Don’t let the Nobel prize fool you. Economics is not a science

The award glorifies economists as tellers of timeless truths, fostering hubris and leading to disaster

Joris Luyendijk in The Guardian


 

‘A Nobel prize in economics implies that the human world operates much like the physical world.’ Photograph: Jasper Rietman


Business as usual. That will be the implicit message when the Sveriges Riksbank announces this year’s winner of the “Prize in Economic Sciences in Memory of Alfred Nobel”, to give it its full title. Seven years ago this autumn, practically the entire mainstream economics profession was caught off guard by the global financial crash and the “worst panic since the 1930s” that followed. And yet on Monday the glorification of economics as a scientific field on a par with physics, chemistry and medicine will continue.

The problem is not so much that there is a Nobel prize in economics, but that there are no equivalent prizes in psychology, sociology, anthropology. Economics, this seems to say, is not a social science but an exact one, like physics or chemistry – a distinction that not only encourages hubris among economists but also changes the way we think about the economy.

A Nobel prize in economics implies that the human world operates much like the physical world: that it can be described and understood in neutral terms, and that it lends itself to modelling, like chemical reactions or the movement of the stars. It creates the impression that economists are not in the business of constructing inherently imperfect theories, but of discovering timeless truths.

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To illustrate just how dangerous that kind of belief can be, one only need to consider the fate of Long-Term Capital Management, a hedge fund set up by, among others, the economists Myron Scholes and Robert Merton in 1994. With their work on derivatives, Scholes and Merton seemed to have hit on a formula that yielded a safe but lucrative trading strategy. In 1997 they were awarded the Nobel prize. A year later, Long-Term Capital Management lost $4.6bn (£3bn)in less than four months; a bailout was required to avert the threat to the global financial system. Markets, it seemed, didn’t always behave like scientific models.

In the decade that followed, the same over-confidence in the power and wisdom of financial models bred a disastrous culture of complacency, ending in the 2008 crash. Why should bankers ask themselves if a lucrative new complex financial product is safe when the models tell them it is? Why give regulators real power when models can do their work for them?

Many economists seem to have come to think of their field in scientific terms: a body of incrementally growing objective knowledge. Over the past decades mainstream economics in universities has become increasingly mathematical, focusing on complex statistical analyses and modelling to the detriment of the observation of reality.

Consider this throwaway line from the former top regulator and London School of Economics director Howard Davies in his 2010 book The Financial Crisis: Who Is to Blame?: “There is a lack of real-life research on trading floors themselves.” To which one might say: well, yes, so how about doing something about that? After all, Davies was at the time heading what is probably the most prestigious institution for economics research in Europe, located a stone’s throw away from the banks that blew up.

 Howard Davies, pictured in 2006. Photograph: Eamonn McCabe for the Guardian

All those banks have “structured products approval committees”, where a team of banking staff sits down to decide whether their bank should adopt a particular new complex financial product. If economics were a social science like sociology or anthropology, practitioners would set about interviewing those committee members, scrutinising the meetings’ minutes and trying to observe as many meetings as possible. That is how the kind of fieldwork-based, “qualitative” social sciences, which economists like to discard as “soft” and unscientific, operate. It is true that this approach, too, comes with serious methodological caveats, such as verifiability, selection bias or observer bias. The difference is that other social sciences are open about these limitations, arguing that, while human knowledge about humans is fundamentally different from human knowledge about the natural world, those imperfect observations are extremely important to make.

Compare that humility to that of former central banker Alan Greenspan, one of the architects of the deregulation of finance, and a great believer in models. After the crash hit, Greenspan appeared before a congressional committee in the US to explain himself. “I made a mistake in presuming that the self-interests of organisations, specifically banks and others, were such that they were best capable of protecting their own shareholders and their equity in the firms,” said the man whom fellow economists used to celebrate as “the maestro”.

