Financial Risk Management

CHAPTER 12Ex‐Post Evaluation of a Risk Model: Backtesting

Backtesting is an essential part of risk management both from a regulatory and an internal perspective. Backtesting is an ex‐post procedure used to check the accuracy of the risk measure/model used by financial institutions. The idea is to compare what the model said in the past with what actually occurred in terms of loss. This explains why it is called “back” testing. We look backward.

As a reminder, to comply with the Basel III regulatory framework (see Part I), a financial institution must compute a daily risk measure over the last 250 trading days or more. With Basel III, the Value‐at‐Risk (VaR) has been replaced by the Expected Shortfall (ES), a more conservative risk indicator. However, the 99% VaR is still used by the regulator for backtesting purposes, because the ES is much more complicated to backtest than the VaR.¹

The backtesting procedure is based on a 1‐day holding period and compares the 99% VaR with the registered daily Profit and Loss (P&L). As the VaR is used to estimate a potential loss that could be experienced over the next 24 hours, it should not underestimate the realized loss too often to be really helpful in terms of risk management. Of course, the VaR is simply an estimate and, as such, it may provide a wrong estimated loss that is lower than the corresponding realized loss. That said, if the VaR estimate deviates too often from what has been historically observed, it becomes dangerous for ...