Felix Salmon has a readable article in Wired called "Recipe for Disaster: The Formula that Killed Wall Street" on David X. Li's wildly popular 2000 financial economics innovation, the Gaussian copula function, which was used to price mortgage-backed securities by estimating the correlation in Time to Default among different mortgages.
Li has an actuarial degree (among others), and that appears to have been his downfall: he assumed mortgage defaults were like Time to Death to a life insurance actuary: largely random events that could be modeled.
Steve Hsu's website Information Processing has a 2005 WSJ article on Li's Gaussian Cupola, for looking at events that are mostly independent but have a modest degree of correlation:
In 1997, nobody knew how to calculate default correlations with any precision. Mr. Li's solution drew inspiration from a concept in actuarial science known as the "broken heart": People tend to die faster after the death of a beloved spouse. Some of his colleagues from academia were working on a way to predict this death correlation, something quite useful to companies that sell life insurance and joint annuities.
"Suddenly I thought that the problem I was trying to solve was exactly like the problem these guys were trying to solve," says Mr. Li. "Default is like the death of a company, so we should model this the same way we model human life."
Uh, maybe, maybe not. There just isn't much in the field of life insurance where selling more life insurance increases the risk of death. The life insurance companies figured out the basics of moral hazard a long time ago: don't let people take out insurance policies on their business rivals or their ex-wives to whom they owe alimony. No tontines. Don't pay out on new policies who die by suicide.
In contrast, giving somebody a bigger mortgage directly raises the chance of default because they need more money to pay it back. Giving them a bigger mortgage because you are requiring a smaller down payment, in particular, raises the risk of default.
His colleagues' work gave him the idea of using copulas: mathematical functions the colleagues had begun applying to actuarial science. Copulas help predict the likelihood of various events occurring when those events depend to some extent on one another. Among the best copulas for bond pools turned out to be one named after Carl Friedrich Gauss, a 19th-century German statistician [among much else].
The Gaussian distribution (a.k.a., normal distribution or bell curve) works like this: Flip a coin ten times. How many heads did you get? Four. Write it down and do it again. Seven. Do it again. Five. As you keep repeating this flip-a-coin-ten-times experiment, the plot of the number of heads you get each time will slowly turn into a bell curve with a mean/median of five.
Now, that's really useful and widely applicable. Processes where you randomly select a sample will tend toward a bell curve distribution.
But the Housing Bubble didn't consist of fairly random events that everybody was trying pretty hard to avoid, like with life insurance. Instead, human beings were responding to incentives. The closest actuarial analogy might be the big insurance payouts that fire insurance companies got stuck with in the South Bronx in the 1970s when decayed businesses that were now worth less than their fire insurance payouts developed a statistically implausible tendency to burst into flames in the middle of the night.
As I said last fall:
Human life really isn't all that random. That's because human beings respond to incentives. If you treat human beings as if they are just mindless probabilistic events, whose risks you can diversify away by dealing with large numbers of them at a time, they will outsmart you. They will put down inflated incomes on their mortgage applications. They will claim to be owner-occupiers when they are just speculators who will rent out the property to Section 8 tenants when they get into a cash flow bind. They will bribe appraisers to report a higher than actual value.
Life insurance companies are in the selection business, not the influence business. Watching other people get rich buying and selling houses, however, influences behavior.
The life insurance actuarial model fails as an analogy for mortgages on other dimensions as well. For example, people die from a very large number of causes, making the distribution of deaths over time more Gaussian. Mortgages, in contrast, are more like being in the earthquake insurance business in California.
Further, Jim Morrison pointed out, the thing about life is that nobody gets out alive. In contrast, lots of people can imagine themselves selling the three houses in Temecula right at the top of the market and retiring to Dallas in comfort.
And there's a tournament aspect to competitive fields, such as homebuying. If you're in the Olympic boxing tournament and you get away with a few defensive lapses in your opening round match against a pudgy guy from Bhutan doesn't mean you can likely get away with them in the gold medal round against the Cuban. Similarly, when the median home price in California gets to $500k, it's not the same as when it was $200k. You can't use default data from when homes cost 40% as much. The margin for error has vanished.
Finally, the idea that just because there hadn't been a giant housing crash since WWII means there can't possibly be a giant housing crash is about 180 degrees backward. It's where there hasn't been a crash lately that you have to worry. What, did everybody expect the government to discourage home buying?
Statisticians need to be good with analogies, as well.