Scandinavian Working Papers in Business Administration

Working Papers,
Örebro University, School of Business

No 2022:15: Estimation of optimal portfolio compositions for small sampleand singular covariance matrix

Taras Bodnar (), Stepan Mazur () and Hoang Nguyen ()
Additional contact information
Taras Bodnar: Stockholm University, Postal: Stockholm University, Matematiska institutionen, SE - 106 91 Stockholm,
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Hoang Nguyen: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden

Abstract: In the paper we consider the optimal portfolio choice problem under parameter uncertainty when the covariance matrix of asset returns is singular. Very useful stochastic representations are deduced for the characteristics of the expected utility optimal portfolio. Using these stochastic representations, we derive the moments of higher order of the estimated expected return and the estimated variance of the expected utility optimal portfolio. Another line of applications leads to their asymptotic distributions obtained in the high-dimensional setting. Via a simulation study, it is shown that the derived high-dimensional asymptotic distributions provide good approximations of the exact ones even for moderate sample sizes.

Keywords: singular Wishart distribution; mean-variance portfolio; Moore-Penrose inverse

JEL-codes: G11

Language: English

19 pages, December 6, 2022

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