The Maverick

15 November 2010

On October 16th Benoît Mandelbrot one of the pioneering mathematicians of our time passed away at the age of 85. It is ironic that at the time of his passing, his theories are more relevant than ever.

Mandelbrot was born in Warsaw in 1924 into a Lithuanian Jewish family, who then fled the Nazis in 1936 and moved to Paris where he attended school. He worked for decades as a researcher at IBM outside the mainstream academic community, before becoming Professor of Mathematics at Yale University.

As a young researcher Mandelbrot encountered the question, 'How long is the coast of Britain?' He argued that the answer depends on the size of one's ruler. From a distance the coastline of an island may look smooth, but zoom in and you reveal jagged edges along the coastline that add up to a longer length of coast. Each time you zoom in further and further you unveil more and more edges and more and more coastline. It was this 'roughness' that is seen in nature, from clouds to cauliflower that came to fascinate him and lead to his development of fractal geometry, a branch of mathematics that could grasp the seeming randomness of nature and find order in chaotic shapes and processes. Many people (Math and computer geeks especially) are familiar with the stunning and strangely organic computer images this field generates.

As Mandelbrot put it, 'Nature has played a joke on mathematicians'. A system can be completely predictable in theory, and completely unpredictable in reality. In a sense Mandelbrot used nature as his starting point, rather than trying to simplify the world to conveniently fit elegant but overly simple mathematics. 'Mountains are not cones, clouds are not spheres, trees are not cylinders, neither does lightning travel in a straight line.'

Mandelbrot then applied his brilliance to finance and made a stunning criticism of the financial markets that time and again proved correct. He suggested that the fundamental assumptions behind models that are used to price stocks and other securities fundamentally understate risk in the world. These models are based on something called 'The efficient markets hypothesis' which my own university thesis examined and which was ironically developed by Mandelbrot's student and protégé, Eugene Fama. Simply stated the theory says that financial markets and prices reflect all available information. In other words, predicting price movements is like trying to predict a coin toss, it can't be done and price movements are random. This stability around a fundamental value determined by the market was used to price securities. During certain reasonably stable periods when markets were behaving efficiently this approach worked well...

Then God stepped in.

Events such as the Iceland volcano, 9/11 and the credit crisis are statistically considered outliers, freak events that are considered improbable and are treated as such by financial models. Reality unfortunately begs to differ and seems to deliver such events on a fairly regular basis. The potential impact of these events on the markets and our society is huge and Mandelbrot therefore concluded that financial models understate or 'sweep under the carpet' such inconveniently difficult to predict events. The world is potentially a lot more risky than investment managers would have us believe.

These inconvenient truths and their inspiration from the natural world gave Mandelbrot something of a maverick reputation amongst the academic community. Among wider audiences he was a mathematical rock star with lecture halls packed out with diverse audiences from all fields. Some have asked why the financial community ignored his warnings so often and the answer is that probably they felt there was little profit in his theories. Essentially Mandelbrot was saying we don't know everything and as the great man said himself, his ideas would mean 'a great amount of work, trouble and effort.' After the recent credit crisis, as commentators once again start to quote Mandelbrot when talking about a need for fundamental reform of the financial system, we see that such effort is absolutely necessary.