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
26 pages, February 1, 2018
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