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An analytical investigation of estimators for expected asset returns from the perspective of optimal asset allocation


  • Frahm, Gabriel


In the present work I derive the risk functions of 5 standard estimators for expected asset returns which are frequently advocated in the literature, viz the sample mean vector, the James-Stein and Bayes-Stein estimator, the minimum-variance estimator, and the CAPM estimator. I resolve the question why it is meaningful to study the risk function in the context of optimal asset allocation. Further, I derive the quantities which determine the risks of the different expected return estimators and show which estimators are preferable with respect to optimal asset allocation. Finally, I discuss the question whether it pays to strive for the optimal portfolio by using time series information. It turns out that in many practical situations it is better to renounce parameter estimation altogether and pursue some trivial strategy such as the totally risk-free investment.

Suggested Citation

  • 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.
  • Handle: RePEc:zbw:ucdpse:110

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    References listed on IDEAS

    1. Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
    2. 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.
    3. Elroy Dimson & Paul Marsh & Mike Staunton, 2003. "Global Evidence On The Equity Risk Premium," Journal of Applied Corporate Finance, Morgan Stanley, vol. 15(4), pages 27-38.
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    More about this item


    Asset allocation; Bayes-Stein estimator; CAPM estimator; James-Stein estimator; Minimum-variance estimator; Naive diversification; Out-ofsample performance; Risk function; Shrinkage estimation;

    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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