AStA Advances in Statistical Analysis

, Volume 101, Issue 3, pp 253–265 | Cite as

A test for the global minimum variance portfolio for small sample and singular covariance

Original Paper
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Abstract

Recently, a test dealing with the linear hypothesis for the global minimum variance portfolio weights was obtained under the assumption of non-singular covariance matrix. However, the problem of potential multicollinearity and correlations of assets constitutes a limitation of the classical portfolio theory. Therefore, there is an interest in developing theory in the presence of singularities in the covariance matrix. In this paper, we extend the test by analyzing the portfolio weights in the small sample case with a singular population covariance matrix. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented.

Keywords

Global minimum variance portfolio Singular Wishart distribution Singular covariance matrix Small sample problem 

Mathematics Subject Classification

91G10 62H12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Taras Bodnar
    • 1
  • Stepan Mazur
    • 2
  • Krzysztof Podgórski
    • 3
  1. 1.Department of MathematicsStockholm UniversityStockholmSweden
  2. 2.Department of MathematicsAarhus UniversityAarhusDenmark
  3. 3.Department of StatisticsLund UniversityLundSweden

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