Market Risks, Internal Models, and Optimal Regulation: Does Backtesting Induce Banks to Report Their True Risks?

In many developed countries, an essential part of a bank's capital requirement may be directly tied to a risk figure taken from the bank's own risk model. When capital is scarce, this creates a conflict of interests because the bank's management may want to manipulate its internal risk model in order to mitigate those capital restrictions. To avoid model manipulation, supervisory authorities require banks to demonstrate the model's accuracy via a procedure known as backtesting, and, when necessary, impose penalty factors to adjust the risk figures. In this paper, we model the relevant trade-off and derive necessary conditions for undistorted risk reporting. We apply our results to the 1996 Amendment of the Basle Capital Accord.