Scandinavian Working Papers in Economics

Working Papers,
Örebro University, School of Business

No 2018:1: Tangency portfolio weights for singular covariance matrix in small and large dimensions: estimation and test theory

Taras Bodnar (), Stepan Mazur (), Krzysztof Podgórski () and Joanna Tyrcha ()
Additional contact information
Taras Bodnar: Stockholm University, Postal: Stockholm University, Department of Mathematics, SE - 10691 Stockholm, Sweden
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Krzysztof Podgórski: Lund University, Postal: Lund University, Department of Statistics, SE - 22007 Lund, Sweden
Joanna Tyrcha: Stockholm University, Postal: Stockholm University, Department of Mathematics, SE - 10691 Stockholm, Sweden

Abstract: In this paper we derive the nite-sample distribution of the esti- mated 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 port- folio where the distribution of the test statistic is obtained under both the null and the 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 sam- ple size increase to in nity. The theoretical ndings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index.

Keywords: tangency portfolio; singular Wishart distribution; singular covariance matrix; high-dimensional asymptotics; hypothesis testing

JEL-codes: C10; C44

26 pages, February 1, 2018

Full text files

wp-1-2018.pdf PDF-file Full text

Download statistics

Questions (including download problems) about the papers in this series should be directed to ()
Report other problems with accessing this service to Sune Karlsson ().

This page generated on 2018-02-05 21:24:21.