The (Mis)behavior of Markets: A Fractal view of Financial Turbulence

By Benoit Mandelbrot

Mandelbrot climbs atop his favorite hobby-horse and works toward a theory of financial markets (and more importantly, financial panics) based on fractal geometry. The initial motivation (and something that seems quite covincing by now) is to debunk the “classical” view of financial markets enshrined in Modern Portfolia Theory and the Captial Asset Pricing Model (CAPM).

Classcally, it is assumed that asset prices are a random walk. That is, price movements are not correlated with past price movements and that the magnitude of any given price movement is normally disrtibuted. Mandelbrot martials various lines of emprical evidence to argue that this is clearly not true, that price changes are not normally distributed and we in fact observe many more large price movements than we would expect if they were gaussian random variables. That much seems fairly uncontroversial to me.

The remainder of his argument is realted to how financial price series have a fractal structure. I'm quite honestly not remotely trained in the underlying mathematical concepts so I'm not sure I followed the postive arguments enough to do them any justice here, but the two emprical observations of financial markets that he (allegedly…) explains are:

1. Financial assets are not a random walk but in fact have a “memory” of past price movements.
2. Volitilty tends to “cluster.” That is, large price movements are more likely after other large price movements.

The second point in particular (base on my very-non rigorous observation of financal markets) seems obviously true. If prices were gaussian, then you wouldn't expect ex ante and “periods of volatility.” Large price swings would of course happen from time to time, but after such a large price shift things should immediately return to normal. But it doesn't seem to work that way. Markets are calm for a while and then they are volatile and there are large price swings from day-to-day (ahem, we're living through one of those periods of volatility right now….) and then things settle back down.

Definitely a fun and interestng read, but as in all trade books on highly technical subjects, caveat emptor.