I don't know if anyone has already linked this (it did not pop up in a cursory search), but there's a great article in, of all places Wired magazine here: http://www.wired.com/techbiz/it/magazine/17-03/wp_quant

(PS- Kudos to my good friend Cecil for bringing this up on his blog: http://werehosed.mvmanila.com/?p=2968 )

The article goes into detail about the main formula (and a little about the guy who developed it, one of the quants on Wall Street) that was used to measure risk of correlated events. Long story short, this was one of the important contributors to the rise of the CDO market, without which the massive securitization of the mortgage market which occurred this decade would not have taken place.

Even without knowing about the formula, I could see what was happening (heck, I can track down posts on TMF commenting on it, it wasn't very hard to notice fer crissakes, and I was hardly the only one). What leapt out at me was how many classical mistakes (often made by traders, but also done in other contexts) were encapsulated in the actions that led up to our current crisis.

My basic analogy for what occurred is the "rubber band" analogy. Long ago and far away, mortgage lenders were predominantly portfolio lenders. Think of the mortgage market as a whole bunch of smallish rubber bands stretched between the fingers on your two hands. As you move your hands further apart from each other, you stretch those rubber bands more and more. Eventually, some of them start to break (as the economy turns down, a factory in Plano, Texas closes, throwing a bunch of people out of work, a substantial number default on their mortgages, and the First National Bank of Plano finds themselves in trouble), which is a sign to stop stretching the rubber bands and start moving your hands closer together again.

With the incredible securitization of the mortgage market, that changed to one great big rubber band. One of the advantages of that is that you can strtech that rubber band much farther than any of the little ones. But when that big rubber band breaks...

Well, guess what, it broke.

Here's one post of mine saying almost exactly that, from back in 2004. I mentioned Fannie and Freddie, not realizing that the growth in the CDO markets and such outside of those institutions was growing at an exponential pace and really pushing the process (and would not crest for another 2 years or so:
http://boards.fool.com/Message.asp?mid=20524454

Of course the rubber band got stretched, because stretching it how financial institutions make money.

So, what went wrong. Several classic mistakes:

1) Inadequate historical data. Imagine trying to determine the risks and rewards inherent in investing in tech stocks, and limiting your dataset to the years 1994 to 1999. Or (I'll use this analogy several times in this post) reviewing data on river levels for five years in trying to determine the hundred year flood plain.

Well, that's essentially what was happening with the parties using David Li's copula formula to determine risk. 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.

Building mathematical strategies based on inadequate historical data is a common problem among beginning traders trying to develop quantitative methods. It's usually not as obvious as I've made it appear here, but it shows up in many ways. And, since market events are notoriously fat-tailed, the consequences can be catastrophic.

2) The improbable is not the same as the impossible
Market participants (which is to say "people") have a habit of treating low probability events as if they were no probability events, at least when those events have a downside (this doesn't apply the other way, or else states would long ago have discontinued lotteries as a way of raising revenue). This can also have dangerous consequences. Again quoting from the story: you can only try to set up a market in which people who don't want risk sell it to those who do. But … people used the Gaussian copula model to convince themselves they didn't have any risk at all, when in fact they just didn't have any risk 99 percent of the time. The other 1 percent of the time they blew up. (emphasis added).

And to paraphrase an old comedy sketch, when they blowed up, they blowed up real good.

3) The activities engaged in by market participants changed the underlying markets themselves.
The analogy I’ll use here, which may be a little obscure, is again that of a river. For millenia, people have tried to build levees along rivers to contain their flooding and exploit the natural fertile floodplains. But a funny thing happens: rivers have a habit of overtopping levees at a rate much greater than would be expected by historical data. Why does this happen?

The short answer is pretty obvious: by building levees all along its banks, the river becomes artificially constrained. Unable to overflow into its floodplain, the river runs even higher in its channel than before. An excellent description (from this superb article on the Mississippi and Older River Control in the New Yorker: http://www.newyorker.com/archive/1987/02/23/1987_02_23_039_T... ) is that a river “begin[s] to stand up like a large vein on the back of a hand.” In so doing, it throws all previous calculations of flood frequencies out the window. “100 year floods” may start occurring every 10 to 20 years, and even a “thousand year flood plain” may now be, say, a fifty year flood. Or less.

In the world of trading and finance, this means that, even with perfect historical data, all your prior measurements are no longer valid. What once was a “six sigma event” may now be a 3 or even two sigma event, and as I’ve commented before, you generally want a lot more sigmas between you and potential economic ruin. This has happened many times before. The explosion of the “junk bond” market and their use in increasingly leveraged LBO’s in the 80’s, the folks at LTCM, and probably dozens of other examples other folks here could come up with.

By engaging in the increasingly aggressive lending practices that they had, based upon risk assessment models that most definitely had NOT been appropriately stress tested, the financial institutions had dramatically changed the underlying dynamics of the housing market. Volatility was present that had never been there before, although in the early part of this decade it was all to the upside. In effect, the river was running higher than ever. Which was fine as long as it stayed within its channel, but once it started overflowing its banks…

4) Costs and benefits removed in place and time
Markets tend to become most distorted (or “least able to be self-correcting”) where costs and benefits are removed in place and time from the parties to a transaction. Such was the case here. Even with perfect risk assessment data, there was a powerful institutional prerogative to continue expanding lending policies. “If we won’t do it, somebody else will/already is.” Someone who held of on lending saw their competitors reaping the profits and share price increases. The benefits were immediate and tangible, while the costs would likely occur in the future. Even the most prescient and upstanding CEO would be faced with the certainty that the consequences of expanding lending practices may well be faced not by them but by their successors, while their refusal to act now would fall on them alone. And so on down the chain at most if not all large financial institutions.
The quickest way to sum this up is an exchange between me and a UBS employee in the elevator where I work. Upon reading that UBS had written off several billion, I said “What, nobody saw this coming?” His response “yeah, but they were too busy making money to care!”

Well, that’s way too brief a summary. I strongly suggest that anyone interested read the article at Wired linked above. I’d also recommend the article on the Atchafayala river, as it addresses risk management in a much different area, but with insights for us all.

Hope the folks at METAR find this useful and hope that it offers at least a little insight.

-synchronicity, still kicking himself for not buying OTM SPY puts back in fall of ’06 when I first started saying we would go into a recession in 2007.