I really can't believe how far this book falls short of what it could have been. I was expecting an in-depth theoretical exploration and practical application of fractal geometry in finance, but instead I got a popular science book written for the general reader.
This book covers the bare minimum about fractal geometry and doesn't advance beyond the superficial discussions (compared to Benoît Mandelbrot's 1982 book The Fractal Geometry of Nature
), at least it seems to me.
Fractals are shapes that reproduce themselves infinitely -- each offshoot of the shape is an approximate miniature of the original shape. Every time you zoom in further, you always find exactly the same shape. It's like a romanesco cauliflower
, each small part of it is exactly the same as the entire cauliflower itself. This property is called self-similarity.
The study of fractals and the math behind them can be traced back to the 17th-century mathematician Gottfried Leibniz, who contemplated the idea of recursive self-similarity. A few mathematicians after Leibniz dabbled in "fractal geometry" (the term wasn't coined until Mandelbrot). Karl Weierstrass in 1872 offered a function whose graph would be considered a fractal; Helge von Koch in 1904 refined Weierstrass's definition and came up with a function that produces the Koch curve.
Mandelbrot didn't start studying fractals and the property of "self-similarity" until the 1960s, while he was working as a research fellow at IBM. Mandelbrot coined the word "fractal" in 1975, and used a computer to construct visualizations.
Fractals look so cool that Mandelbrot came to be known as a stand-up guy in both mathematics and pop culture.
Fractals made by 3D printing:
Perhaps I over-studied mathematics in college (my senior honors thesis was in fractal geometry and chaos theory and I spent a summer at the Institute for Advanced Study in Princeton), or maybe the "maverick mathematician" is either too arrogant or too humble to share his research with the general public, but this book tells me nothing about fractal geometry that I don't already know. I was quite disappointed.
In terms of insights into behavioral finance or market analysis, I don't think I've gained anything new from this book besides re-reading the excessively broad and clichéd conclusions, such as
► markets are turbulent;
► markets are very, very risky -- more risky than the standard theories imagine;
► market "timing" matters greatly;
► prices often leap, not glide;
► markets in all places and ages work alike;
► markets are inherently uncertain, and bubbles are inevitable;
► markets are deceptive;
► forecasting prices may be perilous, but you can estimate the odds of future volatility;
► in financial markets, the idea of "value" has limited value.
His fractal view of finance might have been revolutionary when it first came out, but I find nothing new today.
The author merely provides a generic and repetitive hindsight perspective on the wild price fluctuations in financial markets. I think the fractal patterns in financial markets and their implications for price stability might have been more effectively illustrated by a few representative charts: