When AAA Satisfies Nothing: Impossibility Theorems for Structured Credit Ratings

A credit rating of AAA asserts near-certainty of repayment. This paper asks whether the pre-crisis information environment could have supported that assertion for structured products. Bayes' theorem implies that any reliability target requires a minimum level of statistical discrimination between instruments that will repay and those that will not. At structured-finance base rates, a four-nines reliability target demands discrimination on the order of 10,000 to 1. A three-nines target demands 1,000 to 1. Nothing in the published credit-prediction literature provides an affirmative basis for believing that discrimination of this magnitude was achievable with the data available at rating time. Retrospectively, the realized system fell short of the four-nines benchmark by roughly 90,000-fold. The framework accommodates the historical feasibility of corporate AAA ratings, where high base rates and rich information produce low required discrimination. Illustrative calibrations for contemporary collateralized loan obligations suggest that material tension between the precision target and the information environment persists. The central implication is that the AAA precision claim itself likely exceeded what the available information could support.