**Book By Benoit Mandelbrot**

__Article and __Review__ by GlobalMacroForex__

It’s great to finally read a book by a mathematician who gets economics and market psychology. This book is broken up into 2 sections. The first half he goes into the flaws of traditional financial theory. In the second he proposes fractal geometry as having the potential to help these flaws.

The 3 financial models Mr. Madelbroit criticizes in this book are:

· Sharpe Capital Asset Pricing Model (CAPM)

· Black-Scholes Option Pricing Model

· Harry Markowitz Modern Portfolio Theory

His primary criticism of these theories is using standard deviation in a way that expects/assumes that the statistical data is “Standard Normally Distributed” (Gaussian).

To demonstrate that markets don’t follow a Standard Normal Model, Mr. Mandelbroit took the Dow Jones Industrial average and compared the actual standard deviations with how it should have been under a Standard Normal Distribution (Brownian Motion) Model.

You can clearly see there are clusters of deviations way beyond what a Normal Distribution would predict. In fact, in the following chart, he superimposes the two on each for comparison. You can see the actual Dow movements in black, and the Standard Model in Grey.

Note the large deviation 23+ standard deviations out and the fat tails past 6 standard deviations. In reality, life and markets are not Standard Normally Distributed. Instead, Mr. Mandelbroit proposes the following rules:

__Rule 1. Markets are risky__

Given that they are prone to large drastic swings (24+ standard deviations), traditional academics and the business community at large are drastically underestimating the risks associated with markets. *“Prices often leap, Not glide. That adds to the risk.”*

__Rule 2. Trouble runs in streaks__

Market “Timing” matters greatly. Big gains and losses concentrate into small packages of time. In the Standard Normal Distribution and “Random Walk” theory it’s assumed that tomorrow there’s just as likely a chance of going up as there is down. That is not true in reality. In real markets, there tends to be a lot of volatility in a row. Volatility begets more volatility.

__Rule 3. Markets have a personality__

While all markets around the world trade similar and can be correlated, each market moves in its own unique way.

__Rule 4. Markets mislead__

They are prone to bubbles and busts. The prices may lead some to think its worth more than it really is. Following only other market participants can lead to financial ruin.

__Rule 5. Market time is relative.__

Time is flexible, not linear in markets. Market participants can speak of a “fast-moving market” where volatility and volume are high. They are referring to the market moving on its own time frame, devoid of connection to traditional measurements. If you look at a price chart, you can’t tell the time frame. If you zoom in on a price chart, you might find a pattern in the 1-year chart that’s on a 10-minute chart. It’s all relative to the participants.

__Fractal Geometry__

Although Mr. Mandelbroit does criticize Traditional Market Portfolio Theory, he does little to replace it. His suggestion is fractal geometry, which is a measurement of how “rough” or non-smooth an object is. Although he uses fractal geometry to replicate stock movements * similar* to real stocks, the practical application of this theory is not developed yet for commercial use.