Mortgage-Backed Securities and Risk Magnification

Friend Andrew linked to an amazing Marginal Revolution article about how risk works in the creation of mortgage-backed securities. As Andrew said, this is mandatory reading. Here's the punchline:

Suppose that...we later discover the true probability [of a single mortgage defaulting] is not .05 but .06. In terms of our original mortgages the true default rate is 20 percent higher than we thought--not good but not deadly either. However, with this small error, the probability of default in the 10 tranche jumps from p=.0282 to p=.0775, a 175% increase. Moreover, the probability of default of the CDO jumps from p=.0005 to p=.247, a 45,000% increase!

The article links to the underlying math, but it's mindblowing just how sensitive these "low-risk" instruments are to the estimation of the underlying risk.