The dangerous Gaussian copula function

By Felix Salmon
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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Couldn’t we just boil the implosion of Wall Street down to “overleveraged”? So much easier to understand and pleasantly simple. Even I can understand it.

Posted by Chris08 | Report as abusive

“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.”
it’s not the /modelformula, it’s the people.

Posted by alea | Report as abusive

Yup, I think the point is that it’s not this particular model or any model that “killed” Wall Street. If they hadn’t come up with this one, they would have found another way to juice profits by ignoring and offloading risk. One needs to focus on much larger issues, including the way banks are organized, incentives, regulations, the financialization of our economy, etc. etc. Things you regularly discuss.

This is not to say that it’s not interesting and important to know that particular mechanics by which this latest crash happened, and that research is not therefore valuable. It is rather to say that focusing on the model as the source of Wall Street’s problems — what “killed” it — is too small an answer. Getting rid of that model will not solve the essential societal risk that Wall Street poses to the rest of us. They will find another way to bring down the economy while making themselves rich. The real solution has to come from elsewhere.

Posted by f.fursty | Report as abusive

@Fursty – about this -

“The real solution has to come from elsewhere.”

When you think it all through from every angle, is it possible to realistically conclude that “elsewhere” could be any place that doesn’t involve the barrel of a gun?

Posted by MrRFox | Report as abusive

The problem isn’t that anyone really believed the numbers. The problem is that Wall Street as an institution craves numbers, and if the numbers are unreliable but better numbers aren’t available, they’ll use what they can get. Then the incentive is to maximize whatever costs the numbers don’t measure. This time it was risk, the next time it’ll be something else.

Posted by JayCM | Report as abusive

In other words, most of the people who “modeled” their way to million-dollar bonuses were just as clueless as the people who bought the crap Wall Street was peddling.

Posted by Mitchn | Report as abusive

“She’s a model and she’s looking good.”

Hey, Felix: can anyone actually “touch a CDO?”

Posted by Eericsonjr | Report as abusive

Agree, @fursty — Wall Street was the drunk driver that survived the crash, the economy (the ‘rest of us’) was the victim.

Does anyone in the BACK of the limo ever get hurt?

Posted by EPB | Report as abusive

IIRC, from the prehistory of your various blogs, the guys who marketed the ABN Amro CPDO (and who for a while convinced you that it wasn’t a suicidal product) certainly did appear to believe that their modelling approach showed it couldn’t fail. ( 459977.shtml , blast from the past)

Posted by dsquared | Report as abusive

I think the conclusion of MacKenzie is basically sound:

“The way in which [...] a class of model that was widely disliked, nevertheless helped achieve economically crucial outcomes [...] shows that cultural resources can co-ordinate action even in the presence of widespread scepticism as to their worth.”

Posted by Th.M | Report as abusive

Yes, Gaussian copulas didn’t help. But the main problem is with the CDO model itself. It uses ratings, not empirical data, to forecast total expected pool losses. If the credit is essentially static, fine. If its payment certainty is likely to deteriorate, there is a financial incentive to refinance before the market discovers there’s a problem. Hence the disastrous results of 2003 CBOs and with RMBS CDOs.

The FCIC picked up on this point. Dr. MacKenzie didn’t seem to get it even after he spent half a day with us.

Posted by ARutledge | Report as abusive

I think this an exceptionally informative, helpful comment thread. For better or worse I have elsewhere represented the following as a fair summary of the relationship of the GCF to valuation of derivatives, as they – and it – contributed to mortgage fraud and the run up and crash in housing prices. Am I wrong?

What caused the Great Recession in 2008? A crash in the money supply, which the Greenspan Fed had allowed to grow based on debt derivatives. When the values of those derivatives crashed, the money supply went too. Why had credit derivatives become so important in financial institutions operations? Because they allowed the institutions to escape effective regulation and evaluation of their investment instruments and behavior, and they were very, very, important to the booking of immediate profit on which the bonuses allocated to traders were based.

How did mortgages become involved in this cycle? Mortgages were the most readily available, least regulated, financial instrument which could be used in the creation of credit derivatives. As the demand for credit derivatives grew, the demand for mortgages grew. Traders needed the derivatives to show “profits”, their institutions needed mortgages to create derivatives, mortgage bankers needed borrowers to sell mortgages, borrowers needed housing values inflated by (essentially) fraudulent appraisals to justify the credit they were obtaining.

At the root, the entire cycle depended on the ability of institutions to create, and traders to sell, financial instruments which were rated very highly by – it is now clear – incompetent and complicit credit rating agencies. Much of the valuation and rating of these instruments was supported by mathematical modelling tools which were always suspect, and have now been shown to be dangerous.

Posted by JimPivonka | Report as abusive