The Future of Everything: The Science of Prediction

by David Orrell

  A similar asymmetrical distribution—sometimes known as Pareto’s law, after the nineteenth-century Italian who first discovered it—holds for personal wealth. Perhaps Warren Buffet so distrusted the EMH because if the normal distribution were correct, he shouldn’t exist. Most people would enjoy a uniform degree of financial success; no one would be extremely poor or exceptionally rich. In reality, however, the wealthy are arranged like cities. For every millionaire in the United States, there are about four people with half a million, sixteen with a quarter million, and so on. If heights were arranged in a similar way, then most people would be midgets, but a small number would be giants.

  FIGURE 6.3. The left panel shows a normal distribution, the right a power-law distribution. The horizontal axis could, for example, represent wealth or city size. In reality, the power-law distribution holds only over a certain range, so there are cutoffs in both the vertical and the horizontal axes. In the normal distribution, it is possible to assume that most samples are close to the mean. In a power-law distribution, we cannot ignore the samples in the extreme right-hand tail (because they are the most important in terms of the quantity measured) or those in the left (because there are so many of them).

  The growth of an investor’s assets, or a city’s population, is not a completely random event, but depends on its position in a connected network.45 A person thinking to move is more likely to know people or employers in a large town than in a small town. Big cities draw people to them like moths. Money attracts more money; the rich get richer; strong countries attract investment, while those on the periphery remain vulnerable. The economy consists of both negative feedback loops, like Adam Smith’s invisible hand, and positive feedback loops, which amplify differences. In such situations, Galton’s principle of “regression to the mean” is highly misleading. What goes up needn’t come down.

  Imagine that several different restaurants of similar quality start business on the same day, and that, for some random reason, one restaurant initially attracts a few more customers than the others. (Perhaps its location is slightly better, or the proprietor is well known and popular.) A visitor who lacks detailed information will likely choose the restaurant that holds a few more people, just because that implies that it must be reasonably good. Therefore, the number of customers is amplified by positive feedback: the more customers there are, the more new ones will be generated. As business improves, the proprietor may invest the proceeds in better ingredients (product quality), in advertising (brand equity), or in expanding the restaurant (economies of scale). The restaurant pulls further ahead of its competition. Growth may eventually saturate—when, for example, some of the customers grow bored with the menu. The company therefore follows the S-shaped curve of figure 6.1 (see page 237). Meanwhile, the restaurant down the road, which was just as good to start off with, quietly goes bust within a year or two—as most new businesses do. Positive feedback amplifies changes, be they good or bad, so it can lead to collapse as well as growth.

  The power-law distribution holds, in an approximate fashion, over many different phenomena, from the size of earthquakes to the number of interactions in a biological network (like that in figure 5.4 on page 203).46 Unfortunately, this does not help much with prediction of particular events, because it implies that there is no typical representative. It is no longer possible to predict that an individual sample will be close to the mean, give or take a standard deviation or two. Even the calculation of the mean depends critically on the sample. It has been estimated that if Bill Gates attends a baseball game at Safeco Field in Seattle, the average net worth of those also in attendance increases by a factor of four.47 Leave him out of the calculation, and you miss the most important person. There is no easy mathematical shortcut. Details matter, and nothing is “normal.”

  Like customers choosing a restaurant, investors must be viewed as individual but interdependent agents operating in a highly connected network. The decisions they make can ripple through the entire system. Any accurate model of the economy would have to take into account these intricate social dynamics, which are explicitly ignored by the EMH. Despite these drawbacks, no serious alternative is close to dislodging the orthodox theory from the throne of predictive economics. So why is this the case? And is there anything better available?

  STICKY THEORY

  The orthodox economic theory has proved so resilient because it is both hard to beat—in the sense that other equations do little better at predicting the future or estimating risk—and highly adaptable. More elaborate versions of the basic theory attempt to correct the flaws while retaining the same structure. The field of behavioural economics, for example, addresses psychological effects such as loss aversion. Owners of financial assets hate to sell at a lower price than they paid, so they resist selling after a downturn. Therefore, prices tend to be “sticky” on the way down. Models can be tweaked and adjusted to accommodate these behavioural effects, by incorporating parameterizations of investor psychology, which still treat each investor as having fixed tastes and preferences. These adjustments relax the condition of investor rationality but still assume that investors can be modelled rationally. They therefore do not address the underlying problem, which is that the economy is a social process that cannot be reduced to law.48

  Another approach is to stretch the theory so it better allows for extreme events. Consider, for example, the Mexican peso crisis of 1994–95. The standard deviation of the peso-dollar exchange rate from November 19, 1993, to December 16, 1994, was 0.47 percent. According to random walk theory, someone buying pesos on December 19, 1994, should have expected to lose no more than 3.5 percent of his dollar investment over a two-week period, ninety-nine times out of a hundred. As it turns out, losses were 65 percent, which in principle should not have happened in a billion years.49 The reasons behind the high losses—a peasant uprising in Chiapas and the death of a presidential candidate—were local to Mexico. But the crisis was soon followed by sister crises around the world: the collapse of Asian currencies (1997–98) and Russian bonds (1998).

