You have seen sufficient excerpts of this book on and off at this blog, so that I need say little more about it except to emphasize how very accessible and interesting this whole study is. Mandelbrot is attempting to define a new science of economics and the stock market and admits that he is far from being there; however, the problems he unearths are significant and should give pause to those who argue loudly (and at length) about the privatization of Social Security. The risks involved in even the most conservative stock/bond/cash portfolio far outweigh the perceived advantages until there is a better way of managing risk.
That is largely what the book is about--how does the market really run and how can you best assemble investments to minimize risk and maximize profits. In the process of this discuss Mandelbrot touches on invariant and scalable phenomena in markets, in language, and in the annual flooding of the Nile. That so many disparate phenomena can be looked at through multifractals and brownian motion is interesting in itself. That the common practice of Monte Carlo simulation based on Gaussian rather than Cauchy distributions is a dangerous misstep is made evident throughout.
The main difference between the simple bell curve (Gaussian) and the Cauchy curve is that in a bell-curve an additional bundle of data will not particularly disturb a heavily weighted center. That is, if enough data has been collected, then additional data will not appreciably affect the "center of gravity" of the curve. Large outliers will not affect averages.
With the Cauchy curve it is these large outliers that define the essence of the curve. It is a better measure of rapidly fluctuating environments with inherent turbulence (at least so Mandelbrot implies, and I certainly am not one with the least ability to naysay). As a result, additional data added to the Cauchy distribution will result in significant differences in the measures of central tendency.
Another interesting idea uncovered by Mandelbrot is that it is not only the fluctuations in prices that are important, but also the order in which they occur. And this extends to the study of floods on rivers as well. He pointed out that if the data is entered randomly and stirred together, you end up with a nice well-behaved bell curve distribution. But if the data are analyzed in order, what you find instead are a series of parallel curves that reveal a scalability in the phenomenon that is otherwise invisible.
Mandelbrot argues that as long as outdated means are used to evaluate the market, events like October 1987, and the entire year of 2001, but particularly 9/11 (we're speaking here only of market effects) are inevitable. Bubbles will arise and burst based on old means of buying, holding, and selling stocks. Portfolios will continue to experience rapid fluctuations, even based on very conservative, very deliberate buying and selling. Anyone who went through 2001 realizes what this can mean in a very, very short time.
Mandelbrot's book is required reading for all of those who will propose a means whereby social security will be partially privatized. It is recommended reading for everyone else. Despite Mandelbrot's annoying, but slight, tendency toward focusing the spotlight on himself, the book is quite good. It is one of those eye-opening works where many phenomena of the natural world are brought together and part of the pattern underlying them revealed.
Recommended.
