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

On modelling volatility and mortality for pension schemes

The purpose of this research is to develop volatility and mortality models that could be used in asset liability management in pension schemes. This study provides a comprehensive study of various advance multivariate DCC GARCH models which are used for construction of optimal portfolios in modelling asset return covariances. The effectiveness of using parametric copula in estimating portfolio risk measures are evaluated such that the DCC models are found to have better performance than any other parametric copula models. Several models were developed as extensions to existing mortality models in a single and multiple population, in particular the Lee Carter (LC) mortality model and the Common Age Effect (CAE) model by proposing a modification of singular value decomposition (SVD) and principal component analysis (PCA) methods. Complementing this, a further study on mortality model by applying a range of multivariate DCC GARCH models in modelling the mortality dependence across multiple populations is evaluated. Finally, the proposed models of volatility and mortality are applied to the pension schemes. The volatility models were fitted using multivariate DCC GARCH model to obtain the investment returns and the cohort actuarial tables were produced based on LC approach for the out-of-sample period in the UK population. The fits from the modelling of volatility and mortality were analysed on defined benefit (DB), defined contribution (DC) and hybrid schemes to evaluate the fund value and actuarial liabilities. This research underlined the important role that econometric volatility modelling and stochastic mortality modelling can play in managing pension schemes to ensure that future liabilities can be meet