Monday, August 16, 2010

Physics Envy in Finance

This represents my personal opinion, not the views of the SEC or its staff.

If all you have is a hammer...


I read a New York Times article a while ago on econophysics – the use of the tools of physics in economics – that featured the application of seismology to solve the problems of market crises. I can see the twists of logic that led to this approach: during an earthquake things shake around and fall, and during a market crisis things shake around and fall. Seismology predicts the former, so why not the latter?

This type of logical leap too far is nothing new. I remember the popularity of Kalman filters and the application of the principles of torque to measure the strength of market turns (I’m not kidding) in the seventies. Later came the emergence of chaos theory to model market dynamics and catastrophe theory to model market breaks, the logic being that markets look chaotic, and that market breaks are, well, breaks.

None of these work, and as I will get to in a bit, there is a reason they don’t work. But the use of physics in finance and economics persists, thus the fledgling discipline of econophysics. The reason it persists is first of all, there are not many jobs for physicist in physics, and most of finance is child’s play once you have gone through the rigors of a physics degree, so a lot of physicists end up in finance. Another reason is that most of those in finance really do have physics envy. They want to have the solid structure, the clean answers, and the sexy mathematical models of physics.
So if you are a physicist by training, what is more natural than to take to your new home with your physics hammer, especially if everyone wants you to look at everything as if it is a nail.

Boards don’t hit back
Andrew Lo and Mark Meuller have has a recent paper that addresses the issue of physics envy. They focus on the applicability of the tools of physics as the type of uncertainty becomes more profound, pointing out that while physics can generate useful models if there is well-parameterized uncertainty, where we know the distribution of the randomness, it becomes less useful if the uncertainty is fuzzy and ill-defined, what is called Knightian uncertainty.

I think it is useful to go one step further, and ask where this fuzzy, ill-defined uncertainty comes from. It is not all inevitable, it is not just that this is the way the world works. It is also the creation of those in the market, created because that is how those in the market make their money. That is, the markets are difficult to model, whether with the methods of physics or anything else, because those in the market make their money by having it difficult to model, or, more generally, difficult for others to anticipate and do as well.

In the Bruce Lee movie, Enter the Dragon, Lee faces his arch enemy in a fight. To intimidate Lee, his opponent holds up a board, and splits it in two with his fist. Lee watches passively and says, “Boards don’t hit back”. That gets to the reason physics does not work in finance: markets do hit back.
The markets are not physical systems guided by timeless and universal laws. They are systems based on creating an informational advantage, on gaming, on action and strategic reaction, in a space without well structured rules or defined possibilities. There is feedback to undo whatever is put in place, to neutralize whatever information comes in.

The natural reply of the physicist to this observation is, “Not to worry. I will build a physics-based model that includes feedback. I do that all the time”. The problem is that the feedback in the markets is designed specifically not to fit into a model, to be obscure, stealthy, coming from a direction where no one is looking. That is, the Knightian uncertainty is endogenous. You can’t build in a feedback or reactive model, because you don’t know what to model. And if you do know – by the time you know – the odds are the market has changed. That is the whole point of what makes a trader successful – he can see things in ways most others do not, anticipate in ways others cannot, and then change his behavior when he starts to see others catching on.

For example, I have seen this issue repeatedly in risk management, and it is one reason any risk management model will not cover all the risks. Once the risk model is specified, the traders will try to find a way around it. Are you measuring DV01 risk? Well, fine, then I will do DV01-neutral yield curve trades. Now are you measuring yield curve risk? Fine, then I will do DV01 and yield curve neutral butterfly trades. One of the problems with VaR – and for that matter with any complex model – is that it opens up all the more dimensions for such gaming, and for gaming in a way that is harder to detect. Maybe this can be put into a model, but if it can, it won’t look like how things are modeled in physics.

So it is not by chance that there are so many people trying to add complexity to the markets. Whatever rules are put in place, whatever metrics are devised, traders will try to find ways around them. In an engineering system, if you find a poorly designed valve in a nuclear power plant and replace it with a new and better deigned one, the new valve doesn’t try to figure out ways to make you think it is closed when it is really open. But traders will do that.