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In other words, Greenspan had been unable to imagine that bankers would run their own bank into the ground. Had the maestro read the tiny pile of books by financial anthropologists he may have found it easier to imagine such behaviour. Then he would have known that over past decades banks had adopted a “zero job security” hire-and-fire culture, breeding a “zero-loyalty” mentality that can be summarised as: “If you can be out of the door in five minutes, your horizon becomes five minutes.”

While this was apparently new to Greenspan it was not to anthropologist Karen Ho, who did years of fieldwork at a Wall Street bank. Her book Liquidated emphasises the pivotal role of zero job security at Wall Street (the same system governs the City of London). The financial sociologist Vincent Lépinay’s Codes of Finance, a book about the division in a French bank for complex financial products, describes in convincing detail how institutional memory suffers when people switch jobs frequently and at short notice.

Perhaps the most pernicious effect of the status of economics in public life has been the hegemony of technocratic thinking. Political questions about how to run society have come to be framed as technical issues, fatally diminishing politics as the arena where society debates means and ends. Take a crucial concept such as gross domestic product. As Ha-Joon Chang makes clear in 23 Things They Don’t Tell You About Capitalism, the choices about what not to include in GDP (household work, to name one) are highly ideological. The same applies to inflation, since there is nothing neutral about the decision not to give greater weight to the explosion in housing and stock market prices when calculating inflation.

  Ha-Joon Chang, pictured at the Hay-on-Wye festival, Wales. Photograph: David Levenson/Getty Images

GDP, inflation and even growth figures are not objective temperature measurements of the economy, no matter how many economists, commentators and politicians like to pretend they are. Much of economics is politics disguised as technocracy – acknowledging this might help open up the space for political debate and change that has been so lacking in the past seven years.

Would it not be extremely useful to take economics down one peg by overhauling the prize to include all social sciences? The Nobel prize for economics is not even a “real” Nobel prize anyway, having only been set up by the Swedish central bank in 1969. In recent years, it may have been awarded to more non-conventional practitioners such as the psychologist Daniel Kahneman. However, Kahneman was still rewarded for his contribution to the science of economics, still putting that field centre stage.

Think of how frequently the Nobel prize for literature elevates little-known writers or poets to the global stage, or how the peace prize stirs up a vital global conversation: Naguib Mahfouz’s Nobel introduced Arab literature to a mass audience, while last year’s prize for Kailash Satyarthi and Malala Yousafzai put the right of all children to an education on the agenda. Nobel prizes in economics, meanwhile, go to “contributions to methods of analysing economic time series with time-varying volatility” (2003) or the “analysis of trade patterns and location of economic activity” (2008).

A revamped social science Nobel prize could play a similar role, feeding the global conversation with new discoveries and insights from across the social sciences, while always emphasising the need for humility in treating knowledge by humans about humans. One good candidate would be the sociologist Zygmunt Bauman, whose writing on the “liquid modernity” of post-utopian capitalism deserves the largest audience possible. Richard Sennett and his work on the “corrosion of character” among workers in today’s economies would be another. Will economists volunteer to share their prestigious prize out of their own acccord? Their own mainstream economic assumptions about human selfishness suggest they will not.

The maths formula linked to the financial crash

Black-Scholes: The maths formula linked to the financial crash

By Tim Harford BBC Radio 4, More or Less
 

It's not every day that someone writes down an equation that ends up changing the world. But it does happen sometimes, and the world doesn't always change for the better. It has been argued that one formula known as Black-Scholes, along with its descendants, helped to blow up the financial world.

Black-Scholes was first written down in the early 1970s but its story starts earlier than that, in the Dojima Rice Exchange in 17th Century Japan where futures contracts were written for rice traders. A simple futures contract says that I will agree to buy rice from you in one year's time, at a price that we agree right now.

By the 20th Century the Chicago Board of Trade was providing a marketplace for traders to deal not only in futures but in options contracts. An example of an option is a contract where we agree that I can buy rice from you at any time over the next year, at a price that we agree right now - but I don't have to if I don't want to.

You can imagine why this kind of contract might be useful. If I am running a big chain of hamburger restaurants, but I don't know how much beef I'll need to buy next year, and I am nervous that the price of beef might rise, well - all I need is to buy some options on beef.

