FH-WORKING PAPERS

A NEW COPULA APPROACH FOR HIGH-DIMENSIONAL REAL WORLD PORTFOLIOS

Authors
Wolfgang Aussenegg, Christian Cech
Publication date
01.01.2012
Course of studies
Quantitative Asset and Risk Management
E-Mail
christian.cech@fh-vie.ac.at
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ABSTRACT

The aim of this paper is to generate a new copula based Value at Risk (VaR) approach that can be applied to high-dimensional real world portfolios. Current VaR copula models typically only can deal with portfolios consisting of just a few risk factors. They are, therefore, not suitable for practical applications. This paper tries to fill this gap by presenting a new parsimonious and fast calibration algorithm for the Student t copula model. The new approach provides for the first time the possibility to generate VaR estimates based on Student t copulas for high-dimensional real world portfolios. A portfolio of 21 different financial assets and three additional VaR models (Variance-Covariance, Gaussian copula, and historical simulation) are used to evaluate the suitability of this new Student t copula approach. Almost 20 years of data are used to conduct an out-of-sample hit test based on a rolling window of 250 trading days for model calibration. The results of the hit test reveal that the model performance is highly affected by volatility clustering. Thus, all models perform poorly based on empirical returns, a fact that can be attributed to the underestimation of risk during the financial crisis in 2008. The new Student t copula approach and the historical simulation model perform best, whereas the Variance-Covariance model performs worst in this environment. Accounting for volatility-clustering and applying the models on GARCH(1,1)-innovations rather than on empirical returns considerably improves the performance. Overall, the weaknesses of the Variance-Covariance model stems from three sources: (a) An inappropriate modeling of (univariate) return distributions, (b) an inappropriate modeling of the ‘dependence structure’ (i.e. the copula), and (c) not accounting for volatility clustering. The proposed new Student t copula approach tends to overcome these weaknesses when volatility clustering is accounted for. It is, therefore, a quite promising parametric model alternative for the Variance-Covariance model.
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