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The P&L Attribution Test

We analyse the failure probabilities of the P&L Attribution (PLA) test as defined in the final market risk standard published in January 2016 by the Basel Committee on Banking Supervision. We calculate the failure probabilities from closed-form expressions, derived under the assumption that both the hypothetical and unexplained P&L are normally distributed random variables with zero mean and a prescribed relative variance. We present tabulated results for the probabilities of failing the PLA test within different horizons, as well as the steady-state proportion of desks that a bank might expect to maintain accreditation to use the Internal Model Approach, assuming a minimum period of delay associated with the re-accreditation process subsequent to a desk failing the PLA test. Our analysis concludes that the high failure probability of the PLA test is due to the fact that it is based on calculating a monthly metric from just (roughly) 21 separate daily P&L observations, meaning the resultant ratio distributions have too few degrees of freedom.