How the Gaussian copula got adopted

By Felix Salmon
April 27, 2009

In December 2008, Sam Jones of the FT was kind enough to mention the Gaussian copula function to me. That mention eventually became my Wired magazine cover story, and I always felt a little bit guilty about my story coming out first, since I knew that Sam was working on one too.

Well, Sam’s feature on the copula has now appeared, and it takes a rather different tack than mine; in any case, it’s a great read, so do check it out. Here’s one thing I learned from reading it:

On August 10 2004, the rating agency Moody’s incorporated Li’s Gaussian copula default function formula into its rating methodology for collateralised debt obligations, the structured finance instruments that subsequently proved the nemesis of so many banks. Previously, Moody’s had insisted that CDOs meet a diversity score – that is, that each should contain different types of assets, such as commercial mortgages, student loans and credit card debts, as well as the popular subprime debt. This was standard investing good practice, where the best way to guard against risk is to avoid putting all your eggs in one basket. But Li’s formula meant Moody’s now had a model that enabled it to gauge the interrelatedness of risks – and that traditional good practice could be thrown out of the window, since risk could be measured with mathematical certainty. No need to spread your eggs across baskets if you knew the exact odds of your one basket being dropped. A week after Moody’s, the world’s other large rating agency, Standard & Poor’s, changed its methodology, too.

They’re like Sotheby’s and Christie’s, those two. I’m not sure that “criminal” isn’t too strong a word for the way in which they offer no real alternative to each other, instead chosing to ape whatever the other one does.


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In many ways, we have been all gaussied up.

The article is largely a reprise of WSJ frontpage 12Sep05 “How a Formula Ignited Market That Burned Some Big Investors” by Mark Whitehouse (wrt May05 hiccough in synth CDOs driven by GM/Ford downgrades).

And if they had not adopted a “model that enabled it to gauge the interrelatedness of risks” and it had turned out, as it undoubtedly would have done, that risks which they believed were uncorrelated were not in fact so, you would now be smugly berating them for _that_, instead.

Posted by Ian Kemmish | Report as abusive

Per the previous comment, the Gaussian copula and its inherent risks were outlined in the WSJ in late 2005. Here’s the link: ehouseSlicesofRisk.txt

In the article, Mr. Li, the inventor of the algorithm, acknowledges that his formula was being misused by Wall Street. It just goes to show that there were loud and clear warning signs in the major media about the risks piling up in the financial system. Here are some more thoughts about the media’s role in the crisis: ml

Let me get this straight. You got the idea for your copula story from Sam Jones. You knew he was writing a story on copulas. You scoop him. Why do I not see any reference to Sam Jones in your article?

Is that the level of integrity Reuters has come to?

Speaking of integrity, were you aware of Whitehouse’s 2005 WSJ article? With any kind of diligence, I can’t imagine how you couldn’t have been.

Yes, Congress needs to stop chartering agencies with so much power for destruction.

As a former rating agency analyst in RMBS, I was shocked when I read about the use of the Gaussian cupola was being used at the rating agencies. I didn’t care if Street firms used it for trading or structuring deals, but rating agencies are supposed to be concerned about stressed environments. That was hard enough in mortgage land where we were lucky to be able to look into Houston in the 80′s and LA in the 90′s. Analyze those markets and multiply the bejesus out of them in case they happened across the US.

But evaluating credit correlation across market segments during one of the biggest booms in US history? It was gross negligence. Any experienced statistical analyst knows to consider whether there could be a difference between their sample data and the conditions their models will be asked to perform under. Forget about fat tails. The entire premise of the correlations was not appropriate for risk modeling.

Posted by Wisconsin Bison | Report as abusive

The cupola idea was not new, for the outraged “plagirism” poster. It had been discussed in “The Black Swan”.

The reason all players adopted the cupola is easy, when you have been in business long enough to understand the psychology of the “high flyers”. It gave them an excuse th say that things now fell “up” instead of “down”, and thus make more money, RIGHT NOW, for themselves.

Oh, they knew that there were issues, since one mathemetician after another told them so, but “THEY” were making money.

They figured that they’s have enough in the bank to weather the storm, even if the shite hit the fan. They are probably right. They are certainly right if someone doesn’t ban the key malefactors from future activity in the financial system.

Don’t hold your breath. Expect another bubble within 10 years.

Posted by Tim Connor | Report as abusive

Hi Felix,

I don’t know how significant coming across your article is, but during my Long island confinement in 2006, walking on the beach I got this brilliant idea, which I thought and by the way mentioned it to one of the staff members that I should be getting a Nobel for this, which I named as, THE THEORY OF ASSET AND PRODUCT PROBABILITY VALUATION.

In brief-
While my understanding is that as opposed to Li\’s probability constant is actually a variable quotient leading to a quanta factor of asset and production valuation in close end and open end economic cycles.
A factor which takes in to all quantifiable variables in to account to give a value (+ and -) in a non speculative environment.

