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Performance analysis and optimal selection of large mean-variance portfolios under estimation risk

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  • Francisco Rubio
  • Xavier Mestre
  • Daniel P. Palomar
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    Abstract

    We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings.

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    File URL: http://arxiv.org/pdf/1110.3460
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.3460.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.3460

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    Web page: http://arxiv.org/

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    1. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    2. Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095.
    3. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1998. "Noise dressing of financial correlation matrices," Science & Finance (CFM) working paper archive 500051, Science & Finance, Capital Fund Management.
    4. Hlouskova, Jaroslava & Schmidheiny, Kurt & Wagner, Martin, 2009. "Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 330-336, March.
    5. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    6. Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
    7. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    8. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1999. "Random matrix theory," Science & Finance (CFM) working paper archive 500052, Science & Finance, Capital Fund Management.
    9. 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.
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