But then that leads to a very ticklish problem. How much should I be paying for those beef options? What are they worth? And that's where this world-changing equation, the Black-Scholes formula, can help.

"The problem it's trying to solve is to define the value of the right, but not the obligation, to buy a particular asset at a specified price, within or at the end of a specified time period," says Professor Myron Scholes, professor of finance at the Stanford University Graduate School of Business and - of course - co-inventor of the Black-Scholes formula.

The young Scholes was fascinated by finance. As a teenager, he persuaded his mother to set up an account so that he could trade on the stock market. One of the amazing things about Scholes is that throughout his time as an undergraduate and then a doctoral student, he was half-blind. And so, he says, he got very good at listening and at thinking.

When he was 26, an operation largely restored his sight. The next year, he became an assistant professor at MIT, and it was there that he stumbled upon the option-pricing puzzle.

One part of the puzzle was this question of risk: the value of an option to buy beef at a price of - say - $2 (£1.23) a kilogram presumably depends on what the price of beef is, and how the price of beef is moving around.

But the connection between the price of beef and the value of the beef option doesn't vary in a straightforward way - it depends how likely the option is to actually be used. That in turn depends on the option price and the beef price. All the variables seem to be tangled up in an impenetrable way.
Scholes worked on the problem with his colleague, Fischer Black, and figured out that if I own just the right portfolio of beef, plus options to buy and sell beef, I have a delicious and totally risk-free portfolio. Since I already know the price of beef and the price of risk-free assets, by looking at the difference between them I can work out the price of these beef options. That's the basic idea. The details are hugely complicated.

"It might have taken us a year, a year and a half to be able to solve and get the simple Black-Scholes formula," says Scholes. "But we had the actual underlying dynamics way before."

The Black-Scholes method turned out to be a way not only to calculate value of options but all kinds of other financial assets. "We were like kids in a candy story in the sense that we described options everywhere, options were embedded in everything that we did in life," says Scholes.

But Black and Scholes weren't the only kids in the candy store, says Ian Stewart, whose book argues that Black-Scholes was a dangerous invention.

"What the equation did was give everyone the confidence to trade options and very quickly, much more complicated financial options known as derivatives," he says.

Scholes thought his equation would be useful. He didn't expect it to transform the face of finance. But it quickly became obvious that it would.

"About the time we had published this article, that's 1973, simultaneously or approximately a month thereafter, the Chicago Board Options Exchange started to trade call options on 16 stocks," he recalls.
Scholes had just moved to the University of Chicago. He and his colleagues had already been teaching the Black-Scholes formula and methodology to students for several years.

"There were many young traders who either had taken courses at MIT or Chicago in using the option pricing technology. On the other hand, there was a group of traders who had only intuition and previous experience. And in a very short period of time, the intuitive players were essentially eliminated by the more systematic players who had this pricing technology."

That was just the beginning.

"By 2007 the trade in derivatives worldwide was one quadrillion (thousand million million) US dollars - this is 10 times the total production of goods on the planet over its entire history," says Stewart. "OK, we're talking about the totals in a two-way trade, people are buying and people are selling and you're adding it all up as if it doesn't cancel out, but it was a huge trade."

The Black-Scholes formula had passed the market test. But as banks and hedge funds relied more and more on their equations, they became more and more vulnerable to mistakes or over-simplifications in the mathematics.

"The equation is based on the idea that big movements are actually very, very rare. The problem is that real markets have these big changes much more often that this model predicts," says Stewart. "And the other problem is that everyone's following the same mathematical principles, so they're all going to get the same answer."

Now these were known problems. What was not clear was whether the problems were small enough to ignore, or well enough understood to fix. And then in the late 1990s, two remarkable things happened.

"The inventors got the Nobel Prize for Economics," says Stewart. "I would argue they thoroughly deserved to get it."

Fischer Black died young, in 1995. When in 1997 Scholes won the Nobel memorial prize, he shared it not with Black but with Robert Merton, another option-pricing expert.

