Of Bubbles and Butterflies

Chaos and Financial Markets II

The following story is based on true events. The characters are fictitious. Any resemblance to characters living or dead is entirely unintentional. Close cover before striking.

Rupert and Millie Paltridge, of Silver Springs, Maryland, were considering spec properties in the Phoenix area as a vacation home. “And we could even retire there,” Millie would always say. Prices were at historic highs, thanks to the national boom in real estate. They found a really upscale condo in a new development project outside tony Scottsdale. The year was early 2005. The asking price was $580,000. The development even had its own Starbucks. “We can’t afford this,” Rupert announced. But, friends explained they couldn’t afford NOT to get in on the housing market.

“With subprime and adjustable rate mortgages, no one cares how good your credit is. If anything goes wrong, you can always bail out at a handsome profit. You win. The bank gets their money back. You may not even have to pay a penny of principal for years.”

Rupert and Millie bought. With no down payment, there was plenty of money for furnishings and gee-whiz appliances. They even wintered there in 2005 and 2006. “what fun to be ‘snowbirds’ and make money at it too,” they said. Housing prices started to decline in 2006, though, and the monthly ARM payments started to climb. Then, in early 2008, Rupert lost his job in Silver Springs. It was time to consolidate – to bail out!

They flew out to Phoenix and talked with their realtor. Times were tough. Even if they could find a buyer, they’d still owe the bank about two hundred grand to pay off the mortgage, because they had never really paid it down at all. With tears in their eyes, Rupert and Millie did something they’d never done before in their life. They were ruined, demoralized, and bankrupt. In October 2008, the couple walked away from the mortgage and the home of their dreams, never to return.

The home was later televised nationally as an example of new properties, fully furnished, from which the owners had simply walked away forever, without even taking the family photographs off the wall.

I don’t know a lot about Chaos Theory. Wikipedia explains that it got its kick-start with nineteenth-century French mathematician and physicist Henri Poincare, whose name I associate with wierd mathematical functions I don’t understand. Chaos Theory tries to make sense of complex large scale events that appear totally random to the casual observer.

A popularized illustration of this discipline is known as the “Butterfly Effect“: a butterfly flaps its delicate wings, ever so gently in West Africa, generating ever so small disturbances in the air. Weeks later, a hurricane builds strength over the Caribbean. Although a complex event like a hurricane is the result of the unfavorable confluence of thousands of smaller events, it is easy enough to show in a “thought experiment” that the cascading chain of cause-and-effect might (in theory) be traced backwards to the single event of the butterfly.

Everything has to start somewhere, no matter how inconsequential it seems at first. Somehow this always ends up seeming most true of disasters.

It’s not that we are expected to buy into any notion that the proximal cause of the hurricane was the butterfly. If this was so, the annual 2,000 mile migration of the Monarch Butterfly would be looked upon as one of the most fearsome of deadly natural events. Instead, the Butterfly Effect thought experiment is designed to show how a very “small change in the initial condition of the system” can initiate much greater changes, on a much larger scale. Thus, we envision, the butterfly flaps its wings, and its small wing vortex current drops toward the ground and becomes heated. This displaces heated air already on the ground, rising in a micro updraft which draws in even more warm air. Cooler ocean air is drawn in to replace the rising warm air column, and so forth … In other areas we’re already very familiar with the Butterfly Effect: Smoky the Bear has been warning us of the danger of forest fires for decades, the consequence of one very small cigarette butt, or smouldering remains of last night’s camp fire.

We cannot predict hurricanes, forest fires or financial meltdowns with great accuracy, but we can use chaos theory to help make statistical predictions about the factors that may lead to them. This gives us a degree of control in predicting likelihoods and the consequences of our possible response options.

Fractal pentagram drawn with a vector iteration program.

Fractal pentagram drawn with a vector iteration program (Wikipedia).

In Summitlake.com’s recent 15-essay Financial Crisis series, I meant (but failed) to discuss mathematician Benoit Mandelbrot, best known to most of us for his pioneering work in Fractals: the mathematics of the snowflake, and the complex intricate kaleidoscopic designs found on computer screen-savers and now in the world of art. Each piece of a Mandelbrot fractal pattern is a microcosm of the larger, growing crystal. In fact, each piece of a fractal pattern illustrates why mankind invented the word “pattern” at all. Mandelbrot also applied his theory to the U.S. cotton market, finding “recurring patterns at every scale” in the data.

Even 2000 times magnification of the Mandelbrot set uncovers fine detail resembling the full set

Even 2000 times magnification of the Mandelbrot set uncovers fine detail resembling the full set (Wikipedia)

Mandelbrot also looked at the computerized machinations of the market immediately preceding the current financial meltdown. Like his famous Mandelbrot sets, whether one looked at the big picture or the fine detail, the pattern was everywhere. He pronounced it madness. In a PBS round-table interviewwith Ray Suarez in October 2008, he characterized this as very bad ju-ju:

PAUL SOLMAN: So, getting back to your fundamental work and insight, this is a system that can become turbulent or is inherently turbulent, that doesn’t have enough of a buffer, and that’s the danger?

BENOIT MANDELBROT: That is not well-understood. In fact, that is misunderstood for which tools have been developed which assume that changes are always very small.

