Evaluation of Multivariate GARCH Models in an Optimal Asset Allocation Framework

This paper analyses plethora of advanced multivariate econometric models, which forecast the mean and variance-covariance of the asset returns in order to create optimal asset allocation models. Most existing studies compare the performance of a limited number of Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models, and they are only based on speci fic optimisation models. In this study, we provide an in-depth knowledge of large asset modelling and optimisation strategies for solving a portfolio selection problem. Speci cally, we use symmetric GARCH models and an asymmetric version of it (GJR-GARCH). Several studies have also tried to examine the effectiveness of using parametric copula in estimating portfolio risk measures but their results have been inconclusive. We are interested in evaluating if copula-GARCH could be an optimal model for assessing the performance of a portfolio. This study, therefore, implemented various copula-GARCH based models using the static and dynamic (DCC) estimation of the correlation. By employing different model speci fications, we are able to explore the empirical applicability of the multivariate GARCH models when estimating large conditional covariance matrices. In constructing the optimal portfolios, we evaluate the minimum variance, mean-variance, maximising Sharpe ratio, mean-CVaR, and maximisation of Sortino ratio. We compare the out-of-sample performance for each of the models based on the risk-adjusted performance for a portfolio with and without short sales, consisting eight stocks and four bond indices of 10 years maturity, in the United States (US), United Kingdom (UK), Germany, Japan, Netherlands, Canada and Hong Kong. Our results suggest that the dynamic models are more capable of delivering better performance gains than the static models. These models reduce portfolio risk and improve the realised return in the out-of-sample period. This paper concludes that by adding copula functions to the model, it does not give a better performance model when compared to the dynamic correlation model.