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A risk perspective of estimating portfolio weights of the global minimum-variance portfolio

Author

Listed:
  • Thomas Holgersson

    (Linnæus University)

  • Peter Karlsson

    (Linnæus University)

  • Andreas Stephan

    (Jönköping International Business School)

Abstract

The problem of how to determine portfolio weights so that the variance of portfolio returns is minimized has been given considerable attention in the literature, and several methods have been proposed. Some properties of these estimators, however, remain unknown, and many of their relative strengths and weaknesses are therefore difficult to assess for users. This paper contributes to the field by comparing and contrasting the risk functions used to derive efficient portfolio weight estimators. It is argued that risk functions commonly used to derive and evaluate estimators may be inadequate and that alternative quality criteria should be considered instead. The theoretical discussions are supported by a Monte Carlo simulation and two empirical applications where particular focus is set on cases where the number of assets (p) is close to the number of observations (n).

Suggested Citation

  • Thomas Holgersson & Peter Karlsson & Andreas Stephan, 2020. "A risk perspective of estimating portfolio weights of the global minimum-variance portfolio," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 59-80, March.
    • Handle: RePEc:spr:alstar:v:104:y:2020:i:1:d:10.1007_s10182-018-00349-7
    DOI: 10.1007/s10182-018-00349-7
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    References listed on IDEAS

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    1. Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
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    Cited by:

    1. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. 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.

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    More about this item

    Keywords

    Global minimum-variance portfolio; Portfolio theory; High dimensional; Risk functions;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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