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Sampling Error and Double Shrinkage Estimation of Minimum Variance Portfolios

Author

Listed:
  • Bertrand Candelon
  • Christophe Hurlin
  • Sessi Tokpavi

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

Abstract

Shrinkage estimators of the covariance matrix are known to improve the stability over time of the Global Minimum Variance Portfolio (GMVP), as they are less error-prone. However, the improvement over the empirical covariance matrix is not optimal for small values of n, the estimation sample size. For typical asset allocation problems, with n small, this paper aims at. proposing a new method to further reduce sampling error by shrinking once again traditional shrinkage estimators of the GMVP. First, we show analytically that the weights of any GMVP can be shrunk - within the framework of the ridge regression - towards the ones of the equally-weighted portfolio in order to reduce sampling error. Second, Monte Carlo simulations and empirical applications show that applying our methodology to the GMVP based on shrinkage estimators of the covariance matrix, leads to more stable portfolio weights, sharp decreases in portfolio turnovers, and often statistically lower (resp. higher) out-of-sample variances (resp. Sharpe ratios). These results illustrate that double shrinkage estimation of the GMVP can be beneficial for realistic small estimation sample sizes.

Suggested Citation

  • Bertrand Candelon & Christophe Hurlin & Sessi Tokpavi, 2012. "Sampling Error and Double Shrinkage Estimation of Minimum Variance Portfolios," Post-Print hal-01385835, HAL.
  • Handle: RePEc:hal:journl:hal-01385835
    DOI: 10.1016/j.jempfin.2012.04.010
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    References listed on IDEAS

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    Cited by:

    1. Sarah Perrin & Thierry Roncalli, 2019. "Machine Learning Optimization Algorithms & Portfolio Allocation," Papers 1909.10233, arXiv.org.
    2. Olivier Ledoit & Michael Wolf, 2018. "Robust performance hypothesis testing with smooth functions of population moments," ECON - Working Papers 305, Department of Economics - University of Zurich.
    3. Bertrand Maillet & Sessi Tokpavi & Benoit Vaucher, 2013. "Minimum Variance Portfolio Optimisation under Parameter Uncertainty: A Robust Control Approach," EconomiX Working Papers 2013-28, University of Paris Nanterre, EconomiX.
    4. Michele Costola & Bertrand Maillet & Zhining Yuan & Xiang Zhang, 2024. "Mean–variance efficient large portfolios: a simple machine learning heuristic technique based on the two-fund separation theorem," Annals of Operations Research, Springer, vol. 334(1), pages 133-155, March.
    5. Hafner, Christian & Wang, Linqi, 2020. "Dynamic portfolio selection with sector-specific regularization," LIDAM Discussion Papers ISBA 2020032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    7. Fabrizio Cipollini & Giampiero Gallo & Alessandro Palandri, 2020. "A Dynamic Conditional Approach to Portfolio Weights Forecasting," Econometrics Working Papers Archive 2020_06, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    8. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    9. Bertrand Maillet & Sessi Tokpavi & Benoit Vaucher, 2013. "Minimum Variance Portfolio Optimisation under Parameter Uncertainty: A Robust Control Approach," Working Papers hal-04141193, HAL.
    10. Marco Neffelli, 2018. "Target Matrix Estimators in Risk-Based Portfolios," Risks, MDPI, vol. 6(4), pages 1-20, November.
    11. Thibault Bourgeron & Edmond Lezmi & Thierry Roncalli, 2019. "Robust Asset Allocation for Robo-Advisors," Papers 1902.07449, arXiv.org.
    12. Xing, Xin & Hu, Jinjin & Yang, Yaning, 2014. "Robust minimum variance portfolio with L-infinity constraints," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 107-117.
    13. Ziegelmann, Flávio Augusto & Borges, Bruna & Caldeira, João F., 2015. "Selection of Minimum Variance Portfolio Using Intraday Data: An Empirical Comparison Among Different Realized Measures for BM&FBovespa Data," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 35(1), October.
    14. Simaan, Majeed & Simaan, Yusif & Tang, Yi, 2018. "Estimation error in mean returns and the mean-variance efficient frontier," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 109-124.
    15. Lassance, Nathan, 2021. "Maximizing the Out-of-Sample Sharpe Ratio," LIDAM Discussion Papers LFIN 2021013, Université catholique de Louvain, Louvain Finance (LFIN).

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    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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