Proshare - Facebook Proshare - Twitter Proshare - Google+ Proshare - Linked In Proshare - RSS Feed

How mathematical modelling seduced Wall Street


25 October 2011 by Emanuel Derman    


From apartheid to financial markets, trying to capture messy human behaviour using techniques from science can derail us all


How often are we guilty of a type of naivety both in science and in life by insisting that the things we don't understand really do fit into the boxes of the things we imagine we do; that the facts fit our models of them?


Take the comments by influential biologist and evangelistic atheist Richard Dawkins in the Los Angeles Times in 2007 about the scientific "vandalism" involved in hanging Saddam Hussein: "[his] mind would have been a unique resource for historical, political and psychological research... Psychologists, struggling to understand how an individual... could be so evil... would give their eye teeth for such a... research subject. Political scientists... have now lost key evidence forever."


There is stunning unimaginativeness in these remarks. How little someone must understand the complexities of human nature if they think we can learn to avoid creating monsters by questioning or even dissecting the brains of a Saddam, a Hitler or a Stalin.


Everyday life is also full of examples, some less harmless. Take the South Africa I grew up in during the apartheid era. How convenient for such a government had there been some sort of device to detect and sort people's racial composition to fit its rigid, legal categories of whites, natives (blacks), coloureds and Indians. Racial classification was a tortuous, blatant attempt to impose a hopelessly flawed model of race and genetic origins onto unruly reality.


A while back, to describe this kind of naivety, I coined the word "pragmamorphism". If anthropomorphism is the attribution of human characteristics to inanimate objects, giving inanimate objects the shape of humans, pragmamorphism refers to the attribution of the properties of inanimate things to humans, to giving human minds material qualities.


I must confess that I write from experience, having been guilty of pragmamorphism in using methods drawn from the physical sciences and mathematics to model stock prices, those decidedly non-physical quantities that represent value as determined by humans interacting in markets. Model building isn't necessarily bad, as long as you understand the limitations. In my new book Models. Behaving. Badly, I explain why, on Wall Street and in life, it is crucial to carefully distinguish between theories and models.


I began working life as a physicist, excited by science and filled with a heady mixture of idealism and ambition. I aspired to be another Albert Einstein or Erwin Schrödinger, who intuited the way the universe works. Physics is wonderful at this: in the 17th century, Newton wrote a few compact principles and equations describing nature to an astonishing degree of accuracy. So, in the 20th, did Einstein, Schrödinger and Paul Dirac, whose famous equation describes the measured properties of electrons to an accuracy of 11 significant figures.

In late 1985, I left particle physics for financial research at Goldman Sachs, building physics-style models of options and markets. I was one of the early physicists on Wall Street or POWS, working as a quantitative analyst, or "quant".


Finance was exciting; it seemed a lot like the physics I was used to. The traders were the experimentalists, and I was a theorist working with them. Soon I began to believe it possible to apply the same methods to economics, perhaps even to build a grand unified theory of securities. Along the way I published many papers and built many models, including the Derman-Kani local volatility model, several of which are widely used today. But it takes wise people to use them properly, and I was lucky that most traders I worked with understood how to use them well. Not everyone does.


Theories, as distinct from models, attempt to discover the principles driving the natural world. They need confirmation, but not justification. Successful theories work because they describe how the world really operates. Laws of matter, equations for light, quantum mechanics: like all theories, you can discover them, but you can't ask why they are true. They are a kind of fact. Theories, in short, stand on their own two feet.


Models, however, stand on someone else's feet: they are metaphors or analogies. Calling the brain an electronic computer is a model, as is calling a computer an electronic brain. Models tell you only what something is more or less like, but their necessary simplifications ignore some dimensions of the world.


In economics, there are no true theories: one can make only models. The Efficient Market Model that has gone so badly awry compares stock prices to smoke diffusing through a room, and models them using the physics of diffusion. But these are flawed analogies, neither theory nor fact. The similarity of physics and finance turns out to lie more in their mathematical language - their syntax - rather than their semantics.


Now back in academia, I watch the world struggling with what's happened to economics and markets. Over the past two decades, the US has suffered multiple blows: the decline of manufacturing; ballooning of the financial sector; that sector's capture of the regulatory system; monetary stimulus whenever the economy wavered; taxpayer-funded bailouts of large corporations; a pervasive crony capitalism bordering on corruption; private profits and public losses; the redemption of the rich and powerful by the poor and weak; ratings agencies giving unrealistically good ratings as part of their business strategy; state policies trying to cure insolvency by branding it illiquidity (as in Greece); and the widespread use of obviously poor economic models.


The internecine feuds in the daily papers show economics is largely about what is good for society - and how to get it. We used to put economics with politics and philosophy as PPE, the moral sciences. Now it's MPNE, with mathematics, psychology and neuroscience, the traditionally value-free sciences. There is nothing wrong with them, but if economics is about what's good and how to get it, it can't be value-free. Its mathematical models are vastly inadequate metaphors. Its papers read like Euclid, with axioms and theorems, its false rigour inversely proportional to its minimal efficacy.


The truth is that no model invented can tell how any stock or share price will perform. The worm at the heart of economics has been its dark love of inappropriate scientific elegance and scientism. We forget at our peril that markets and prices are generated by human behaviour. And the greatest danger in modelling human behaviour is a kind of pragmamorphism, in imagining that someone can write a theory encapsulating behaviour and thereby relieve us of the constant difficulty of complex thinking. To confuse a limited model with a theory is to embrace a future disaster driven by the belief that humans obey mathematical rules.


Economists think matter is simple, and that people can be modelled similarly. But Schrödinger, father of the quantum mechanical wave equation, knew the apparent solidity of matter disguises the mystery beneath. In What is Life?, he wrote: "My body functions as a pure mechanism according to the Laws of Nature. Yet I know, by incontrovertible direct experience, that I am directing its motions... in which case I feel and take full responsibility for them." Like Schrödinger, we should recognise the great puzzle of scientific success. On the one hand, scientists have the ability to discover nature's mechanistic laws; on the other, to discover them we have to assume that scientists have autonomy, they can tell right from wrong, they are not mechanical beings. In short, to find the laws, we must assume we are not subject to them.


Even if you don't see things Schrödinger's way, it's essential to understand that models in the social sciences, and in finance particularly, are very different from models in the physical sciences. They should be accompanied by a health warning to ensure that no one forgets.




Emanuel Derman is head of financial engineering at Columbia University, New York City. His first book, My Life as a Quant, detailed his time as head quantitative analyst at Goldman Sachs. This essay is based on his new book, Models. Behaving. Badly (Wiley/Freepress) and on his blog at



Source: New Scientist



Related News