The Quant who Killed your IRA: David X. Li and the Guassian Copula Function: The Risk Management Model that Imploded

When the economy started to collapse, one of the first things I wondered was how it could happen so fast, in so many sectors. I was baffled that so many bright math & finance minds did not seem to have the tools to communicate the depths of the problem in a way that decision-makers could understand.

At that point in time, pre- Bernie Madoff, I still had some faith in our system, but still, I wondered how so many math "geniuses" could be asleep at the wheel, all at the same time! I came across an article by Saul Hansell in the New York Times in September 2008 that explained things just enough to open my eyes to the reality of the situation: "How Wall Street Lied to Its Computers: So where were the quants?"

Well, that was five months ago.The economy continues to plummet, gasping for breath from time-to-time. The article below does a good job of explaining some of the more confusing sets of events:

Recipe for Disaster: The Formula That Killed Wall Street Felix Salmon, Wired Magazine, 02/23/09

"Here's what killed your 401(k) David X. Li's Gaussian copula function as first published in 2000. Investors exploited it as a quick—and fatally flawed—way to assess risk. A shorter version appears on this month's cover of Wired."

Probability Specifically, this is a joint default probability—the likelihood that any two members of the pool (A and B) will both default. It's what investors are looking for, and the rest of the formula provides the answer.	Survival times The amount of time between now and when A and B can be expected to default. Li took the idea from a concept in actuarial science that charts what happens to someone's life expectancy when their spouse dies.	Equality A dangerously precise concept, since it leaves no room for error. Clean equations help both quants and their managers forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness.
Copula This couples (hence the Latinate term copula) the individual probabilities associated with A and B to come up with a single number. Errors here massively increase the risk of the whole equation blowing up.	Distribution functions The probabilities of how long A and B are likely to survive. Since these are not certainties, they can be dangerous: Small miscalculations may leave you facing much more risk than the formula indicates.	Gamma The all-powerful correlation parameter, which reduces correlation to a single constant—something that should be highly improbable, if not impossible. This is the magic number that made Li's copula function irresistible.

More from the Wired article:

"Li's copula function was used to price hundreds of billions of dollars' worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared."

Related:

"Responding to FAQ: What is Tranching?" Mark Chu-Carroll, Bad Math, Good Math blog, 9/19/2007

"In many cases, the investors have no clue how many levels of re-bundling are going on to create their top-tranch low-risk bond. And you've got all sorts of people who thought they were buying conservative investments who are now stuck with their money invested in bundles of low-tranch shit loans."

Conde Nast's Interactive Graphic: What's a CDO? 5/5/07

The Rise of the Machines & another look at the role of "quants" in the current financial downturn.

I came across an article on-line from the New York Times, written by Op-Ed Contributor Richard Dooling, "The Rise of the Machines",

Dooling mentions at the beginning of the article that Warren Buffett called derivatives "weapons of mass destruction". I guess time will tell. The article was published on October 11, 2008. Nearly two months later, things continue to combust.

"Somehow the genius quants — the best and brightest geeks Wall Street firms could buy — fed $1 trillion in subprime mortgage debt into their supercomputers, added some derivatives, massaged the arrangements with computer algorithms and — poof! — created $62 trillion in imaginary wealth. It’s not much of a stretch to imagine that all of that imaginary wealth is locked up somewhere inside the computers, and that we humans, led by the silverback males of the financial world, Ben Bernanke and Henry Paulson, are frantically beseeching the monolith for answers. Or maybe we are lost in space, with Dave the astronaut pleading, “Open the bank vault doors, Hal." '

Richard Dooling is the author of "Rapture of the Geeks: When AI Outsmarts IQ"

I've assembled a few related articles that focus on the role of the quant and some additional information that might assist in our understanding of what has been unfolding during the current economic recession:


Quants Gone Wild - The Subprime Crisis (3/27/08; A.W. Bodine and C.J. Nagel)
"The “best & brightest” quantitative analysts on Wall Street became so technologically advanced that many of the principals running investment firms simply didn’t understand the arcane risk models their “quants” developed – and sadly neither did the quants. We recall the comment made during a recent presentation at Concordia College by Don Gogel, President and CEO of Clayton, Dubilier and Rice. He noted that this “toxic cocktail” was something that even the “mixologists themselves didn’t understand” let alone those trading in them. Bryant Urstadt writing in MIT’s Technology Review in December 2007 also notes, “The more quants learn, the farther away a unified theory of finance seems. Human behavior, as manifest in financial markets, simply resists quantification, at least for now.” We should here also do homage to the investing approach of the sage Warren Buffet—that he does not invest in anything he doesn’t understand. Investment houses should note this simple truth."

On Becoming a Quant (pdf) May 2008; Mark Joshi

Hiring the Next Generation of Quants, Finance Tech, 3/31/2006; Ivy Schmerken

""An MBA does not cut it because operating in today's markets requires more quantitative skills than a typical MBA can offer," contends Linda Kreitzman, director of the Masters in Financial Engineering (MFE) program at the Haas School of Business at the University of California at Berkeley. "Trading is getting more complex, especially in structured products," she adds, citing as examples fixed income, mortgage-backed securities and asset-backed securities, as well as credit and equity derivatives and volatility trading. ""

Here is an article, written by Tom Davenport, in the Discussion Leader, Havard Business Publishing, that offers a a few ideas for solutions:

10 Principles of the New Business Intelligence

"I've argued for a while that organizations need to increase their focus on decision-making. In particular, they need to think again about the relationship between information and decision-making."