Survey_JSS_2003

Abstract

The data set considered here contains data from all thirteen German banks that used internal models for regulatory purposes in the year 2001. The data set for each bank consists first of VaR forecasts and second, the so-called clean, or hypothetical P&L for all 253 trading days of the year 2001. Most of the following figures and tables are based on the normalized P&L and VaR time series. I.e., they are divided by the banks' full sample standard deviation of P&L to insure condentiality. Table 1 shows summary statistics of each bank's data. The coe cient of variation (i.e., the ratio of the standard deviation and the mean) of VaR in column 5 shows that for the ma jority of the banks the variability of the VaR is relatively small compared to its mean. Only banks A, E, and I have a coe cient of variation that is two times larger than the average coe cient of variation of all banks. The last column reports the average loss anks. exceeding VaR, i.e., the estimate of the expected shortfall E[Ct Vtj Ct > Vt ]. Note, that for the standard normal distribution, the expected shortfall is approximately 0.34 for the 99% condence level. The comparatively large average losses exceeding VaR indicate the presence of outliers. Three out of the thirteen banks had more than four violations and only four had no violations at all. For reasons of condentiality, the individual numbers of violations are not reported here.