Felix Salmon published a great article in Wired that looks at the Recipe for Disaster: The Formula That Killed Wall Street. The article looks at the widespread use of the Gaussian copula function. In assessing the risks in mortgage backed securities.
The theory behind Gaussian copula function tries to overcome the difficulty in assessing the multitude of correlations among all the risks in a pool of mortgages. David X. Li came up with the Gaussian copula function that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, uses historical prices from the Credit Default Swaps market. Li wrote a model that used the price of Credit Default Swaps, rather than real-world default data as a shortcut to determining the correlation between risks. There is an inherent assumption that the CDS markets can price default risk correctly.
I did not do well in my college statistics class. (It was on Friday afternoon, close to happy hour.) But I do remember two concepts. One, correlation does not equal cause and effect. Two, you always need to challenge the underlying assumptions and methodology, because they can have dramatic effects on the data. (and third, do not schedule difficult classes on Friday afternoon.)
According to Felix’s story, Wall Street seemed to miss some of the underlying assumptions in the Gaussian copula function. Since the risk profile was based on the CDS market, the data was only looked as far back as the CDS market existed. That was less than ten years. During that time, home prices did nothing except skyrocket. Unfortunately, the last real estate crash was before that period.
Li’s formula was used to price hundreds of billions of dollars worth of mortgaged-backed securities. As we now see, Wall Street got it wrong.
It looks like I did not waste my time with statistics and that I got the key knowledge. Look closely at correlation to see why things are moving together. Challenge the underlying assumptions and make sure you understand how they effect the end product of your results. Those are good lessons for anyone involved in enterprise risk management.
As a recovering economist, this is an interesting concept. I thought only ivory tower econ professors made such leaps of faith. People have always questioned why economists aren’t all rich. Now we now why. Just because a math formula sounds sophisticated and powerful, does not mean you shouldn’t question the assumptions.
Nice post.
Toby –
Thanks for stopping by.
It sounds like the dynamic of having an ultra-smart economist coming up with a formula being used by managers who do not understand the underlying weaknesses and assumptions in using the formula. It is pretty clear form the fall-out on Wall Street (and the survivors) as to who understood the math.
In a truly free market there are supposed to be multiple buyers and sellors and they are not all supposed to be using exactly the same model. This greatly increases the odds of red flags popping up. Part of the problem with “too big to fail” is that those institutions are “too big to succeed”. If diversification matters for individual investors – then it matters for the rest of the marketplace too. When everyone is going the same direction – whether following the same formula, or a single guru, or a government mandate, then on occasion everyone will be wrong – and it is that failure case that invites disaster. It is not that Merrill Lynch improperly assessed the risk of mortgage backed securities, it is that virtually everyone used the same risk model.
Dhlii –
I do not think it is the lack of a free market. I think it is illustrative of the herd mentality on (what is left of) Wall Street. It overreacts to good news, oversells for bad news and abuses the same strategies.