  To account for such sudden changes in volatility, more sophisticated risk-assessment techniques have been developed, such as the generalized autoregressive conditional heteroskedasticity (GARCH).50 The last word, to you and me, means changing variability; autoregressive means that the changes depend on past behaviour. In its most basic form, GARCH produces a distribution of price changes that better accounts for extreme events, but at the expense of two new parameters. These add to the number of unknowns, as well as the number of Greek letters in the equations, and still cannot begin to account for the inherently social and political nature of the market (there is no parameter for peasant uprising). As Mandelbrot put it, “The high priests of modern financial theory keep moving the target. As each anomaly is reported, a ‘fix’ is made to accommodate it. . . . But such ad hoc fixes are medieval. They are akin to the countless adjustments that defenders of the old Ptolemaic cosmology made to accommodate pesky new astronomical observations.” 51 In practice, it seems hard to find numerical techniques that improve greatly on the orthodox methods, which is why they are still orthodox. Forecasters can always try to get around shortcomings in the model output by applying their subjective judgment. One currency trader said that pricing techniques such as Black-Scholes only represent the numerical approach to the problem: “Although used as a first cut, the actual price quoted takes non-quantitative factors into account.”52

  Another reason for the theory’s endurance is the lock-in effect: it has become entrenched in academic circles and elsewhere. Just as the perfect model hypothesis in weather forecasting enables researchers to do complicated, pseudo-probabilistic analyses of the atmosphere, so orthodox theory allows the development of intimidating and authoritative financial techniques. As the economist Paul Ormerod wrote, “Maximizing behaviour, for all its faults, is a valuable security blanket for many economists. It enables the mathematics of differential calculus to be applied to their theories, a
nd for some intellectually satisfying results to be obtained. It has the side-benefit, too, of inducing mortal terror in many scholars from other disciplines in the social sciences who lack the required amount of mathematical training.”53 This is reminiscent of Iamblichus’s statement about the Pythagoreans: “Their writings and all the books which they published were not composed in a popular and vulgar diction, so as to be immediately understood, but in such a way as to conceal, after an arcane mode, divine mysteries from the uninitiated.”54

  One defence of the orthodox theory is that it correctly predicts that the market is unpredictable. If, it is argued, the market is irrational, then a rational investor would be able to consistently outsmart it.55 But while an efficient market implies unpredictability, the opposite is not true. It is actually rather strange that unpredictability is cited as evidence of logical calm. A drunken man’s stumbling (the original inspiration for the random walk) might be unpredictable, but we wouldn’t call his behaviour hyper-rational.

  Perhaps the greatest attraction of orthodox theory lies in its subtext. It allows economists to maintain the illusion that the economy is fundamentally rational, and that their models are correct. The causes of error are externalized to random external shocks. The tenets of the theory—that investors are independent and fixed in their tastes, and can look into the future to calculate value—reflect the Pythagorean ideals of an ordered universe. They are also exactly the assumptions that need to be made if economic models are to be considered accurate and economists are to maintain any oracular authority. As soon as we admit that the economy is a complex set of interactions in a huge connected network, and that it involves individuals whose “beliefs, interpretations and justifications evolve and transform themselves continuously,” then the idea of accurate mathematical models begins to seem, to paraphrase Immanuel Kant, a little absurd. The system is uncomputable, and there is no Apollo’s arrow to fly into its future. It is interesting that Bachelier, whose work was at first spurned, was not allowed back in the fold until his random walk hypothesis was reconciled with this image of a rational marketplace.

  Indeed, a huge amount of effort has gone into explaining rationally why the market is rational. This leads to the kind of double- think that allowed astronomers to retain the notion of perfectly circular motion, despite much evidence to the contrary, for about 2,000 years.56 Another example of double-think occurred during the summer of 1988, when a severe drought in the United States Midwest affected the supply of corn and soybeans. As time went on and the drought continued, prices of these commodities rose to extreme heights. Then one day, Chicago experienced a tiny, insignificant amount of rain—one imagines a few drops sprinkled on the balding pate of a broker as he headed out to work in the morning— and prices collapsed. Some saw this as a sign that markets might be a touch on the manic, oversensitive side, but efficient-market enthusiasts disagreed. One top economist insisted that the response in the market was quite rational, because investors know that weather tends to be persistent, so they all updated their forecasts with this new information and concluded that the drought would not continue. 57 Given the uncertainty in weather forecasts of any type, it seems to be stretching the meaning of the word “rational” to allow a few rain clouds to so drastically change expectations for the future.

  THE PSYCHOLOGY OF ECONOMICS

  Here are some factors that behavioural psychologists believe affect investors:

  Compartmentalizing.Investors divide problems into parts and treat each separately, instead of looking at the big picture. Losing ten dollars on the street feels worse than losing the same amount in a stock portfolio because each event is handled in a different mental compartment.