If one of them comes, nothing bad happens. If several of them come together, very bad things have happened. And the theory does not take account of that, and the theory doesn’t take account of very large and sudden changes in anything.

The theory thinks that things move slowly, gradually, and can be corrected as they change, whereas, in fact, they may change extremely brutally.

In our 15-part Financial Crisis series, we looked at several examples of runaway “chaos”, or large-scale disequilibrium, from exploding-star supernovas, to coal furnace explosions, to the effects of toxic debt on the U.S. economy. We found that these phenomena can be explained by enumerating all of the contributory causes as components of a chain of events.

We find a corroborative piece of the puzzle in the February 2009 Scientific American. In “Labor and the Catch of the Day“, writer Paul Raeburn looks at the work of mathematician George Sukihara in studying declining U.S. coastal fisheries:

Sugihara, a mathematician and theoretical ecologist at the Scripps Institution of Oceanography in La Jolla, Calif., analyzed that data and came to a surprising conclusion: both potential explanations of the sardine collapse were wrong.

His conclusion, in a study published in Nature in 2006, was that the problem was the harvesting of too many big fish. Fishing boats were leaving behind a population of almost all juveniles. Sugihara showed that mathematically such populations are unstable. A slight nudge can create a boom — or a catastrophic collapse.

In other words, throwing back the little ones is exactly the wrong thing to do. A population of juvenile fish lacks the body mass and fat reserves to ride out even moderate swings in the boom-bust of food chain cycles. It’s counterintuitive, but leaving the big guys in the ocean stabilizes the herd. To breed the next catch, we have been culling out the strong and throwing back the weak. The fishing fleet captains still may not get it, but any cattleman can tell you what’s wrong with that.

Sugihara, too, looked at global financial markets:

Sugihara sees fisheries as a complex, chaotic system, akin to financial networks. They are so alike that the global financial giant Deutsche Bank lured Sugihara away from academia for a time; there, from 1996 to 2001, he successfully used the analytical techniques that he would later call on for his sardine work to make short-term predictions about market fluctuations.

We tend to look at investment and fishery populations as standalones, isolated from the bigger pictures, and that has been our greatest mistake. Ultimately we may learn more of practical use about our economy from the mathematicians and ecologists than from Adam Smith and John Maynard Keynes. “Market Forces” really does not explain anything, you know. But we already knew actions have consequences.

We need to stop thinking of the economy as a single stable, steady-state engine. Changes in one subsystem, such as the auto fuel subsystem, can have far-reaching consequences for the whole system. Adjusting the engine to a leaner fuel mixture means a hotter and more efficient burn. In the desert, then, will this car go further, or will the cooling system become overwhelmed and seize up the engine?

Just because we can’t always predict the long-range course of market streams doesn’t mean we should stop trying to assess the short-term impacts of the diversion of thousands of branched, interrelated tributaries. Good for us, or bad for us? The big picture is not as chaotic as we thought, and we’re seeing this in scores of unexpected places of nature. The financial interaction of billions of individuals is no different.

In a financial meltdown, the loss is worse than simply burning up a sum of money, or pouring it down down the black hole of a failed war. We spent $3 trillion on that historical horror of the Iraq war, but in our domestic economy, not only did we throw away $14 trillion in mortgage debt, we suffered the cascading loss of expected income and growth it might have generated if invested rationally. We expect the loss in case of  fire or war, but in the meltdown we destroy the growth that was already anticipated (and probably spent).

Once again, there’s no credible “I told you so” moral here. We don’t alway need a butterfly effect theory to explain the financial meltdown, caused by irresponsible lending policies and toxic debt, accelerated by irrational computer trading programs – we had one hell of a huge “butterfly”. The piece the mathematicians are contributing is still vital to the explanation. In effect, the economy collapsed for the same reason as the fisheries: we pulled all the healthiest ones out of the sea.

Rupert and Millie Paltridge didn’t see it coming. But this little instability in their personal lives cascaded into a national crisis. They didn’t cause the crisis, but analysts with the right tools could have forecast it early enough to allow damage control. There was certainly no shortage of butterflies.

Nancy Pelosi didn’t see it coming. Neither did Rush Limbaugh. I sure didn’t. You probably didn’t. It seems only a couple of Wall Street Cassandras and two eccentric mathematicians could see not only that something was wrong, but what. If there’s any silver lining to the cloud that blackens the economic outlook today, it’s that a lot of very bright, capable people are starting to listen and ask all the right questions.

I recently lost my own job, like millions of others, in the national wave of corporate layoffs. Fortunately, I was close enough to retirement that I was able to decide to just go for it. This is just the set-up for the anecdote: earlier in my life, I was teased for being the “perfect consumer”. If it was a cutting-edge gadget, from stereo to electronic mosquito repellant, I had to have it. Today, that lifestyle of course came to a screeching halt. As I find myself musing how the nation’s stores and mail order houses are going to survive without me, I realize it just isn’t that funny any more: retailers have lost most of the purchasing power of millions of households.

Rupert and Millie, whoever and wherever you are, take heart. Certainly, it has been said that home buyers like you could have known better, and maybe should have. But our realtors, bankers and legislators didn’t seem to know better either. Move forward from here. Things will get better. I won’t see you in Scottsdale, but maybe we’ll bump into each other at Trader Joe’s in the more downscale Tempe. Good luck to you!

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