I’m currently sitting in a lecture by Benoit Mandelbrot. The father of ?fractals? is at Microsoft ostensibly to promote his book, ?The Misbehavior of Markets?. He hasn’t actually touched on markets yet, though. He is reviewing his life work and explaining how it all fits together. He calls his overarching passion, ?the science of roughness?, and titles the presentation ?the rough and the smooth?.
Much of this you may have read elsewhere. He has lots of interesting pictures. He was initially interested in turbulence. Explaining how most of the natural world is ?rough?, but geometry and mathematics initially arose from the ?smooth?. Demonstration that self-similarity is a feature of roughness, and reflected in many man-made things throughout history. Showing Hokusai Fuji pics.
Now discussing the discovery that outer bounds of brownian motion forms a cluster with dimension 1.33. Discussing the way that the proof forthis was developed.
Now showing pictures of the first computer printouts of the Mandelbrot set. Explaining how he might not have even noticed it if not for a mistake. Same low resolution, striped dot-matrix output of my first Mandelbrot pictures.
Describing some cases of fractal patterns in nature.
Now talking about financial markets (however, he will not discuss ?politics, sex, religion, or portfolio?). First became interested in the sixties, understanding the fluctuation of cotton prices. The theory at the time was that prices for commodoties follow gaussian fluctuation. Cotton prices were different than gaussian white noise, though; sometimes rise or fall violently. Showing several price history charts, amplitude of price changes varies. Ten sigma to hundred sigma variations ?happen every day?. Explaining how people tried spectral analysis.
Goal became to ?describe it? without necessarily ?explaining it?. Goal not to be a Newton; Marx and Freud tried to be Newton. Explaining how tempting it is to use averaging, fixpoints, spans; but ?you have to wait the whole of human history to see if it ever averages?. Showing how to approximate near identical level of randomness using a very simple fractal.
Arguing that his model is the only model that attempts to describe movement of financial markets. There are many other models around, but they all have the caveat that they are only valid in the ?long run? with ?large numbers?, etc. Quotes Keynes, ?in the long run we shall all be dead?.
Q & A.
Q. If Gaussian does not represent reality, does that invalidate Black-Scholes?
A. Nobody uses Black-Scholes anyway. Everyone fudges volatility to get what they want. I used to be more polite about this, but everyone knows it is wrong.
Q. Some black-box companies claim to outperform the market. Do they use fractal investing?
A. Many claim to, but when I talk to them I have no evidence that they even understand the concepts. Not very reputable. Some large institutions understand.