  Trend following.Extrapolating from current conditions tends to fuel bubbles because when the market is going down, people expect it to stay down, and when it is going up, the sky is the limit.

  Loss aversion.People take less pleasure in winning ten dollars than they do pain in losing the same amount. A consequence is that investors will avoid selling assets at a loss.

  Denial.Investors maintain beliefs even if they are at odds with the evidence. This results in cognitive dissonance.

  Suggestion.They are overly influenced by the opinions of others.

  Status quo bias.They tend to avoid change. It means that transactions, which always involve some kind of change, have a hidden extra cost.

  Illusory correlations.Investors look for patterns where they don’t exist. This is also called superstition.

  Interestingly, such psychological effects—denial, the power of suggestion, status quo bias, and fear of loss—may also explain why human beings cling to their predictive models even when the results don’t agree with reality.

  INVESTMENT STORIES

  Of course not all economists, and certainly not all traders, agree with the hypothesis that the market is without even pockets of predictability. People such as the former hedge fund manager George Soros do quite well by following their intuitive feel for market sentiment, and betting against trends. It is interesting to compare the EMH vision of rational investors with Soros’s notion of “radical fallibility,” which contends that “all the constructs of the human mind . . . are deficient in one way or another.”58 (This includes investment ideas or stories—such as South Sea gold, Internet stocks, and indeed abstract economic theories like the EMH—which grow and reinforce themselves in a positive feedback loop as they become established in the investment community.) Profit opportunities arise when you can spot the flaw in the story and bet against it. Because the market is constantly changing and adapting, investment strategies and mental models are themselves nothing but “fertile fallacies” that must be fixed or discarded when they no longer work.

  The dangers of excessive confidence in models were amply illustrated by the 1998 collapse of Long-Term Capital Management LP. This hedge fund had a number of economics luminaries on its ticket, including Myron Scholes (of the Black-Scholes formula). It used efficient-market theory to construct complicated and highly leveraged financial bets, which worked well until August 1998, when the Russian government decided to throw efficiency to the winds and default on its bonds. The subsequent market collapse, unanticipated by the equations, meant that to avoid an even greater crisis, the firm had to be rescued in a $3.6-billion bailout.

  Attempts are still made to develop investment techniques based on quantitative, predictive models, but they tend to be data-driven rather than model-driven. These can involve classical statistical techniques, which search for correlations in data, or biology-inspired techniques involving neural networks and genetic algorithms. The first biology-inspired approach simulates the way that the brain works by setting up a network of artificial “neurons” that learn to detect patterns in streams of financial data. The latter approach sets alternative algorithms into competition, then chooses the winner in a process akin to natural selection. The aim is not to simulate the underlying economy, but to seek trends in the financial data itself. Such methods may analyze anything at all—say, the dollar-sterling exchange rate and the price of pork bellies—to detect patterns that (for good reason) elude most investors. In the world of finance, even a tiny advantage can lead to substantial profits—at least if you are backed by a large bank, so that positions can be heavily leveraged and transaction costs controlled. The Prediction Company, set up by physicists and funded by the Swiss bank UBS AG, is one firm which uses such techniques.59 It is hard to judge the firm’s success in the somewhat opaque world of financial prediction, but it is still around after more than fifteen years.

  Ultimately, though, all such models, like those of the chartist, depend on the future’s resembling the past. They seem more alchemy than science. One trader at a major New York investment firm, which employs a large team of about a hundred “quants,” or quantitative analysts, told me that it was a “matter of debate” within the firm whether research into predictive mathematical models, beyond simple valuation tools, was worthwhile for them.
This is also why the chairman of the U.S. Federal Reserve has yet to be replaced by a machine. The market is a social process that deals in fictions as well as reality, words as well as numbers. Mathematical models certainly have their uses, but they only give part of the story and can be misleading if taken out of context. In the markets, number is not all. Just as computers are not good at spotting social trends or interpreting stories, they do not seem brilliant at making market predictions. For most investors, the teachings of the EMH are quite useful— diversify among different asset classes, avoid expensive management fees, and be wary of prophets who claim to foretell the future. To which could be added: risks may be larger than they appear.

  THE LIVING ECONOMY

  Even if models are not predictive, they can still be used to capture aspects of the economy’s dynamics in a more realistic way. Models have been produced of a hypothetical stock market, for example, in which individual agents are assumed to have their own preferred investment strategy.60 Some will tend to follow the current psychology and accentuate market swings (positive feedback), while others base their decisions on value analysis and go against trend when they feel the market is too high or too low (negative feedback). The price at any time represents a dynamic balance between these forces: subjective greed or panic versus “objective” calculations of value. The behaviour gets interesting when the market participants are allowed to influence one another: if a majority thinks that the market is going to tank, then this mood eventually deflates the most optimistic chart-follower. Predictions therefore affect the future in a self-reinforcing, positive feedback loop. Tastes and preferences are treated as dynamic rather than fixed. The result is an inherently unstable system that mimics typical market behaviour, including booms and busts. There is no invisible hand to guide it to equilibrium; no such equilibrium even exists.