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Saturday 26 June 2010

Physics Risk Isn't Market Uncertainty

Physics Envy

The idea that economics should be modelled on the concepts of physics has been prevalent for the best part of a century. It’s a deliciously engaging idea, that the steadfast and unbending rules of science should be the template for the queen of the social sciences. The only trouble is that in economics human beings are part of the system and don’t tend to behave as economists would wish them to.

On the other hand the ideas generated by analogies between physics and economics have generated a whole bunch of truly great economic ideas and are the basis of the whole of microeconomics. Although it’s tempting to argue that these ideas don’t truly make sense it’s actually quite hard to make this accusation stick. Economics and physics are connected - only just not quite the way economists like to imagine.

Random Walks

The links between economics and physics have a very long history, right back to the seminal work of Louis Bachelier in 1900, when he created a model of economics that predated Einstein’s similar work on Brownian motion – the original random walk theory – by half a decade. Bachelier’s ideas then lay forgotten for half a century until they were rescued and resurrected by Paul Samuelson.

Samuelson is by far the most important economist of the second half of the twentieth century and his PhD thesis, Foundations of Modern Economics Analysis, is the most important work of that age. Samuelson was more or less the first person since Bachelier to start from the premise that there are analogies to be drawn between science and economics that can usefully be applied to generating economic theories, a position from which he then proceeded to develop a whole range of new insights into economics.

From Quals to Quants

Samuelson’s approach led directly to the replacement of high minded qualitative ideas about economics with numerical precision: these theories allowed economists to mathematically model their concepts rather than merely engaging in frantic handwaving. In many ways Samuelson is the economic equivalent of Issac Newton, who was the first scientist to solve problems in physics through mathematics, as he turned the dismal science into a quantifiable and manageable set of premises and axioms.

The weakness in this approach is that showing an analogy between economics and physics isn’t the same as proving that they can be treated in the same way. As any philosopher knows, an argument from analogy is a dangerously weak one. Assuming analogies on the basis of external similarities has led to many arguments which on the surface appear to be valid but which fall apart once we peer under the covers at mechanisms.

The most famous of these analogies was William Paley’s famous argument from design in which he argued that just as a complex artefact like a watch required a designer so a complex organism like a human being also required a designer. It took Darwin to expose the mechanisms and therefore the failings of this argument, but the general problem is well understood: analogy is a poor basis for a powerful proposition.

Heat and not much Light

So, for example, the Black-Scholes option pricing model is directly based on the physical law of thermodynamics in a direct line from Bachelier’s models of financial speculation (although as this paper points out the analogy isn't exact). Yet we know that this model has failed catastrophically under extreme conditions in a way that Brownian motion never does: the behaviour of molecules is predictable, en masse, the behaviour of financial derivatives is not. So what’s the difference?

Well, the main issue is people, of course, whose range of behaviour is simply not as predictable as those of elementary particles. In a fascinating paper by Andrew Lo and Mark Mueller – in fact it’s almost a book – entitled WARNING: Physics Envy May be Hazardous to Your Wealth the authors propose that the main difference between these types of system is down to uncertainty.

Knight's Uncertainty

Uncertainty is the type of randomness in systems that can't be predicted by statistical analysis, which is contrasted with risk, which is randomness that can be predicted. This distinction was originally made by Frank Knight and focussed on the difference between, say, the volatility of stock prices you see in so-called equilibrium conditions – when the variation in prices is statistically quantifiable – and the affects of an event like 9/11. The former is risk, the latter uncertainty. Physics is essentially about measurable risk while economics is about risk and unmeasurable uncertainty which means that there's always a chance that any nice statistical models will be wrecked by the random behaviour of human beings.

It’s of course a bit surprising that it took economists quite so long to wake up to the fact that their risk quantifying models were failing to handle the fundamental uncertainty of the world. Certainly it rather looks like the overt focus on mathematical models and the spurious comfort that this provided practitioners rather overwhelmed the more obvious lessons of psychology that were there for everyone to see, had they been prepared to open their minds.

Danger, Dumb Management

The underlying issue is that markets are artefacts of human behaviour, not fundamental postulates of the physical world. The best we can say about such artefacts is that they often operate as though they’re not subject to uncertainty. On the other hand this is a statement of the bloody obvious – if the world didn’t frequently work as though uncertainty doesn’t exist the models wouldn’t work at all and it would be impossible to make the claims that economists often do for the power of their wayward children.

What Lo and Mueller argue is that too much weight has been given to those areas that can be mathematically quantified and too little to those that can’t. So even if the quantitative models that failed during various financial crises would have succeeded eventually they were bound to fail in the short term due to failures of management or of investor nerve. These were not failures of the risk models but failures to model risk, situations which the researchers argue:
“requires managers who understand both the business environment and the limitations of models and the consequences of their failure. When senior management is missing one of these two perspectives, the consequences can be disastrous.”
No Hiding Place for Economists

However, they also go on to point out that the failures of economic models and the failures of the models of physics generally lead to quite different outcomes. When the latter go wrong the scientists retreat to a dark corner and try and figure out what to do next, largely untouched by the behaviour of politicians, media commentators and the public. In the former case economists have no such leeway – failures of economic models are generally very public and generate public expectations.

The failures of quantitative models are, in the researchers’ view, not a reason to stop developing and using such models. Rather, they argue, it’s necessary that everyone relying on them in the management chain should understand their inherent limitations. As they say “managers in positions of responsibility should no longer be allowed to take perverse anti-intellectual pride in being quantitatively illiterate in the models and methods on which their businesses depend”.

Of course, we might hope that economists would make clear the limitations of their models before letting them loose on the public. But perhaps that's a step too far? Or perhaps not.

Uh Oh, CEO

Anyway, the idea that they might have to take responsibility for the risky behaviour of their corporations is going to be a bit of a shock to a generation of technology blind CEO’s who are incapable of opening attachments on their Blackberries, let alone understanding the possible ramifications of Gaussian copulas. However, it’s doubtful that this would help because as the reseachers also point out there had been a seventy year period prior to the property price implosion during which US home prices didn’t decline significantly. Given that disaster myopia – the tendency to assume small probabilities of disaster are actually zero – kicks in within much shorter periods that this it would've taken some heroic risk management to have kicked against the traces when everyone else was making money hand over fist on what appeared to be a one way bet.

Lo and Mueller believe that we need more and better quantitative modelling to improve the models, not less. They’re right of course, but along with this we need better management and understanding of what these models mean. We could start by making the CEOs of organisations personally responsible for the risks in their businesses. Don’t hold your breath though, mathematical analysis doesn’t tend to be high on the list of skills valued in chief executives.

Related Articles: Ambiguity Aversion: Investing Under Conditions of Uncertainty, Econophysics, Consciousness and Cosmic Karma, Darwin's Stockmarkets


  1. Confidence sells. Humility works.


  2. The problem is not a lack of mathematical knowledge amongst CEOs; it is precisely the fact that their lack of mathematical knowledge makes them unwilling to challenge mathematical models. Humility and a tendency to explain 'where the model will fail' are not notable qualities amongst modellers. However, this does not stop quantitative financiers from complaining that they had been 'misunderstood'. This is nonsense; Quants are more responsible than anybody else for allowing people to work on the basis of a single, "probable" (according to some sophisticated model), 'expected' outcome, rather than understanding that the actual outcome is hardly ever that expected. (The expected value of a one dollar bet on the toss of a coin is zero - but that outcome will never happen).