Risk evaluation in financial risk management: prediction limits and backtesting

ABSTRACT Inappropriate forecasting methods can systematically lead to an underestimation of market risk which can result in real losses. The purpose of our paper is to quantify the magnitude of risk underestimation by measuring the rate in which the value-at-risk and the expected shortfall exceed an upper prediction limit based on bootstrapping. The resulting ex ante exceedance rates are related to the ex post failure rates which result from the number of exceptions in the backtesting procedure of the Basel II regulation. An empirically grounded analysis reveals a systematic underestimation risk which clearly differs between common forecasting models. With regard to underestimation risk our paper unfolds the necessity for an adjustment of the Basel II guidelines.