This Wired.com article Recipe for Disaster: The one formula that killed Wall St is probably the closest to answering the question I always wanted the answer for. “How could so many brilliant bankers go wrong?”

Before quant models came along, investors have no way of knowing the correlations between different variables that will impact the chances of default on a bond. For example if you default on a loan what is the probability that your neighbors will default on their loan too?. When calculating the value of a mortgage backed security the variables that lead to default are many. So there were no means to price an exotic MBS. Faced with the challenge of not having the right formula to calculate such probabilities investors were just happy to put their money in safe mortgage bonds (like from Freddie Mac and Fannie Mae in US). There are no variables required here as the bonds are guranteed by the government. Well they didnt have to to buy those boring bonds for long.

Sometime in early 2000 a chinese born quant guru came up with a neat trick to calcualte the probability of default using a formula later known as Gaussian Coupla Function. What is this formula all about?

Li wrote a model that used Credit Default Swaps prices rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly) to calculate a single correlation constant. Hesaid there will be no need to analyze huge amounts of historic data to calculate correlation between default variables. He said the only thing that matters is the final correlation number—one clean, simple, all-sufficient figure that sums up everything. That is the value gamma in his formula. (Read the article)

A brilliant simplification like this elecrified the markets. Overnight contracts worth $billions were written for CDO (collateralized debt obligations) and then for CDS (Credit Default Swaps) insuring those contracts. The two contracts fed on each other and grew multi fold from 2000. I remember having long discussons in 2005 about the CDO&CDS markets and the huge contract volumes. Most of the banks simply didnt have the resources to even price and process those contracts. The market exploded from then. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.(and so are the bonuses of the bankers)

Well how did the honeymoon for the bankers end.

Li formula has some fundamental weaknesses which the banks chose to ignore.

1. How could we use 10 years worth of CDS data to model housing default rates. The default data for housing market goes back at least 100 years. Could we take the last 10 year data, when US market has seen a dream real estate run, to create a model on default rates. (Isnt it Survivorship bias in statistics?)
2. Could correlations ever be constant. Arent they changing with the environment? Could the relationship between 2 variables ever be reduced to one constant number. Even Einstein’s model E=mc2 has a residual function.

It turns out that there were early warnings including from Li himself. But the managers chose to ignore those warnings. They didnt want to get into quant nuances. Besides who cares when the business is doing good?

Well I dont think Li’s formula is the sole culprit here. I will probably post an article soon refuting the single killer formula theory.