Scholes' work had inspired a generation of mathematical wizards on Wall Street, and by this stage both he and Merton were players in the world of finance, as partners of a hedge fund called Long-Term Capital Management.

"The whole idea of this company was that it was going to base its trading on mathematical principles such as the Black-Scholes equation. And it actually was amazingly successful to begin with," says Stewart. "It was outperforming the traditional companies quite noticeably and everything looked great."

But it didn't end well. Long-Term Capital Management ran into, among other things, the Russian financial crisis. The firm lost $4bn (£2.5bn) in the course of six weeks. It was bailed out by a consortium of banks which had been assembled by the Federal Reserve. And - at the time - it was a very big story indeed. This was all happening in August and September of 1998, less than a year after Scholes had been awarded his Nobel prize.

Stewart says the lessons from Long-Term Capital Management were obvious. "It showed the danger of this kind of algorithmically-based trading if you don't keep an eye on some of the indicators that the more conventional people would use," he says. "They [Long-Term Capital Management] were committed, pretty much, to just ploughing ahead with the system they had. And it went wrong."

Scholes says that's not what happened at all. "It had nothing to do with equations and nothing to do with models," he says. "I was not running the firm, let me be very clear about that. There was not an ability to withstand the shock that occurred in the market in the summer and fall of late 1998. So it was just a matter of risk-taking. It wasn't a matter of modelling."

This is something people were still arguing about a decade later. Was the collapse of Long-Term Capital Management an indictment of mathematical approaches to finance or, as Scholes says, was it simply a case of traders taking too much risk against the better judgement of the mathematical experts?

Ten years after the Long-Term Capital Management bail-out, Lehman Brothers collapsed. And the debate over Black-Scholes and LTCM is now a broader debate over the role of mathematical equations in finance.

Ian Stewart claims that the Black-Scholes equation changed the world. Does he really believe that mathematics caused the financial crisis?

"It was abuse of their equation that caused trouble, and I don't think you can blame the inventors of an equation if somebody else comes along and uses it badly," he says.

"And it wasn't just that equation. It was a whole generation of other mathematical models and all sorts of other techniques that followed on its heels. But it was one of the major discoveries that opened the door to all this."

Black-Scholes changed the culture of Wall Street, from a place where people traded based on common sense, experience and intuition, to a place where the computer said yes or no.

But is it really fair to blame Black-Scholes for what followed it? "The Black-Scholes technology has very specific rules and requirements," says Scholes. "That technology attracted or caused investment banks to hire people who had quantitative or mathematical skills. I accept that. They then developed products or technologies of their own."

Not all of those subsequent technologies, says Scholes, were good enough. "[Some] had assumptions that were wrong, or they used data incorrectly to calibrate their models, or people who used [the] models didn't know how to use them."

Scholes argues there is no going back. "The fundamental issue is that quantitative technologies in finance will survive, and will grow, and will continue to evolve over time," he says.

But for Ian Stewart, the story of Black-Scholes - and of Long-Term Capital Management - is a kind of morality tale. "It's very tempting to see the financial crisis and various things which led up to it as sort of the classic Greek tragedy of hubris begets nemesis," he says.

"You try to fly, you fly too close to the sun, the wax holding your wings on melts and you fall down to the ground. My personal view is that it's not just tempting to do that but there is actually a certain amount of truth in that way of thinking. I think the bankers' hubris did indeed beget nemesis. But the big problem is that it wasn't the bankers on whom the nemesis descended - it was the rest of us."

Additional reporting by Richard Knight

The mathematical equation that caused the banks to crash

 Ian Stewart in The Observer 21-02-12

It was the holy grail of investors. The Black-Scholes equation, brainchild of economists Fischer Black and Myron Scholes, provided a rational way to price a financial contract when it still had time to run. It was like buying or selling a bet on a horse, halfway through the race. It opened up a new world of ever more complex investments, blossoming into a gigantic global industry. But when the sub-prime mortgage market turned sour, the darling of the financial markets became the Black Hole equation, sucking money out of the universe in an unending stream.

