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Wednesday 11 February 2009

Newton's Financial Crisis: the Limits of Quantification

Issac Newton's Nail
“To the man with only a hammer, every problem looks pretty much like a nail”
The blame for the crisis in today’s financial markets lies, in my opinion, with one man. Isaac Newton.

The observant among you may spot a potential flaw in this theory. The great English scientist has been dead for two hundred and eighty two years. But let’s not let a matter of such insignificant detail delay us, the genesis of the credit crunch can clearly be traced back to the man whose balls swing so freely on many a stressed executive’s desk.

The Start of Mathematical Modelling

Newton’s Theory of Gravity was a landmark in the history of science. It wasn’t just that he was able to describe the mechanics of celestial movement from a study in rural, plague-ridden Oxfordshire by dint of observing a falling apple. That was pretty spectacular - as was his casual invention of calculus and the fact he was so busy sticking needles in his eye and attempting to coax gold out of bits of coal, lead and mouse droppings that he lost the original proof of his theory and had to be bribed by Edmond Halley (he of the comet) to write another one.

No, the most amazing thing was that he described his theory using mathematics. Today this seems perfectly natural – no theory in physics has much credibility until the mathematical models that describe it can be proven – but in Newton’s time it was revolutionary (in both senses of the word). By modelling his theory using maths he was able to develop something that didn’t just describe the observed motions of the heavens but which was also able to predict them and in so doing ushered in the whole gamut of modern science.

Professional Science and Peer Review

This had a couple of fairly immediate effects that we can still see the impact of today. Firstly doing science rapidly became equivalent to doing mathematics. Before Newton physics was descriptive and dominated by amateurs. After Newton a class of professional scientists started to develop for whom mathematical modelling was the key to understanding the universe. This change happened pretty rapidly – Robert Hooke, the hunchbacked polymath who was Newton’s contemporary (and who is a particular hero of mine) spent the rest of his life claiming that Newton had stolen his idea to develop gravitational theory. In fact there’s some evidence that Hooke did give Newton a key insight into centripetal motion but Hooke’s ideas were purely descriptive. It was Newton’s unique mathematical approach that won him the plaudits, a key place in history and set the scene for the rise of mathematical modelling.

What this movement into maths meant, however, was that science became increasingly remote from ordinary people and, more and more, we had to rely on the scientists themselves to check their own work. Fortunately most scientists have egos the size of the US’s budget deficit so if they actually ever agree on anything there’s a fairly high degree of probability it’s near enough right. Anyway, the process of peer review which governs modern science has grown up to provide a basis for accepting new work and the norm of the rest of us taking the experts at their words has grown along with it.

Physics Envy

The second impact of Newton’s new approach was to establish physics as the gold standard to which other disciplines should aspire. Predictive, mathematical, science was long held in much higher regard than descriptive subjects like sociology and psychology and it became a fairly natural progression for other subjects to attempt to develop similar processes. So much so that “science” is now roughly equated with “prediction”. If you can’t predict you ain’t scientific, is the general idea.

Unfortunately these two features – the esteem of the predictive sciences and the general population’s ignorance of the underlying maths that underpins them have conspired to make lots of quite nasty things happen without much debate. Some of these led to eugenics and the gas chambers and others to I.Q. testing and mass sterilization. And yet others led to the Efficient Market Hypothesis, quantitative investment analysis and the wholesale destruction of the modern financial system.

The Efficient Market Hypothesis

The Efficient Market Hypothesis is one of the great blights of modern investment analysis. What it says is that markets price efficiently, all the time. So all known information is already in the price of stocks or bonds or whatever which means that unless you know something that’s not in the public domain you can’t, on average, profit by trading. The corollary of this is that you can develop mathematical models to describe – and predict – market movements.

Charlie Munger, the octogenarian billionaire Vice-Chair of Berkshire Hathaway has a name for the Efficient Market Hypothesis. He calls it “bonkers”.

On one hand it’s perfectly obvious that markets are pretty efficient most of the time. The whole point of a market is to find a price at which an instrument will clear – where buyers and sellers are matched. However, the key is in that critical “most of the time”. From time to time things go spectacularly wrong: think South Sea Bubble, Wall Street Crash and dotcom mania. There are plenty of other examples. Unfortunately “most of the time” doesn’t model very well in maths. It comes up with things like “this model will only go wrong once every million years”. Whereupon it does, usually more or less immediately.

Imprecise Investment Analysis

What we can see here is investment analysis modelling itself on physics by clothing itself in the garments of precision. Sadly this is illusory – just because you can model something doesn’t mean it’s correct. Unfortunately it seems the leaders of the world’s major financial corporations are as wide-eyed as the rest of us when it comes to implicitly believing people armed with a white coat, weird hair and a supercomputer. Although given the accuracy of some of the models used to predict the valuation of collateralised sub-prime mortgages one is left with the sneaking suspicion that this was actually the work of a couple of geeks in a basement armed with an Excel spreadsheet. Anyway, the trouble with this goggle-eyed acceptance of these quantitative approaches is that, unlike science, there’s no peer review. The lunatics had truly taken over the asylum.

Someone who invests purely on the basis of the Efficient Market Hypothesis and mathematical models is like the man with a hammer: when faced with a problem that isn’t a nail they hammer on regardless. Munger describes this as the quest for spurious precision: the inappropriate application of the models of the hard sciences to domains where it’s simply not appropriate.

Newton's Money Madness

Isaac Newton ended up running the Royal Mint but like many of today’s financial guardians he had no idea about investing because at root it’s not mathematics that rules the markets, it’s human behaviour. He lost a load of money in the bust of the South Sea Bubble of 1720 and learned the hard way that although you can take humanity out of the models you can’t take it out of the markets. His lament rings as true today as it did three centuries ago:
“I can calculate the motions of the heavenly bodies, but not the madness of people”.

Related articles: Perverse Incentives are Daylight Robbery, Alpha and Beta: Beware Gift Bearing Greeks, The Tragedy of the Financial Commons, Seven Psychological Quirks that Destroy Returns


  1. Newton's second law is not easily implied from his Principia. I think you are thinking too highly of someone who used infinitesimals and then set them to zero. It took a lot of work to justify mathematically Newton's ideas, which were implanted in him by Hook mainly. Euler basically derived the second law. Newton's law of gravity was known for a while but nobody coudld prove it. Eevn Feynman admitted that he could not follow Newton's proof.

  2. A fair point, although Newton explicitly stated that he wanted the Principia to be hard to understand so that people wouldn't bother him. Newton's achievement was certainly built on that of others, Hooke included, but it was his mathematical formulation of the proofs that gave him primacy, and established the subsequent quantitative approach of all scientific proof.

    Feynman did indeed give up on the Principia, but being Feynman he went off and developed his own proof as documented in Feynman's Lost Lecture: The Motion of Planets Around the Sun.