A generalized precision matrix for non-Gaussian multivariate distributions with applications to portfolio optimization

34 Pages Posted: 6 Apr 2022 Last revised: 25 Oct 2023

See all articles by Emanuele Taufer

Emanuele Taufer

affiliation not provided to SSRN

Karoline Bax

Technische Universität München (TUM) - TUM School of Management

Sandra Paterlini

University of Trento - Department of Economics and Management

Date Written: October 19, 2023

Abstract

We introduce the concept of Generalized Precision Matrix (GPM), based on a general measure of dependence, which might be valid for any statistical distribution. Beside showing that in the Gaussian case, the GPM coincides with the inverse of the covariance matrix, we derive the GPM analytically for the multivariate t, multivariate skew-normal and multivariate skew-t distributions, moving beyond Gaussianity.
Therefore, we argue that using the derived GPMs might be preferable when data show asymmetry and heavy tails, supporting our claim through simulation analysis. As financial times series are leptokurtic, we propose then an application to the Markowitz minimum variance portfolio, which exhibits superior fitting of the multivariate skew-t model during crisis periods.

Keywords: Generalized Precision Matrix, heavy tails, multivariate t distribution, multivariate skew-normal and skew-t distributions, minimum-variance portfolio

JEL Classification: C46, C58, G11

Suggested Citation

Taufer, Emanuele and Bax, Karoline and Paterlini, Sandra, A generalized precision matrix for non-Gaussian multivariate distributions with applications to portfolio optimization (October 19, 2023). Available at SSRN: https://ssrn.com/abstract=4063255 or http://dx.doi.org/10.2139/ssrn.4063255

Emanuele Taufer

affiliation not provided to SSRN

Karoline Bax (Contact Author)

Technische Universität München (TUM) - TUM School of Management ( email )

Freising
Germany

Sandra Paterlini

University of Trento - Department of Economics and Management ( email )

Via Inama 5
Trento, I-38100
Italy

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