A scale-and-level complement to the FRTB profit and loss attribution test

The profit and loss attribution test of the Basel market risk standard compares the hypothetical and the risk-theoretical profit and loss of a desk through a Spearman correlation of the levels and a Kolmogorov-Smirnov distance, with zones that a faulty-model desk can pass. On a generator with a known true risk model, a model fed a volatility twenty days old is flagged by neither statistic in any of 1,000 replications. We propose a complement added beside the regulatory zone: a Mincer-Zarnowitz regression of the hypothetical on the risk-theoretical profit and loss with a joint Wald test under an HC3 covariance, the Spearman correlation of the absolute values, and of their 20-day rolling means, each with a critical value read from a simulated null. At a family size of 1% the complement flags the stale-volatility model in 99.9% of 1,000 replications (95% Wilson interval 99.4 to 100.0%) with a held-out false-alarm rate of 0.9% (0.5 to 1.7%); the regulatory zone flags 0.0%. Against published comparators the rolling-mean statistic has the largest area under the ROC curve at lags of 5, 10 and 20 days, but it is weak against a wrong correlation (4.5%, flagged by the union only through the Wald test) and a one-day misalignment (42.3%, flagged in 100.0% by the absolute-value and Wald statistics). The stated size does not transfer to desks with more persistent or more dispersed volatility (4.0% and 6.2%) or a larger pricing noise (99.0%): thresholds need each desk's own null. Repository and reproducible pipeline (MIT): https://github.com/fsantibanezleal/CAOS_Contraste .