Scandinavian Working Papers in Business Administration

Working Papers,
Örebro University, School of Business

No 2021:13: Tangency portfolio weights under a skew-normal model in small and large dimensions

Farrukh Javed (), Stepan Mazur () and Erik Thorsén
Additional contact information
Farrukh Javed: 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
Erik Thorsén: Stockholm Universtity, Postal: Department of Mathematics, Stockholm University, SE-10691 Stockholm, Sweden

Abstract: In this paper, we investigate the distributional properties of the estimated tangency portfolio (TP) weights assuming that the asset returns follow a matrix variate closed skew-normal distribution.We establish a stochastic representation of the linear combination of the estimated TP weights that fully characterize its distribution. Using the stochastic representation we derive the mean and variance of the estimated weights of TP which are of key importance in portfolio analysis. Furthermore, we provide the asymptotic distribution of the linear combination of the estimated TP weights under the high-dimensional asymptotic regime, i.e. the dimension of the portfolio p and the sample size n tend to infinity such that p/n → c ∈ (0, 1). A good performance of the theoretical findings is documented in the simulation study. In the empirical study, we apply the theoretical results to real data of the stocks included in the S&P 500 index.

Keywords: Asset allocation; high-dimensional asymptotics; matrix variate skew-normal distribution; stochastic representation; tangency portfolio

JEL-codes: C13; G11

27 pages, June 10, 2021

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