The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward
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- Create Date：2021-04-30 11:55:41
- Update Date：2025-09-06
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- Author：Benoît B. Mandelbrot
- ISBN：1846682622
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Summary
This international bestseller， which foreshadowed a market crash， explains why it could happen again if we don't act now。 Fractal geometry is the mathematics of roughness: how to reduce the outline of a jagged leaf or static in a computer connection to a few simple mathematical properties。 With his fractal tools， Mandelbrot has got to the bottom of how financial markets really work。 He finds they have a shifting sense of time and wild behaviour that makes them volatile， dangerous - and beautiful。 In his models， the complex gyrations of the FTSE 100 and exchange rates can be reduced to straightforward formulae that yield a much more accurate description of the risks involved。
Reviews
Oxanne
，
This book explains financial markets in a way that makes sense。 The author tries to warn us that the financial markets are far riskier than we believe they are。 He explains the weaknesses of math models we use in finance （that are based on a bell curve and dont consider long-term dependence）。 Theorists use those models and dont think about the real risk exposure in the market。 I encourage everyone to read this book。
James K Worswick
，
Benoit Mandelbrot， whom influenced Nassim Taleb and taught Eugene Fama， provides insight on the market; and the history of how CAPM， Black Scholes， and the Efficient Market Hypothesis came to be。 In this book， cases against each of these tools that the financial analysts use are explained。 He also introduces his own theory， that the market is multi-fractal， and that each small action causes a larger reaction， like the butterfly effect:"The size of the price changes clearly cluster together。 Big Benoit Mandelbrot， whom influenced Nassim Taleb and taught Eugene Fama， provides insight on the market; and the history of how CAPM， Black Scholes， and the Efficient Market Hypothesis came to be。 In this book， cases against each of these tools that the financial analysts use are explained。 He also introduces his own theory， that the market is multi-fractal， and that each small action causes a larger reaction， like the butterfly effect:"The size of the price changes clearly cluster together。 Big changes often come together in rapid succession， like a fusillade of cannon fire; then come long stretches of minor changes， like the pop of toy guns。 There is scaling here， too: If you zoom in on an individual cluster of big changes， you find it is made up of smaller clusters。 Zoom again， and you find even finer clusters。 It is a fractal structure。 Nor is it just the price changes of interest; at times， the price levels also exhibit some kind of irregular regularity。 The charts sometimes rise or fall in long waves， or with small waves superimposed on bigger waves。 " 。。。more
Daniel Walton
，
Interesting book that challenges the orthodox theories of finance。 I found the historical and biographical segments most interesting。 I think it's important for the fields in economics to face scrutiny from outsiders， particularly mathematicians。 They bring fresh ideas and different perspectives that help identify our blind spots。 Mandelbrot was an important voice in pointing out non-normality of returns distributions， non-stationarity， and dependence of increments。 These are all important point Interesting book that challenges the orthodox theories of finance。 I found the historical and biographical segments most interesting。 I think it's important for the fields in economics to face scrutiny from outsiders， particularly mathematicians。 They bring fresh ideas and different perspectives that help identify our blind spots。 Mandelbrot was an important voice in pointing out non-normality of returns distributions， non-stationarity， and dependence of increments。 These are all important points that have been incorporated into asset pricing theory to some degree。 I appreciate his fondness for fractals， fractional BM and time-scaling， but they aren't necessarily the best tools for the job， though they are cool。 。。。more
Pedro Ceneme
，
