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Viewpoint: The Perils of Equating Bankers to Bees

March/April 2010


Pablo TrianaBy Pablo Triana

One of the most influential mathematical finance models ever is the so-called Gaussian Copula model. Now consigned to the dustbin of failed experiments, the Gaussian Copula enjoyed untold stardom in the early years of this century, becoming central in the valuation and rating of the convoluted mortgage-related assets that unleashed the credit crisis.

The formerly glorious concoction promised to accurately estimate the joint default probabilities and default correlations of a bunch of debt securities pooled together. It was widely embraced around the financial industry as a trusted indicator of the likelihood that a lot of the (often dodgy) mortgages making up those infamous Collateralized Debt Obligations would turn nasty concurrently. Due to its technical intricacies, the Gaussian Copula typically delivered bland default correlation estimates, facilitating the confidence-building AAA-ing of junky subprime investments. As is now only too obvious, the model failed drastically as numerous clustered defaults took place rather more habitually than theoretically predicted.

The model’s failure would not seem that surprising to those aware of the original rationale for its embedding in Finance-land. David Li, the father of the hitherto reputable mathematical baby, initially got his inspiration from academics engaged in modeling the “broken heart” effect (calculating the odds of a person dying once their significant others have passed away, an important concept in actuarial science). Believing that “default is like the death of a company, so we should model this the same way we model human life,” Li saw it only fit to apply the mathematics of death correlation to the tackling of default correlation. That is, the quantitative device that aided and abetted the lethal trading in toxic mortgage stuff first made its entry into the markets because someone saw nothing wrong with equating financial activity with the workings of the human body. That’s as odd as concluding upon seeing stock prices go up and down that the science behind elevator-building should be used to forecast the S&P 500.

Lecturing to Birds, Pablo TrianaAs would be plain to a 10-year old, just because companies, like people, can “die,” that doesn’t imply that, barring the complete loss of our common sense, we can analyze debt defaults as the loss of a human life. No wonder the Gaussian Copula suffered an unmitigated defeat out there in the heartless markets.

Unfortunately, David Li’s is not the only instance of wildly inappropriate analogies when it comes to financial modeling. Mathematicians and theoreticians appear incapable of not attempting to equate market activity to all sorts of odd, insultingly unrelated fields. For decades we’ve heard financial economists and assorted scientists tell us that market pros are like molecules, and that if you know physics then you’ve got the markets mapped. The ignored ramblings of hopeless cranks? Far from it. Models borrowing from exactly such oddness have been furiously applauded, embraced and granted the Nobel. Meanwhile, markets and real traders kept busy trotting along in a notoriously non-molecular fashion, naturally.

These days, “biological finance” appears to be the new “in” phrase. Bank portfolios should be modeled on savannahs (apparently tropical rainforests are to be avoided at all costs). Regulators should heed the dictums of marine experts. In epidemiologists apparently lies the solution to “too-big-tofail.” Mathematical biologists, mirroring the now-prevalent physicists, are reportedly trying to jump into the financial bandwagon, attempting to succeed where so many other brainiacs fell by the wayside before. Upon contemplating such process, the rest of us should worry.

Bad things have afflicted the world following the adoption of the creations of those bent on treating finance as something else. The crash of October 1987 was caused by the use of a theory that espouses that stock prices behave like dust particles. The recent mayhem owes a lot of its misery not just to mathematically confusing corporate bankruptcy with human mortality, but also to assuming market activity to be a realm of chaos-devoid calmness. We should aim to prevent the next big troubles from emerging via the adoption of a formula that depicts hedge fund managers as pollinating bees.

A big reason why we know that the odd mathematical homologies are unsound is that the process would certainly not work backward. Would a financier (even if quantitatively skillful) be able to accurately map the physical terrain, based solely on his market career? Be able to model death? Be able to model the survival rate of an ecosystem? Of course not. For the simple reason that financial practice has little to do with the science of physics, mortality or biology. Just like a career trader would not be considered an authority on fisheries management or atomic studies, should non-financiers bearing irremediably weird theorems be given credence in Financeland?

Pablo Triana ( is the author of “Lecturing Birds on Flying: Can Mathematical Theories Destroy The Financial Markets?”


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