One story that's going around on Wall Street is that the financial industry landed itself, and us, in the fix we're all now in by erecting a massive structure of derivatives and interlocking claims which no one really understood, and which now has the effect that a collapse anywhere puts the whole structure at risk of toppling like a house of cards. Viz. the quote of the day:

Mr. Blinder, the former Fed vice chairman, holds a doctorate in economics from M.I.T. but says he has only a "modest understanding" of complex derivatives. "I know the basic understanding of how they work," he said, "but if you presented me with one and asked me to put a market value on it, I'd be guessing."

Which is to say, the soi-disant rocket scientists of Wall Street gave themselves a complicated job, and then did it badly.

Me, I'm not so sure. Some of the mistakes involved no math at all. And in cases where the math should have been easy, they still blew it badly.

To begin with, a lot of the structure was based on implicit trust in ratings agences which, as others have noted, were blowing the simple stuff. Consider "mortgage-backed securities," which is where the rot first set in. This is a field in which conventional wisdom had been that buyers who didn't put in a substantial down payment, relative to the cost of the property, were at elevated risk of default; financially, they'd have nothing to lose if they defaulted, and if the value of the property dropped at all, they'd even have something to gain. In the year 2000, as Conan O'Brien would say, Standard and Poor's decided to set aside decades, if not centuries, of experience, and say that arrangements with no down payment were not at elevated risk. By the time they went back on it, the collapse was already underway.

But beyond that, let's consider cases where a little math was involved: the now infamous mortgage-backed securities.

The basic idea of these is that when you've got a lot of risky loans with more or less similar properties, you can predict roughly what's going to happen to them in aggregate, and take advantage of that. So, let's say you think that there's between a 10% and 30% chance that any individual borrower will default. That means that 70% are very likely to keep making their payments, another 20% are in doubt, and the last 10% are toast --- but you don't know which 70%. So, how can you get certain returns? By creating a security that gets payments from whoever's still paying, up to 70%, no matter which loans those are. (So long as more than 70% of the borrowers are still paying, the other payments go to buyers of riskier "tranches" of the payment pool; when they stop, the buyers of those tranches are out of luck, but they knew they were buying concentrated risk going in.) Since you're assuming that no more than 30% of them will default, it's basically a sure shot that enough of them will keep paying to keep that first-dip revenue stream going, which is how you make an absolutely solid, AAA-rated security out of a whole bunch of individually bad loans.

That is, in fact, the basic argument for the AAA-ratings on a whole bunch of mortgage-backed securities. It's all entertainingly outlined in this well-circulated slideshow, or if you want more detail with musical accompaniment look here. And yet losses on these things are now bleeding major banks white.

So, could there be something wrong with the analysis? In fact, the argument contains an elementary mathematical error that bites a lot of people hard on the ass in probability 101. If you haven't seen it already, you might want to go back and see if you can spot it, because I'm going to spoil it for you in the next paragraph.

Here's the problem: The whole arrangement implicitly assumes that the failures of the individual loans are independent. That is, we're assuming that each borrower has between a 70% and 90% chance of keeping up with the payments whatever the others do. And the world might just not be like that. Let's suppose, instead, that there's some event --- let's say, just for kicks, a meteor strike on the town --- that might (with between 10% and 30% probability) make all of the borrowers default, all at once. In this situation, each individual loan still has the same chance of defaulting as it does if they're independent. But pooling this risk buys you nothing: if the meteor hits, the loans default all at once, and it doesn't matter how the payments have been divvied up, because they've all ceased.

That's a nice mathematical curiosity unless someone can point to events likelier than meteor strikes which might have this kind of mass effect. But by the time the real estate bubble was really going, there was such an event, which was almost certain to happen: a rise in interest rates. Lots of borrowers, particularly in the subprime range, were taking loans with variable interest rates which would "reset" up at some future date. If they couldn't pay after the reset, they'd have to sell the house fast. But, at the same time, it was common in the bubble to judge affordability by the monthly payment, and if rates go up, the same monthly payment buys you less house. So, in the event of a rise in rates, the borrower can't make the payments (because the rates have gone up), and they can't sell to a similar buyer for as much as they paid (because any similarly situated buyer can now afford less). In such a case, default is what's going to happen, because it's the only thing that can happen. To all of them. All at once.

By the way, did I mention that interest rates in mid-bubble were at historic lows, and had nowhere to go but up?

Were the soi-disant rocket scientists of Wall Street and the Connecticut hedge funds trying to defraud anyone with this stuff? I'd say probably not. As others have noted, placing big bets against nasty events is a great strategy for a fund manager, even if you're sure to lose big eventually, so long as you don't acknowledge what you're doing. (In the meantime, you get to pocket your fees, which can be colossal.) And the easiest way to do that is to convince yourself that you're doing something else that genuinely does "add value" --- which is a particularly easy job if the flaw is concealed within pages of ornate mathematical bafflegab. As someone once said, it is difficult to get a man to understand something if his salary depends on his not understanding it.

I'll admit I'd be slightly more credible here if I had scribbled this down a few years ago, so I could be quoting myself now. Instead, I just decided to stay the hell out of the real estate market. But I think the argument stands on its own. [Update: Then again, here's somebody else who did call it at the time. But he's got a Ph.D. In economics!]

One last note on housing questions --- my last post on the subject got a few comments blaming people who put themselves in hock up to their eyebrows, borrowing more and more against houses they already owned to pay for vacations, fancy cars and glitzy junk. And they exist. From the depths of Orange County, IrvineRenter dredges up a spectacular examples on a regular basis. But that wasn't everybody. Probably not even most of 'em, except in isolated enclaves like Irvine (where most of the buyers weren't really subprime, though many made the same mistakes, and where there's reason to believe that the real bleeding hasn't even started yet). So, I hope before posting one of those again, folks will take a good look at a story of another type. (And yes, the poor woman signed legal papers in a language she didn't understand. She speaks Spanish, and lives in the U.S. Does she have a choice?)