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The Misbehavior of Markets: A Fractal View of Financial Turbulence Annotated Edition

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

4.5 1,318 ratings

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A groundbreaking mathematician presents a new model for understanding financial markets

Benoit B. Mandelbrot is world-famous for inventing fractal geometry, making mathematical sense of a fact everybody knows but that geometers from Euclid on down had never assimilated: Clouds are not round, mountains are not cones, coastlines are not smooth. To these insights we can now add another example: Markets are not the safe bet your broker may claim.

Mandelbrot, with co-author Richard L. Hudson, shows how the dominant way of thinking about the behavior of markets--a set of mathematical assumptions a century old and still learned by every MBA and financier in the world--simply does not work. He uses fractal geometry to propose a new, more accurate way of describing market behavior. From the gyrations of the Dow to the dollar-euro exchange rate, Mandlebrot shows how to understand the volatility of markets in far more accurate terms than the failed theories that have repeatedly brought the financial system to the brink of disaster. The result is no less than the foundation for a new science of finance.

ISBN-10

0465043577
ISBN-13

978-0465043576
Edition

Annotated
Publication date

March 7, 2006
Language

English
Dimensions

6 x 0.92 x 9.25 inches
Print length

368 pages
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Editorial Reviews

Review

“The deepest and most realistic finance book ever published.”―Nassim Nicholas Taleb

About the Author

Benoit B. Mandelbrot was the inventor of fractal geometry, whose most famous example, the Mandlebrot Set, is one of the most iconic images in mathematics. He was Sterling Professor Emeritus of Mathematical Sciences at Yale University and a Fellow Emeritus at IBM's Thomas J. Watson Laboratory and the recipient of the Wolf Prize in Physics and the Japan Prize in science and technology, as well as awards from the U.S. National Academy of Sciences, the IEEE, and numerous universities in the U.S. and abroad.

His books include Fractals: Form, Chance and Dimension, which was later expanded into the classic The Fractal Geometry of Nature, and a memoir, The Fractalist, which was published posthumously.

Richard L. Hudson was the managing editor of the Wall Street Journal's European edition for six years, and a Journal reporter and editor for twenty-five years. He is a 1978 graduate of Harvard University and a 1991 Knight Fellow of MIT. Now the CEO and editor of Science Publishing Ltd., he lives in Brussels, Belgium.

Product details

Publisher ‏ : ‎ Basic Books; Annotated edition (March 7, 2006)
Language ‏ : ‎ English
Paperback ‏ : ‎ 368 pages
ISBN-10 ‏ : ‎ 0465043577
ISBN-13 ‏ : ‎ 978-0465043576
Item Weight ‏ : ‎ 13.9 ounces
Dimensions ‏ : ‎ 6 x 0.92 x 9.25 inches

Best Sellers Rank: #61,680 in Books (See Top 100 in Books)
- #11 in Fractal Mathematics
- #19 in Business Statistics
- #39 in Statistics (Books)

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4.5 1,318 ratings

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Brian Dickinson

Buy it for Finance, Love it for the Fracticality

Reviewed in the United States on June 21, 2023

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What a wonderfully written book. I don't recall who said it, but I once heard someone say that much of scientific literature is, "written not with an intent to be understood, but instead, written to not be wrong." This book is clearly written to be *understood* by any intelligent reader, regardless of their background in mathematics. There are no formulae, equations, etc. in this book (you can find those on Wikipedia, if you are interested). Indeed, the beauty of his fractal geometry is that it is inherently visual.

I would liken his determination to truly communicate his (sometimes complex) ideas to that of RIchard Feynman -- which is one hell of a compliment.

A representative example: "The probability of that happening...was less than one in 10^50 [read: 10 to-the-power-of 50] -- odds so small they have no meaning. It is a number outside the scale of nature."

It may not sound like a mind blowing explanation, but "odds so small they have no meaning" and "a number outside the scale of nature" to me are ideal, pithy, digestible ways of explaining the value of a number like that to a general audience. To those who don't have a background in physics, math, or some fields of engineering, a number like 10^50 is just another viable number. But he makes sure to put it in proper perspective with an economy of words that I envy. Most authors would just say 1:10^50 and expect you to be wowed. He makes sure you get it before moving on.

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muddy glass

everything you were ever taught about finance is a lie!

