Modern portfolio theory is based on the assumption that changes in stock prices are normally distributed (follow a bell curve). Benoit Mandelbrot and Nassim Nicholas Taleb disagree with this assumption, and believe market crashes like that of 1987 are much more likely to occur than standard theory predicts.
For my spring 2006 U.C. Berkeley Extension Statistics class I created a presentation Are Daily Changes in Stock Prices Normally Distributed? I analyzed MSFT (used in the standard MBA Finance textbook as an example of normality!), BRKA, and the S&P 500 index over various date ranges. I found none of them satisfied statistical tests for normality.
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