Title: A new non-Gaussian factor GARCH model
Authors: Patrick Walker - University of Zurich (Switzerland) [presenting]
Marc Paolella - University of Zurich (Switzerland)
Pawel Polak - Columbia University (United States)
Abstract: A new orthogonal factor GARCH model for a multivariate set of skewed, heavy-tailed asset returns is proposed. Conditional returns are modeled by a multivariate generalized hyperbolic (MGHyp) distribution and the covariance matrix specification makes use of the eigendecomposition of principle component analysis (PCA). Due to the mixing structure of the MGHyp distribution, the filtered residuals are Gaussian and common market shocks to asset volatilities, which manifest themselves in leptokurtic tails, are accounted for. The leading eigenvalues of the orthogonal decomposition, representing those unobserved statistical factors that explain most of the assets' covariances, are endowed with univariate GARCH dynamics, while the remaining eigenvalues are assumed constant over time in order to preserve invertibility. Joint maximum likelihood estimation of all model parameters is carried out by a fast expectation conditional maximization either (ECME) algorithm. An application to portfolio optimization with daily rebalancing shows the superiority of the new model compared to several benchmark models and the naive diversification strategy. In addition, we observe lower portfolio turnover of our new model compared to multivariate GARCH models with constant conditional correlations (CCC), translating into possibly lower transaction costs.