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The distribution of sample mean-variance portfolio weights

Author

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  • Kan, Raymond

    (Rotman School of Management, University of Toronto)

  • Lassance, Nathan

    (Université catholique de Louvain, LIDAM/LFIN, Belgium)

  • Wang, Xiaolu

    (Ivy College of Business, Iowa State University)

Abstract

We present a simple stochastic representation for the joint distribution of sample estimates of three scalar parameters and two vectors of portfolio weights that characterize the minimum-variance frontier. This stochastic representation is useful for sampling observations efficiently, deriving moments in closed-form, and studying the distribution and performance of many portfolio strategies that are functions of these five variables. We also present the asymptotic joint distributions of these five variables for both the standard regime and the high-dimensional regime. Both asymptotic distributions are simpler than the finite-sample one, and the one for the high-dimensional regime, i.e., when the number of assets and the sample size go together to infinity at a constant rate, reveals the high-dimensional properties of the considered estimators. Our results extend upon [T. Bodnar, H. Dette, N. Parolya and E. Thorst ́en, Sampling distributions of optimal portfolio weights and characteristics in low and large dimensions, Random Matrices: Theory Appl. 11 (2022)].

Suggested Citation

  • Kan, Raymond & Lassance, Nathan & Wang, Xiaolu, 2023. "The distribution of sample mean-variance portfolio weights," LIDAM Discussion Papers LFIN 2023006, Université catholique de Louvain, Louvain Finance (LFIN).
    • Handle: RePEc:ajf:louvlf:2023006
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    References listed on IDEAS

    as
    1. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    2. Raymond Kan & Xiaolu Wang & Guofu Zhou, 2022. "Optimal Portfolio Choice with Estimation Risk: No Risk-Free Asset Case," Management Science, INFORMS, vol. 68(3), pages 2047-2068, March.
    3. Raymond Kan & Daniel R. Smith, 2008. "The Distribution of the Sample Minimum-Variance Frontier," Management Science, INFORMS, vol. 54(7), pages 1364-1380, July.
    4. Taras Bodnar & Yarema Okhrin & Nestor Parolya, 2022. "Optimal Shrinkage-Based Portfolio Selection in High Dimensions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 140-156, December.
    5. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
    6. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    7. Mengmeng Ao & Li Yingying & Xinghua Zheng, 2019. "Approaching Mean-Variance Efficiency for Large Portfolios," Review of Financial Studies, Society for Financial Studies, vol. 32(7), pages 2890-2919.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Portfolio choice ; estimation risk ; stochastic representation ; high-dimensional asymptotics ; minimum-variance frontier;
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