Most investment analysis is based on the assumption that returns follow a Gaussian or Normal distribution. However, examinations of available data show that returns don’t exactly follow this pattern. Benoit Mandelbrot of fractal fame suggested the Cauchy distribution as an alternative that may agree better with real-life investment data.
To illustrate the difference between these two theories, suppose that you invest money over a period of time, and based on historical data, you expect to have $1 million on a certain date. Suppose further that historical data suggests there is a one in ten chance that you'll actually have $750,000 or less. What is the chance that you'll actually end up with $250,000 or less?
The Gaussian distribution says that the odds of this bad outcome are less than one in a billion. However, the Cauchy distribution says that the odds of this bad outcome are just over 2%! This is an enormous difference.
The available evidence shows that real life investing is wilder than the Gaussian distribution, but not as wild as the Cauchy distribution. Beware any investing advice based too strongly on calculations using just one of these distributions.