The Misbehavior of Markets: A Fractal View of Financial Turbulence

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."

Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions. Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model. This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market. The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right. I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter. There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community. All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader. Well worth a look.

The author shows how modern financial theory underestimates risk in financial markets. Famous as "the father of fractal geometry," Mandelbrot is less well-known for his contributions to financial market theory. He is the tour de force behind Taleb's "Black Swan" writings. "Misbehavior" is more of an introduction to fractal finance than a textbook about how to implement Mandelbrot's ideas into trading systems. Nevertheless, it provides a foundation and introduction to new methods that many may find useful, with enough detail to begin incorporating same into quantitative models. Other works by Mandelbrot go much deeper into the "how to" side of fractal finance. Benoît (pronounced "ben-wah") Mandelbrot writes in a clear, conversational style. The text avoids mathematical formulas, using instead a combination of written descriptions and entertaining analogies to explain. Chapter notes in an appendix present the mathematical formulas behind his descriptions, along with further (clear, simple) explanations. The book divides into three parts: The Old Way, The New Way, and The Way Ahead. The first part describes the history leading up to modern finance as still taught in most business schools. It describes contributions by key figures such as Louis Bachelier, Paul Samuelson, William Sharpe, Harry Markowitz, Myron Scholes, and Fischer Black. I found this summary quite interesting, a valuable lesson history. Although we learned MPT (modern portfolio theory) in my MBA finance classes, it's background and potential shortfalls were not addressed. The second part steps back to examine the nature of markets (turbulent, not Gaussian), identify contradictions between observation and modern theory (extreme events way more common than predicted), and then develop a better, multi-fractal (i.e. scalable) view of finance. Here Mandelbrot excels. Illustrations ("cartoons") help get points across while entertaining analogies (e.g. "Noah, Joseph, and Market Bubbles") and a true story of engineering genius (H.E. Hurst's analysis of Nile River floods) lead to insight into market trends useful to trend-followers. The third part looks to the future. It summarizes the previous material in "Ten Heresies of Finance" and points the way for future research. Overall, I loved this book. Obviously, Nassim Nicholas Taleb did too ("...the first book in economics that spoke directly to me.") It contains valuable information for every investor, professional or amateur, experienced or novice. Rather than something for advanced-level traders, I think it is the first book for anyone interested in investing or trading. It will open your eyes like no other, and inject a dose of realism and humility about money and markets that otherwise might cost a lot more than this book's price.

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.

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.

This book was written before the current financial crisis, and recently reissued with a new preface on the financial crisis. The most noteworthy features of this book are (a) its clear presentation of traditional financial theory without any equations, and (b) a systematic critique of the major premise of this theory, which the authors take to be the assumption that error terms are normally distributed when in fact they are often Cauchy distributed (and therefore have "fat tails" leading to high volatility and higher risk exposures than suggested by the standard theory). Despite the title and numerous photo plates in the book, there is nothing `fractal' about Mandelbrot's explanation of financial theory. However, the authors show clearly that financial markets exhibit a degree of volatility incompatible with the Capital Assets Pricing Model. They also show that, despite the standard notion that only the beta of a stock can be stable across time, the degree of volatility of a stock can also be forecast, and has strong implications for profitable buying and selling. The authors almost always stress that this book should be no comfort for the poor misguided souls who believe they can `beat the market' by analyzing stock movement history. This is a very important point, and authors who deny this are, I believe, misguided or evil. Nevertheless, they cannot resist leveling the standard "critique" that some investors do phenomenally well, consistently making profits where the standard theory says they should not (e.g., their homage to Peter Lynch, p. 103), even though this contradicts their basic message. It is a very attractive property of a book that its basic argument is correct and important, but it is also nice if the book is well crafted. With the exception of the lucid description of the standard model and clear critique of this model, the book is a scattershot of arguments of tangential relevance and quite excessively too long. The same points are belabored again and again. It is safe to say that the first or second time you come across a repetitive paragraph, you may put the book down for good. You won't have missed much, if anything, of relevance. The authors do go beyond their rather academic critique of modern finance theory to suggest that bad financial theory was largely responsible for the economic crisis, with the implication that if we reform our economic theory of financial markets, there will be no future bubbles of the sort that recently almost destroyed several economies. This claim does not ring true. Bloated state mortgage institutions (Freddy and Fanny), the Federal Reserve Board's complicity in flooding the economy with cheap credit, the irrational present-oriented incentive structure of financial services, the complicity of auditing firms with their clients, and mystical financial innovations such as credit default swaps also contributed to financial fragility.

