In 2004, the book The (Mis)behaviour of Markets by Benoit Mandlebrot was published – well ahead of the financial mess in 2008. And it’s a shame more financiers didn’t read it.
In it Mandelbrot lays out the history of his challenge to the traditional way of thinking about risk in finance. He shows very clearly that the use of models based on ‘tossing a coin’ and a ‘random walk’ that fit very nicely in a spreadsheet, underestimate the likelihood of extreme events.
And he draws his evidence and his mathematics from nature itself. Indeed, he is credited with creating a new branch of mathematics called ‘fractal geometry’.
Now, rather than get drawn into a complex explanation of how we should measure risk, I’ll try to get my point across by using two pictures linked to the name of a celebrity.
That celebrity is Fern Britton, who as well as demonstrating a little risk awareness in the video at the end of this blog, shares her name phonetically with two common examples of fractal maths.
To state the obvious, one is a fern leaf and the other the coast of the Britain. And both the leaf and the coastline hold clues to the fractal geometry that more adequately explains the risks in the world we live in.
If you look at the simple structure of a fern leaf you can see that the shape of the overall leaf is mirrored in each individual leaflet. And that shape is then copied again within the leaflet…and so on. In other words the design repeats, scaling up and down. You can clearly see the pattern of its growth.
But it can also be applied to more complicated examples. The pattern of the coastline is far ‘rougher’ than the leaf, but fractal geometry still allows us to describe it – to give it a number that shows how rough it is. And we can do this by assuming we are measuring the length of the coastline with different lengths of ruler – the shorter the ruler, the longer the overall measurement of the coastline will be. I hope this is obvious since a shorter ruler would fit into more nooks and crannies.
And it turns out when you compare the resulting measurements you also get a scaling number or fractal. The UK coastline has a fractal dimension of 1.25 and the smoother Australian coastline 1.13. But the important point to take away is that a similar approach can also give us insight into the roughness or risk of other naturally occurring complex events like flooding and turbulence.
The book describes the similar work of H.E Hurst, a British civil servant sent to study the flooding of the Nile in the 50s. He found the range from highest Nile flood to lowest was far wider than you would expect if was a random event, like tossing a coin. Also, extreme events seemed to cluster – a flood would be followed by another flood. As a result, if you were to build a dam, it would need to be higher than suggested by traditional theory – you should expect more extreme values, more often.
The ‘Nile Pattern’ that Hurst saw and Mandelbrot describes with fractals is also replicated in finance. And as we headed into the recent financial crisis the traditional banking dams were based on efficient market theory and were not high enough. They had even been effectively lowered with all their off-balance sheet activity and light regulation.
Unfortunately, even if you had been aware of this in advance, it didn’t mean you could pick the perfect day to sell all your investments. However, you did have a major advantage. You were able to see that risk was being severely under-priced, especially by banks, and you could adjust your own exposure accordingly. And it’s beginning to be the case again – encouraged by governments borrowing stability from the future.
As investors does this mean we run for the hills? Well, it’s important to realise that the extremes work both ways – positive economic developments are also not distributed like the roll of a dice. It just means it’s especially important to be disciplined and choose investments with as much financial integrity and transparency as possible – be very wary of chasing yield.
Finally, as promised, here is Fern in her own words, describing the risks of closing a sash window (from 30 seconds in). She clearly is a fellow sufferer of that most debilitating of afflictions – ‘the giggles’. It’s got me in a bit of bother a few times, but that’s for another post.
- past performance is no guide or guarantee of future returns;
- the value of stock market investments can rise and fall over time, so it is quite possible to get back less than what you put in, depending upon timing