Reviewed in the United States on August 21, 2011

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everything you were ever taught about finance is a lie! (or maybe not.) "the (mis)behavior of markets" is an excellent introduction to mandelbrot's unorthodox ideas on the house of modern finance. this book was written for a general audience and was written late in mandelbrot's life, after he's had decades to polish his thoughts. if you want an introductory book to read about how the stock market is possibly related to fractals, then this is the book to pick up.

fractals are the by now familiar mathematical objects that display self-similarity when scaled larger or smaller. their progenitors are those weird constructs, such as peano's space-filling curve and the cantor set, that were introduced in the late nineteenth century and subsequently sparked a revolution in logic. all of these animals of pure mathematical fancy were designed to challenge the conventional notions of the time and forced mathematicians to revisit the foundations of their craft. indeed, this line of thought led to the strange notion of non-integer fractional dimensions.

so what does all of this have to do with finance? the dimension of a fractal is given by a power law. a lot of economic and financial data seem to fit power laws as well. fractals are characteristically self-similar. charts of stock prices exhibit self-similarity. yada yada yada and thus, markets are governed by fractals. wait a minute. that's actually not quite logical!

ok, so there are some speculative aspects fueling this enterprise. this is the source of most of the negative criticism mandelbrot receives for this book. in my opinion, laying out some speculative avenues of thought is not a crime. scientists should dare to dream! mandelbrot himself acknowledges that this circle of ideas is merely in its infancy. he hopes others will pursue this path of inquiry and continue his life's work. and just why would anybody pick up that banner? well, because our current understanding of finance is deeply flawed while mandelbrot offers a (very rough) potential alternative.

in the first part of the book, mandelbrot does an outstanding job presenting data contradicting conventional financial theories. the punchline: markets are much riskier than people think. in particular, he attacks the use of the so-called "normal" probability distributions in finance. this foundational attack threatens modern portfolio theory, the capital asset pricing model, the black-scholes formula for pricing options, etc. essentially, all the major developments in finance in the second half of the twentieth century are in jeopardy. some of the creators of these theories have won nobel prizes in economics, so a lot is at stake here. (an understatement!) note that mandelbrot's arguments in part one are valid even if the fractal speculations presented afterward turn out to be unfounded.

mandelbrot uses plain language and analogies in his exposition throughout the book. he purposefully avoided equations, but he partially makes up for it through the use of pictures. mandelbrot was a very visual thinker and it shows in this book. for example, on p.179 mandelbrot offers a diagram of what "removing the trend" means in hurst's research. stare at the picture for a little while and the meaning should become clear to anyone with an interest in math and science. similarly, mandelbrot doesn't really explain how multifractal time works since the given father-mother-child analogy is fuzzy at best. however, the "fractal market cube" diagram on p.214 explains the concept of multifractal time in one picture. anyone familiar with projections should be able to understand this diagram without any problems. this compromise approach of offering analogies for a general audience while providing supplementary mathematical content in the pictures is suitable for an introductory book aimed at a wide audience, in my opinion.

the best feature of this book for me was the autobiographical chronicling of a sharp mathematical mind at work. mandelbrot was able to see patterns and connections between seemingly unrelated fields and then he pursued these links relentlessly over decades of time. his individuality and perseverance allowed him to carry on even when the rest of the establishment were pursuing contrary ideas. mandelbrot also doesn't hide the moments when he was in the dark or when he saw connections that turned out to be trickier than his first instinct suggested. after all, this train of thought spanned a lifetime. and amazingly, some of his greatest insights came from pure serendipity. mandelbrot received a major breakthrough from reading a paper that was pulled out of a garbage can!

in the interest of fairness, there are some relatively minor oversights in this book. this was the only real negative i could think of and it's easily forgivable. for example, mandelbrot incorrectly states that peter lynch's stellar performance as manager of fidelity's magellan fund was most significant when the fund was small. it's actually the opposite: market impact costs become a burden when a mutual fund grows too large, making it much easier to outperform the market when a fund's assets are small, especially with lynch's trading style. in spite of this minor criticism, i found this book to be a page turner written by an obviously extraordinary thinker.

it's always a good idea to read the masters. if you want to understand the spirit of passive investing, read jack bogle. if you want to partake in value investing, read ben graham. and if you want to know why the house of modern finance might stand on shaky foundations, read mandelbrot. read, think, then judge for yourself. lastly, if you were hoping to make a fortune from fractals, read the following quote from p.6 of the book:

"i see a pattern in these price movements -- not a pattern, to be sure, that will make anybody rich; i agree with the orthodox economists that stock prices are probably not predictable in any useful sense of the term."

