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on July 11, 2014
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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on March 14, 2017
Great book (albeit incomplete if you're looking for definitive answers) that discusses the shortcomings of risk assessments for financial products and portfolios. As others have said, the author has posed several questions regarding the validity of financial practitioners' existing tools in corporate finance (valuation), options, and portfolio theory. One answer: multifractal theory; which the author posits could be the foundation for the next class of financial economists (best case).

My key takeaway from this book is that market participants' tools underassess risk and thus market participants should be wary of becoming model-dependent.

Additionally, supporting research and proofs are in the appendix or on the book's designated website for the more curious readers.
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on April 17, 2017
Mandelbrot shows that modern finance has a problem.

He examines CAPM, MPT, and Black-Scholes and shows that these models have major issues, mainly rigid assumptions.

He then shows that fractals provide a more realistic approach.

Before reading this book, I have only heard about fractals. It is interesting that fractals can be used in finance.

However, as the other reviews suggest fractals have some issues as well (large subjectivity!).

Overall, the book is still a good read because Mandelbrot shows the issues in modern finance and tries to

suggest a better approach (fractals).
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on August 21, 2011
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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Top Contributor: Swimmingon January 20, 2012
This book is both entertaining and instructive. It is also a more approachable text for those who don't have the background to enjoy his collection of papers published in "Fractals and Scaling in Finance".

It is instructive because a good part of the text is a very generalized presentation of the math theories used in Finance to model the market. Most of the Finance books present the math without a complete analysis. Mandelbrot does an excellent job instructing the reader about the theories and how they are applied to market models. And he presents the flaws which exist. You may not agree with his overall thesis, however, it is still very instructive.

People may not agree with his point of view, but his research from the 1960's is interesting and still relevent today.

As far as his assertions, I personally agree with him, and so does a large part of wall street. Random walk is not employed by traders, and the market makes most of its major moves in very short discrete periods of time. And Wall Street employs alot of math types to develop trading models to exploit patterns. Of course the patterns change as more systems exploit the pattern.

The flaws in modern finance theories are more based on the fact that there are standardized methods like the CAPM, which become worthless once everyone is forced to employ them.
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on December 8, 2011
The one downside about this book (and I find other books like this) is that it ends up being long for the level of detail contained. An 15 page essay could probably capture the most salient points of the book quite easily. Regardless, I'm partial to the book because I find it a relatively rational and clearheaded approach to markets. Many theorists these days who have seen the efficient market theory fail pounce on the opportunity and hail their theory as the new lens through which markets should be studied -- Soros, Lo, Talib, and the list goes on. Mandelbrot is no different, but he identifies the shortcomings of his theory in a much more palatable fashion than I've seen from some other authors, easing you into his ideas. He plainly says that his theory is a new mathematical approach to securities prices, and not a mechanism by which to make money (at least not yet). His application of fractals from nature to securities prices does make intuitive sense. His work in other fields shed light on what you may find in the book: "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line" -- neither do security prices follow smooth curves. He leaves the math out of this book, but certainly embarks on a fresh approach without sounding like he's found the Holy Grail.
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on October 6, 2010
Benoit Mandelbrot's The (Mis) Behavior of Markets is a splendid read and very informative. As many reviewers have noted, Mandelbrot invented fractal geometry. He has also been on the cutting edge (some would say fringe, but he's thinking and questioning) in multiple disciplines, as his curiosity seem to know no bounds. Mandelbrot does a good job of describing the inadequacies of the efficient market hypothesis and CAPM and other sacrosanct theories in finance, and he offers for our consideration an alternative view. His view is based on his assertion of reality; namely that the world of finance is turbulent (as indeed, the world is turbulent), and linear tools relying on reliability and rational man will never tell the full story.

Mandelbrot, to his credit, warns the reader early on that his is not an investment guide. He simply offers his ideas, and admits that some don't offer as much insight currently as he wishes. He is, however, optimistic that his philosophies and his alternative (edge-type) thinking will prevail in some form.

Truly wish I read this before b-school, as he explains why I scratched my head through a good portion because the theories didn't look "right." As a couple of other reviewers have noted, the first part of the book is best, and sort of stumbles to find itself in the second half. All that said, this is a valuable contribution and highly recommended.
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on October 12, 2012
The Misbehavior of Markets

This is an outstanding book in financial literature. I read it after reading Taleb's Black Swan. Naturally, Professor Mandelbrot has a point arguing that financial markets do not behave normally (nowadays everyone immerse in financial markets should be aware about this!). You bet! It only takes to turn back and remember october 1987 to realize the fact. I would recommend this book to any person who is curious about the developments that Mandelbrot and his disciples have made in fractal geometry applied to economics and finance. Also, if you are a technical reader, this book could help you as a warm up to more sofisticated books on the topic. READ IT!
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on October 23, 2007
I am a risk manager. The challenges that Mandelbrot has undertaken both politically, socially and intellectually are breathtaking and highly relevant. I am routinely found plodding through dense math texts, trying to remember my greek alphabet and often hoplessly lost in teh terminology. Mandelbrot does a great service to us all when he keeps the language understandable for the laity and eschews the complex formulas. You can tell that he does not need to sound overly smart because he is overly smart.

This book toes together so much history and so many concepts in such an elegant style that it is very hard to oversell the work. I have a hard time imagining a field in which this knowledge is not applicable in some way. And anyone who has even a baseline sense of curiosity will find the interweaving of the many great stories compelling.

I would imagine that some math majors will find that the information is somewhat basic, but only if they are exposed to a lox on non linear problems in a complexity theory or econophysics field. For everyone else, this is a masterpiece, an entertaining, accessible masterpiece.

Oh, and for any of you who like Nassim Taleb's work, this is absolutely essential reading. I also suggest diving into network and sync theories which fill in the gaps left by Mandelbrot. Much good work has been done since he wrote this. "Linked" and "sync" are especially good and accessible.
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on June 19, 2007
This book should be required reading for all of Wall Street's money managers. It would have saved billions of their clients' money.

Let's look at the Long Term Capital disaster. Intelligent people, Nobel laureates, so what went wrong? The answer is simple: fat tails! (The concept that supposedly one-in-a-billion events are, in fact, not unusual). Clearly, it was not lack of intelligence that caused their downfall, but a childish reliance on flawed financial theories.

Mandelbrot identifies and explains the flaws. True, he does not provide an alternative theory, but perhaps the whole point is that financial markets, being chaotic systems, are not predictable.

Let's look at another chaotic system, the weather. Here the parameters such as temperature, wind speed, humidity, are easily measurable. Yet, we still cannot predict the weather accurately for more than a day or two. How then can the stock market, which is far more complex than the weather, be predictable, when most of the parameters that affect it are not measurable, and some are not even known?

Perhaps the weakest part of the book is the beginning of a theory that Mandelbrot tries to found. He suggests that fractal equations produce charts that look and feel like real stock price charts, and that there might be some connection that can be exploited to predict or describe financial markets. He does not, however, go beyond this suggestion and hopes that someone else would develop his theory.

Bottom line: Mandelbrot's "fat tail" theory explains the financial disasters suffered by many "brilliant" money managers. It does not predict the market, but explains the risks of conventional capital market theories. It saves you money, and after all a penny saved is a dollar earned.
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