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Portrait of Krzysztof Podgórski. Photo.

Krzysztof Podgórski

Professor, Head of the Department of Statistics

Portrait of Krzysztof Podgórski. Photo.

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

Author

  • Taras Bodnar
  • Stepan Mazur
  • Krzysztof Podgórski

Summary, in English

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.

Department/s

  • Department of Statistics

Publishing year

2017-07

Language

English

Pages

253-265

Publication/Series

AStA Advances in Statistical Analysis

Volume

101

Issue

3

Document type

Journal article

Publisher

Springer

Topic

  • Probability Theory and Statistics

Keywords

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

Status

Published

ISBN/ISSN/Other

  • ISSN: 1863-8171