Discussion Paper, Series 2: Banking and Financial Supervision 2005,02
The Value at Risk of a portfolio differs from the sum of the Values at Risk of the portfolio's components. In this paper, we analyze the problem of 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 twelve German banks for the period from 2001 to 2003, we estimate the Value at Risk of the entire portfolio. We assume a reduced-form model and neglect the effects of a potential bankruptcy of one of the banks. We analyze different models for the cross-correlation of the banks? profits and losses. In an empirical study, we apply backtesting methods to determine which aggregation model leads to the best out-of-sample estimates for the portfolio's economic risk figure. Our 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) During "normal" times, the portfolio's Value at Risk is much lower than the sum of the single Values at Risk. (iii) The relative marginal risk contribution depends on the bank in question and is between 0.05 and 0.62.
Value at Risk portfolio cross-correlation market risk regulation risk forecast model validation