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Dominating Estimators for Minimum-Variance Portfolios

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  • Gabriel Frahm

    ()
    (University of Cologne - University of Cologne)

  • Christoph Memmel

    ()

Abstract

In this paper, we derive two shrinkage estimators for minimum-variance portfolios that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of assets and number of observations . The small-sample properties of the shrinkage estimators as well as their large-sample properties for fixed but and but are investigated. Furthermore, we present a small-sample test for the question of whether it is better to completely ignore time series information in favor of naive diversification.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number peer-00741629.

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Date of creation: 15 Oct 2010
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Publication status: Published, Journal of Econometrics, 2010, 159, 2, 289
Handle: RePEc:hal:journl:peer-00741629

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Related research

Keywords: C13; G11; Covariance matrix estimation; Minimum-variance portfolio; James-Stein estimation; Naive diversification; Shrinkage estimator;

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References

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  1. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
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  3. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, Elsevier, vol. 10(5), pages 603-621, December.
  4. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, Elsevier, vol. 15(5), pages 850-859, December.
  5. Lorenzo Garlappi & Raman Uppal & Tan Wang, 2007. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 20(1), pages 41-81, January.
  6. Vasyl Golosnoy & Yarema Okhrin, 2007. "Multivariate Shrinkage for Optimal Portfolio Weights," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 13(5), pages 441-458.
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  16. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, INFORMS, vol. 9(2), pages 277-293, January.
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Citations

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Cited by:
  1. Yen, Yu-Min & Yen, Tso-Jung, 2014. "Solving norm constrained portfolio optimization via coordinate-wise descent algorithms," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 737-759.
  2. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2014. "Estimation of the Global Minimum Variance Portfolio in High Dimensions," Papers 1406.0437, arXiv.org.
  3. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2013. "On the equivalence of quadratic optimization problems commonly used in portfolio theory," European Journal of Operational Research, Elsevier, Elsevier, vol. 229(3), pages 637-644.
  4. Zhou, Qing & Faff, Robert & Alpert, Karen, 2014. "Bias correction in the estimation of dynamic panel models in corporate finance," Journal of Corporate Finance, Elsevier, Elsevier, vol. 25(C), pages 494-513.
  5. DeMiguel, Victor & Martin-Utrera, Alberto & Nogales, Francisco J., 2013. "Size matters: Optimal calibration of shrinkage estimators for portfolio selection," Journal of Banking & Finance, Elsevier, Elsevier, vol. 37(8), pages 3018-3034.
  6. Hao Liu & Winfried Pohlmeier, 2013. "Risk Preferences and Estimation Risk in Portfolio Choice," Working Paper Series, The Rimini Centre for Economic Analysis 47_13, The Rimini Centre for Economic Analysis.
  7. Francisco Rubio & Xavier Mestre & Daniel P. Palomar, 2011. "Performance analysis and optimal selection of large mean-variance portfolios under estimation risk," Papers 1110.3460, arXiv.org.
  8. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2012. "A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function," Papers 1207.1003, arXiv.org.
  9. Vahe Avagyan & Andrés M. Alonso & Francisco J. Nogales, 2014. "Improving the graphical lasso estimation for the precision matrix through roots ot the sample convariance matrix," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws141208, Universidad Carlos III, Departamento de Estadística y Econometría.
  10. Taras Bodnar & Arjun K. Gupta & Nestor Parolya, 2013. "On the Strong Convergence of the Optimal Linear Shrinkage Estimator for Large Dimensional Covariance Matrix," Papers 1308.2608, arXiv.org, revised Jun 2014.
  11. Frahm, Gabriel, 2010. "An analytical investigation of estimators for expected asset returns from the perspective of optimal asset allocation," Discussion Papers in Statistics and Econometrics 1/10, University of Cologne, Department for Economic and Social Statistics.
  12. Olivier Ledoit & Michael Wolf, 2014. "Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks," ECON - Working Papers, Department of Economics - University of Zurich 137, Department of Economics - University of Zurich.

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