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Mean--variance portfolio optimization when means and covariances are unknown

  • Tze Leung Lai
  • Haipeng Xing
  • Zehao Chen
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    Markowitz's celebrated mean--variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to portfolios that may perform poorly and have counter-intuitive asset allocation weights; this has been referred to as the "Markowitz optimization enigma." After reviewing different approaches in the literature to address these difficulties, we explain the root cause of the enigma and propose a new approach to resolve it. Not only is the new approach shown to provide substantial improvements over previous methods, but it also allows flexible modeling to incorporate dynamic features and fundamental analysis of the training sample of historical data, as illustrated in simulation and empirical studies.

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    File URL: http://arxiv.org/pdf/1108.0996
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    Paper provided by arXiv.org in its series Papers with number 1108.0996.

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    Date of creation: Aug 2011
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    Publication status: Published in Annals of Applied Statistics 2011, Vol. 5, No. 2A, 798-823
    Handle: RePEc:arx:papers:1108.0996
    Contact details of provider: Web page: http://arxiv.org/

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    1. Mark Britten-Jones, 1999. "The Sampling Error in Estimates of Mean-Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, 04.
    2. Yusif Simaan, 1997. "Estimation Risk in Portfolio Selection: The Mean Variance Model Versus the Mean Absolute Deviation Model," Management Science, INFORMS, vol. 43(10), pages 1437-1446, October.
    3. Niko Canner & N. Gregory Mankiw & David N. Weil, 1994. "An Asset Allocation Puzzle," NBER Working Papers 4857, National Bureau of Economic Research, Inc.
    4. 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.
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