Krzysztof Podgórski
Professor, Head of the Department of Statistics
Tangency portfolio weights for singular covariance matrix in small and large dimensions : Estimation and test theory
Author
Summary, in English
In this paper we derive the finite-sample distribution of the estimated weights of the tangency portfolio when both the population and the sample covariance matrices are singular. These results are used in the derivation of a statistical test on the weights of the tangency portfolio where the distribution of the test statistic is obtained under both the null and alternative hypotheses. Moreover, we establish the high-dimensional asymptotic distribution of the estimated weights of the tangency portfolio when both the portfolio dimension and the sample size increase to infinity. The theoretical findings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index.
Department/s
- Department of Statistics
Publishing year
2019
Language
English
Pages
40-57
Publication/Series
Journal of Statistical Planning and Inference
Volume
201
Document type
Journal article
Publisher
North-Holland
Topic
- Probability Theory and Statistics
Keywords
- High-dimensional asymptotics
- Hypothesis testing
- Singular covariance matrix
- Singular Wishart distribution
- Tangency portfolio
Status
Published
ISBN/ISSN/Other
- ISSN: 0378-3758