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How is Finance like a Sand Pile?

Why is it that nobody in the mainstream media seems to know anything about economic theory or the dynamics of financial markets? This morning's Washington Post contained yet another column asking why it is that economists failed to predict last fall's financial crash. The title lays the blame squarely at economist's feet: "Economists out to Lunch."

As if these economists were sitting at the controls of a machine they fully and completely understand. As if something like the crash we experienced could be predicted. As if the financial system had levers to pull or buttons to push that would yield predictable outcomes.

This all seems quite ludicrous to me. Even though I am not an economist, it seems clear that our economic and financial system is a complex system, with all the ramifications that has for predictability--or lack of predictability. It is a system comprised of multiple, nested feedback loops. These types of systems self-organize and display dynamic behavior that is well-understood from complex systems theory.

Not that you would ever know that from reading the newspapers.

One type of self-organized behavior that has been considered by those seeking to describe the dynamics of financial markets is exemplified by a sand pile fed from the top by a stream of sand grains. The dynamics of this sand pile exhibit what is known as self-organized criticality, or SOC.

The grains tumble slowly down the sides of the sand pile, coming to rest at various points along the slope. The pile slowly grows as sand is dribbled onto the top until, suddenly, the system becomes unstable and a small avalanche occurs. A rush of sand tumbles to the bottom, returning the remaining pile to a situation where additional sand can be added--but only for awhile. Small avalanches occur at random intervals and it is never entirely predictable when they will happen.

The sand pile's SOC dynamics exist because this system has an attractor that is simultaneously stable and unstable. This type of attractor is known as a critical point. It is essentially a mountain pass in the hilly terrain that characterizes the dynamic landscape for the system.

This mountain pass is a saddle point: if we stand at the point and look in one direction, the mountain slopes upward. Turn ninety degrees, though, and the mountain slopes down. Another ninety and it slopes up again. Completing the circular spin as we stand at our saddle point, we see the mountain sloping downward again. Sand grains roll down the mountain slopes toward this saddle point but when the resulting sand pile becomes too big, it collapses and rushes away into the surrounding valleys.

SOC has been suggested as the explanation for a variety of phenomena: forest fires, earthquakes, and, yes, financial markets. The common feature in systems that are governed by SOC is that they are driven by a persistent external force. In the case of the sand pile, it is the stream of sand. In the forest fire example, it is thought to be the slow accumulation of dry fuel. In the earthquake example, it is the constant pressure from colliding tectonic plates pushing on a fault line that will, at a random and unpredictable time, slip, causing a quake.

I would love to see a thoughtful discussion of the possible role of SOC in economics and financial systems. Nobelist Paul Krugman's ideas come close, but he seems to shy away from precise scientific language that would make it clear to me that he agrees with the idea that economic systems are complex, self-organizing and, thus, subject to the natural laws for these fascinating types of systems. I will keep looking, but please post links if you know of any relevant work.


  1. Hi Raima,

    My name is Mark and I stumbled across your blog while doing some research into fractals. I'm an independent trader in the capital markets and I have spent the last 3 years studying the fractal behavior of financial markets. Benoit Mandelbroit wrote a book "The Misbehavior of Markets" in 2007 that sort of laid the groundwork for studying asset markets as fractal phenomena. Benoit built much of his fractal theory on his studies of the pricewave in cotton back in the 1960s. He wrote a couple of earlier books on the subject and a couple of others have touched on the fractal market idea over the past 10 years or so, but it remains VASTLY understudied and is still considered (at best) a curiosity by most of academia and Wall Street. You can find the Misbehavior of Markets on Amazon for about 10 bucks. It's an easy read and Mandelbroit clearly proves the market is fractal in nature and that the efficient market hypothesis is total BS. And the recent financial crisis has only added to the weight of evidence that the market is fractal, not efficient.

    I've been working on building my own model for capturing the fractal nature of the momentum of the pricewave in markets (and when I say markets I mean all markets...any large sufficiently liquid stock, bond, currency, or commodity). All markets behave by these same fractal rules.

    If you are interested in learning more about my work or discussing the fractal nature of markets, I'd be more than willing to share my model with you in an off the public internet way via email. You can email me at

    I find it very curious that you come from the world of complexity science and I come from the world of trading yet we both see a sort of big gaping hole in the general understanding of how financial markets really work. I look forward to hearing from you.


