AR-GARCH-EVT-Copula for securitised real estate: an approach to improving risk forecasts?

Abstract

ABSTRACT This study presents a quantitative analysis of the so-called AR-GARCH-EVT-Copula model aimed at forecasting risk metrics for multi-asset portfolios, including securitised real estate positions. The model incorporates a non-linear dependence structure and time-varying volatility in asset returns. Accordingly, an empirical study using data from six major global markets is carried out. The approach is applied to forecast risk metrics, in comparison to classical methods like historical simulation and variance-covariance models. Forecasts are then compared with realised returns, to calculate hit sequences and conduct statistical interference on the respective models. It is empirically shown that, the AR-GARCH-EVT-Copula model provides a superior forecast concerning risk metrics. This is mainly due to the usage of copulas, allowing us to individually model the dependence structure of random variables. Back testing and test results confirm the superiority of our model in comparison with classic methods such as historical simulation and Variance-Covariance approach. The decomposition of the univariate and multivariate models of the target model reveal the necessity to allow for high order and thus long-lasting autoregressive modelling as well as asymmetric tail dependence and rotated copulae across different portfolios.