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.