Under Basel III, the current international banking regulation, banks must maintain two Tier 1 capital ratios that treat risky assets differently. The Basel Committee uses the critical average risk weight (CARW) framework developed by the Bank of England to determine which ratio is the binding constraint. This methodology, which implicitly assumes that each asset is subject to a uniform shock, consists in comparing the implied average risk weight of a bank to a regulatory critical threshold. Using a stress test approach, we examine whether, and under which conditions, the CARW framework identifies the correct binding capital ratio. We find important errors that are attributable to a series of simplifying assumptions made by the regulator. We finally generalize the methodology used by the Basel Committee and show how our stress-test approach can be used to determine which ratio is binding when only a (single class of) asset(s) is shocked.