In reflection of present ongoing economic crisis, which I had been able to fallow and predict since 2004, after six months of my arrival to US from India( housing and real estate bust)the potential for an economic crisis.
Here is the copy of my correspondence with G20 summit.
From: G20uk
To: indra karan ; G20uk
Sent: Thursday, April 23, 2009 10:34:54 AM

Dear Mr. Karan,

Thank you for your email expressing your views.

G20 Secretariat.

—–Original Message—–
From: indra karan []
Sent: 03 April 2009 20:51

HM Treasury.
Your Excellency,

The solution to the present world economic crisis lies in a The New Global Economic Initiative-A fixed margin, self sustainable open end economic, industrial investment derivatives is the most viable solution as opposed to the stagnant self destructive, speculative multi level financial instruments with a redundant unregulated real estate economies, mostly born out of primitive quasi industrial business model is what has become the plague of not only the west but also that of many industrial nations, who have modeled their economies based on out of the line consumerist capitalism.

The only way out and solution this predicament which will onset industrial lethargy and the glut of unwanted consumer products from china would haunt the developed nations for a long time, Claiming one victim after another leading to a devastating dynamics of asymmetrical worldwide crisis and a potential showdown of aggression and protectionist wars, which are most likely beyond the abilities of money managers, political leaders, administrators, business economists and even Army Generals alike in a global scenario.

The crisis also has a potential for shift in economies that have far more fundamentalist, anti industrial underdeveloped social and consumer structures, making it further more difficult in facing the challenges in a divided world, also causing a shift in emphasis on to societies that have more religious and fundamentalist agendas affecting liberal( secular) , democratic and open societies in an unconventional mode that might pose far more greater threat and a potential third world war in search of markets for the present industrial nations.
The beginnings and apparent failure to tackle such crisis by the West and by it European allies is all ready showing its weariness and human and economic toll and human rights crisis in addition the failure of turning around the nations and economies like Iraq and Afghanistan to more democratic and liberal dynamics in to an integrative world socio- political and economic order , including the ongoing Israel and Palestine conflict along with many other middle eastern nations which are proving to be far more problematic beyond the military and diplomatic powers of the developed nations as envisaged, leading to a crisis and conflict of civilizations snowballing in to a imminent world crisis.

The continuation of the redundant economic and industrial policies and globalization has all ready made it very clear that the world economies are in crisis and the present industrial economies with their out of the place economic measures are leading to a self destructive mechanism evidently showing \’the capitalistic economic model\’ in poor light in addition to triggering unscientific and superstitious protectionist measures, where the remaining potential of the economies and forex is consumed in toxic assets and production of further industrial consumerist products which would glut world markets with no potential or need for such.

In a classic case of double jeopardy, which in addition to leading consumer industrialist nations like china and other developed Asian economies for want of their depleting growth and market would doubly add to the ongoing crisis with no solution in the offing and also forcing the continuation of the false and speculative consumerist economies to the extent of backlash and deepening of crisis in the growing disparities of living standards within the economies of developed nations, forcing the world marooned in a distress and gloom, leading to primitive protectionism and social unrest.

Most of the recent economic measures by the leading world economies and the resolution of the ongoing G-20 summit are just a reflection and false symptoms of the deep economic crisis but not the solution of the disease the plagues the world industrial economies and most likely destroy underdeveloped nations.

In addition to Consumerist industrial economies like China and other Asian nations with their economic growth on the decline , with vast reserves of unwanted consumer products and lacking in market for the goods, further adding to a crisis beyond the control of world nations needs some extra ordinary radical measures , where political will and vision, measures free of protectionism and corruption are much needed to begin with, in addition to a most probable and viable realistic approach to revitalizing the world economies, which is not about stimulus and increased spending and strengthening of market forces but, but a new world economic and industrial initiative.

A global investment model with potential to sustain 500 million population over the next 10 years, consisting of modulated economic derivatives that are non speculative, self regulative, needing less intervention, fixed cap profit-open ended, environmental global networks with a support of knowledge and research base and the collectives of multi ethnic, multinational, secular, open society participatory, self supportive healthy societies, that are highly productive and self sustaining is most likely the most viable future economic model based on a functional , scientific , futuristic theory-


A theory which give us a realistic understanding of these modulated economies in a live environment and a proper framework for planning and evolving productive future economies with a scientific and non speculative, verifiable open solutions.

In addition to a scientifically accurate probability value of each initiative planned and the dynamics its functioning in a synchronized networked environment in real time environment, where the supply and demand are optimized in addition to the understanding and planning of definitive life cycles of each industrial derivatives( module) and products.

(The detailed explanation and understanding of this economic theory and scientific frame work can be made available up on further correspondence and in consultation of economic experts from around the world, before a working model is proposed for consideration).

Thanking you,
With warm regards,

Raja Indra karan.