Monday, August 25, 2008

How the Gnome of Zurich Got It Wrong

Last week I was at a conference in Zurich, Switzerland, site of the HQs of all those Swiss banks. At Einstein's alma mater, the Swiss Federal University of Technology (ETH) there is a mathematics professor named Paul Embrechts whom I like to think of as being the actual Gnome of Zurich. About a decade ago he succeeded in convincing the leading Swiss banks to use the mathematical entity known as a copula as the basis for measuring risk. They did so, and from them it spread to become the most widely used method in the financial world, displacing the Black-Scholes formula, although one is hard pressed to find a definition of it in any financial economics textbooks. I will say that it is based on a stationary distribution that attempts to take into account more fully covariances among events. It also has the advantage of actually admitting that there are lots more extreme events than does the Gaussian normal that underlies Black-Scholes, which after the 1987 crash most of the practitioners knew was garbage. So, it admits the stylized fact that all asset markets exhibit "fat tails" or kurtosis, those more frequent extreme events.

However, it turns out that the copulas have not proved sufficient to deal with the events of the last year, with most funds and banks and whatnot still getting into trouble. One of the conference participants was an econophysicist colleague of Embrechts, Didier Sornette, who runs an "Observatory of Financial Crises." While he has made some not so accurate public forecasts himself (see my "Econophysics and Economic Complexity," available at, Sornette described the problem with the copulas: they do not take into account how herding can happen. So, they can give the right probability that a 10% decline in a market can happen in one day, but will understate the probability that this might happen for three days in a row. This would suggest that Nassim Taleb with his black swans might be right, although anybody trying to follow his "barbell strategy" to make money on really big crashes would probably have lost money over most of the last several years, despite the big crashes that have been going on over the past year.


Myrtle Blackwood said...

I don't understand why so much intellectual effort goes into such formulas and so little on the nature and definition of value in our world. (I know, I know. Just repeating myself!)

"Not all that is very useful commands high value (water, for
example) and not everything that has a high value is very useful (such as a diamond).
This example expresses not one but two major learning challenges that society faces today. Firstly, we are still learning the “nature of value”, as we broaden our concept
of “capital” to encompass human capital, social capital and natural capital. By recognizing and by seeking to grow or conserve these other “capitals” we are working our way towards sustainability. Secondly, we are still struggling to find the “value of nature”....

The Economics of Ecosystems and Biodiversity

Environmental damage and species loss costs between $A2.2 trillion and $A5 trillion every year.

Throw in a dog-eat-dog neoliberal game where western corporations practice imperialism on a scale never seen before. Well, it's not so surprising that the casino stock market will eventually reveal the tale.

reason said...

Your quote just adds to the confusion. The confusion is between value and price and it uses high value where it means high price.

Surely there is some part of value that is intrinsic, but price is situational.

Anonymous said...

How about someone who had put options on Freddie and Fannie...? said...


There is an old wisecrack that economists know the price of everything and the value of nothing. Of course, conventional theoretical economists do not usually see any distinction between the two.


I have not followe the market closely enough to say. So much of this is a matter of timing and the degree to which one is doing naked puts or complicating things with further finagles. I would guess that there were some time periods recently when one could have made good money on the bet you pose.

BTW, I note that the copula that spread througout the financial world, especially for use in collaterized debt obligations, was of the simplest sort, the Gaussian binomial. There are broad families of copulas that link distributions together, this being the key, the nature of the dependency between distributions that are mixed. Just too simple, for all the secrecy surrounding the nature of these beasts as they have been used by specific firms.

reason said...

Surely the difference between price and value is consumer surplus? (And I always heard it was traders who know the price of everything and the value of nothing.) said...


I think the standard textbooks would call that "net welfare." However, one could certainly argue that the full integral under a demand curve is the "value," which to get the "net value" or "net welfare" one must subtract off what was paid, that is, the price.

Much of this is indeed definitional, and again, in standard current economics, the terms "price" and "value" are often simply viewed as one and the same thing, although sometimes "value" is thought of as being the competitive equilibrium price. Hence, referring to the thread on Cartan, the title of Gerard Debreu's magnum tome on general equilibrium theory is _Theory of Value_. Of course for Marxists, value is the socially necessary amount of labor time it takes to produce something, and this can certainly deviate from price, either equilibrium or otherwise.

Anonymous said...

I don't see how that makes Paul Embrechts a "gnome" or why you would go to personal attack. You could simply state what you think is wrong about copula application in finance and maybe propose something better?! Also, unlike the typical suspects, Prof. Embrechts actually is rather cautious about the application of the theory if you read his books or listen to his lectures.