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The (Mis)Behaviour of Markets: A Fractal…

The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward (original 2004; edition 2008)

by Benoit B. Mandelbrot, Richard L. Hudson (Author)

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Title:The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward
Authors:Benoit B. Mandelbrot
Other authors:Richard L. Hudson (Author)
Info:Profile Books, London, Paperback, 352 pages
Collections:Your library
Tags:Risk, Probability, Financial markets

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The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot (2004)

Recently added byalifwahid, sunrise_hues, Embarquer, private library, guy.bogaarts, BravoZulu, tdeden, Phil_Crocker



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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:

( )
  sunrise_hues | Jun 21, 2015 |

Mandelbrot is the "father of fractal geometry." He's a mathematician who has spent much of his career looking at prices and markets. He argues pretty forcefully that any of the risk management techniques used by Wall Street are based on false assumptions and have been proven to fail time and again.

Mandelbrot is Nassim Taleb's mentor. I've gotten to the point where I wonder if, as a Christian, I can still teach economic orthodoxy (much less finance classes like risk management) with a clear conscience. The models and systems that modern finance uses to calculate risk are unrealistic and fail. Econometric modeling is guilty of the same sins.

It shakes the foundations of my learning to the core. Here's another blogger's review of the book, the comments are very insightful.

4.5 stars out of 5. ( )
  justindtapp | Jun 3, 2015 |
Just a few bits about those wonderful fractals and an interesting lot about Mandelbrot's demolition of many financial market theories. ( )
  Johannes99 | Dec 9, 2012 |
In these turbulent economy we seem to be victims of the financial markets. Benoit Mandelbrot, famous mathematician and inventor of fractal geometry, joined forces with Richard Hudson, to write a book about financial theory. “The (Mis)behavior of Markets” falls in the popular science genre. It is low on formulas, instead you can find lots of historical anecdotes and opinions.

1. Risk, Ruin and Reward

We start with a brief history of finance. The author asks us to play a game. Out of 4 charts we need to select the ones that are real and the ones that are fake.

2. By the Toss of a Coin or the Flight of an Arrow?

Chance is important in finance. There is the mild form of chance, described by the bell curve. On the other hand, there is the more extreme Cauchy probability distribution. Financial theory follows the mild path, but Mandelbrot is convinced that this is wrong and a more wild variability is to be expected.

3. Bachelier and His Legacy

The third chapter is about Bachelier and his coin-tossing view of finance. His work led to the theory of the efficient market. According to this theory, the market is so efficient that all information is directly reflected in the price of financial assets.

4. The House of Modern Finance

People who helped build the house of modern finance and their theories are mentioned – Markowitz, Sharpe, Black and Scholes. Even though some received Nobel Prizes, they still lost a lot of money in the markets.

5. The Case Against the Modern Theory of Finance

Mandelbrot tries to demolish the house of modern finance starting with shaky assumptions. He tries to disprove these assumptions. More evidence is presented, such as the low price earnings and price book anomalies. These anomalies are in direct conflict with current theory.

6. Turbulent Markets: A Preview

Turbulence is a nice metaphor for trading. Mandelbrot tries to convince us, that we should be thinking of fractals, when we look at stock charts. He uses cartoons of stock charts to achieve that.

7. Studies in Roughness: A Fractal Primer

Fractal geometry deals with roughness. It introduces a measure called fractal dimension, which is similar to the normal dimension in geometry, but is not an integer.

8. The Mystery of Cotton

This chapter describes a research project of Mandelbrot, when he worked at an IBM laboratory. He discovered a power law in the log returns of cotton prices. The evidence pointed at a L-stable probability distribution with features somewhere between a normal and Cauchy distribution.

9. Long Memory, from the Nile to the Marketplace

Hurst, a famous hydrologist, faced the challenge of figuring out a pattern to the Nile river. Hurst discovered a long term dependence in his data set. It is suggested, that the so called Hurst exponent could be a new yardstick, that would explain better long memory effects in financial markets.

10. Noah, Joseph, and Market Bubbles

The author refers to characters in the Bible to describe different forms of wild variability. For people familiar with the Bible this is a good example. In my opinion we can call it a shaky assumption at best.

11. The Multifractal Nature of Trading Time

Some days are slow, some days just fly by. Apparently this applies to trading too and it is due to the multifractal nature of time.

12. Ten Heresies of Finance

A list of ten big errors in financial theory. Markets are riskier, than we thought. Timing matters. Prices often leap.

13. In the Lab

Mandelbrot warns us that fractal finance is not mature yet. However, it is superior to the mainstream theories, since they dangerously underestimate risk.

The book ends with notes containing formulas and bibliography listing scientific articles. A thrilling book, that I could not put down, until I read it cover to cover. It is the finance equivalent of “A Brief History of Time”. I give it 5 stars out of 5. ( )
  IvanIdris | Feb 8, 2012 |
This book offers some key points on fractals, by the pen of it's creator (the person that formalized it into a theory, more correctly), it offers a fruitful introduction to the topic, and what it lacks in rigor, it makes up in relating theory to events in the real world. ( )
  RamiFaour | Sep 19, 2009 |
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Amazon.com Product Description (ISBN 0465043577, Paperback)

Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns. What many of his followers don't realize is that he has also been watching patterns of market change. In The (Mis)Behavior of Markets, Mandelbrot joins with science journalist and former Wall Street Journal editor Richard L. Hudson to reveal what a fractal view of the world of finance looks like. The result is a revolutionary reevaluation of the standard tools and models of modern financial theory. Markets, we learn, are far riskier than we have wanted to believe. From the gyrations of IBM's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate--Mandelbrot shows that the world of finance can be understood in more accurate, and volatile, terms than the tired theories of yesteryear.The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With The (Mis)Behavior of Markets, he puts the tools of higher mathematics into the hands of every person involved with markets, from financial analysts to economists to 401(k) holders. Markets will never be seen as "safe bets" again.

(retrieved from Amazon Thu, 12 Mar 2015 18:16:16 -0400)

(see all 2 descriptions)

"Together with Richard L. Hudson, Benoit Mandelbrot turns a fractal eye to the behavior of financial markets and overturns the "random walk" theory that is the underpinning of all contemporary financial analysis. Markets, we learn, are far riskier than we have wanted to believe." "The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With his fractal models, the (mis)behavior of the world's markets - from the gyrations of IMB's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate - can be understood in more accurate terms than the tired theories of yesteryear." "The (Mis)Behavior of Markets is a reevaluation of the standard tools and models of modern financial theory. Mandelbrot's fresh insights explode the false assumptions that have caused millions of investors, traders, and managers to underestimate the real risk, of the market."--Book jacket.… (more)

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