  2. This world is quite the big place and to encounter a story such as this one just puts me out of my ordinary. I gotta hand it to whoever wrote this, you've really kept me updated! Now, let's just hope that I can come across another blog just as interesting.

  3. There is a more philosophical question implied here: since the economy IS a complex system, why do governments and the Federal Reserve believe they can 'manage' it?

    The Austrian school of economics stipulates that it is not possible at all, and that fractal reserve banking is a silly notion that ensures periodic recessions. They also suggest that emergence demands allowing firms to fail to allow innovation and creative destruction to advance. Famous Austrian economists like Hayek and Mises talk about complex systems often.

    Of course as a school of economics they remain in the minority, since our societies are by now increasingly hierarchical and statist. People like Krugman become famous partly because they encourage management of economies. This is the inherent issue with large governments imposing simplistic answers to complex systems; it is impossible to predict their effect on other variables, including sustainability, culture, profitability, etc.

    "Understanding complex systems converts one to a free market libertarian." I would appreciate your reaction to such a statement.

  4. Looking at this post two years later, and see I didn't respond to all the comments. So sorry! @WhiskeyJim suggests that taking a complex systems approach when trying to understand financial systems will convert one into a "free market libertarian." I can see how one might arrive at that conclusion, but it assumes that the government is completely separate from the financial market, when in reality it is actually a part of the market. There is no way to have a "free market," and I'm not convinced it would be any better. It would certainly behave according to the same principles of complex dynamics, but just without the higher-level organizing structures that governments (and governments working together) provide.

  5. I forgot I made this post:) Surely I was too vague. I agree that governments are very much involved in financial markets; they do not protect or nurture a complex system (which would be a free market); for years the GSEs wrote more than half the mortgages at reduced rates and profiles, and the FED kept interest rates artificially low.

    I should have realized something was structurally wrong when Greenspan said they had tamed risk. Of course one can not do that; one only displaces it. And a complex system learns at least partly by responding to it.

    My earlier point was that there were lessons learned from the financial collapse. Large complex economies will always malinvest and like any complex system, need to readjust to new realities. Think of an ant colony that periodically depletes a food source and must look for another one.

    In this sense artificially spurring such systems with GSEs and interest rates by imperfect models exacerbates such adjustments since they allow the malinvestment to continue too long, making the adjustment more painful.

    International banking laws like Basil do the same in a different way, since they dissuade duplication and variety that spurs emergence or innovation; any weakness of the law spreads throughout the system. It is no coincidence that Canadian banks ignored both Basil and MBSs and needed no bail-outs.

    A market in interest rates alone would have self-corrected years before, containing the recessionary correction in a much smaller arena.

    So I disagree with you Raima, that a complex system would not be better. Markets explore and make mistakes. But the mistakes would be smaller before self-correcting because they are inherently more adaptive than bureauracies (notice that legislative changes including the FSB have been relatively small and driven by politics). And the threat of bankruptcy in the shadow of fractal reserve banking would almost immediately force banks into a more reserved stance. It is the regulation itself that allows them so much gearing.

    What we learned I think, was that the idea of 'managing' the economy or the financial system is in effect a fools game, especially using an infantile social science such as economics. The two choices are clear; either the government should nurture a complex system, or drastically increase control of the financial system to a dull and dreary role with virtually no innovation at all, much like the insurance industry.

    Playing around in the middle with governments and financial systems writing their own regulation is actually the worst of both worlds. And the pain we suffer from their mistakes is too great.

  6. I guess I was too vague, too! :) I agree with much of what you say, but my point is that the financial system IS a complex system, despite what people might wish to believe. There really aren't levers and buttons one can push to make the markets do what we want (and managing risk sounds pretty much impossible) but people act as if the financial system is some sort of machine that can be adjusted at will, rather than an organism that is growing and changing (which is, I think, a better way of looking at it.)

    When I said the government is not separate from the market, what I meant is that the government (actually, this should be plural: governments) are part of the complex system. So, I'm no really sure what you're disagreeing with, when you say "I disagree with you that a complex system would not be better." I'm not saying it's better or worse, I'm just saying we HAVE a complex system whether policy makers know that or not, and the governments are part of this system, since they react and adjust to changes just like corporations and individuals do.

    And I totally agree that it makes no sense to "manage" the financial system unless the people who are making policies acknowledge that it is a complex system we have here and try to "nurture" it, as you say. I would love to see people who are in positions of power acting as if they understood this.

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