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A Bayesian information criterion for portfolio selection

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  • Lan, Wei
  • Wang, Hansheng
  • Tsai, Chih-Ling
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    Abstract

    The mean-variance theory of Markowitz (1952) indicates that large investment portfolios naturally provide better risk diversification than small ones. However, due to parameter estimation errors, one may find ambiguous results in practice. Hence, it is essential to identify relevant stocks to alleviate the impact of estimation error in portfolio selection. To this end, we propose a linkage condition to link the relevant and irrelevant stock returns via their conditional regression relationship. Subsequently, we obtain a BIC selection criterion that enables us to identify relevant stocks consistently. Numerical studies indicate that BIC outperforms commonly used portfolio strategies in the literature.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 1 (January)
    Pages: 88-99

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:88-99

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Bayesian information criterion Minimal variance portfolio Portfolio selection Risk diversification Selection consistency;

    References

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    1. Ravi Jagannathan & Tongshu Ma, 2002. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," NBER Working Papers 8922, National Bureau of Economic Research, Inc.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
    3. William N. Goetzmann & Alok Kumar, 2008. "Equity Portfolio Diversification," Review of Finance, European Finance Association, vol. 12(3), pages 433-463.
    4. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
    5. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(03), pages 621-656, September.
    6. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    7. Alexander Kempf & Christoph Memmel, 2006. "Estimating the global Minimum Variance Portfolio," Schmalenbach Business Review (sbr), LMU Munich School of Management, vol. 58(4), pages 332-348, October.
    8. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
    9. Olivier Ledoit & Michael Wolf, 2001. "Improved estimation of the covariance matrix of stock returns with an application to portofolio selection," Economics Working Papers 586, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    11. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September.
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