Misspecified Dependency Modelling: What Does It Mean for Risk Measurement?

Forecasting portfolio risk requires both, estimation of marginal return distributions for individual assets and dependence structure of returns as well. Due to the fact, that the marginal return distribution represents the main impact factor on portfolio volatility, the impact of dependency modeling which is required for instance in the field of Credit Pricing, Portfolio Sensitivity Analysis or Correlation Trading is rarely investigated that far. In this paper, we explicitly focus on the impact of decoupled dependency modeling in the context of risk measurement. We do so, by setting up an extensive simulation analysis which enables us to analyze competing copula approaches (Clayton, Frank, Gauss, Gumbel and t copula) under the assumption that the “true” marginal distribution is known. By simulating return series with different realistic dependency schemes accounting for time varying dependency as well as tail dependence, we show that the choice of copula becomes crucial for VaR, especially in volatile dependency schemes. Albeit the Gauss copula approach does neither account for time variance nor for tail dependence, it represents a solid tool throughout all investigated dependency schemes.