Anyone who has followed the crisis will understand that the real economy of businesses and commodities is being upstaged by complicated financial instruments known as derivatives. These are not money or goods. They are investments in investments, bets about bets. Derivatives created a booming global economy, but they also led to turbulent markets, the credit crunch, the near collapse of the banking system and the economic slump. And it was the Black-Scholes equation that opened up the world of derivatives.

The equation itself wasn't the real problem. It was useful, it was precise, and its limitations were clearly stated. It provided an industry-standard method to assess the likely value of a financial derivative. So derivatives could be traded before they matured. The formula was fine if you used it sensibly and abandoned it when market conditions weren't appropriate. The trouble was its potential for abuse. It allowed derivatives to become commodities that could be traded in their own right. The financial sector called it the Midas Formula and saw it as a recipe for making everything turn to gold. But the markets forgot how the story of King Midas ended.

Black-Scholes underpinned massive economic growth. By 2007, the international financial system was trading derivatives valued at one quadrillion dollars per year. This is 10 times the total worth, adjusted for inflation, of all products made by the world's manufacturing industries over the last century. The downside was the invention of ever-more complex financial instruments whose value and risk were increasingly opaque. So companies hired mathematically talented analysts to develop similar formulas, telling them how much those new instruments were worth and how risky they were. Then, disastrously, they forgot to ask how reliable the answers would be if market conditions changed.

Black and Scholes invented their equation in 1973; Robert Merton supplied extra justification soon after. It applies to the simplest and oldest derivatives: options. There are two main kinds. A put option gives its buyer the right to sell a commodity at a specified time for an agreed price. A call option is similar, but it confers the right to buy instead of sell. The equation provides a systematic way to calculate the value of an option before it matures. Then the option can be sold at any time. The equation was so effective that it won Merton and Scholes the 1997 Nobel prize in economics. (Black had died by then, so he was ineligible.)

If everyone knows the correct value of a derivative and they all agree, how can anyone make money? The formula requires the user to estimate several numerical quantities. But the main way to make money on derivatives is to win your bet – to buy a derivative that can later be sold at a higher price, or matures with a higher value than predicted. The winners get their profit from the losers. In any given year, between 75% and 90% of all options traders lose money. The world's banks lost hundreds of billions when the sub-prime mortgage bubble burst. In the ensuing panic, taxpayers were forced to pick up the bill, but that was politics, not mathematical economics.

The Black-Scholes equation relates the recommended price of the option to four other quantities. Three can be measured directly: time, the price of the asset upon which the option is secured and the risk-free interest rate. This is the theoretical interest that could be earned by an investment with zero risk, such as government bonds. The fourth quantity is the volatility of the asset. This is a measure of how erratically its market value changes. The equation assumes that the asset's volatility remains the same for the lifetime of the option, which need not be correct. Volatility can be estimated by statistical analysis of price movements but it can't be measured in a precise, foolproof way, and estimates may not match reality.

The idea behind many financial models goes back to Louis Bachelier in 1900, who suggested that fluctuations of the stock market can be modelled by a random process known as Brownian motion. At each instant, the price of a stock either increases or decreases, and the model assumes fixed probabilities for these events. They may be equally likely, or one may be more probable than the other. It's like someone standing on a street and repeatedly tossing a coin to decide whether to move a small step forwards or backwards, so they zigzag back and forth erratically. Their position corresponds to the price of the stock, moving up or down at random. The most important statistical features of Brownian motion are its mean and its standard deviation. The mean is the short-term average price, which typically drifts in a specific direction, up or down depending on where the market thinks the stock is going. The standard deviation can be thought of as the average amount by which the price differs from the mean, calculated using a standard statistical formula. For stock prices this is called volatility, and it measures how erratically the price fluctuates. On a graph of price against time, volatility corresponds to how jagged the zigzag movements look.

