The Calculus of Expected Loss: Backtesting Parameter-Based Expected Loss in a Basel II Framework

The dependency structure of credit risk parameters is a key driver for capital consumption and receives regulatory and scientific attention. The impact of parameter imperfections on the quality of expected loss (EL) in the sense of a fair, unbiased estimate of risk expenses however is barely covered. So far there are no established backtesting procedures for EL, quantifying its impact with regards to pricing or risk adjusted profitability measures. In this paper, a practically oriented, top-down approach to assess the quality of EL by backtesting with a properly defined risk measure is introduced. In a first step, the concept of risk expenses (Cost of Risk) has to be extended beyond the classical provisioning view, towards a more adequate capital consumption approach (Impact of Risk, IoR). On this basis, the difference between parameter-based EL and actually reported Impact of Risk is decomposed into its key components. The proposed method will deepen the understanding of practical properties of EL, reconciles the EL with a clearly defined and observable risk measure and provides a link between upcoming IFRS 9 accounting standards for loan loss provisioning with IRBA regulatory capital requirements. The method is robust irrespective whether parameters are simple, expert based values or highly predictive and perfectly calibrated IRBA compliant methods, as long as parameters and default identification procedures are stable.