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Making Markowitz's Portfolio Optimization Theory Practically Useful

Author

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  • BAI, ZHIDONG
  • LIU, HUIXIA
  • WONG, WING-KEUNG
Abstract
The traditional estimated return for the Markowitz mean-variance optimization has been demonstrated to seriously depart from its theoretic optimal return. We prove that this phenomenon is natural and the estimated optimal return is always $\sqrt{\gamma}$ times larger than its theoretic counterpart where $\gamma = \frac 1{1-y}$ with $y$ as the ratio of the dimension to sample size. Thereafter, we develop new bootstrap-corrected estimations for the optimal return and its asset allocation and prove that these bootstrap-corrected estimates are proportionally consistent with their theoretic counterparts. Our theoretical results are further confirmed by our simulations, which show that the essence of the portfolio analysis problem could be adequately captured by our proposed approach. This greatly enhances the practical uses of the Markowitz mean-variance optimization procedure.

Suggested Citation

  • Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:74360
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    File URL: https://mpra.ub.uni-muenchen.de/74360/1/MPRA_paper_74360.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Optimal Portfolio Allocation; Mean-Variance Optimization; Large Random Matrix; Bootstrap Method;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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