Scandinavian Working Papers in Economics

Working Papers,
Örebro University, School of Business

No 2023:11: A test on the location of tangency portfolio for small sample size and singular covariance matrix

Svitlana Drin (), Stepan Mazur () and Stanislas Muhinyuza ()
Additional contact information
Svitlana Drin: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Stanislas Muhinyuza: School of Business and Economics Linnaeus University, Postal: School of Business and Economics, Linnaeus University, 35195 Växjö, Sweden

Abstract: In this paper, we propose the test for the location of the tangency portfolio on the set of feasible portfolios when both the population and the sample covariance matrices of asset returns are singular. We derive the exact distribution of the test statistic under both the null and alternative hypotheses. Furthermore, we establish the high-dimensional asymptotic distribution of that test statistic when both the portfolio dimension and the sample size increase to infinity. We complement our theoretical findings by comparing the high-dimensional asymptotic test with an exact finite sample test in the numerical study. A good performance of the obtained results is documented.

Keywords: Tangency portfolio; Hypothesis testing; Singular Wishart distribution; Singular covariance matrix; Moore-Penrose inverse; High-dimensional asymptotics.

JEL-codes: G11

Language: English

17 pages, October 18, 2023

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