The Implicit Constraints of Fundamental Review of the Trading Book Profit-and-Loss-Attribution Testing and a Possible Alternative Framework

The Fundamental Review of the Trading Book (FRTB) is a relatively new regulatory framework, proposed by the Basel Committee on Banking Supervision and dedicated to market risk. Its major innovation is the profit-and-loss-attribution (PLA) test, a tool designed to verify the alignment between theoretical changes in a trading desk portfolio’s value, based on an institution’s risk-measurement model (risk theoretical profit-and-loss (RTPL)), and hypothetical changes in a trading desk portfolio’s value, based on an institution’s accounting/front-office pricing model (hypothetical profit-and-loss (HPL)). The theoretical and numerical results presented in this paper highlight the very strong, implicit constraints embedded in PLA and the generally low probability of conducting a successful PLA test; these results support industry concerns related to the proposed regulatory requirements. Moreover, numerical tests aimed at assessing whether RTPL and HPL are sufficiently close show that the proposed alternative framework based on statistical hypothesis testing, together with the imposition of a minimum correlation level between RTPL and HPL, appears to be a robust approach in terms of statistical discriminatory power, reactivity and sensitivity to outliers.