The AMA method - analytical foundations of its failure

In 2024, the Basel Committee on Banking Supervision, implementing the CRR III regulation, withdrew the Advanced Measurement Approach for operational risk (AMA) — a model built on an actuarial foundation — ending its twenty-year history in the banking sector. The official justification was excessive dispersion of model results across institutions, undermining comparability of capital requirements. This article argues that such dispersion was merely a symptom — the deeper problem being a structural inconsistency of the framework, embedded in its assumptions from the outset. Three structural properties of the AMA framework are derived. Property (1) concerns the domination of distant quantiles of the aggregate loss distribution by a single extreme loss when heavy-tailed severity distributions are applied. Property (2) demonstrates that the AMA model outcome is determined by quantiles of the severity distribution higher by one or more orders of magnitude than the regulatory quantile of 0.999. Property (3) indicates the dependence of the extreme loss value — which determines the model outcome — on the count of minor, negligible operational events. The occurrence of these properties was verified by a numerical Monte Carlo experiment. The results indicate that the combined effect of the derived properties led to the necessity of estimation at quantiles of the order 0.9999, 0.99999 and higher — levels beyond the capabilities of reliable statistical modeling given data volumes available in banking practice. Also critical was the ambiguity in the definition of rarity, and the transfer of that concept onto the single loss distribution axis — a transfer arising from the joint occurrence of properties (1), (2), and (3). Rarity readings on this axis depended on the quantile positioning of extreme losses, which could itself depend on the count of low-value, negligible losses. The observed dispersion of results across institutions may therefore have been a consequence of these unintended structural inadequacies, rather than the result of modeling errors.