Wednesday, March 4, 2009

The Meltdown Formula

Wired magazine brings us Recipe for Disaster: The Formula That Killed Wall Street.

So cool to see it.

This formula provides an answer to the question "What is the chance that two members of the same pool will default on their loans?"

The point of the equation is to calculate the probability that A and B both default in our time period. Investors used this equation to choose investments A and B so that this probability that they both default is as small as possible.

Most of the magic seems to lie in two places:
  1. The probability distributions (the F variables), which describe how long each investment is likely to survive.
  2. The correlation parameter (gamma), which describes how the two investment survival probabilities rise or fall together.
I could go into the mathematics of it all, but I will let the geeks among you check out the article. Basically, this formula helped people (like the folks at AIG's Financial Products group) setup credit default swaps and arrange packages of securities that were supposed to have well-balanced risks. If they had a risky investment they wanted to try, they could balance it by investing in something that had very small correlation with it. The problem is that when the base of the house of cards started to crumble, everything ended up having high correlation to everything else.

Anyway, it is interesting to see the actual formula. It feeds into my scepticism about people trying to push epistemological limits. Maybe we can't solve everything with equations. Just because you can associate a number with it, doesn't mean the number really has any meaning. These quantitative masters of finance thought they could control risk by associating formulas and numbers with everything, but ultimately risks can't be controlled by numbers.

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