The market goes up nice and steadily and everyone agrees it ought to go up because analysts have underestimated growth in companies’ earnings. Then out of the blue we get a 10 per cent sell-off and everyone is worrying about whether the eurozone will collapse.
If you have looked at computer animations of fractals such as the Julia or Mandelbrot sets, you probably put them in the box labelled amazing and wonderful. But, according to their inventor, fractals make sense of this familiar pattern of complacency and panic in the stockmarket. He says fractals have an ominous message for investors and the stockmarket, threatening levels of risk far greater than conventional models suggest.
Benoit Mandelbrot is not a typical professor. His ideas led him to explore a range of phenomena from cosmology to dripping taps, from coastlines to share prices. With an academically suspect refusal to specialise, he was long regarded as a maverick by his peers. Now he is a household name and his Fractal Geometry of Nature is possibly the best-selling maths book ever published.
Mandelbrot was one of the first to point out, way back in the 1960s, that investment returns do not fall into a bell curve or Gaussian distribution, as is required for modern portfolio theory to work.
But it was not until he wrote his last book that he really laid into the conventional models of risk. In The Misbehaviour of Markets, Mandelbrot says that markets do not exhibit the “mild risk” of the bell curve but the “wild risk” of fractals, which are as different as Mars and Venus.
Since fractals are a universal feature of nature, the idea that they may be found in financial markets is not that far-fetched. Fractals measure the roughness of real objects in the way that the geometry we learned in school measures ideal objects.
That roughness means that features tend to cluster, in the way extreme fluctuations in share prices did in August 1998 or October 2008, creating an irregular but not random alternation of chaos and order rather than being evenly distributed as MPT requires.
Many economists are attempting to characterise the world as returning to normality after the crunch. This is a pattern we want to believe in, since it conforms to the once in a generation view of crises and means we do not have to worry about another one coming along for a long time. Mandelbrot completely disagrees with this.
In his fractal model, the next bit of chaos could be just around the corner (euro crisis, sterling crisis, oil crisis, China crisis, etc).
The classic fractal is a Cornish coastline. A series of closely linked rocky outcrops is followed by a long smooth beach, then more rocks.
This is what Mandelbrot means when he says risk is fractal and in scale – the risk is proportionately the same whether the timescale is a day, a week, a year or a decade and it is not randomly distributed but comes in clumps.
This is not what advisers learn in their investment exams. It makes the world of investment much riskier than current theories say, and implies a much greater need for measures to avoid disasters. But it is a model being used by more and more of the smartest traders, who, like Black Swan author and trader Nassim Taleb, have proved that MPT does not work. The quiet advance of absolute return investing suggests that despite learning all the MPT algebra, advisers understand the need to damp down risk to well below what the old models say is necessary.
Chris Gilchrist is director of Churchill Investments and editor of The IRS Report