Fat-Tails Once More (and not the last time)
My favorite quote is from Mills (1927) (it tells it all)
”A distribution may depart widely from the Gaussian type because the influence of one or two extreme price change.”
Mandelbrot went deeper into fat-tails in the early 1960s. Then in the 60s and 70s there was a series of so called great discoveries in academic finance, they all based their models on Gaussian. Empirical facts was pushed under the carpet, this to get every theoretical model consistent with each other (CAPM, Black-Scholes-Merton, Sharpe Ratio etc.)
For example the idea behind the Sharpe ratio was great: to get a simple quantitative measure of risk versus returns. The problem was the way the Sharpe ratio measure risk (sigma alone) was basically useless. To use Sharpe ratio is simply dangerous, still most funds use it as marketing device (for often naiive investors). But it must be better than nothing? Well before the Sharpe ratio researcher evidently at least looked at the whole historical distribution (for as much data they had), far from good but at least better (at least it forced you to think).
Do we need a global credit contraction and melt down of finacial markets to make people once agian rember and understand what Mills and others pointed out in early 1900 ? Everybody on Wall Street claim they understand fat-tails, but from recent market blow ups (from only moderate moves) this do not seem to be the reality....
References
Mandelbrot, B. (1962): “The Variation of Certain Speculative Prices,” Thomas J. Watson Research Center Report NC-87: The International Re- search Center of the International Business Machine Corporation.
Mitchell, Wesley, C. (1915): “The Making and Using of Index Numbers,” Introduction to Index Numbers and Wholesale Prices in the United States and Foreign Countries (published in 1915 as Bul letin No. 173 of the U.S. Bureau of Labor Statistics, reprinted in 1921 as Bul letin No. 284, and in 1938 as Bul letin No. 656).
Mills F. (1927) The Behaviour of Prices, National Bureau of Economic Research.
Oliver, M. (1926): Les Nombres Indices de la Variation des Prix. Paris doc- toral dissertation.
more details also in my chapter 1: Derivatives Models on Models