This is a good introduction into fractal theory and its insights without heavy mathematical jargon。 Mandelbrot writes clearly and punctuates his arguments with anecdotes， pictures， and graphs throughout the book， which help greatly to get into the nonintuitive conclusions he draws from his theory。 For those looking for more academic rigor， the notes section goes into more （mathematical） depth about the models and hypothesis he uses。 This book interesting because its format and narrative represen This is a good introduction into fractal theory and its insights without heavy mathematical jargon。 Mandelbrot writes clearly and punctuates his arguments with anecdotes， pictures， and graphs throughout the book， which help greatly to get into the nonintuitive conclusions he draws from his theory。 For those looking for more academic rigor， the notes section goes into more （mathematical） depth about the models and hypothesis he uses。 This book interesting because its format and narrative represent somewhat Mandelbrot argument for nonlinear systems: often I was dulled and puzzled by the choice in words and analogies and then， suddenly， after a specific paragraph the concept clicked。 While some readers may get discouraged by this style of composition， I would suggest one persists through it for such insights that pop suddenly。 Having recently read Scale by Geoffrey West， I was specifically draw by the concepts of distinct time scales that financial markets operate， as well as Mandelbrot elegant and simple breakdown of the market between “Noah” and “Joseph” systems， that is， for one-off/huge impacts that dissipate quickly and persistent trickle-down effects that reverberate for a long time。 However， you will be frustrated if you are looking for explanations as to why these systems behave fractally as they do: while Mandelbrot offers some potential accounts for the dominion of power laws， he is much more concerned in designing experiments and determining models that accurate depict reality than speculating in what causes it。 Nonetheless， a lot of the book seems a bit repetitive if you are somewhat familiar with economics history and financial theory。 As such， I would recommend more seasoned readers to skip directly to Chapter VI （or Chapter V if in need of a quick recap of the limitations of Modern Portfolio Theory/Efficient Market Hypothesis）。 Also， Mandelbrot frequently inserts autobiographical aspects in his arguments， which can take a nice chunk of his claims。 While some of it can contribute to the nonlinear effect of explaining his models as I mentioned before， I felt that some could be suppressed。 The book ends with a summary on the “Ten Heresies of Finance”: the biggest limitations of the current consensus for explaining financial markets， how this can increase our risk of ruin and how fractal theory can improve our perception of risk。 While the discussion of uncertainty here is interesting， the author does this in very broad strokes。 As such， for a better meditation on the topic I would recommend either The Black Swan or Antifragile by Nassim Taleb。 。。。more
Richard
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Good book。 I am surprised that other mathematically-inclined would not see the simplicity。
Abir Kar
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A good place to start if you know nothing about fractals and the inability of standard financial models at predicting tail events。 Mandelbrot spends a lot of time talking about how everyone else is wrong and very little about how his own method is better。 Still not a bad book by any standards - I just wish there was a bit more math and real life examples。
Otávio Ziglia
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Incredible how this totally unorthodox book about finance has become basically mainstream in the 2020s。
JEFFERY VERNETTI
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One of a few books that I will read again， and I have no doubt that I will glean new information the next time that I read it。
Luke Deacon
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Mandelbrot sets out to overthrow the philosophy that undergirds modern finance。 His key theses are:1） Markets are far more turbulent and risky than we often assume （they aren't normal， they don't follow the Gaussian bell-shaped curve）; 2） their parts scale fractally; 3） big market action is concentrated in smaller amounts of time （or: big gains/losses almost always happen very quickly）; 4） prices often leap rather than glide （thus rendering Bachelier， Markovitz， Sharpe， and Black-Scholes mathema Mandelbrot sets out to overthrow the philosophy that undergirds modern finance。 His key theses are:1） Markets are far more turbulent and risky than we often assume （they aren't normal， they don't follow the Gaussian bell-shaped curve）; 2） their parts scale fractally; 3） big market action is concentrated in smaller amounts of time （or: big gains/losses almost always happen very quickly）; 4） prices often leap rather than glide （thus rendering Bachelier， Markovitz， Sharpe， and Black-Scholes mathematics all wrong， as their math relies on the continuous change of prices）; 5） prices are long-range dependent， meaning that a trend， once started， tends to keep going in that direction （persistent） or undo itself （anti-persistent）; 6） we can't （yet） forecast prices， but we can get an idea of how volatile the market is going to be - this won't necessarily help us make a lot of money， but it will help us avoid the market's worst punches; 7） we need to do a lot more work to figure out how the fractal scaling of market movements can help us understand finance better。 Enjoyable book and I'm thankful he made it easy for the average layman to understand， but I think it could have been more concise。 There are also no answers， so don't read it if you're looking for a "how to invest" guide - it's definitely not that。 。。。more
