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

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.

KEYWORDS:

• Dependence modelling
• real estate risk management
• AR-GARCH-EVT-Copula
• back-testing
• price risk forecasting

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. As well as EVT application to the fat tails, which will be reproduced in detail below.

2. Tail dependence of the individual copula families will be discussed in detail below.

3. For a more technical approach on the details of the methodology in the broader stock market, we recommend the study of Wei and Zhang (2004).

4. The transformation methodology differs across the copula families; nonetheless, the basic idea is consistent. See Wang et al. (2010) for more details on differences for elliptical and Archimedean copulae.

5. Accordingly, the approaches to back-test the $CVa{R}^{\alpha }$ are still subject to debate. See Nolde and Ziegel (2017) and Acerbi and Szekely (2017) for a detailed discussion.

6. Implementing the AR-GARCH-EVT-Copula model leads to a load of typical estimates. Since the estimates change over time due to the usage of rolling windows, those estimates can only be illustrated in figures. These figures for AR-GARCH estimates, scale and shape as well as copula parameters are available upon request.

7. The results for the portfolios containing stocks and bonds are available upon request.

8. With an interesting outlier of US stocks, with a total number of zero times for the highest fit of order zero.