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mtspace

A Random Walk Gets More "Wiggly"

Reviewed in the United States on July 11, 2014

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Mandelbrot sets out to demolish most of the theoretical bases of financial theory that led to several of the financial crises in the last several decades, foremost of which is that the random motions in prices of commodities and stocks can be assumed to be normally distributed. This sounds like an esoteric sort of argument, but anyone who wishes to win in any game of chance must have some solid notion of how to deal with risk. If one uses the standard model employing the normal (Gaussian) distribution, one will always underestimate the probability of rare events. This can lead to ruin, sometimes on a small scale. As an example, Mandelbrot talks about the rise and fall of the mother of all hedge funds - Long Term Capital Management which took a measly $3.6 billion bailout in the late 1990's because it underestimated risk. But it can happen on a much larger scale as in the crash of 2008 when many large financial institutions in the US held leveraged positions in mortgage security debt instruments. Long story short, everyone underestimated the risk of the unexpected happening, and it nearly crashed western civilization. The cost of that mistake will be measured in the $trillions.

Mandelbrot goes through the models that set up the whole thing: Bachelier, Sharpe, Black-Scholes, and standard portfolio theory. He briefly discusses their power. It's a great, if somewhat sketchy overview of what tools financiers and bankers often use. But in each case, lurking in the background are the assumptions of normality in price movements, and of statistical independence between time periods and between different asset classes.

There is no question that Mandelbrot proves that cotton price fluctuations are badly described by the normal distribution. The quantitative and qualitative information he brings to other asset classes is much less robust. He gives us very good arguments as to why other classes behave as does cotton; but It is hard to say that he brings the same level of quantitative rigor to these. For those of us who want the argument to end with everyone believing the fractal story, it's a bit of a disappointment. What he does do, though, is to describe the Cauchy distribution function which, with some slight generalizations can produce distribution functions that will accurately characterize time series price data whose variation obeys power-laws in the tails of the distribution. The upshot is that anyone with a solid understanding of college level statistics could go on to derive their own Black-Scholes formula.

His publisher appears to have set two rules: 1) no math of any sort in the body of the book, and 2) only simple algebraic equations in the notes. These prohibitions have several consequences. One is that the book is quite readable to anyone, even someone who has not finished eighth grade algebra. A reader can get a vague sense for what Mandelbrot is saying without the math. The flip side is that people who have finished eighth grade algebra may find the arguments hand-wavy when they could be much more solid. Anyone who has a solid background in statistics is likely to be able to fill in the gaps much better, but they will find the arguments fall far short of the kind of proof that one would expect in a 300 page book written by a world-famous mathematician. The people who have studied Black-Scholes, understand its derivation, and use it everyday will likely want a little bit more data and a lot more math before they kill the beast that writes their paychecks. Specifically, they will want a replacement method, which Mandelbrot only hints at.

I found the text here to be a little bit discursive and somewhat repetitive. I often enjoyed his anecdotes, but I did find myself skipping paragraphs, pages, and even chapters. I bought the book knowing that markets have fractal behavior, and hoping to be able to make my own mathematical models based on information in this book. It did allow me to make the intuitive connection between power-law behavior and fractal behavior. And I believe the book has gotten me to the point where I can do all the steps required to price risk and characterize random motions in the prices of assets; although I think a six page monograph that admitted mathematical notation would have been more than sufficient.

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JONATAS DOS SANTOS SILVA

Divisor de águas.

Reviewed in Brazil on July 18, 2023

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Sua abordagem e compreensão intelectual da matemática financeira envolvida nos mercados jamais será a mesma, absolutamente.

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ROBIN

Surprisingly readable…

Reviewed in the United Kingdom on March 30, 2024

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…from this eminent mathematician. A fundamental introduction to fractals for any student of Financial Analysis.

A Buyer

Cover is good. Not fake print

Reviewed in India on February 16, 2024

Verified Purchase

This review is for the paperback. The book is in good condition and binding appears intact. Print is original.

Content - yet to read, but this is highly recommended reading and I'm sure I will learn a thing or two.

Amazon Customer

Great book

Reviewed in Canada on April 30, 2021

Verified Purchase

Must read for analysts and advanced investors alike. Really great view of risk with a simplified use of math - much more theory than equations.

finmath

Useful and interesting reading

Reviewed in Italy on July 16, 2018

Verified Purchase

This book is an interesting treatment of the theory of financial markets using a very original approach. It provides several examples from the past and the criticism to models currently used, and it slowly introduces the key concepts of fractals. The book is always readable and doesn't require a strong mathematical background. Personally, I would have liked a more formal exhibition to the theory, but I understand this is not the author's objective. The book encouraged me to deepen the subject and delve into further research.

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