Value at Risk and Backtesting

Value-at-Risk (VaR) is probably the most commonly known measure for quantifying and controlling the risk of a portfolio. Establishing VaR is of central importance to a credit institute. The description of risk is attained with the help of an “internal model”, whose job is to reect the market risk of portfolios and similar uncertain investments over time. The objective parameter in the model is the probability forecast of portfolio changes over a given period. Whether the model and its technical application correctly identify the essential aspects of the risk, remains to be seen and verified. The backtesting procedure serves to evaluate the quality of the forecast of a risk model by comparing the actual results to those generated with the VaR model. For this the daily VaR estimates are compared to the results from hypothetical trading that are held from the end-of-day position to the end of the next day, the so-called “clean backtesting”. The concept of clean backtesting is differentiated from that of “mark-to-market” profit and loss (“dirty P&L“) analyses in which intra-day changes are also observed. In judging the quality of the forecast of a risk model it is advisable to concentrate on the clean backtesting.