Aaron
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Much ado over very little。 Mandelbrot seems to derive much of his personality from being a contrarian， which itself is not of much interest — his ideas are interesting， but his stories about why nobody believes him because he’s such a revolutionary are much less so。 He’s also got an ego on him， with constant name dropping （take a shot every time he mentions Harvard， MIT， IBM， or UChicago）。 It’s not a good look on anyone， and even less so on someone who is already popularly successful — see Feynm Much ado over very little。 Mandelbrot seems to derive much of his personality from being a contrarian， which itself is not of much interest — his ideas are interesting， but his stories about why nobody believes him because he’s such a revolutionary are much less so。 He’s also got an ego on him， with constant name dropping （take a shot every time he mentions Harvard， MIT， IBM， or UChicago）。 It’s not a good look on anyone， and even less so on someone who is already popularly successful — see Feynman as an example of doing this kind of thing better。A whole lot of time is dedicated to the existing thoughts in economics， which is nice， but not too exciting。 The main purpose of this is to show how fractal models fit the situation better， but the problem is that while fractals can make compelling models， their pragmatic usefulness as anything past faking a realistic chart is questionable。 They do make reasonable models with Monte Carlo simulations for risk assessment， but the problem remains the same as other models — they don’t really predict much in reality。On the plus side， I learned how fractals work， and their application here is reasonable-ish。 I suspect models with smarter distribution functions + momentum mechanisms could beat out a fractal approach， but maybe not？ It’s an interesting idea， but I see why the establishment wasn’t ready to scrap everything and start from this instead。 Mandelbrot seems baffled that this hasn’t happened， of course。 。。。more
Brahm
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Mandelbrot is a mathematician who is fascinated by fractals （let's call it a form of geometric repetition， like a fronds of fern， florets of cauliflower， branches of a tree）， coined the modern term "fractal"， and invented the mathematical field of fractal geometry。 If you want to see fractals in a set of images， go to this Wikipedia page and check out the images。 In this book Mandelbrot applies fractal geometry to the study of market behaviour， with the thesis that traditional market models are Mandelbrot is a mathematician who is fascinated by fractals （let's call it a form of geometric repetition， like a fronds of fern， florets of cauliflower， branches of a tree）， coined the modern term "fractal"， and invented the mathematical field of fractal geometry。 If you want to see fractals in a set of images， go to this Wikipedia page and check out the images。 In this book Mandelbrot applies fractal geometry to the study of market behaviour， with the thesis that traditional market models are all essentially wrong because they're based on bell curves， which consistently underestimate or exclude the possibility of catastrophic risk。 This is basically the same fat tails/black swans argument my favourite modern philosopher Nassim Nicholas Taleb makes in his books （he in fact references Mandelbrot） but with fewer brash anecdotes and meandering philosophical side-tracks。 The background chapters on fractals were fascinating: one of Mandelbrot's explanations is they are a study of roughness， and interesting to note that humanity has studied "perfect" shapes and geometry since the ancients， but we have neglected roughness and recursion until the modern era。 The "fractality" of market prices can be demonstrated with a simple example: remove the x and y axes from a stock ticker's price and you cannot tell if you're looking at an hour， day， week， year， or decade's worth of data。 Fractal geometry cannot predict market outcomes （what can？） but it can be used to better quantify and forecast risk， measure variability， and build models to test hypotheses。 It's another tool available than the oft-misused Gaussian bell curve。 Mandelbrot goes against the grain and rails against most modern economists， so would recommend to fans of Taleb or those who enjoy reading an argument that goes against the establishment。 While I enjoyed the book I felt the conclusion was weak or nonexistent: it ended with a 10-point "listicle" and a couple examples of current applications of fractal geometry being applied to study markets， but I would have liked to see a concise summary or conclusion of his thesis。 。。。more
Tobias Myhre
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Time， price & volatility ✔
