Posted on Categories Expository Writing, Finance, Opinion

# It is not all the quants’ fault.

There is plenty of blame to go around from the current global financial crisis. But, I would like to point out that it is not “all the quants’ fault.” We are all now, unfortunately, sitting in the middle of a high quality (and extremely expensive) lesson in financial mathematics. I would hate for some of the truly important points to be lost to paying too much attention to some of the shiny details.

One fascinating article ( Recipe for Disaster: The Formula That Killed Wall Street by Felix Salmon, Wired, February 2009) has so popularized assigning blame to one formula (and one mathematician) that posting the image of a formerly obscure statistical formula (called a “copula”) is now considered good for a laugh.

A copula formula.

However, the original mathematical paper being castigated (“On Default Correlation: A Copula Function Approach” by David X Li, Risk Metrics (2000)) is in fact good work. What is wrong is not the formula but the over-reliance on the formula. If we place all the blame on “copulas” we will be too ready to repeat the current disaster with some other “better” model.

We need to think more like Michael Lewis and use specific failures as miniature laboratories to learn larger lessons. A great example is his write-up of the Iceland financial collapse ( Wall Street on the Tundra by Michael Lewis, Vanity Fair, April 2009 ) which, if you read carefully, contains a general indictment of speculative greed and getting rich by pushing around bits of paper (instead pursing activities that create actual value).

So back to the copulas: what is to be learned (now at great expense) there? I would like to work through some of the important points of Dr. Li’s paper and explain some of the painful points in our current lesson. In my opinion none of the flaws are mathematical (or in the paper)- the flaws are all deep defects in logic and reason (and found in the later behavior of traders).

The main purpose of Dr. Li’s paper was to figure out how to price a newer and more complicated financial instrument (the credit default swap) in terms of older underlying instruments (mortgages). In addition to developing the necessary mathematics the paper contains several clever ideas based on the logic of reasonable markets. As the markets became very large and very unreasonable the logic no longer applied. That is what went wrong.

Credit default swaps (in their simplest form) essentially started as insurance policies against mortgages defaulting. Unfortunately, credit default swaps were unregulated financial instruments instead of regulated insurance policies. Credit default swaps degenerated into “bets” (or derivative securities) when they were separated from the underlying mortgages. You could, in essence, buy or sell insurance on your neighbor defaulting on their mortgage.