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

Taras Bodnar, Stepan Mazur and Krzysztof Podgórski
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Taras Bodnar: Stockholm University
Krzysztof Podgórski: Lund University

AStA Advances in Statistical Analysis, 2017, vol. 101, issue 3, No 2, 253-265

Abstract: 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; 91G10; 62H12 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s10182-016-0282-z

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