Joey
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In addition to a （well-trodden but nonetheless robust） critique of EMH/MPT， Mandelbrot highlights the empirical observation that markets tend to exhibit “memory” of ST and LT patterns， specifically that price volatility （both up and down） appears in clusters。
Josh Friedlander
，
I once interned somewhere where I worked with a bright French guy， who had previously graduated from a grande école and worked as a quant。 We chatted during breaks about the Efficient Markets Hypothesis， algotrading， and Harry Markowitz （he was not a fan）。 "Economics still needs its Galileo， its Newton，" he said。 It's possible that he had read this book， which contains a very similar idea。Mandelbrot was a peripatetic and intellectually omnivorous scholar， who moved from Poland to France to the U I once interned somewhere where I worked with a bright French guy， who had previously graduated from a grande école and worked as a quant。 We chatted during breaks about the Efficient Markets Hypothesis， algotrading， and Harry Markowitz （he was not a fan）。 "Economics still needs its Galileo， its Newton，" he said。 It's possible that he had read this book， which contains a very similar idea。Mandelbrot was a peripatetic and intellectually omnivorous scholar， who moved from Poland to France to the United States， and worked on meteorology， computer graphics （at a job at IBM）， finance， and a host of other fields， in addition to his main focus of pure maths （where he is best known for inventing the concept of fractal geometry）。 It was his openness to practical problems that led him to the US; when he got his PhD French mathematics was in the grip of the Bourbaki （of which his uncle and brother were members）， which was too much "math for math's sake" for his taste。 His uncle gave him a book by George Zipf describing the distribution of word frequency in common corpuses， as Pareto had done earlier for income distributions。 Neither Pareto nor Zipf were right about the specifics， but the basic idea - that seemingly chaotic data could be modeled buy surprisingly simple patterns - seemed promising。 Thus a career was born。Mandelbrot's hero in some ways is Louis Bachelier， the first mathematician to analyse financial data seriously， modelling it as a random process。 He used the concept of Brownian motion （then a fairly edgy idea in statistical mechanics， recently revived by a young Albert Einstein） to model the chaos of options prices in the Third Republic。 As with Mandelbrot， his interest in finance was seen as not comme il faut by the theory-oriented world of French maths， and - despite being championed by Poincaré - he struggled to find a teaching post。 In fact one of Mandelbrot's central claims is that the randomness of financial markets is not Brownian: impossibly rare events seem to happen all too often。 Like the phases of matter， there are different types of randomness， he claims。 Mild randomness is Brownian motion， a coin toss， or a random walk （as in Malkiel's book）， and modeled by the Gaussian bell curve and the Black-Scholes formula。 By contrast， there is also slow and then "wild" randomness， found in turbulent flow and stock prices， and modeled by fractal geometry。 Such information doesn't help make one rich - the mathematics don't allow simple prediction - but they do disprove some of the more egregious simplifications of financial maths。 （Mandelbrot thinks there is some merit in fundamental analysis， but considers technical analysis akin to astrology。） Some of this may be less surprising nowadays when it is common to find Wall Street firms full of physics PhDs crunching out algorithms。 But some of Mandelbrot's ideas are also still controversial。 （His style， a bit long on self-promotion， can be off-putting。）One of the best bits of this book is the frequent use of illustrations， something Mandelbrot became accustomed to while working at IBM。 He notes that Lagrange and Laplace bequeathed to science a suspicion of illustrations， partly because of their desire for analytical proof， but also because the illustrations in their time were not so precise。 However， computer graphics can be made with any degree of precision desired， and actually help the scientist apprehend connections which can be proven later。 （Keep going， belief will follow， D'Alembert said of the calculus; here it is the opposite。） This is another case where today's explosion of "data vis" has caught up with Mandelbrot。 He uses "cartoons" （in the art historical sense） to illustrate his ideas; one example is the Koch curve， （"this lamentable plague of a function with no derivatives" in the words of one contemporary mathematician）。Mandelbrot criticises the currently popular time-series prediction models like SARIMAX and GARCH （"a name only a statistician could love"）， and suggests instead a "multifractal generative model"， with some sketches and real-life examples。 But the book is not exactly a prescription for financial modelling， more a critique of the current state， and a proposal that statistical tools for modelling options prices and portfolio risk are still in their infancy: Galileo still awaits。 。。。more
