Time Dynamic and Hierarchical Dependence Modelling of an Aggregated Portfolio of Trading Books : A Multivariate Nonparametric Approach

From a banking supervisory perspective, this paper analyzes aspects of market risk of a supervisory trading portfolio comprised of the trading books of eleven German banks with a regulatory approved internal market risk model. Based on real, clean profit-and-loss data and value-at-risk estimates, the paper specifically models and analyzes the portfolio's dependence and diversification structure. Such an analysis is indispensable for financial stability studies. The high sensitivity of market risk measurements with respect to the dependence structure of the underlying portfolio is now a well-known fact. However, few techniques for high-dimensional and hierarchical dependence analysis have been studied in the financial literature thus far. This paper develops multidimensional (asymptotic) test statistics based on the copula theory for detecting significant changes of the portfolio's dependence over time. Furthermore, a statistical hypothesis test is proposed to identify the distinct contributions of subportfolios toward the overall level of dependence. The utilized techniques are distribution-free and, in particular, are invariant with respect to the marginal return distributions