On the non-Gaussianness of finanical markets

In 2002, Malcolm Gladwell published an essay in the New Yorker called Blowing Up: How Nassim Taleb turned the inevitability of disaster into an investment strategy.

It is sort of a soft profile of 1) Victor Niederhoffer and 2) Nassim Taleb and his hedge fund (Empirica). Taleb's investment strategy begins by noting that people tend to be risk-averse in an asymmetric way (favoring smaller but steady gains and erratic but larger losses (which, I am inferring, shows up in the behavior of the stock market)) [as shown by Kahneman and Tversky]. Also stock market fluctuations do not really follow a normal distribution/Gaussian distribution/bell curve (which describes the statistics of a bunch of identical but independent things...This was one of the assumptions of the Markowitz model.). If you look at the tails (where the largest fluctuations occur), you find that these large fluctuations are much more likely than a Gaussian distribution would predict (as in, they happen perhaps once every few years rather than once very few millennia). This is referred to casually as "fat tails". Eugene Fama first discovered this, and the mathematician Benoit "Fractal Guy" Mandelbrot wrote a book analyzing this discrepancy and proposing an alternative model of financial markets.

Mandelbrot's calculations show that a Cauchy distribution (a.k.a, Lorentzian distribution) is a better model for such market fluctuations. But is there something better? Probably there are more sophisticated models that require more computation. Fama's collaborator French talks about performing calculations without assuming a distribution. I am looking at academic papers to try to learn more.

Today, Fama argues though that the average passive investor really needs only to know that the Cauchy fat tails mean that market crashes and surges are more likely than many expect. Unfortunately, many non-passive investors operating in the fat tails without understanding them are believed to be responsible for the collapses of Long Term Capital Management, and more recently, AIG.

According to posts on the Bogleheads forum, Taleb's hedge fund had to close because (back in 2004) the excess market volatility that they were betting on was simply not there to earn sufficient profit from.