In recent weeks I have described how people think about risk. They use approaches very different from those implied by the models of quantitative finance and decision theory. They are influenced by what is salient, rather than what is probable. Events that are phenomenally unlikely – the winning of a large prize in the lottery or a child’s abduction by a paedophile – influence their thinking to a disproportionate degree because they grab attention. Few people think of uncertainty in terms of statistical distributions and are able to attach probabilities that add up to one to a well defined set of disparate outcomes. They tell stories about the future instead.
We do these things not because we are irrational – in any ordinary sense of the word – or because we are mathematically illiterate, although many people who make decisions, big and small, are indeed irrational and ignorant of basic maths. We do these things because it is impossible to cope with a complex world and the plethora of information about it we encounter in other ways.
Everyone knows of John Maynard Keynes’s ideas on macroeconomic policy but far fewer know of his contributions to the theory of probability. This was the subject of his fellowship dissertation at King’s College, Cambridge before the first world war. Keynes got the post, and quickly established himself as a public figure. After he had walked out in disgust from the Versailles conference that – temporarily – brought the war to an end, he turned the exercise into a book. His biographer, Robert Skidelsky, believes that understanding Keynes’s approach to probability is key to understanding much of the rest of his work, and I think he is right.
Keynes believed that the financial and business environment was characterised by “radical uncertainty”. The only reasonable response to the question “what will interest rates be in 20 years’ time?” is “we simply do not know”. And this was a prescient comment: 20 years after the publication of Keynes’s A Treatise on Probability takes us to 1941, when Britain was struggling for continued existence at a crucial stage in the second world war. Keynes had seen the future more clearly than most but when it came to how specific events would unfold, he simply did not know. Like everyone else.
For Keynes, probability was about believability, not frequency. He denied that our thinking could be described by a probability distribution over all possible future events, a statistical distribution that could be teased out by shrewd questioning – or discovered by presenting a menu of trading opportunities. In the 1920s he became engaged in an intellectual battle on this issue, in which the leading protagonists on one side were Keynes and the Chicago economist Frank Knight, opposed by a Cambridge philosopher, Frank Ramsey, and later by Jimmie Savage, another Chicagoan.
Keynes and Knight lost that debate, and Ramsey and Savage won, and the probabilistic approach has maintained academic primacy ever since. A principal reason was Ramsey’s demonstration that anyone who did not follow his precepts – anyone who did not act on the basis of a subjective assessment of probabilities of future events – would be “Dutch booked”.
Some scholars from the Netherlands have sought, without success, to track down the origins of this offensive phrase. A Dutch book is a set of choices such that a seemingly attractive selection from it is certain to lose money for the person who makes the selection.
I used to tell students who queried the premise of “rational” behaviour in financial markets – where rational means are based on Bayesian subjective probabilities – that people had to behave in this way because if they did not, people would devise schemes that made money at their expense. I now believe that observation is correct but does not have the implication I sought. People do not behave in line with this theory, with the result that others in financial markets do devise schemes that make money at their expense.
In fact, that is what a depressing proportion of financial market activity is about. The largest and most famous Dutch book would be the collection of ingenious structured products RBS acquired when it bought the Amsterdam-based bank ABN Amro. We know what followed.