Lo and Mueller conclude their paper by considering that “the study of economics may be closer to disciplines such as evolutionary biology, ecology, and meteorology”. And indeed, an increasingly popular alternative to borrowing from the tools of physics is to push finance into a biological model. The argument is that in the biological sphere, there is the interaction and feedback that physics lacks. Evolution is the result of this dynamic, of one species changing over time to best another species, just as one trader will change strategies to best another trader. But this model also does not fit. Evolution is not a conscious process. It is a winnowing out of the poorly designed and emergence of the better designed on the basis of the process of natural selection. In contrast, in finance the process is conscious and intelligent.

A better analogy than physics or biology is a military one. The point is that there is a strategy of intelligent reaction to any action, an arms race to leapfrog one another in information gathering and technology, to know what others are doing, and to react in a way that they will not anticipate. This is the point where I could pull out quotes from The Art War about seeing into the mind of the enemy, attacking when your opponent believes you will retreat, and the like. That is not physics.

28 comments:

  1. It sounds like you are talking about Game Theory (which has been applied to everything from war to biology).

    On a side note Physics envy seems to infiltrate into every facet of finance (in my case corporate management being asked why we I cannot calculate and measure every financial risk) and for our clients or managers wanting to know the exact ramifications years from now.

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  2. Interesting post.

    Could you please elaborate more on the view that Chaos theory is not working. The move cited by Lo that finance is going more in the direction of biology, meteorology seems to suggest the contrary. But why would intelligence exclude non-linearity.

    I would be interested in your views on this.

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  3. You write: "[the trader] can see things in ways most others do not, anticipate in ways others cannot, and then change his behavior when he starts to see others catching on."

    Really? It seems to me that what makes a trader successful is either luck or illegal activity. Is Warren Buffet a genius or just the one lucky survivor of all his peers?

    It seems to me that the trouble with any metaphor other than game theory is that these fields of study are concerned with non-linear, but not random, systems. Chaos is often misinterpreted to mean random, but this is exactly the opposite of what it means.

    Financial markets, however, can be seen as random, rather than non-linear. There is no useful underlying equation, probabilistic or otherwise, to explain the day-to-day movements. The best we seem to do is broad generalizations, which everyone sees, and present no arbitrage opportunity.

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  4. @Tyler;

    Game theory is unlikely to be much help for this type of uncertainty because most experiments show that labeling the strategies, players, etc makes a difference. Game theory was built on the premise that these were irrelevant.

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  5. This sounds almost like it's saying the EMH is spot on?

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  6. Rick, you may be interested in the black swan group on linked in. We have a few good discussions around risk, knightian uncertainty "the edge of modelling" and behaviour. http://www.linkedin.com/groups?mostPopular=&gid=80474

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  7. I have read you book and appreciate your background and that generally you think things through... but with with regard to the statement you make in the first paragraph you would be better off reading Didier Sornette's full bibliography and the observations of Log-Periodic behavior accross a wide range of processes including facture, birth and the stockmarket. While the application of many physical science methods have not fared well, tossing off comments like your first paragraph without bothering to read and understand Sornette's work does not reflect the type of writing and thinking that I would have come to expect from your previous writings

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  8. Here are some thoughts in resonse to the posts above.

    On chaos theory: The market is not simply a nonlinear dynamical system. It does not follow a non-linear process, for the reasons I mention in the post, and is not deterministic.

    On game theory: Game theory can give insights into behavior in a situation like we have in the market, but it has not shown the ability to be practical in describing the behavior of loosely structured and randomly changing systems with gaming opportunities. The reason, I think, is one that I mention in the post: While there is strategy and gaming behavior in the markets, it is not within a well-specified system. You can't apply game theory when the rules of the game are not known.

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  9. A better analogy than physics or biology is a military one.

    Perhaps that's true as a descriptive matter, but would a military analogy really be better for us from an instrumental standpoint? The motivations for this post are mysterious to me.

    Nobody who builds models -- neither physicists nor economists -- is apt to confuse them with the phenomena those models are meant to describe. That models made by people trained as physicists fail for the same reasons (assumptions of linearity, &c.) as models made by people trained as economists is not surprising, and is no real critique of physicists. We don't know what we don't know, and dismissing whole categories of new models does not seem promising as a learning strategy.

    History too belies the argument that physicists have failed at producing useful economic theory. There is a long line of productive economists who were trained in physics, from Tinbergen and Samuelson to Larry Summers. Have military strategists made the same contribution?

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  10. This post is essentially noise. All it says is that it's difficult to predict human behavior as reflected in market prices, as far as I can tell. And that's true. Many other human behaviors are predictable in a statistical sense, from physical and mental development to distributions of firm sizes, city sizes, etc. And the stories that motivate the power law stuff econophysics has done (their best results, IMHO) are deeply insightful in, yes, an evolutionary and biological kind of way.

