IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v53y2007i6p1005-1015.html
   My bibliography  Save this article

Performance of Portfolios Optimized with Estimation Error

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1060.0664
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1060.0664?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    2. Frankfurter, George M. & Phillips, Herbert E. & Seagle, John P., 1971. "Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1251-1262, December.
    3. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    4. Clarkson, Pete & Guedes, Jose & Thompson, Rex, 1996. "On the Diversification, Observability, and Measurement of Estimation Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 69-84, March.
    5. Pastor, Lubos & Stambaugh, Robert F., 2000. "Comparing asset pricing models: an investment perspective," Journal of Financial Economics, Elsevier, vol. 56(3), pages 335-381, June.
    6. Fomby, Thomas B & Samanta, Subarna K, 1991. "Application of Stein Rules to Combination Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 391-407, October.
    7. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-278, July.
    8. 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.
    9. Jorion, Philippe, 1991. "Bayesian and CAPM estimators of the means: Implications for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 15(3), pages 717-727, June.
    10. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    11. Green, Richard C & Hollifield, Burton, 1992. "When Will Mean-Variance Efficient Portfolios Be Well Diversified?," Journal of Finance, American Finance Association, vol. 47(5), pages 1785-1809, December.
    12. Jonathan Lewellen & Jay Shanken, 2002. "Learning, Asset‐Pricing Tests, and Market Efficiency," Journal of Finance, American Finance Association, vol. 57(3), pages 1113-1145, June.
    13. Tu, Jun & Zhou, Guofu, 2004. "Data-generating process uncertainty: What difference does it make in portfolio decisions?," Journal of Financial Economics, Elsevier, vol. 72(2), pages 385-421, May.
    14. Cheol S. Eun & Bruce G. Resnick, 1994. "International Diversification of Investment Portfolios: U.S. and Japanese Perspectives," Management Science, INFORMS, vol. 40(1), pages 140-161, January.
    15. Mark Britten‐Jones, 1999. "The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
    16. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    17. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Antonio Díaz & Carlos Esparcia, 2021. "Dynamic optimal portfolio choice under time-varying risk aversion," International Economics, CEPII research center, issue 166, pages 1-22.
    2. 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.
    3. Taras Bodnar & Mathias Lindholm & Vilhelm Niklasson & Erik Thors'en, 2020. "Bayesian Quantile-Based Portfolio Selection," Papers 2012.01819, arXiv.org.
    4. Kamesh Korangi & Christophe Mues & Cristi'an Bravo, 2024. "Large-scale Time-Varying Portfolio Optimisation using Graph Attention Networks," Papers 2407.15532, arXiv.org.
    5. 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.
    6. 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.
    7. 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.
    8. Sharma, Udayan & Karmakar, Madhusudan, 2023. "Measuring minimum variance hedging effectiveness: Traditional vs. sophisticated models," International Review of Financial Analysis, Elsevier, vol. 87(C).
    9. 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).
    10. 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.
    11. 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.
    12. 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.
    13. Bodnar, Taras & Lindholm, Mathias & Niklasson, Vilhelm & Thorsén, Erik, 2022. "Bayesian portfolio selection using VaR and CVaR," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    14. 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, December.
    15. Lord Mensah, 2016. "Asset Allocation Brewed Accross African Stock Markets," Proceedings of Economics and Finance Conferences 3205757, International Institute of Social and Economic Sciences.
    16. Taras Bodnar & Nikolaus Hautsch & Yarema Okhrin & Nestor Parolya, 2024. "Consistent Estimation of the High-Dimensional Efficient Frontier," Papers 2409.15103, arXiv.org.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Raymond Kan & Daniel R. Smith, 2008. "The Distribution of the Sample Minimum-Variance Frontier," Management Science, INFORMS, vol. 54(7), pages 1364-1380, July.
    22. 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.
    23. 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.
    24. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2020. "Company classification using machine learning," Papers 2004.01496, arXiv.org, revised May 2020.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    2. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    3. Mishra, Anil V., 2016. "Foreign bias in Australian-domiciled mutual fund holdings," Pacific-Basin Finance Journal, Elsevier, vol. 39(C), pages 101-123.
    4. Jun Tu & Guofu Zhou, 2011. "Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies," CEMA Working Papers 715, China Economics and Management Academy, Central University of Finance and Economics.
    5. Lorenzo Garlappi & Raman Uppal & Tan Wang, 2007. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 41-81, January.
    6. Guillaume Coqueret, 2015. "Diversified minimum-variance portfolios," Annals of Finance, Springer, vol. 11(2), pages 221-241, May.
    7. Frank Fabozzi & Dashan Huang & Guofu Zhou, 2010. "Robust portfolios: contributions from operations research and finance," Annals of Operations Research, Springer, vol. 176(1), pages 191-220, April.
    8. David Stefanovits & Urs Schubiger & Mario V. Wüthrich, 2014. "Model Risk in Portfolio Optimization," Risks, MDPI, vol. 2(3), pages 1-34, August.
    9. Tu, Jun & Zhou, Guofu, 2010. "Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(4), pages 959-986, August.
    10. Meade, N. & Beasley, J.E. & Adcock, C.J., 2021. "Quantitative portfolio selection: Using density forecasting to find consistent portfolios," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1053-1067.
    11. Kellerer, Belinda, 2019. "Portfolio Optimization and Ambiguity Aversion," Junior Management Science (JUMS), Junior Management Science e. V., vol. 4(3), pages 305-338.
    12. Mishra, Anil V., 2017. "Foreign bias in Australia's international equity holdings," Review of Financial Economics, Elsevier, vol. 33(C), pages 41-54.
    13. Tu, Jun & Zhou, Guofu, 2011. "Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies," Journal of Financial Economics, Elsevier, vol. 99(1), pages 204-215, January.
    14. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    15. 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.
    16. Bodnar Taras & Schmid Wolfgang, 2011. "On the exact distribution of the estimated expected utility portfolio weights: Theory and applications," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 319-342, December.
    17. Mishra, Anil V., 2015. "Measures of equity home bias puzzle," Journal of Empirical Finance, Elsevier, vol. 34(C), pages 293-312.
    18. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    19. Tomohiro Ando, 2012. "Bayesian portfolio selection under a multifactor asset return model with predictive model selection," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 14(1/2), pages 77-101.
    20. Roskelley, Kenneth D., 2008. "Cromwell's Rule and the Role of the Prior in the Economic Metric: An Application to the Portfolio Allocation Problem," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 227-236, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:53:y:2007:i:6:p:1005-1015. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.