There is an old joke that if you asked three economists for their opinions, you'd get four different answers. The point, of course, is that there is a high amount of ambiguity in the field of economics; for predictive ability, it is not quite as bad as consulting tarot cards, but it does lack the typically clean rules of a science like physics. The money (quite literally) is in the economic model that can best predict the future and let investors know what and when to buy and sell. The laws of physics works well in virtually all situations, getting only tricky in isolated circumstances (such as black holes). Economics, on the other hand, has much fuzzier rules in almost all circumstances. To put it in physics terms, Mandelbrot's contention would be that the science of economics is Newtonian (or maybe even pre-Newtonian) in an Einstein world. And with medieval rigidity, the powers-that-be will stay with their basic dogma (refining only as necessary) and will dismiss more modern ideas as heresy. In particular, Mandelbrot points to the fact that economists, by relying on bell-curve models, are failing to plan for extreme swings in the market. Aberrations in market activity are much more common than these models predict, which points out their flaws. Mandelbrot's alternative - based on his own work in fractals - is based on something called power laws, which better take into account the "natural" turbulence of the market. Mandelbrot is clear that his ideas will not make people richer, but it may keep them from getting poorer by understanding how markets work better. His writing (or that of his collaborator) is entertaining and informative without getting too technical (these details are saved for the notes). On the other hand, he is too close to this subject to be truly objective, and I was often left wondering if his ideas were truly better or if he merely did a good job of making them seem like they were. Even Mandelbrot admits that his ideas may seem heretical, but that in themselves doesn't make them right or wrong. While good and thought-provoking, this book should be taken more as a well-supported opinion piece than scientific truth.

This is another in a series of books written by Benoit Mandelbrot that deserves to have a 6 star rating.The current foundation of practically all financial analyses ,excepting the "safety-first"approach of Roy and Charnes and Cooper,is the mean-variance(standard deviation)approach which is incorporated into more advanced versions such as the capital asset pricing model(capm)and the Black-Scholes options pricing model for puts and calls.All of these models assume that all price movements in all financial markets are approximately the same small size,are independent of each other,are homogeneous and satisfy the law of large numbers and the central limit theorem.This leads directly to the assumption that all price movements can be modeled as(as if)being normally distributed.The reader should note that practically all classical and neoclassical economic theory is currently based on subjective expected utility(SEU)theory which bases much of its practical results on the applicability of the normal probability distribution.The entire argument made by Milton Friedman and Robert Lucas,jr.,that all false trading(contracting)at disequilibrium(nonequilibrium)prices cancels out in the long run over time ,is based on the claim that such price movements are normally distributed around the market clearing equilibrium price.This equilibrium market clearing price is automatically interpreted as being the mean of a normal probability distributiion.Such a price is thus an optimal price since the average of a normal probability distribution is also the maximum outcome possible.The entire claim that price adjustments lead to an optimal outcome in all(private sector) markets means that the socalled"INVISIBLE HAND"of the market is nothing more than a normal probability distribution.Any type of skewed and/or nonnormal distribution of price movements means automatically that such adjustments do not lead to an optimal outcome.Mandelbrot has thrown down the gauntlet,not only to the current purveyors of basic risk management,portfolio analysis,but to much of the economics profession as well.Mandelbrot does this by simply presenting massive amounts of empirical evidence showing that the commodity,futures,money,stock,and other markets price movements are not generally normally distributed.All of Mandelbrot's research has been replicated and duplicated by many other researchers in many other countries besides the USA.Since the mid-fifties,Mandelbrot has carefully and patiently presented his results in a series of widely cited scholarly articles and books.In this book,Mandelbrot has decided to take his case directly to the general public.The book is straightforward and easy to read and absorb.The only technical knowledge needed by a reader is some basic familiarity with the normal distribution and an understanding of the basics of calculating a Z-score.I can't recommend this book too highly.

Ottimo testo

B. Mandelbrot tears down the whole house of classic economy, showing how it stands on wrong fundaments. Then goes on suggesting alternative foundations. I do hope someone is working on building an alternative edifice on this basis. There's a prophetic passage at some point: when describing how the random variables in economic are far from memoryless, an old trader who lived through Black Friday and the Great Depression is quoted saying that once his generation will be gone, the caution they had will also disappear from Wall Street. This was written well before 2008.

I loved it. A masterpiece from the inventor of Fractals. A classic. Highly recommended.

I couldn’t read this book in a single sitting; not even a few chapters went by before I had to keep it down and vent anger at 2 things: 1. The ignoramuses who founded MPT, CAPM, and Black-Scholes, sure, but even more us, the modern practitioner who continues to use these models (I happen to be another unfortunate victim of years wasted learning modern finance in college and afterwards). Not a page will go by when you think how different the world would be if Bachelier’s work had remained undiscovered. 2. The fact that this book has been lying on my desk for 11 YEARS, unread. I first found Mandelbrot when I was 19, a student of accounting and finance. Maybe it was the hormones of youth, or my lack of comprehension skills that I never completed reading it. Memories of the jagged graphs in the book luckily brought me back to it. This is mandatory reading for everyone who has a bank account.

Delightfully clearly written discussion of the mathematics of the turbulent discontinuities that characterise asset and financial markets by the man who brought us mathematical measures of “roughness” (i.e. fractals).