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Performance of Portfolios Optimized with Estimation Error

Author

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  • Andrew F. Siegel

    (Business School, University of Washington, Mackenzie Hall, Box 353200, Seattle, Washington 98195-3200)

  • Artemiza Woodgate

    (Business School, University of Washington, Mackenzie Hall, Box 353200, Seattle, Washington 98195-3200 and Russell Investment Group, Tacoma, Washington 98402)

Abstract

We explain the poor out-of-sample performance of mean-variance optimized portfolios, developing theoretical bias adjustments for estimation risk by asymptotically expanding future returns of portfolios formed with estimated weights. We provide closed-form non-Bayesian adjustments of classical estimates of portfolio mean and standard deviation. The adjustments significantly reduce bias in international equity portfolios, increase economic gains, and are robust to sample size and to nonnormality. Dominant terms grow linearly with the number of assets and decline inversely with the number of past time periods. Under suitable conditions, Sharpe-ratio maximizing tangency portfolios become more diversified. Using these approximation methods it may be possible to assess, before investing, the effect of statistical estimation error on portfolio performance.

Suggested Citation

  • Andrew F. Siegel & Artemiza Woodgate, 2007. "Performance of Portfolios Optimized with Estimation Error," Management Science, INFORMS, vol. 53(6), pages 1005-1015, June.
    • Handle: RePEc:inm:ormnsc:v:53:y:2007:i:6:p:1005-1015
    DOI: 10.1287/mnsc.1060.0664
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    References listed on IDEAS

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    1. Taras Bodnar & Holger Dette & Nestor Parolya & Erik Thors'en, 2019. "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions," Papers 1908.04243, arXiv.org, revised Apr 2023.
    2. Díaz, Antonio & Esparcia, Carlos, 2021. "Dynamic optimal portfolio choice under time-varying risk aversion," International Economics, Elsevier, vol. 166(C), pages 1-22.
    3. Jonathan Fletcher, 2009. "Risk Reduction and Mean-Variance Analysis: An Empirical Investigation," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 36(7-8), pages 951-971.
    4. Clara Calvo & Carlos Ivorra & Vicente Liern & Blanca Pérez-Gladish, 2021. "Grading Investment Diversification Options in Presence of Non-Historical Financial Information," Mathematics, MDPI, vol. 9(6), pages 1-11, March.
    5. Sharma, Udayan & Karmakar, Madhusudan, 2023. "Measuring minimum variance hedging effectiveness: Traditional vs. sophisticated models," International Review of Financial Analysis, Elsevier, vol. 87(C).
    6. Carmine De Franco & Johann Nicolle & Huyên Pham, 2019. "Dealing with Drift Uncertainty: A Bayesian Learning Approach," Risks, MDPI, vol. 7(1), pages 1-18, January.
    7. Bodnar, Taras & Lindholm, Mathias & Niklasson, Vilhelm & Thorsén, Erik, 2022. "Bayesian portfolio selection using VaR and CVaR," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    8. Francis In & Sangbae Kim, 2012. "An Introduction to Wavelet Theory in Finance:A Wavelet Multiscale Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8431, October.
    9. Lord Mensah, 2016. "Asset Allocation Brewed Accross African Stock Markets," Proceedings of Economics and Finance Conferences 3205757, International Institute of Social and Economic Sciences.
    10. Taras Bodnar & Nikolaus Hautsch & Yarema Okhrin & Nestor Parolya, 2024. "Consistent Estimation of the High-Dimensional Efficient Frontier," Papers 2409.15103, arXiv.org.
    11. Huang, Hung-Hsi & Lin, Shin-Hung & Wang, Ching-Ping & Chiu, Chia-Yung, 2014. "Adjusting MV-efficient portfolio frontier bias for skewed and non-mesokurtic returns," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 59-83.
    12. Füss, Roland & Miebs, Felix & Trübenbach, Fabian, 2014. "A jackknife-type estimator for portfolio revision," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 14-28.
    13. David Bauder & Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2021. "Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 221-242, February.
    14. James Mcdonald & Richard Michelfelder & Panayiotis Theodossiou, 2010. "Robust estimation with flexible parametric distributions: estimation of utility stock betas," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 375-387.
    15. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2020. "Company classification using machine learning," Papers 2004.01496, arXiv.org, revised May 2020.
    16. Taras Bodnar & Mathias Lindholm & Vilhelm Niklasson & Erik Thors'en, 2020. "Bayesian Quantile-Based Portfolio Selection," Papers 2012.01819, arXiv.org.
    17. Kamesh Korangi & Christophe Mues & Cristi'an Bravo, 2024. "Large-scale Time-Varying Portfolio Optimisation using Graph Attention Networks," Papers 2407.15532, arXiv.org.
    18. Yudong Wang & Chongfeng Wu & Li Yang, 2015. "Hedging with Futures: Does Anything Beat the Naïve Hedging Strategy?," Management Science, INFORMS, vol. 61(12), pages 2870-2889, December.
    19. Fabozzi, Frank J. & Huang, Dashan & Jiang, Fuwei & Wang, Jiexun, 2024. "What difference do new factor models make in portfolio allocation?," Journal of International Money and Finance, Elsevier, vol. 140(C).
    20. Taras Bodnar & Solomiia Dmytriv & Yarema Okhrin & Nestor Parolya & Wolfgang Schmid, 2020. "Statistical inference for the EU portfolio in high dimensions," Papers 2005.04761, arXiv.org.
    21. Pan, Zhiyuan & Wang, Yudong & Yang, Li, 2014. "Hedging crude oil using refined product: A regime switching asymmetric DCC approach," Energy Economics, Elsevier, vol. 46(C), pages 472-484.
    22. Alexandros Kostakis & Nikolaos Panigirtzoglou & George Skiadopoulos, 2011. "Market Timing with Option-Implied Distributions: A Forward-Looking Approach," Management Science, INFORMS, vol. 57(7), pages 1231-1249, July.
    23. Raymond Kan & Daniel R. Smith, 2008. "The Distribution of the Sample Minimum-Variance Frontier," Management Science, INFORMS, vol. 54(7), pages 1364-1380, July.
    24. Jonathan Fletcher, 2009. "Risk Reduction and Mean‐Variance Analysis: An Empirical Investigation," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 36(7‐8), pages 951-971, September.

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