Don’t expect markets to bend it like Beckham

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What is important in billiards is the result, not the play: and what matters in business and finance is the outcome, not the process. In business and finance, as in billiards, the imperfections are critical and you can anticipate the result, or understand the outcome, only by appreciating these imperfections.

Several years ago, The Daily Telegraph made an unlikely claim about Britain’s most famous footballer. Under the headline “David Beckham a physics genius”, the paper reported a study describing the differential equations that must be solved to compute the trajectory of the ball in a famous Beckham goal.

The relationship between intention and outcome in sport had been highlighted many years earlier in a much cited joint article by the doyen of Chicago economics, Milton Friedman, and the great statistician Leonard Jimmie Savage. Friedman and Savage suggested that the shots of an expert billiard player would be those an accomplished physicist would calculate using knowledge of equations of motion. Like Beckham, the billiard player might not be capable of actually making such calculations, but the assumption that he did would accurately describe his play.

Friedman and Savage were defending the use of unrealistic assumptions in economic reasoning. The only thing that mattered, they claimed, was the accuracy of predictions. Friedman built on these ideas in another article, “The methodology of positive economics”. Fifty years later, economists continue to claim justification for implausible assumptions on the basis of his argument.

The analogy Friedman and Savage used applies only to expert billiard players. If you try to predict my own play using the assumption of perfect calculation, you will not predict well: you might do better to assume that the ball will move randomly. But expert billiard players are those who make excellent shots and they do so even if neither they nor we quite understand how they do it. This is what enables us to recognise them as expert.

The unrealistic assumption of perfect shots works only because of a process of selection in which players like me are eliminated. Thanks to the mathematical work of evolutionary biologists over the past 50 years, we now understand that arguments such as this can be extremely powerful. Darwin’s insight was to show that evolution could produce outcomes beyond the scope of even the most complex calculations. Results might seem to be the outcome of extensive optimisation even though no one had done, or could do, the maths.

Selection processes are found in social life, in sport, in business and finance, as well as in biology. Natural selection is seen in the commercial world: only profitable companies survive, and only successful traders keep trading. But the context of natural selection defines the narrow limits of the argument that Friedman and Savage developed. Their example does not establish a general case for accepting theories based on unrealistic assumptions. In fact, it shows the limits of such an argument.

The assumption that the shot played is the best available is useful in explaining the strokes made by a single expert billiard player. But that assumption is useless for explaining the interaction between two expert billiard players. A high-level game between experts is impressive because their play is nearly perfect, yet exciting and involving only because their play is not perfect. To predict the outcome of a match, you need to focus on the imperfections.

What is important in billiards is the result, not the play: and what matters in business and finance is the outcome, not the process. In business and finance, as in billiards, the imperfections are critical and you can anticipate the result, or understand the outcome, only by appreciating these imperfections.

Most profit-making opportunities in business have already been taken. The people who make money, either as entrepreneurs or as traders, are those who find those profit opportunities that have not already been taken. In securities markets the efficient market hypothesis is largely true but attractive investment opportunities are found only when the efficient market hypothesis is not true. And it is when the hypothesis is not true that we observe market dislocations.

The imperfections of markets explain who makes money, and who loses it; why economic growth sometimes falters, and how it then recovers. Friedman and Savage’s metaphor was designed to explain how we might predict economic events by assuming perfect knowledge even if that assumption of perfect knowledge was unrealistic. But their metaphor illustrates even more clearly why economic predictions based on the assumption of perfect knowledge are so often misleading.

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