A Non-Elliptical Orthogonal GARCH Model for Portfolio Selection under Transaction Costs

33 Pages Posted: 27 Sep 2019

See all articles by Marc S. Paolella

Marc S. Paolella

University of Zurich - Department of Banking and Finance; Swiss Finance Institute

Pawel Polak

Stony Brook University-Department of Applied Mathematics and Statistics; Institute for Advanced Computational Science

Patrick S. Walker

University of Zurich, Department of Banking and Finance; OLZ AG

Date Written: September 25, 2019

Abstract

Covariance matrix forecasts for portfolio optimization have to balance sensitivity to new data points with stability in order to avoid excessive rebalancing. To achieve this, a new robust orthogonal GARCH model for a multivariate set of non-Gaussian asset returns is proposed. The conditional return distribution is multivariate generalized hyperbolic and the dispersion matrix dynamics are driven by the leading factors in a principle component decomposition. Each of these leading factors is endowed with a univariate GARCH structure, while the remaining eigenvalues are kept constant over time. Joint maximum likelihood estimation of all model parameters is performed via an expectation maximization algorithm, and is applicable in high dimensions. The new model generates realistic correlation forecasts even for large asset universes and captures rising pairwise correlations in periods of market distress better than numerous competing models. Moreover, it leads to improved forecasts of an eigenvalue-based financial systemic risk indicator. Crucially, it generates portfolios with much lower turnover and superior risk-adjusted returns net of transaction costs, outperforming the equally weighted strategy even under high transaction fees.

Keywords: Dynamic Conditional Correlations; Multivariate GARCH; Multivariate Generalized Hyperbolic Distribution; Principle Component Analysis; Financial Systemic Risk

JEL Classification: C32; C53; G11; G17

Suggested Citation

Paolella, Marc S. and Polak, Pawel and Walker, Patrick S., A Non-Elliptical Orthogonal GARCH Model for Portfolio Selection under Transaction Costs (September 25, 2019). Swiss Finance Institute Research Paper No. 19-51, Available at SSRN: https://ssrn.com/abstract=3460049 or http://dx.doi.org/10.2139/ssrn.3460049

Marc S. Paolella

University of Zurich - Department of Banking and Finance

Plattenstr. 14
Zürich, 8032
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Pawel Polak

Stony Brook University-Department of Applied Mathematics and Statistics ( email )

Stony Brook University
Stony Brook, NY 11794
United States

Institute for Advanced Computational Science ( email )

100 Nicolls Rd
Mailstop 5250
Stony Brook, NY 11794
United States

HOME PAGE: http://https://sites.google.com/view/pawelpolak/

Patrick S. Walker (Contact Author)

University of Zurich, Department of Banking and Finance ( email )

Plattenstrasse 14
Zürich, CH-8032
Switzerland

HOME PAGE: http://www.bf.uzh.ch/

OLZ AG ( email )

Gessnerallee 38
Zurich, Zurich 8001
Switzerland

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