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The Distribution of the Sample Minimum-Variance Frontier

Author

Listed:
  • Raymond Kan

    () (Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

  • Daniel R. Smith

    () (Faculty of Business Administration, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada)

Abstract

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier, and we propose an improved estimator of the population frontier. In addition, we provide the exact distribution of the out-of-sample mean and variance of sample minimum-variance portfolios. This allows us to understand the impact of estimation error on the performance of in-sample optimal portfolios.

Suggested Citation

  • Raymond Kan & Daniel R. Smith, 2008. "The Distribution of the Sample Minimum-Variance Frontier," Management Science, INFORMS, vol. 54(7), pages 1364-1380, July.
  • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:7:p:1364-1380
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    File URL: http://dx.doi.org/10.1287/mnsc.1070.0852
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Kourtis, Apostolos, 2014. "On the distribution and estimation of trading costs," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 104-117.
    2. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2017. "Portfolio selection with mental accounts and estimation risk," Journal of Empirical Finance, Elsevier, vol. 41(C), pages 161-186.
    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. Kourtis, Apostolos & Dotsis, George & Markellos, Raphael N., 2012. "Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2522-2531.
    5. Maller, Ross & Roberts, Steven & Tourky, Rabee, 2016. "The large-sample distribution of the maximum Sharpe ratio with and without short sales," Journal of Econometrics, Elsevier, vol. 194(1), pages 138-152.
    6. Gopal K. Basak & Ravi Jagannathan & Tongshu Ma, 2009. "Jackknife Estimator for Tracking Error Variance of Optimal Portfolios," Management Science, INFORMS, vol. 55(6), pages 990-1002, June.
    7. Yen, Yu-Min & Yen, Tso-Jung, 2014. "Solving norm constrained portfolio optimization via coordinate-wise descent algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 737-759.
    8. 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.
    9. Huang, Xiaoxia & Ying, Haiyao, 2013. "Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations," Economic Modelling, Elsevier, vol. 30(C), pages 61-66.
    10. David Bauder & Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2018. "Bayesian mean-variance analysis: Optimal portfolio selection under parameter uncertainty," Papers 1803.03573, arXiv.org.
    11. Bodnar Taras & Schmid Wolfgang & Zabolotskyy Tara, 2012. "Minimum VaR and minimum CVaR optimal portfolios: Estimators, confidence regions, and tests," Statistics & Risk Modeling, De Gruyter, vol. 29(4), pages 281-314, November.
    12. repec:eee:finana:v:52:y:2017:i:c:p:240-251 is not listed on IDEAS

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