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

Bodnar, Taras ; Mazur, Stepan LU and Podgórski, Krzysztof LU (2017) In AStA Advances in Statistical Analysis 101(3). p.253-265
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.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Global minimum variance portfolio, Singular covariance matrix, Singular Wishart distribution, Small sample problem
in
AStA Advances in Statistical Analysis
volume
101
issue
3
pages
253 - 265
publisher
Springer
external identifiers
  • wos:000406350700002
  • scopus:84995767761
ISSN
1863-8171
DOI
10.1007/s10182-016-0282-z
language
English
LU publication?
yes
id
2faf1ab9-9bb4-4ee5-9b39-5eae0c771bc9
date added to LUP
2016-12-05 07:29:43
date last changed
2025-02-09 21:24:11
@article{2faf1ab9-9bb4-4ee5-9b39-5eae0c771bc9,
  abstract     = {{<p>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.</p>}},
  author       = {{Bodnar, Taras and Mazur, Stepan and Podgórski, Krzysztof}},
  issn         = {{1863-8171}},
  keywords     = {{Global minimum variance portfolio; Singular covariance matrix; Singular Wishart distribution; Small sample problem}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{253--265}},
  publisher    = {{Springer}},
  series       = {{AStA Advances in Statistical Analysis}},
  title        = {{A test for the global minimum variance portfolio for small sample and singular covariance}},
  url          = {{http://dx.doi.org/10.1007/s10182-016-0282-z}},
  doi          = {{10.1007/s10182-016-0282-z}},
  volume       = {{101}},
  year         = {{2017}},
}