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Building portfolios of stocks in the S\~ao Paulo Stock Exchange using Random Matrix Theory

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  • Leonidas Sandoval Junior
  • Adriana Bruscato
  • Maria Kelly Venezuela
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    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 are 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. The results show that the use of regression to subtract the market effect on returns greatly increases the accuracy of the prediction of risk, and that, although the cleaning of the correlation matrix often leads to portfolios that better predict risks, in periods of high volatility of the market this procedure may fail to do so.

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    File URL: http://arxiv.org/pdf/1201.0625
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1201.0625.

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    Date of creation: Jan 2012
    Date of revision: Mar 2013
    Publication status: Published in Physica A 410 (2013) 94-109
    Handle: RePEc:arx:papers:1201.0625

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    Web page: http://arxiv.org/

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    1. 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.
    2. Tola, Vincenzo & Lillo, Fabrizio & Gallegati, Mauro & Mantegna, Rosario N., 2008. "Cluster analysis for portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 32(1), pages 235-258, January.
    3. Pafka, Szilárd & Kondor, Imre, 2003. "Noisy covariance matrices and portfolio optimization II," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 319(C), pages 487-494.
    4. 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, INFORMS, vol. 55(5), pages 798-812, May.
    5. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 21(03), pages 279-292, September.
    6. Ester Pantaleo & Michele Tumminello & Fabrizio Lillo & Rosario N. Mantegna, 2010. "When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators," Papers 1004.4272, arXiv.org.
    7. 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, Cambridge University Press, vol. 7(01), pages 1423-1424, January.
    8. Dickinson, J. P., 1974. "The Reliability of Estimation Procedures in Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 9(03), pages 447-462, June.
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    Cited by:
    1. Dalibor Eterovic & Nicolas Eterovic, 2012. "Separating the Wheat from the Chaff: Understanding Portfolio Returns in an Emerging Market," Working Papers, Adolfo Ibáñez University, School of Government wp_025, Adolfo Ibáñez University, School of Government.

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