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Risk Preferences and Estimation Risk in Portfolio Choice

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  • Hao Liu

    (CoFE, University of Konstanz, Germany)

  • Winfried Pohlmeier

    ()
    (CoFE, University of Konstanz, Germany; ZEW, Germany; RCEA, Italy)

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Abstract

This paper analyzes the estimation risk of efficient portfolio selection. We use the concept of certainty equivalent as the basis for a well-defined statistical loss function and a monetary measure to assess estimation risk. For given risk preferences we provide analytical results for different sources of estimation risk such as sample size, dimension of the portfolio choice problem and correlation structure of the return process. Our results show that theoretically sub-optimal portfolio choice strategies turn out to be superior once estimation risk is taken into account. Since estimation risk crucially depends on risk preferences, the choice of the estimator for a given portfolio strategy becomes endogenous. We show that a shrinkage approach accounting for estimation risk in both, mean and covariance of the return vector, is generally superior to simple theoretically suboptimal strategies. Moreover, focusing on just one source of estimation risk, e.g. risk reduction in covariance estimation, can lead to suboptimal portfolios.

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Bibliographic Info

Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 47_13.

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Date of creation: Aug 2013
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Handle: RePEc:rim:rimwps:47_13

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Keywords: efficient portfolio; estimation risk; certainty equivalent; shrinkage;

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References

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  1. 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.
  2. Gabriel Frahm & Christoph Memmel, 2010. "Dominating Estimators for Minimum-Variance Portfolios," Post-Print hal-00741629, HAL.
  3. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
  4. 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.
  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. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
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