    When it comes to intellectual integrity, however, the physicists win hands down. Finance and economics professors have proven themselves to be ideological cheerleaders of the worst kind as a group, and have done more damage than good. Efficient markets, marginal productivity theory, all the Establishment-serving orthodox mythologies of neoclassical economics... Fischer Black... Merton... Scholes... the Fed... virtually all their fruit is vanity and waste.

    I'm an former academic economist, BTW, now a practitioner, and yes, I envy the physicists' tool kit--they are smarter than we are--but even more, a certain high-mindedness I've never found in economists.

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  11. LOL! I'm a Meteorologist. Meteorology is within the domain of Atmospheric Physics. In essence, anyone who gets a full academic degree in Meteorology is essentially getting a degree in Physics. A Ph.D in Physics once said he thinks Meteorology is somewhat harder than rocket science! An even more rarefied related specialty is Climatology. Witness the multitudes of people who don't understand physics let along Climatology who think they know something about climate change. You're right that "most of finance is child’s play once you have gone through the rigors of a physics degree" but finance clearly is a different animal of complexity. By the way, the late Ed Lorenz who was a pioneer of chaos theory was a Meteorologist :-)

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  12. It's very strange to write a paper about physics envy without even refering to Philippe Mirowski Masterpiece "More Heat than light : Economics as Social Physics, Physics as Nature's Economics. See chapter 7 "The ironies of Physics envy".

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  13. Taking your train of thought one step further in the line of a "military analogy": when simulating tactical maneuvers for military purposes, the latest trend is using intelligent agents. Does this type of "model" also fall under your critique? Or is there a more robust "feedback" in creating "adversaries" and seeing how they would react to your moves (in your opinion)?

    (I must say, as a physicist, it is interesting to hear these well-argued comments, contrasting all the hype that is thrown around a lot.)

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  14. Unfortunately we have raised a generation of financiers so fixated with this nonsense that our capital markets have become dysfunctional. Capital is being misallocated on a massive scale so geek SD wannabes can play video games.

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  15. Michael,

    Tinbergeb, Samuelson, and Summers used quantitative methods (from physics and elsewhere) to transform economics from within. The econophysics movement now is trying to do its own separate thing. That does not mean the econophysics are wrong, but it does mean that the historical analogy is not applicable.

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  16. Dear Richard,

    Thank you for keeping up with the public dialogue.

    As you well know, I chronicle the array language tool makers. And of course, my folks are using the languages to develop biological computing models as well as physics models, so I'm model neutral, in this sense.

    My interest is where your thesis centres around the hammer/nail analogy.

    Is the hammer accountable for the hitting?

    I don't have clarity myself, though if we're talking about guns, it seems obvious that someone without a gun cannot shoot.

    And even in war, we have the Hague.

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  17. On Ervik's comment:

    Perhaps something along the lines you suggest will get us closer to where we want to go. I think one place to look is with agent based models. But up to this point, they have been mostly toys to show how simple rules can lead to complex behavior and create patterns that in some respects look like what we see in markets (i.e. with momentum, booms and busts).

    And the question is how you imbue the agents with intelligence and an ability to react by thinking outside the box.

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  18. As I commented over at FTAlphaville: Well put; ecological analogies fit markets better than physical analogies. And like ecologies, economies resist prediction and control.

    I've tried to explain all this to my brighter Ph. D. in physics father-in-law, with modest success. People adapt, inanimate objects don't.

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  19. Nice post Rick. If the economy or economics is not simply a non linear dynamical system, not deterministic and not following non linear processes , how would you characterize it? I view it as an example of a complex,adaptive and evolving, dynamic, non linear system subject to positive and negative feedback, random events and changing variables under the governance of all the chaotic emotions in the human prefrontal cortex. No wonder it is impossible to model accurately!! It should be mentioned that what we think of as classical economics began in the mid 19th century, an exciting time with nascent concepts of energy,matter, electricity and light being hashed out by towering fathers of modern physics. The ancestors of modern economics, non physicists, convinced themselves that analogues for physical concepts must exist in economics and they adopted and transliterated these physical concepts across to their evolving ideas of economics, a blunder that we are still living with today. I agree with the meteorologist that economics and markets share characteristics with complex fields like climate and meteorology. Economics is probably a beast unto itself perhaps more under the control of sorcery than game or chaos theory.

