Credit rating agencies in 2008 literally did not have enough math to justify their AAA labels.
April 24, 2026
Original Paper
When AAA Satisfies Nothing: Impossibility Theorems for Structured Credit Ratings
arXiv · 2604.20877
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The Takeaway
Mathematical insufficiency, rather than just corruption or bad judgment, made the ratings for structured credit products unreliable before the financial crisis. The information available to agencies at the time was statistically too thin to support the high confidence levels they claimed for complex mortgage bonds. While the public blamed greedy analysts, the underlying data simply lacked the signal required for such precise predictions. This impossibility theorem shows that some financial products are too complex to be accurately rated by any model. Investors should view high ratings on opaque assets as mathematical guesses rather than objective facts.
From the abstract
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,