The Black Swan: The Impact of the Highly Improbable
by Nassim Nicholas Taleb
Allen Lane ₤20, 400 pages
FT bookshop price: ₤16

Nassim Nicholas Taleb’s last book, Fooled by Randomness, argued that there is a human tendency to recognise false patterns and attribute causes in random processes. It was full of anecdotes, irretrievably opinionated and informed by a range of reading. You would expect these war stories and strength of views from a trader and hedge fund manager, but not the erudition.

Taleb’s new book, The Black Swan, develops a theme from that earlier work. Everyone substantially underestimates the significance of extreme events in contemplating the future. Taleb calls these extreme events ”black swans”, not imaginable until they are seen.

Taleb writes of two worlds: Mediocristan and Extremistan. The mathematics of Mediocristan is the algebra of classical statistics and probability theory. Distributions are normal, curves are bell-shaped. A carpet looks like a brush if you lie face down on it, with every tuft distinguishable. At a distance, it just looks like a carpet; individual variation averages out.

The mathematics of Extremistan is the fractal geometry described by Benoit Mandelbrot. Distributions follow a power law. The pictorial representation of Extremistan is a rugged landscape. It looks rugged whether you see it close up or from a distance - like a snowflake, which has the same shape whatever the degree of magnification.

The law of large numbers applies in Mediocristan. No single event matters, only accumulations and agglomerations. But in Extremistan every observation can make a large difference to the overall outcome. For risk analysis, it matters a lot if you are in Mediocristan, the province of standard statistics texts, or Extremistan, the territory of newer theories associated with chaos and complexity.

Taleb claims that there are too many extreme events in securities markets for such markets to be located in Mediocristan. The black swan of October 1987, when the Dow Jones index fell by about 20 per cent, was the first trigger for his personal reassessment. The event was simply outside the realms of possibility in classical statistics. Taleb would first substitute power laws and the mathematics of extreme statistics for the reassurance of normal distributions. But this still gives more credence to economists and financial analysts than he allows. Probabilities can be defined and predictions made only if the events that are the subject of the probabilities and predictions can be described. Donald Rumsfeld distinguished known unknowns and unknown unknowns. Statistics, old and new, deal with known unknowns. Taleb’s world is determined by unknown unknowns - black swans.

No one, he says, could have predicted the invention of the wheel or measured the probability that the wheel would be invented, because if you could do either of these things you would already have invented the wheel. The invention of the wheel was a black swan.

It is simply meaningless to ask what, on September 10, 2001, was the probability that the events of September 11 would occur. Meaningless because knowledge of such possible events would dramatically affect the likelihood that they would occur. Meaningless because the probability that the exact sequence of events that took place the following day would occur is vanishingly small. The best we might do is ask what the probability of an incident like 9/11 would be. But that question dissolves into a fruitless discussion of what is meant by ”like”. September 11 was a one-off. These events defy prediction. Taleb laughs at a correspondent who, impressed by the argument, asks what are the 10 most likely black swans? To pose the question is to miss the point completely.

Taleb doesn’t only live in Extremistan when it comes to statistics. With few exceptions, the writers and professionals he describes are knaves or fools, mostly fools. His writing is full of irrelevances, asides and colloquialisms, reading like the conversation of a raconteur rather than a tightly argued thesis. But it is hugely enjoyable - compelling but easy to dip into.

Yet beneath his rage and mockery are serious issues. The risk management models in use today exclude the very events against which they claim to protect the businesses that employ them. These models import a veneer of technical sophistication, the result of the simultaneous development of modern finance theory and information technology. Quantitative analysts have lulled corporate executives and regulators into an illusory sense of security. Beware the black swan.

John Kay is the author of ”The Hare and the Tortoise: An Informal Guide to Business Strategy” (Erasmus)