Time dynamic and hierarchical dependence modelling of an aggregated portfolio of trading books: a multivariate nonparametric approach

From a banking supervisory perspective, this paper analyses aspects of market risk of an aggregated trading portfolio comprised of the trading books of 11 German banks with a regulatory approved internal market risk model. Based on real, clean profit and loss data and Value-at-Risk estimates of the 11 banks, the paper specifically models and analyzes the portfolio's dependence and diversification structure, indispensable for financial stability studies. The high sensitivity of market risk measurements with respect to dependence structure of the underlying portfolio is nowadays a well-known fact. However, only few techniqques for high-dimensional and hierarchical dependence analysis have been proposed and studied in the financial literature so far. One reason is certainly the increasing complexity of the statistical theory, which is commonly referred to as the curse of high-dimensionality. The present paper develops and applies multidimensional (asymptotic) test statistics based on the copula theory with the aim of detecting significant long-term level changes in the supervisory portfolio's dependence over time. Furthremore, a statistical hyphothesis test is proposed to identify the distinct contributions of sub-portfolios towards the overall dependence level in ahiercharchical manner. The utilized techniques are distribution-free and, in particulaar, are invariant with respect to the maarginaal return distributions.