# Did math formula cause financial crisis?

### 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.

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