Supervisor's Portfolio : The Market Price Risk of German Banks from 2001 to 2004: Analysis and Models for Risk Aggregation

We analyze how a single economic risk figure for the Value at Risk of a hypothetical portfolio composed of different commercial banks might be obtained for a supervisor. Using the daily profits and losses and the daily Value at Risk figures of German banks for the period from 2001 to 2004, we determine the Value at Risk of the entire market risk portfolio by assuming a reduced-form model and neglecting effects of a potential bankruptcy of one of the banks. We propose different models for the cross-correlation of the banks' profits and losses and apply in an empirical study backtesting methods to determine which aggregation model leads to the best out-of-sample estimates for the quot;supervisor's portfolio'squot; economic risk figure. The main findings can be summarized in three statements. (i) The portfolio's Value at Risk can be estimated from time series data very well. (ii) Diversification effects are significant during 'normal' times. (iii) The relative marginal risk contribution depends on the bank in question and is between 0.07 and 0.62