Secret Formula That Destroyed Wall Street
These were the headlines in the March (2009) issue of Wired. The headlines caught my eye, as I was one of the many who saw their life savings quickly evaporate like a drop of water on a hot day.
Prob[TA<1,TB] = Φ2(Φ-1(FA(1)),Φ-1(FB(1),γ)
where the equation determines the joint default probability of investors A and B, TA and TB represent the "amount of time between now and when A and B can be expected to default," Φ2 merges the "individual probabilties associated with A and B," FA and FB are the "probabilities of how long A and B are likely to survive," and γ is the "all-powerful correlation parameter, which reduces correlation to a single constant."
The subsequent article claimed that one secret mathematical formula "destroyed Wall Street," or "how one simple equation made billions for bankers--and nuked your 401(k)." What was this formula...and who created it?
The creator was David X. Li, a mathematician/economist working for JPMorgan Chase in 2000. His creation was a "Gaussian copula function" designed to assess risk... that was fatally flawed. In statistics, "copula" implies the linking of behavior of two variables. The actual formula was:
Do I understand all of this...no! But it is interesting that our financial downfall can be traced to a single mathematical equation. The flaws lie in four areas. First, the equality. As described in the Wired article, equality is "a dangerously precise concept, since it leaves no room for error. Clean equations help...forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness." Second, the copula Φ aspect is quite sensitive..."Errors here massively increase the risk of the whole equation blowing up." Third, the gamma γ "reduces correlation to a single constant--something that should be highly improbably, if not impossible." And fourth, the formula's simplicity and elegance "excited" investment bankers, who "lacked the math skills to understand what the models were doing or how they worked."
As the financial market now struggles to rebound to a respectable level, David X. Li has moved to Beijing and is no longer working in the world of finance. But, Li did talk about his equation or model: "The most dangerous part is when people believe everything coming out of it."
For more information about this equation, its underlying model, its flaws, and its impact, please read the Wired article. And, share some of this information with students, who tend to fall in the trap cautioned by Li!
Source: Felix Salmon's "A Formula for Disaster," Wired, MArch 2009, pp. 74-79, 112