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

Authors

  • Taras Bodnar Department of Mathematics, Stockholm University, Roslagsvagen 101, SE-10691 Stockholm, Sweden
  • Stepan Mazur Department of Statistics, Lund University, Tycho Brahes vag 1, SE-22007 Lund, Sweden
  • Krzysztof Podgórski Department of Statistics, Lund University, Tycho Brahes vag 1, SE-22007 Lund, Sweden

Keywords:

global minimum variance portfolio, singular Wishart distribution, singular covariance matrix, small sample problem

Abstract

Bodnar and Schmid (2008) derived the distribution of the global minimum variance portfolio weights and obtained the distribution of the test statistics for the general linear hypothesis. Their results are obtained in the case when the number of observations n is bigger or equal than the size of portfolio k. In the present paper, we extend the result by analyzing the portfolio weights in a small sample case of n < k, with the singular covariance matrix. The results are illustrated using actual stock returns. A discussion of practical relevance of the model is presented.

Downloads

Issue

2015

Section

Working Papers in Statistics