Dr.  Svetlozar Rachev is author of Fat-Tailed and Skewed Asset Return Distributions, a book outlining the issues with applying a bell curve to market returns and the implications of its use in traditional asset allocation. Below is a inteview with Dr. Rachev by Risk Manager.

Abstract

The traditional models and analysis procedures for portfolio optimization are, in most cases, based on the assumption that the distribution of returns of an asset is normal. This means that in practice, a portfolio of stocks undergoes small percentage daily losses and gains much more often than negligible or extreme fluctuations.

The German mathematician, astronomer, geodesist, and physicist Johann Carl Friedrich Gauss developed the normal distribution to describe exactly this occurrence. The corresponding density function for this distribution is thus called the Gauss-function or bell curve. B. Mandelbrot, a French mathematician of Polish origin who is known for his research in the field of fractal geometry, opposes the applicability of the normal distribution in explaining the reality of financial markets. He suggests that extreme movements are much more likely than the commonly used models in finance predict. This is why traditional methods in risk management and finance are being increasingly criticized. 

“Zari” Rachev and Stefan Mittnik are dedicated to the development of alternative quantitative models beyond the scope of the normal distribution. Scientists show that the Gaussian model would predict that a crash, like the one that occurred in 1987, would occur only once in 1087 years. Empirical observations, however, give evidence to show that such crashes can possibly occur once every 38 years.

Interview-Rachev Parting with the Bell Curve.pdf