Depends on which model you mean. The banks were holding higher tranches of the securitised mortgage pools. While those pools had traditional levels of defaults

Depends on which model you mean. The banks were holding higher tranches of the securitised mortgage pools. While those pools had traditional levels of defaults, the tranches had their expected value. As the defaults accelerated beyond historic levels, they plummeted in value. In both cases the same model said the instrument had/didn't have value. As these instruments are fair value accounted the fact that they were still bringing in cash didn't help any. However, as the mortgage market started to go south, the default models underestimated the level of defaults, particularly in the equity release market. This underestimation was endemic in the industry at the time, from the banks to the regulators and ratings agencies. There is, of course, a very strong argument to say that the ignorance was willful, everyone was on quite a nicer earner and reacted late to the evidence as it started appearing. So there wasn't really a paradox. The banks were holding tranches while the expected defaults were within historic levels. Once it became clear that that wasn't a good predictor anymore, they tried to limit the effect but it turned out that so many participants were in the same boat that there weren't enough buyers. I have to say I'm not entirely sure what this has to do with ad analytics but I'm not writing a book on the subject so maybe that's not too surprising.