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CN 34-1054/N

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The optimal portfolio with modified covariance matrix using clustering method

  • Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.03.014
  • Received Date: 30 October 2012
  • Accepted Date: 13 January 2013
  • Rev Recd Date: 13 January 2013
  • Publish Date: 30 March 2014
    Abstract

  • Abstract

    The Markowitz optimal portfolio was introduced and the reason why the result was unstable was analyzed.Based on this analysis, a new method was presented: Using the clustering method to modify the sample covariance matrix to get a better investment option. To prove the new methods reasonableness, real data from the Chinese stock market were used to simulate “real investment”. It was found that the portfolio obtained from this method was better in both mean return and stability than the traditional method， which can be further verified by using risk prediction.

    Abstract

    The Markowitz optimal portfolio was introduced and the reason why the result was unstable was analyzed.Based on this analysis, a new method was presented: Using the clustering method to modify the sample covariance matrix to get a better investment option. To prove the new methods reasonableness, real data from the Chinese stock market were used to simulate “real investment”. It was found that the portfolio obtained from this method was better in both mean return and stability than the traditional method， which can be further verified by using risk prediction.
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    • References(10)
  • [1]
    Markowitz H.Portfolio Selection:Efficient Diversification of Investment[M].New York:Wiley,1959.
    [2]
    Pafka S, Kondor I. Noisy covariance matrices and portfolio optimization[J].The European Physical Journal B,2002,27(2): 277-280.
    [3]
    Jorion P. Portfolio optimization in practice [J]. Financial Analysts, 1992, 48(1):68-74.
    [4]
    Ledoit O, Wolf M. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection[J].Journal of Empirical Finance,2003,10(5):603-621.
    [5]
    Markowitz H. Portfolio analysis with factors and scenarios [J]. Journal of Finance, 1981, 36(4): 871-877.
    [6]
    Frost P A,Savarino J E.An empirical Bayes approach to efficient portfolio selection[J].Journal of Financial and Quantitative Analysis,1986,21(3):293-305.
    [7]
    Jorion P. Bayesian and CAPM estimators of the means:Implications for portfolio selection[J]. Journal of Banking and Finance,1991,15(3): 717-727.
    [8]
    Merton R C. Ananalytic derivation of the efficient portfolio frontier[J]. The Journal of Financial and Quantitative Analysis,1972,7(4):1 851-1 872.
    [9]
    Laloux L,Cizeau P, Bouchaud J P, et al. Noise dressing of financial correlation matrices[J].Physical Review Letters,1999,83(7):1 467-1 470.
    [10]
    Plerou V, Gopikrishnan P, Amaral L N, et al.Random matrix approach to cross correlations in financial data[J]. Physical Review E, 2002,65:066126.
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    [1]
    Markowitz H.Portfolio Selection:Efficient Diversification of Investment[M].New York:Wiley,1959.
    [2]
    Pafka S, Kondor I. Noisy covariance matrices and portfolio optimization[J].The European Physical Journal B,2002,27(2): 277-280.
    [3]
    Jorion P. Portfolio optimization in practice [J]. Financial Analysts, 1992, 48(1):68-74.
    [4]
    Ledoit O, Wolf M. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection[J].Journal of Empirical Finance,2003,10(5):603-621.
    [5]
    Markowitz H. Portfolio analysis with factors and scenarios [J]. Journal of Finance, 1981, 36(4): 871-877.
    [6]
    Frost P A,Savarino J E.An empirical Bayes approach to efficient portfolio selection[J].Journal of Financial and Quantitative Analysis,1986,21(3):293-305.
    [7]
    Jorion P. Bayesian and CAPM estimators of the means:Implications for portfolio selection[J]. Journal of Banking and Finance,1991,15(3): 717-727.
    [8]
    Merton R C. Ananalytic derivation of the efficient portfolio frontier[J]. The Journal of Financial and Quantitative Analysis,1972,7(4):1 851-1 872.
    [9]
    Laloux L,Cizeau P, Bouchaud J P, et al. Noise dressing of financial correlation matrices[J].Physical Review Letters,1999,83(7):1 467-1 470.
    [10]
    Plerou V, Gopikrishnan P, Amaral L N, et al.Random matrix approach to cross correlations in financial data[J]. Physical Review E, 2002,65:066126.
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