I've discussed Power law distributions in the context of music, box office and other charts and the danger of modelling them with gaussians - you over weight the 'top ten' hits, and ignore the 'long tail' of many smaller creators.
The stock market has a complementary problem. Options pricing is done using a model known as Black-Scholes, that has as a key parameter historical volatility, and the variance of price fluctuation is used for this. Now it has long been noticed that Stock market price fluctuations are not distributed as a gaussian - Mandelbrot pointed out they follow a scale-free Power law distribution decades ago..
However, gaussians are still used all the time in quant analysis. In this case it is the other end of the curve that fails - they see the small fluctuations and model them, but the big disturbances are far more common than is predicted. It is essentially this error that caused the LTCM collapse. The quant's dismiss this effect as acts of god, and unmodellable, but these are exactly the events that destroy your portfolio.
Malcolm Gladwell wrote a profile of Nassim Taleb, one trader who does use power laws rather than gaussians, and does well out of it.