How the Gaussian Copula Function humbled a Giant Financial System

The formula opened a new door of opportunities for many large financial firms helping them to market the complex financial instruments known as credit derivatives, including what risk they faced, what strategies they needed to minimize the risk and what return they should demand. Using Li’s formula, rating agencies (such as Moody’s) could determine how safe or risky a tranche was based on a single correlation number. Bankers were able to bundle anything and create a triple A-rated bond from car loans, bank loans and corporate bonds, to mortgage-backed securities. These pools were better known as collateralized debt obligations (CDOs).

“The CDS and CDO markets grew together, feeding on each other. At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrocketed to more than $62 trillion. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006,” said Salmon.

However, cautionary advice against using the Gaussian copula function and against using correlation as a deciding factor for investment or as a tool for risk management were clearly voiced by many in the finance industry. The main argument against the formula was that it made no allowance for unpredictability and assumed correlation was a constant rather than a variable, resulting in a lot of uncertainty in the end-result. This also suggests that the implications of using the formula were well understood before the financial crisis began, yet managers continued to misuse the formula because it mainly allowed them to capitalize on huge returns.

Another flaw with the copula formula was that it used CDS prices to calculate correlation in a time, when house prices were rising and thus where default correlations were at their lowest. But, when the housing bubble popped, house prices began to drop across the country and default correlations started to escalate. This meant that the formula was highly sensitive to changes in house prices. Bankers took advantage of the formula’s sensitivity to house-price appreciations by continuing to create more CDOs.

Many bankers were unaware that large changes in the correlation number were a result of small changes in their underlying assumptions. The results they were seeing were not as volatile as they should have been, suggesting the risk shifted elsewhere. The main problem was that the managers were responsible for all asset-allocation decisions and lacked the quantitative skills to understand the models in terms of what they did and how they worked. They also made their decisions based on outputs from “black-box” computer models and not on common sense.

“Very few people understand the essence of the model. The most dangerous part is when people believe everything coming out of it,” Li once said of his own model.

In all, most in the finance industry fail to realise the reality, nor understand the impact, their figures can have on the markets. Worse, many bankers, especially managers, simply don’t grasp the mathematical workings of such financial models like the Gaussian Copula function. No model can perfectly represent reality. Therefore, common sense must come into play when making sound investment and asset-allocation decisions.

The copula function was an elegant way to model risk, provided the underlying assumptions were met. A debate continues as to whether Li or those who misinterpreted his formula should be personally blamed for the Housing Meltdown. But in reality, this may be just the tip of the iceberg.

ARB Team

Arbitrage Magazine

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