The dangerous Gaussian copula function

June 21, 2012
tattooed across his arm, or Donald MacKenzie titling his latest paper after my Wired story on that function.

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I’m not sure which is more flattering: someone getting the Gaussian copula function tattooed across his arm, or Donald MacKenzie titling his latest paper after my Wired story on that function.

MacKenzie is a very smart sociologist, who understands quants and copula functions much more deeply than I ever did. (And, like most journalists, I forgot nearly all of what I ever knew about them within weeks of writing the article.) His paper is largely sociological, and I wouldn’t recommend reading it if you don’t like running across phrases like “the beginnings of a typology of mechanisms of counterperformativity”. But the good news is that if you want an English-language translation, Lisa Pollack has done an amazing job of extracting the interesting bits, and there’s no reason for me to try to replicate what she’s already done so well.

Here’s how Lisa sums it up:

The quant community also didn’t, and doesn’t, rate the Gaussian copula model highly at all. In fact, we’re putting that very mildly if the statements from quants interviewed by the researchers are anything to go by.

Furthermore, this was a view held by many before the financial crisis hit. But even in the face of this rejection, the model has stayed in use through multiple crises and is still in use.

I’m going to push back here a little bit. For one thing, although the “many” is implied, it’s never quite stated. Yes, MacKenzie interviewed 29 people before the crisis, including 24 quants. But all the interviews took place after the “correlation crisis” of 2005, when the weaknesses of the Gaussian copula function first became obvious. And in fact MacKenzie cites only one pre-crisis interview with a quant who was very skeptical of the function — and that was with “a quant who had contributed importantly to its technical development”.

My reaction to this is that of course anybody who contributed to the technical development of the Gaussian copula function was highly aware of its weaknesses. In fact, that was a theme running through my article, as summed up in the quote with which I ended it, from David Li, the inventor of the function. “The most dangerous part,” he said, “is when people believe everything coming out of it”.

What I suspect, here, but don’t know for sure because MacKenzie doesn’t really describe his interviewees, is that the people he talked to for this paper tended to be the most senior, worldly, introspective, and successful quants — not to mention the ones who spoke good English. Every bank has graybeards who love to talk about how tools like Gaussian copula functions or value-at-risk are massively inadequate. Those graybeards get a lot of lip-service. But in practice, both senior management and the traders in the trenches end up using the quick-and-dirty measures because they don’t have the time or the sophistication to do anything else.

MacKenzie doesn’t buy the idea of “F9 monkeys” — people who just input a security, press F9, and out pops a price. But he seems much more interested in making a broader sociological point:

In our research experience, the ‘model dope’ exists, but not as an actual person: rather (in the form of, e.g., ‘sheet monkey’ or ‘F9 model monkey’) it is a rhetorical device that actors deploy. It is a way of describing someone as different from oneself: a way of ‘othering’ them. There is no clear evidence in our research of model-dope behaviour or beliefs. (For example, none of the 29 interviews we conducted prior to the crisis contains anything approaching an unequivocal endorsement of Gaussian copula models.) Any satisfactory notion of ‘culture’, it seems to us, must treat the cultural dope and its local equivalents such as ‘sheet monkey’ as forms of othering, not adequate conceptualizations of the actor. Nor are ‘cultures’ equivalent to sets of meanings, symbols and values: they encompass practices, including the most material of practices. Ultimately, culture should be treated as a verb, not a noun (it is unfortunate that use of the verb is currently restricted to its biological sense): people do cultures, rather than culture existing as a thing causing them to act as they do.

I’ll leave the discussions of verbing culture and “othering” to MacKenzie, but I do still believe that on a day-to-day basis, banks were full of people who were happy to just accept whatever the model spit out — especially, as MacKenzie demonstrates, if doing so did wonders for their end-of-year bonus. And while MacKenzie draws distinctions between banks and investors, and between credit-based and asset-backed securitizations, even he admits that there were people managing enormous CDOs who didn’t even know what a correlation model was, let alone have a deeply skeptical attitude towards it.

The fact is, as MacKenzie demonstrates, that there were enormous numbers of people whose bonuses depended on believing that the numbers thrown out by the Gaussian copula function were accurate:

In the early years of the credit derivatives market it was not unusual for traders to sell a deal ‘at par’ – 100 cents in the dollar – when their ‘bank[‘s] system would have told them that this was worth about 70 cents’. A single trade ‘would make [$]20 million of P&L.’)

While it’s possible, in that context, for a determined researcher in an in-depth interview to elicit doubts about the utility of the function from relatively senior people, it’s really not possible for those doubts to get acted on, or even to really exist in the bank itself, as opposed to in discussions down the pub after work.

MacKenzie doesn’t like the way my article simplified the sociology of Wall Street:

The seventh section then returns to the question posed by Salmon’s article, enquiring into the extent to which the Gaussian copula family of models ‘killed Wall Street’. An adequate answer, we posit, demands both a differentiated understanding of that family of models and also, more importantly, a grasp of the fact that a model never has effects ‘in itself’ but only via the material cultures and organizational processes in which it is embedded.

I genuinely have no idea what a “material culture” might be; I’ll leave that kind of thing to MacKenzie. And I’ll admit that the “Wall Street” of my title was a broad church, including not only investment banks but basically anybody who might ever touch a CDO. If MacKenzie wants to make the case that Gaussian credulity was found much more on the buy side and at the credit rating agencies than at the sell side, I’ll happily give him that.

But the fact is that the Gaussian copula function was invidious, and did cause enormous losses all over the world. The way I like to think about it is that value-at-risk allowed banks to ignore tail risk, and the Gaussian copula function did a magnificent job in maximizing that tail risk. The two together were lethal. And while there are surely many other models which inhabit Wall Street in much the same way, I sincerely hope that none of them are remotely as dangerous as the Gaussian copula function turned out to be.


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