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Risk Preferences and Estimation Risk in Portfolio Choice

Author

Listed:
  • Hao Liu

    (CoFE, University of Konstanz, Germany)

  • Winfried Pohlmeier

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

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.

Suggested Citation

  • Hao Liu & Winfried Pohlmeier, 2013. "Risk Preferences and Estimation Risk in Portfolio Choice," Working Paper series 47_13, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:47_13
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    File URL: http://www.rcea.org/RePEc/pdf/wp47_13.pdf
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    References listed on IDEAS

    as
    1. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    2. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    3. Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. 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.
    6. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    7. repec:hal:journl:peer-00741629 is not listed on IDEAS
    8. Frahm, Gabriel, 2010. "An analytical investigation of estimators for expected asset returns from the perspective of optimal asset allocation," Discussion Papers in Econometrics and Statistics 1/10, University of Cologne, Institute of Econometrics and Statistics.
    9. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    10. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    11. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    efficient portfolio; estimation risk; certainty equivalent; shrinkage;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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