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Did math formula cause financial crisis?

Felix Salmon, blogger for Portfolio.com

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The Gaussian Copula Function, created by David X. Li, prices collateral debt obligations.

TEXT OF INTERVIEW

KAI RYSSDAL: With Wall Street down to somewhere near half of where it was 18 months ago, there is an understandable temptation to try and figure out why. Inevitably that's a complicated question. And the answer's pretty complicated too.

The cover story in this month's Wired magazine suggests one possibility. A guy named David Li and a formula he came up with to help Wall Street figure out how risky one set of bonds might be as compared with another -- and what happens when those bonds default.

Felix Salmon wrote that article. He also sometimes helps us wrap up the week on Friday afternoons as well. Felix, good to talk to you.

FELIX SALMON: Good to talk to you, Kai.

RYSSDAL: This guy, David Li, what was he trying to do?

SALMON: What David Li was trying to do was look at lots of different bonds and try and work out whether they were all moving in the same direction or not. Whether they were correlated or not. Whether they were independent of each other or not. And he created this astonishing piece of mathematics called the Gaussian copula function, which sought to answer that very question.

RYSSDAL: What does that mean -- Gaussian copula? I mean, if I can just take a little sidebar here for a second.

SALMON: People get very scared when they hear the word Gaussian. But this is just one way of looking to see whether one set of probabilities is associated with another set of probabilities. The really key part of the Gaussian copula function is the copula bit. It's what's known as a multivariant copula. You can take lots of different bonds or stocks or any kind of securities you like, and you can throw them all into one big equation and out the end get a single number which is easily manipulable and trackable as they say in the world of quantitative finance.

RYSSDAL: It comes across in the article that this formula is a little bit like the Grand Unified Field Theory of financial economics. Once this guy figures out correlation between when bonds default and when they don't, well then Wall Street says, "Holy cow. We found it. We just have to look at this one simple thing and now we can trade a million different securities.

SALMON: Exactly. You can throw this formula at so many different problems and get this very elegant, simple number out the other end. And it made it far too easy for people to be able to just say, "Hey, we've solved this problem, and let's go away and start trading lots of money." And, eventually, what happens is that in their desire for things to trade, they end up buying huge amounts of debt, which they really shouldn't have been buying.

RYSSDAL: And they were buying it because this formula said: Well, this correlates to that, and everything should be fine.

SALMON: The slogan has it that in a crisis all correlations go to one -- it's something which no one really thought about during the good years.

RYSSDAL: That is to say, all those correlations going to one means everything moves together. And even bad things can move together.

SALMON: Especially, bad things move together. So, if you have one mortgage defaulting, then suddenly you have 100 mortgages defaulting. And even though you could cope quite happily with one or two mortgages defaulting, what you can't cope with is mortgages across the state and across the country all defaulting at the same time.

RYSSDAL: Alright, but let me ask you this, then, Felix. Here's this guy. He's a statistics PhD. He comes up with this formula. He thinks it works. Turns out, in reality, it has a fatal flaw. But is the fault his, or is the fault with the application that Wall Street did with it?

SALMON: The fault is really with Wall Street. The way you get bubbles on Wall Street is when everyone does the same thing at the same time. If no one used the formula, then it would have had no damage. If only a few people had used it, then they would have lost money. But the whole system would have been OK. The problem was the whole system started using the formula.

RYSSDAL: Obviously it's not David Li's fault that Wall Street took his formula and did all this crazy stuff with it. But do you get a sense at all that he wishes maybe he hadn't come up with it?

SALMON: I think he's built a really rather successful career on the back of this formula. And given that most people who know about it don't blame him personally for the meltdown of the global financial system, I think he's probably done all right for himself.

RYSSDAL: Felix Salmon blogs at Portfolio.com. He's writing on paper this month -- the cover story on Wired magazine, about the Gaussian copula formula. Felix, thanks a lot.

SALMON: A pleasure.

Sitthikone Assourin's picture
Sitthikone Assourin - Jan 20, 2011

He didn't invent the game though... so...

Eduardo León's picture
Eduardo León - Sep 15, 2009

The problem doesn't require any moral explanation (greed?). It reduces to blindly using a formula without having a deep understanding of what it means and what its limitations are.

