Must Read Article on the Financial Meltdown
Via Tyler Cowen at Marginal Revolution, an excellent article in Wired about how one formula, embodying one assumption, catalyzed the meltdown. I recommend you read it and ponder it. There are many useful lessons for modeling complex systems in general.
However, I will summarize for those of you short on time. A fundamental problem in securitization is figuring out how different components of a security are related. Think of it as measuring how well the components are diversified. The more independent the components, the less risk embodied in the security. Thus AAA rated tranches of mortgage-backed securities are supposed to be very safe because the components are supposed to be highly independent.
A Chinese mathematician named David X. Li had an insight. You don’t have to analyze the dependencies directly, you just have to observe the correlations in the market prices of the components. Then you can compute these really tight sounding confidence intervals on the correlations of various components because you have all this market data. Of course, the market can’t take into account what it doesn’t understand. So you see a bunch of 25-sigma events. At least, your model says they are 25-sigma. Oops!