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Sampling Error and Double Shrinkage Estimation of Minimum Variance Portfolios

Author

Listed:
  • Candelon Bertrand
  • Hurlin Christophe
  • Tokpavi Sessi

    (METEOR)

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 to introduce a new framework useful to improve the stability of the GMVP based on shrinkage estimators of the covariance matrix. 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, montecarlo 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

  • Candelon Bertrand & Hurlin Christophe & Tokpavi Sessi, 2011. "Sampling Error and Double Shrinkage Estimation of Minimum Variance Portfolios," Research Memorandum 002, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2011002
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. repec:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9266-z is not listed on IDEAS
    3. 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.
    4. repec:sbe:breart:v:35:y:2015:i:1:a:21453 is not listed on IDEAS
    5. repec:eee:reveco:v:56:y:2018:i:c:p:109-124 is not listed on IDEAS
    6. 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.

    More about this item

    Keywords

    monetary economics ;

    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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