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.

摘要

这项研究对所谓的AR-GARCH-EVT-Copula模型进行了定量分析，旨在预测多资产组合（包括证券化房地产头寸）的风险指标。该模型结合了非线性依赖结构和资产收益率随时间变化的波动性。因此，使用来自六个主要全球市场的数据进行了实证研究。与传统方法（例如历史模拟和方差-协方差模型）相比，该方法适用于预测风险指标。然后将预测与已实现的回报进行比较，以计算命中序列并在各个模型上进行统计干扰。从经验上可以看出，AR-GARCH-EVT-Copula模型提供了有关风险指标的出色预测。这主要是由于使用了copulas，让我们可以对随机变量的依存结构进行单独建模。回溯测试和测试结果证实了我们的模型与经典方法（例如历史模拟和方差-协方差方法）相比的优越性。目标模型的单变量和多变量模型的分解表明，有必要进行高阶且因此持久的自回归建模，以及不对称尾部依赖性和跨不同投资组合的旋转系。