random matrix to noise, we simulate a set of data and add different volumes of random noise. Having ascertained that the eigenspectrum is independent of the standard deviation of added noise, we use RMT to determine the noise percentage in a correlation matrix based on real data from S&P500. Eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart. Finally, we attempt to separate the noisy part from the non-noisy part of C. We apply an existing technique to cleaning C and then discuss its associated problems. We propose a technique of filtering C that has many advantages, from the stability point of view, over the existing method of cleaning.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 335 (2004)
    Issue (Month): 3 ()
    Pages: 629-643

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    Handle: RePEc:eee:phsmap:v:335:y:2004:i:3:p:629-643

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Random matrix theory; Portfolio optimization; Correlation matrix; Eigenvalues and eigenvectors;

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    Citations

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    Cited by:
    1. Thomas Conlon & Heather J. Ruskin & Martin Crane, 2010. "Random Matrix Theory and Fund of Funds Portfolio Optimisation," Papers 1005.5021, arXiv.org.
    2. 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.
    3. Conlon, T. & Ruskin, H.J. & Crane, M., 2007. "Random matrix theory and fund of funds portfolio optimisation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 565-576.
    4. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    5. Yin, Yi & Shang, Pengjian, 2013. "Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6442-6457.
    6. Stephan Süss, 2012. "The pricing of idiosyncratic risk: evidence from the implied volatility distribution," Financial Markets and Portfolio Management, Springer, vol. 26(2), pages 247-267, June.
    7. Conlon, T. & Ruskin, H.J. & Crane, M., 2009. "Cross-correlation dynamics in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 705-714.
    8. Leonidas Sandoval Junior & Adriana Bruscato & Maria Kelly Venezuela, 2012. "Building portfolios of stocks in the S\~ao Paulo Stock Exchange using Random Matrix Theory," Papers 1201.0625, arXiv.org, revised Mar 2013.
    9. Sandoval, Leonidas Junior & Bruscato, Adriana & Venezuela, Maria Kelly, 2012. "Building portfolios of stocks in the São Paulo Stock Exchange using Random Matrix Theory," Insper Working Papers wpe_270, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    10. Jushan Bai & Shuzhong Shi, 2011. "Estimating High Dimensional Covariance Matrices and its Applications," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 199-215, November.
    11. Thomas Conlon & Heather J. Ruskin & Martin Crane, 2010. "Cross-Correlation Dynamics in Financial Time Series," Papers 1002.0321, arXiv.org.
    12. Coronado Ramírez Semei Leopoldo & Porras Serrano Jesús & Sandoval Bravo Salvador, 2013. "Aplicación de bicorrelación cruzada al rendimiento diario del precio del café," Contaduría y Administración:Revista Internacional, Accounting and Management: International Journal, vol. 58(1), pages 117-129, enero-mar.
    13. Wang, Gang-Jin & Xie, Chi, 2013. "Cross-correlations between Renminbi and four major currencies in the Renminbi currency basket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1418-1428.
    14. 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.

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