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  20. Hhhmmm...Isn't it the other way around? It seems to me physicists have economics envy.

    To David Merkel: Inanimate objects aren't. There's a lot going on down there.

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  21. I very much enjoyed this post.

    It’s a topic that I’ve been thinking about a lot and I’ve recently written an article on what economics can learn from models used by ecologists. I don’t know if you’re familiar with the work of Robert May at all, but he was the man who effectively destroyed the notion in ecology that complexity in and of itself was a good thing. He used a toy model, which (ironically) borrowed from a theorem in physics and which was what could fairly be termed an agent-based model in that the species in the model affected outcomes through their interactions, to show that complexity was only good up to a point, and that the relationship between complexity and stability was in fact non-linear. He has now applied the model to the financial system in an article for a Scientific journal called Interface.

    Andrew Haldane, who’s the executive director for financial stability at the Bank of England, in a speech called ‘Rethinking the Financial Network’ which, I think, owes a lot to his familiarity with May’s ideas, posited that this same non-linear relationship between complexity and stability exists in financial systems. Complexity resulted in the financial system responding well to the bursting of the dotcom bubble, for instance, but almost led to its collapse when hit with the failure of Lehman Brothers. I’d be interested to hear your views on Haldane’s speech.

    I was also interested in the following passage:

    Evolution is not a conscious process. It is a winnowing out of the poorly designed and emergence of the better designed on the basis of the process of natural selection. In contrast, in finance the process is conscious and intelligent.

    I’m not sure it matters for the purposes of making better economic models whether poor business models are winnowed out and better ones emerge as a result of a conscious or unconscious process. What matters, I think, is that borrowing models of ecosystems enables economists to create agent-based models in which interactions between different financial players can play a key role in determining and influencing outcomes.

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  22. When I was in high school, my physics teacher liked to open with "suppose you had a pair of frictionless roller skates". I usually spent the rest of the class daydreaming about all the trouble I could get into with frictionless roller skates and how I would get rich having some sweat shop factory in the far east mass produce them for me (I hadn't taken business law at that point, so I was still optimistic).

    To paraphrase George EP Box "Essentially, all models are wrong, but some are useful."
    Here in lies the correct application of frictionless roller skates. Perhaps closed system models are wrong for finance, but they do open the debate. I believe that rational economic games go a long way toward explaining financial behavior. I also believe in using the tools of physics, more to think about the open ended problems as opposed to solving them.

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  23. In all of these speculations -- and among economists in general -- it is striking that no one asks what justifies economics as a science, since it cannot reliably predict very important events. Economics takes off as a science from Adam Smith and the law of supply and demand, which is dubbed a scientific principle because it analogizes Newton's Third Law - handed down from the 17th Century. Newton's laws apply perfectly to perpetual motion machines, but economics is stuck with a nasty, ultimately irreducible inefficiency called "profit" -- which we believe makes the case to reformulate economics as a thermodynamic - a thermo-economic -- system fueled by consumers' dollars. How thermo-economically apt it is that end-users are fuel-burning "consumers"! This brings us at least into the 19th century. Among the benefits of a thermo-economic reformulation is the ease with which profit may be construed as "Shannon entropy", a capacity to convey information. Now we have arrived at least into the late 20th Century. Please visit our work very much in progress at profitandentropy.com, and tell us what you think. Our email addresses are there - we will have a comment posting capacity ASAP.
    Richard Goldwater

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  24. Perhaps this might be of interest:
    “’Physics envy’ – physics abysmally misconstrued!” – http://www.repiev.ru/articles/Physics-Envy.htm

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  25. This comment has been removed by a blog administrator.

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  26. Here is the challenge, any explanations that seek predictability and reliability and empirical relevance must tie to the already discovered best predictable models of experience we have. Those come from the sciences and laws of biology, chemistry and physics.

    Reality is all about electron exchanges after all.

    If econ cannot ultimately tie back to neuroscience and other laws of those disciplines -- it is just story-telling.

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  27. What works and does not work has always been an issue. The fact that people use it does not validate a method. The fact that people reject it does not invalidate a method. Astrology works in predicting the markets but, few use it even when the records show high accuracy demonstrated by some such as W D Gann.

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  28. It becomes less useful if the uncertainty is fuzzy and ill-defined, what is called Knightian uncertainty.

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