Rick Nonsense
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So uh， talk about timing。 Pretty much the day I finished this book the whole Gamestop saga began kicking off。 Perhaps the highest praise I could give this book is that after reading it no one should find those types of shenanigans surprising。 Mandelbrot uses a mixture of hardcore first order mathematics and philosophy to shred the theories of financial orthodoxy and replace them with much more useful （and less iatrogenic） concepts。 If anyone wants to get into finance or side trading， I would str So uh， talk about timing。 Pretty much the day I finished this book the whole Gamestop saga began kicking off。 Perhaps the highest praise I could give this book is that after reading it no one should find those types of shenanigans surprising。 Mandelbrot uses a mixture of hardcore first order mathematics and philosophy to shred the theories of financial orthodoxy and replace them with much more useful （and less iatrogenic） concepts。 If anyone wants to get into finance or side trading， I would strongly urge them to read this book before any others。 。。。more
Gregory Gandy
，
The Misbehavior of Markets by Benoît B。 Mandelbrot provides some unique insights into the flaws of modern financial theory and advocates for adopting multifractal analysis in the financial sector。 Mandelbrot manages to explain the fundamentals of multifractal analysis in a clear and relatively concise way。 See my notes below for more content details。I gave the book four instead of five stars because I found aspects of the style to be off-putting at times。 Mandelbrot frequently complains about ho The Misbehavior of Markets by Benoît B。 Mandelbrot provides some unique insights into the flaws of modern financial theory and advocates for adopting multifractal analysis in the financial sector。 Mandelbrot manages to explain the fundamentals of multifractal analysis in a clear and relatively concise way。 See my notes below for more content details。I gave the book four instead of five stars because I found aspects of the style to be off-putting at times。 Mandelbrot frequently complains about how the financial sector hasn't widely adopted his ideas。 I was also disappointed that Mandelbrot doesn't provide a path forward， resources， or advice， for the reader interested in experimenting with multifractal analysis， especially given that multifractal analysis is still a very niche topic in finance。--------------------Some of my notes:- Randomness has multiple states （pg。 30）。 Gaussian vs。 Cauchy （pgs。 33 to 42）。 Bachelier， random walk （pg。 44）。Mandelbrot argues that modern financial theory relies on the following assumptions: - Investors are rational， this has been disproven by behavioral economics。 - Homogeneous expectations， studies have shown that if there are two types of investors （fundamentalists and chartists） the two groups interact in unexpected ways， and the market becomes a chaotic nonlinear system in which the factors interact。 - Price changes are continuous， price changes jump and lead to order imbalances in which market indigestion leads to sell and buy orders not matching。 - Price changes follow a Brownian motion。 Brownian motion assumes independence， random walk （fad effect evidence）， statistical stationary of price changes， gaussian distribution （fat tails on the bell curve evidence）。 Mandelbrot argues that orthodox financial theory is still used despite the obvious flaws that it’s assumptions rest on because it gives a false confidence of precision and competence。 Most orthodox， modern financial， financial theories rely on each other and cannot be separated from the whole。 Compares modern financial theory fixes， like APT and GARCH， to Ptolemaic astronomers accommodating new observations that didn’t fit their theories by adding epicycles to cycles。 Mandelbrot uses the concept of fractal geometry， the study of roughness， to incorporate turbulence into a new method of financial analysis。 Fractals can be used to measure how convoluted and irregular something is。 For more on fractals， see pgs。 126 to 131。Power laws， Pareto （pg。 153）。 H is a measure of far an asset will randomly run （long memory， goes against random walk） （pg。 187）。 If H is bigger than 0。5， it will roam far。 If it is less than 0。5 ， it will roam less （pg。 187）。 A higher H indicates a risky momentum play while an H barely above 0。5 indicates a boring stock （pg。 192）。 Two types of wild variability: Almost-cycles， long range dependence influences the random fluctuations of the present （pg。 200）。 Abrupt change （discontinuity）， hierarchy of turbulence， a pattern that scales with time （pg。 201）。 Rescaled range （R/S） analysis is a non-parametric test that is a measure of long-term dependence （pg。 202）。 Best model of how a market works is Multifractional Model of Asset Returns （pg。 217）。 Price is a function of trading time which is a function of clock time。 The baby theorem （pg。 213）。 Convert clock time to trading time with binomial bending of time with multiplicative cascade （pg。 215）。 Some practitioners think that multifractal thinking is most useful for risk-protection （pg。 260）。 Fractal fingerprint （pg。 264）。 Monte Carlo Simulation （pg。 267）。 。。。more
