There’s an interesting story in the New York Magazine by Michael Osinski–the author of the main software package used to create the CMOs and CDOs that have helped cripple the financial system.

Osinski’s story is worth a read in its own right. But what I found curious about it was that he appears unaware of a flaw that existed in those products from the outset–the presumption that the standard mathematics of risk and return could be applied to financial assets. He doesn’t even mention this topic, but statements like the following imply that his software used a standard probability distribution to calculate risk and return for a given bond:

“Working with another programmer, I wrote a new mortgage-backed system that enabled investors to choose the specific combinations of yield and risk that they wanted by slicing and dicing bonds to create new bonds. It was endlessly versatile and flexible. It was the proverbial money tree…”

Though these distributions don’t have to be “Gaussian”–the “Normal Distribution” that lies behind the ubiquitous “Bell Curve”–all these distributions “tend” towards that one, and they certainly share one feature: they have finite variances around the mean outcome.

Sorry for some of the statistical jargon so far: the basic point is that, if some process–like rolling dice at a casino–follows one of these distributions, then you can calculate both the average score (which for a roll of two dice is 7) and the odds of a particular score (say 12, the odds of which are one in 36) coming up. You can also calculate that some outcomes are so rare as to be effectively impossible–such as rolling 12 twelve times in a row (such an outcome would occur only once in every 5 million trillion attempts).

The problem is that mortgage defaults aren’t like dice rolls. Which face on one dice turns up on the top doesn’t affect what the other dice do: a 6 on one dice has absolutely no impact on the likelihood of another dice also turning up 6. But if your neighbour defaults on a housing loan, you are more likely to do so too–because her mortgagee sale will depress the likely price for your house, and her disappearance from the neighbourhood will decrease incomes there, indirectly affecting yours, and so on.

Crucially, price rises in an asset market are also correlated: a rising asset market leads to the rising expectations that Minsky’s “Financial Instability Hypothesis” describes so well, and a falling one puts the process in reverse.

In this sense, asset price movements have more in common with earthquakes than with dice rolls. The best stylised model of an earthquake was built by a physicist called Per Bak–he called it “the sandpile model”.

Consider a child building a mound of sand at a beach by smoothly pouring dry sand out of a bucket. Initially, the sand spreads wide, then it gets to the point where sideways movement requires more force than each sand grain can impart, so the mound begins to rise up. It gets steeper–approaching a pyramid shape–and as it gets steeper, the structure gets precarious. Then another grain is added, and the whole structure suddenly collapses in an avalanche. The avalanche then stops, the pyramid is much less steep, the sand pile broader. The child continues adding sand, it pyramid rebuilds, then collapses at some trigger point, and so on.

The process building the sand pile doesn’t change–it’s always more sand grains dropping out of the bucket–but at somewhat unpredictable moments, the behaviour of the aggregate sand pile changes, from building upwards to collapsing, and then rebuilding again.

The pattern replicates what we see with earthquakes: movements in the earth’s tectonic plate occur all the time, and most of the time, each movement just adds to the existing level of tension between those plates. But every now and then, one additional movement occurs, the whole mass shifts, and a major earthquake results. As Per Bak put it, “a big earthquake is a small one that doesn’t stop”.

The pattern of movements you get from such a process can look superficially like a Normal distribution–the famous Bell Curve–but it differs from it in two fundamental ways. Firstly, there are many more movements near the average; secondly, there are also many more movements way, way away from the average–so many more that, in what is known as a pure “Power Law” distribution, the standard deviation is infinite: any scale event can occur, and will occur given enough time.

What does that mean for CDOs and CMOs? Since they presumed a “Normal” distribution (or at best one drawn from the class of statistical distributions where standard deviations are finite), they categorically ruled out the possibility of “large events”–such as, for example, house prices falling 10% in a year.

There is no example of the numbers Osinski’s programs may have used, but for example if a bond had assumed that house prices move up at 5% a year with a standard deviation of 2% around that trend, then a 5% fall in house prices would only occur once every 3.5 million years. A 10% fall would only occur once every 31 **trillion** years–it simply couldn’t happen.

Yeah, right.

In fact, in a Power Law process, movements of that scale will occur, and far more frequently than predicted by these standard probability functions. Osinski shows no awareness of this:

It hurts when people say I caused this mess. I was and am quite proud of the work I did. My software was a delicate, intricate web of logic. They don’t understand, I tell myself. Perhaps it was too complicated. But we live in a world largely of our own device. How to adjust and control these complexities, without stifling innovation, is the problem.

He couldn’t be proud of what he has done, had he known that he had used a fundamentally inappropriate model as the foundation of how risk and return were calculated. As usual, ignorance rules in this folly.

I’ll return to this topic in more detail in next month’s Debtwatch.