Financial Crisis, Value-at-risk Forecasts and the Puzzle of Dependency Modeling

Forecasting Value-at-Risk (VaR) for financial portfolios is a staggering task in financial risk management. The turmoil in financial markets as observed since September 2008 called for more complex VaR models, as ”standard” VaR approaches failed to anticipate the collective market movements faced during the financial crisis. Hence, recent research on portfolio management mainly focussed on modeling return interdependencies via dynamic conditional correlations (DCC, Engle (2002)) volatility spillover (e.g. the BEKK model, named after Baba, Engle, Kraft and Kroner, (1995)) or copulas (Embrechts et al. (2002)). In this paper, we analyze VaR estimates based on extreme value theory (EVT) models combined with parametric copulas. Tails of the return distributions are modeled via Generalized Pareto Distribution (GPD) approaches applied to GARCH filtered residuals to capture excess returns. Copula models are used to account for tail dependence. Drawing on this EVT-GARCH-Copula approach, we evaluate portfolios consisting of German Stocks, market indices and FX-rates, with a data sample covering both calm and turmoil market phases. Moreover, models accounting for variable and invariant dependency schemes are evaluated using statistical backtesting and Basel II criteria . The results strongly support the EVT-GARCH-Copula approach, as 99% VaR forecasts clearly outperform estimates stemming from alternative models accounting for dynamic conditional correlations and volatility spillover for all asset classes in turmoil market times.