I mentioned in a previous blog, "Fractals and Self-Organized Criticality" about the fractal nature of many natural systems. That is, the self-similarity observed in nature over many scale lengths. It turns out that fractals can be quite useful to describe financial systems as well. However, they are rarely used and this leads to many misconceptions about the markets. Let me explain.



When we discuss variability or probability distributions, we generally resort to simple Gaussian statistics ("bell curve" statistics). That is, when you take a sample, say, a population and plot out something such as their heights on an xy plot, there are some very tall people, some very short, but basically, there is an average height and the curve looks something like a church bell. Hence the name. This works very well for heights or weights or university grades or other such things that vary within set limits. Therefore, we don't have to worry about a single mile-high person messing up our nice bell curve. There are natural limits imposed on human heights, as it were. However, other statistical distributions are not necessarily confined to any arbitrary limit. Such is the case with the market. But, much to our misfortune, fractal statistics are almost never used to describe or explain the behaviour of the markets. We are shown graphs or pie charts of historical trends or mathematical predictions about future market tendencies. So, how much faith can we have in our financial advisers, the majority of which have never studied fractal distributions in relation to the free market economy?

There has been a lot of buzz these days about the economy. This year started off with spiking oil prices (some 50%), and talk about a global recession. Now, the rhetoric has gone from recession to depression or even collapse. What's going on here? What do I do with my investments? Should I be putting my money in my mattress? How will the price of oil effect the price of food or other economic needs? I must admit that I am far from qualified to comment satisfactorily on the implications of global economic collapse. However, I will say that I am pessimistic about the future of civilization continuing on in the way it has been during the "cheap oil fiesta" we have been fortunate to live through over the past 150 years or so. The turmoil we see in the markets now is heavily related to the price of oil, but also to the laissez-faire free market economics and its misleading mathematical foundation. The future may be one of energy shortages, but it doesn't have to be bad. Civilization has persisted for thousands of years without the gadgets we are familiar with today, including the laptop I am typing this on. But, I am optimistic that we will adjust to our new set of circumstances, live more locally and be happy with less "cargo". :)

I drew most of the information for this blog in the form of a summary (as I understand it) from an article I read by Benoit Mandelbrot and Nassim Nicholas Taleb called, - "How The Finance Gurus Get Risk All Wrong". Benoit Mandelbrot is a mathematician and is celebrated as the "father of fractals". It's a short article... check it out if you're interested.

Peace,
Grant