Testing backtesting : an evaluation of the Basle guidelines for backtesting internal risk management models of banks

Internal risk management models and downside-risk measures such as Value-at-Risk (VaR) play an important role in contemporary banking practice. VaR measures the maximum loss born by a bank or other financial institution over a certain time period and given a certain level of confidence. Following the Basle guidelines for bank supervision, many supervisory institutions require banks to use such models and to report VaR measures on a regular basis. Capital requirements for the bank are then directly related to its reported VaR figure. In principle, following the Basle guidelines based on the internal models approach, banks are allowed to design their own risk management models for computing their VaR. This raises the question whether banks have any impetus to come up with correct models in the sense that the VaR predicted by the model matches the true VaR. This question is addressed in the present paper. In our model, banks assign negative utility to required capital reserves due to opportunity costs. Using a stylized representation of the Basle guidelines for backtesting internal risk models, we investigate whether banks are inclined to choose overly prudent or overly risky internal models. We check the robustness of the result by varying the planning horizon of the bank and the degree of fat-tailedness of the bank’s asset and liability portfolio. It generally turns out that banks have a strong incentive to use internal models that underestimate the true VaR of the bank’s portfolio. Monetary penalties should be set substantially higher by supervisory institutions to realize a closer match between reported and actual VaR.