Black-Scholes implements Bachelier's vision. It does not give the value of the option (the price at which it should be sold or bought) directly. It is what mathematicians call a partial differential equation, expressing the rate of change of the price in terms of the rates at which various other quantities are changing. Fortunately, the equation can be solved to provide a specific formula for the value of a put option, with a similar formula for call options.

The early success of Black-Scholes encouraged the financial sector to develop a host of related equations aimed at different financial instruments. Conventional banks could use these equations to justify loans and trades and assess the likely profits, always keeping an eye open for potential trouble. But less conventional businesses weren't so cautious. Soon, the banks followed them into increasingly speculative ventures.

Any mathematical model of reality relies on simplifications and assumptions. The Black-Scholes equation was based on arbitrage pricing theory, in which both drift and volatility are constant. This assumption is common in financial theory, but it is often false for real markets. The equation also assumes that there are no transaction costs, no limits on short-selling and that money can always be lent and borrowed at a known, fixed, risk-free interest rate. Again, reality is often very different.
When these assumptions are valid, risk is usually low, because large stock market fluctuations should be extremely rare. But on 19 October 1987, Black Monday, the world's stock markets lost more than 20% of their value within a few hours. An event this extreme is virtually impossible under the model's assumptions. In his bestseller The Black Swan, Nassim Nicholas Taleb, an expert in mathematical finance, calls extreme events of this kind black swans. In ancient times, all known swans were white and "black swan" was widely used in the same way we now refer to a flying pig. But in 1697, the Dutch explorer Willem de Vlamingh found masses of black swans on what became known as the Swan River in Australia. So the phrase now refers to an assumption that appears to be grounded in fact, but might at any moment turn out to be wildly mistaken.

Large fluctuations in the stock market are far more common than Brownian motion predicts. The reason is unrealistic assumptions – ignoring potential black swans. But usually the model performed very well, so as time passed and confidence grew, many bankers and traders forgot the model had limitations. They used the equation as a kind of talisman, a bit of mathematical magic to protect them against criticism if anything went wrong.

Banks, hedge funds, and other speculators were soon trading complicated derivatives such as credit default swaps – likened to insuring your neighbour's house against fire – in eye-watering quantities. They were priced and considered to be assets in their own right. That meant they could be used as security for other purchases. As everything got more complicated, the models used to assess value and risk deviated ever further from reality. Somewhere underneath it all was real property, and the markets assumed that property values would keep rising for ever, making these investments risk-free.
The Black-Scholes equation has its roots in mathematical physics, where quantities are infinitely divisible, time flows continuously and variables change smoothly. Such models may not be appropriate to the world of finance. Traditional mathematical economics doesn't always match reality, either, and when it fails, it fails badly. Physicists, mathematicians and economists are therefore looking for better models.

At the forefront of these efforts is complexity science, a new branch of mathematics that models the market as a collection of individuals interacting according to specified rules. These models reveal the damaging effects of the herd instinct: market traders copy other market traders. Virtually every financial crisis in the last century has been pushed over the edge by the herd instinct. It makes everything go belly-up at the same time. If engineers took that attitude, and one bridge in the world fell down, so would all the others.

By studying ecological systems, it can be shown that instability is common in economic models, mainly because of the poor design of the financial system. The facility to transfer billions at the click of a mouse may allow ever-quicker profits, but it also makes shocks propagate faster.

Was an equation to blame for the financial crash, then? Yes and no. Black-Scholes may have contributed to the crash, but only because it was abused. In any case, the equation was just one ingredient in a rich stew of financial irresponsibility, political ineptitude, perverse incentives and lax regulation.

Despite its supposed expertise, the financial sector performs no better than random guesswork. The stock market has spent 20 years going nowhere. The system is too complex to be run on error-strewn hunches and gut feelings, but current mathematical models don't represent reality adequately. The entire system is poorly understood and dangerously unstable. The world economy desperately needs a radical overhaul and that requires more mathematics, not less. It may be rocket science, but magic it's not.
Ian Stewart is emeritus professor of mathematics at the University of Warwick.