Misbehavior of the Markets and other things
January 25, 2007 10:55 AM   Subscribe

I have a few questions about Benoit Mandelbrot's "(Mis)behavior of the Markets", fractal finance and Gaussian distribution.

(1) Does this school (which seems to be very aligned with Taleb's Popperian skepticism in its approach) of thought have a name for it? It seems to successfully reject Bachelier's original paper and all papers and equations that rely on the Gaussian distribution (or take it as a given).

(2) Are his findings widely accepted among academics? Or practitioners (e.g., most leading Wall Street institutions)? It seems that true Gaussian distribution was never widely accepted, but used anyway as it works until it doesn't.

(3) While his antithesis of modern finance seems quite convincing, are his fractals applicable? I am trying to figure out if he manages to prove anything beyond constructing a visually pleasing example of a stock chart. Fractal generation manages to show the similar bubbles and long-tails that are characteristic of a real market (and not in some platonic Brownian market), but that does not prove that fractals can be used to better manage risk.

I've read a few papers on Mandelbrot's site, but nothing explaining a little more in depth his ideas. I studied the BlackÔÇôScholes model in school and was taught on using models which in their forms are based on a normal Gaussian distribution. I never liked this for reasons that Mandelbrot and Taleb managed to express. Any journals that I can subscribe to which follow that line of thought more closely? I have been reading the JFE but will take on more if they are interesting.
posted by geoff. to Science & Nature (3 answers total) 6 users marked this as a favorite
This is on my list. I have not read it yet but it might interest you:

Fractals and Scaling In Finance
by Benoit B. Mandelbrot
Publisher: Springer; 1 edition (April 20, 2005)
ISBN-10: 0387983635

I think his research is well known. One of the problems is that BS works with the assumption that stocks follow a Brown-motion but a Levi flight would actually be a better describtion. However, AFAIK the mathematics get to tricky to get this into the BS model.
posted by yoyo_nyc at 11:35 AM on January 25, 2007

Best answer: "Gaussian distribution was never widely accepted, but used anyway as it works until it doesn't."

I'm not sure I totally agree with this statement. We use the Gaussian distribution because it's simple, and easily defined in terms of two moments - the mean and the standard deviation.

But we all know it doesn't truly describe the distribution of returns in many markets - for example equities. The 1987 stock market crash - a single drop of roughly 22% or some 520 points - according to a normal distribution would be 20 standard deviation event (IIRC)!! Or something that should only happen once every billion years or so.

Then there is the asymmetry of returns, again particularly in the equity markets; we know they move a hell of a lot faster DOWN than they do up. This is the entire idea behind Asymmetric GARCH models, for example. This reality hardly is consistent with the simplified, not to mention symmetrical Gaussian view.

But getting back to why the normal distribution is used - its a simple concept and easily explained. Who reading this doesn't understand the Bell Curve? And tools exist to convert a normal distribution to certain other distributions (accounting for skewness and kurtosis of course), so analysis can be carried out using a normal distribution and the results converted.

Finally, and perhaps most importantly - keep in mind under Basel II and other regulatory regimes, models must be explained to regulators. If you've got a precise idea of the true return distribution of an asset class, you've probably spent a crapload of money arriving at this conclusion and the last thing you want to do is explain your research to a Central Bank. You're gonna trade the hell out of this advantage. So many desks do understand more precise return distributions of the assets traded, and they ain't talking.
posted by Mutant at 12:19 PM on January 25, 2007

Mathematician here, not an economist.

The justification for the Gaussian distribution is the Central Limit Theorem. Basically, if some random variable is a combination of many different same- (or similarly-) distributed random variables, the combined one tends towards being Gaussian.
posted by CrunchyFrog at 1:00 PM on January 25, 2007

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