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

Listed author(s):
  • Leonidas Sandoval Junior
  • Adriana Bruscato
  • Maria Kelly Venezuela
Registered author(s):

    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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    Paper provided by 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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    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. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
    4. 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.
    5. 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.
    6. 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.
    7. Dickinson, J. P., 1974. "The Reliability of Estimation Procedures in Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(03), pages 447-462, June.
    8. 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(01), pages 1423-1424, January.
    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.
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