As any statistician knows (and even some non-statisticians, like me), the normal distribution assumption works better when you're in the middle of the distribution, not in the tails. Either you have a good model predicting what happens in those extremely rare but possible disasters (an extremely difficult task, which serves no practical purpose unless you have a lot of information), or you take decisions that are disaster-proof (to a level of confidence, of course).

Everybody used this guy Li's formula as if it were the solution to everything and, when the assumptions of his model no longer worked, the whole system was brought down.

richard blythe's picture
richard blythe - Mar 24, 2009

Mathematics with the purpose of making Accounting Inscrutable.

blonde accountant's picture
blonde accountant - Mar 6, 2009

Garbage in, garbage out. You can't blame Li for inventing the thing, I mean, look at the atom bomb. It's how it's used. Still, Li must feel guilty, cuz he's not talkin. Of course, when he told them it didn't do everything, they didn't listen.

Bankers price risk and built the world. The problem is this generation of bankers need to get richer quicker and easy fixes do the trick. Until they make up their minds to go clean and get off the greed drug, suffer through the withdrawal, it's not goin to get any better for any of us goin thru it with em. Since they've always been on the greed drug--it's their generational thing--it's not going to get any better. We just gotta wait til they die off and the next one comes to power. Except we'll be done it by then. Geez I'm sorry I had kids.

Carl W's picture
Carl W - Mar 3, 2009

Ferrari can build you a race car, but you better send an ambulance if you put someone with much less skills than Michael Schumacher to drive it!

Jim Hayes's picture
Jim Hayes - Mar 2, 2009

There is an old adage that "statistics don't lie, but statisticians do." Don't you think this applies here?
Why don't we start looking where the money went - into the pockets of those writing bad mortgages, packaging bad mortgages and selling them as "securities" (what a dumb name!) and taking home big bonuses.
Why don't we look into UBS's 52,000 customers with Swiss bank accounts for some payback? Ask Phil Gramm, he knows about them!

anonymous coward's picture
anonymous coward - Feb 28, 2009

yes, well, i believe mr li is a convenient scapegoat here. the rating agencies were corrupt and full of people of low moral character.

what im trying to say here is that greed is bad. greed is not what built this nation. people who want to go out, take, kill, conquer, and exploit, they do not create anything, but only destroy.

without a moral backbone or some kind of moral philosophy underlying your actions, we backslide into barbarity and animalism... and no technology, formula, gizmo or gadget will save us from that fate.

david hill's picture
david hill - Feb 25, 2009

Both the solutions and the reasons why we are in this fine mess is because we do not go any further than the perceived wisdom that got us all into these disastrous affairs. In this respect we try to fix the problem by going back every time to the very people who actually got us into this whole debacle in the first place. Even Einstein said in as many words that we couldn’t solve our problems by the very means that caused our dilemma. Therefore why is it that the Media are not brought into the blame game as well as they are still even today, after all has been laid bare, pandering completely to the ill-informed wisdom of those who were and still are the culprits of this whole financial and economic disaster.

This thinking of going back to those every time who have brought the world to its knees (which will happen over the next two years I am sure) is complete madness. Indeed, what is really required is new innovative thinking and outside the 'box'. In this respect, it is a well documented situation in the history of science and technology that main stream thinking was never the reason why major technological breakthroughs happened. In this respect it has been estimated that 75% of all the inventions that have made the modern world what is it is today emanated outside advanced thinkers and from the minds of independent inventors. The TV (Baird, an amateur radio ham), Jet Engine Whittle an RAF officer), the chip (KIlby had a personal private interest not ordered by the company to invent the chip as they were totally involved with tube/valve making - now the basis and driving a $1.5 trillion global annual industry), the car (Daimler a mechanic), the airplane (Wright Bros. who were mechanics), email(Tomlinson invented it for himself not the company) , WWW(Tim Berners-Lee's thinking not CERNs'), etc, etc are examples of a non-ending list.

Therefore the media has to start being innovative and not be just stuck in the mud with the old guard that has got us all into this 'mother' of all messes.
The sooner they grasp this and let independent thinkers put their views across the sooner we shall solve the present situation. Is the media listening, I wonder? Probably not and where they will perpetuate the whole situation by not doing so.

Therefore the villains in this whole affair are,
1. Politicians
2. The Bankers
3. The Media

and in that order, and why, the G20 Summit in April 09 will fail also.