Crisis and risk dependencies

The knowledge of the multivariate stochastic dependence between the returns of asset classes is of importance for many finance applications, such as asset allocation or risk management. By means of goodness-of-fit tests, we analyze for a multitude of portfolios consisting of different asset classes whether the stochastic dependence between the portfolios’ constituents can be adequately described by multivariate versions of some standard parametric copula functions. Furthermore, we test whether the stochastic dependence between the returns of different asset classes has changed during the recent financial crisis. The main findings are: First, whether a specific copula assumption can be rejected or not, crucially depends on the asset class and the time period considered. Second, different goodness-of-fit tests for copulas can yield very different results and these differences can vary for different asset classes and for different tested copulas. Third, even when using various goodness-of-fit tests for copulas, it is not always possible to differentiate between various copula assumptions. Fourth, during the financial crisis, copula assumptions are more frequently rejected. However, the results also raise some concerns over the suitability of goodness-of-fit tests for copulas as a diagnostic tool for identifying stressed risk dependencies.

► Rejection of copula null hypotheses crucially depends on asset class and time period.
► Different goodness-of-fit tests for copulas can yield very different results.
► During the financial crisis, copula assumptions were more frequently rejected.
► Ability of goodness-of-fit tests to identify stressed risk dependencies seems doubtful.