Mandelbrot‏, by Ralph Vince

June 25, 2010 |

I have been re-reading Mandlebrot's book The Mis(behavior) of Markets.

Mandelbrot's notions regarding prices (and I have no reservation about saying this) do NOT pertain to us because we have a horizon, a finite period of time to trade in.

Secondly, and more importantly, price changes on the long side are bounded. I KNOW what the worst case can be — and this certain information I can use (overwhelmingly) to my advantage.

If Mandelbrot batted 1000 in his trading, I would listen to what his ideas were. Anything shy of that is silly for me (or anyone else) to listen to or consider.

Although I have never given the fractal gnome a chance to physically acost me I do have a peeve with him. His fractal theory has a certain beautiful appeal. However his fractal theory as he applies it to the markets has some serious flaws.

The most important flaw is the /*assumption* /of infinite variance in his form of the four parameter Levy distribution. Mandelbrot argues that because his form fits the cotton data reasonably well that proves the variance is infinite. However a four power rational polynomial fits the normal distribution reasonably well, However the analytical form of the normal is well known not to be a rational polynomial. Just because a form fits does not prove that it /*is*/ that form.

Assuming infinite variance obviates any attempt to do empirical significance testing because it would be meaningless. So you never see significance testing in a paper from the fractal school. They cannot do rigorous empirical testing and that is no way to do science. But it is a pretty theory.

The fractal gnome was F@m@'s Ph.D coach.

Ralph Vince writes:

Let's assume the worst — that Mandelbrot is correct and there IS infinite variance in the distribution of price returns (i.e. c1 / c0).

The Old Frenchman would say, "Who gives a rat's butt?" and he would be correct.

What we experience is a transformation of the distribution of the returns of prices by our trading rules — in other words, we take a pair of scissors to this paper distribution, paring off parts of it as we see fit.

Does a binomial option have infinite variance? Come on!