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Building portfolios of stocks in the São Paulo Stock Exchange usingRandom Matrix Theory

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  • Leonidas Sandoval Junior
  • Adriana Bruscato
  • Maria Kelly Venezuela

Abstract

By using Random Matrix Theory, we build covariance matrices between stocks of the BM&F-Bovespa (Bolsa de Valores, Mercadorias e Futuros de S˜ao Paulo), which is cleaned of some of the noise due to the complex interactions between the many stocks and the finiteness of available data. We also use a regression model in order to remove the market effect due to the common movement of all stocks. These two procedures are then used to build stock portfolios based on Markowitz’s theory, trying to obtain better predictions of future risk based on past data. This is done for years of both low and high volatility of the Brazilian stock market, from 2004 to 2010.

Suggested Citation

  • Leonidas Sandoval Junior & Adriana Bruscato & Maria Kelly Venezuela, 2012. "Building portfolios of stocks in the São Paulo Stock Exchange usingRandom Matrix Theory," Business and Economics Working Papers 161, Unidade de Negocios e Economia, Insper.
    • Handle: RePEc:aap:wpaper:161
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    References listed on IDEAS

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    1. Tola, Vincenzo & Lillo, Fabrizio & Gallegati, Mauro & Mantegna, Rosario N., 2008. "Cluster analysis for portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 235-258, January.
    2. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    3. Dickinson, J. P., 1974. "The Reliability of Estimation Procedures in Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(3), pages 447-462, June.
    4. Frankfurter, George M. & Phillips, Herbert E. & Seagle, John P., 1972. "Estimation Risk in the Portfolio Selection Model: A Comment," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(1), pages 1423-1424, January.
    5. 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.
    6. Pafka, Szilárd & Kondor, Imre, 2003. "Noisy covariance matrices and portfolio optimization II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 487-494.
    7. Frankfurter, George M. & Phillips, Herbert E. & Seagle, John P., 1971. "Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1251-1262, December.
    8. Ester Pantaleo & Michele Tumminello & Fabrizio Lillo & Rosario Mantegna, 2011. "When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1067-1080.
    9. 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, vol. 335(3), pages 629-643.
    10. Laurent Laloux & Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Random Matrix Theory And Financial Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 391-397.
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