Brad Crossen
，
Taleb explains it better。
Marius Heje Mæhle
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Helt klart en av de beste finansbøkene som finnes
Ben Verhaeghe
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MehI didn't find this book worth the time it took me to read it。 Concept is at first interesting but it gets repeated over and over too many times MehI didn't find this book worth the time it took me to read it。 Concept is at first interesting but it gets repeated over and over too many times 。。。more
Alexander Aleksandrov
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Great book that once against highlighted how useless my finance bachelor's degree was。 Great book that once against highlighted how useless my finance bachelor's degree was。 。。。more
☘Misericordia☘ ⚡ϟ⚡⛈⚡☁ ❇️❤❣
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A premodern take on time series data， the markets behavious and whether the natural concepts still apply to them。 Affinity and walking through a whole maze of philosophical concepts。 Uni- and multifractality。 Recursive and non-recursive models of the market。 While I would've loved it to be more hands on （ie， supply the calcs where applicable， for instance）， I can't really be too grumpy since this is a very old work that turned out to be fascinating in light of how far we have taken our market BS A premodern take on time series data， the markets behavious and whether the natural concepts still apply to them。 Affinity and walking through a whole maze of philosophical concepts。 Uni- and multifractality。 Recursive and non-recursive models of the market。 While I would've loved it to be more hands on （ie， supply the calcs where applicable， for instance）， I can't really be too grumpy since this is a very old work that turned out to be fascinating in light of how far we have taken our market BS。 。。。more
Dominik Duda
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Very interesting and well-described insight into randomness as seen in markets。My mind was totally blown by the fact that there is this different type of randomness （turbulent one） which is not describable by standard distribution。This book will make you better manage your expectations in markets and help you look at price datasets from the only correct perspective。
Sav
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Excellent intro to the current models used in financial markets， and how to improve on them。 I wish it had gone into the weeds a little more - it’s pretty high level。
John Curtice
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Generic history of mathematical finance and models
Dipanshu Gupta
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Mandelbrot’s thesis: Abandon the Gaussian and embrace power laws。 He’s the father of fractals， a very powerful tool in every discipline of science I have encountered。 The problem with finance is that our mathematical tools and systems are ill-equipped to understand it， even though we have poured trillions into it。 To paraphrase Mandelbrot， we know why earthquakes occur but we cannot explain what leads to a man’s financial ruin。 His interest is not of a speculator， but a mathematical modeller。 Ha Mandelbrot’s thesis: Abandon the Gaussian and embrace power laws。 He’s the father of fractals， a very powerful tool in every discipline of science I have encountered。 The problem with finance is that our mathematical tools and systems are ill-equipped to understand it， even though we have poured trillions into it。 To paraphrase Mandelbrot， we know why earthquakes occur but we cannot explain what leads to a man’s financial ruin。 His interest is not of a speculator， but a mathematical modeller。 Having read his student Taleb’s work first， I was aware of the ideas that Mandelbrot proposes。 Reading the teacher’s first-hand account improved my understanding of it。 And his humour keeps you engaged。 。。。more
Luke Ingalls
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This book was good。 This is really the first book I’ve read about financial forecasting so it was tough learning about the classic theories at the same time I was learning what was wrong with them。 I’d suggest a python installation to accommodate this text。 I found myself constantly creating simulations to implement what Mandelbrot discussed。
Peter Deegan
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+ clear！！ （really difficult subject matter communicated extremely well）， economic nuance is not lost despite being written by a journalist， puts arguments from different eras in conversation with each other - I didn't quite understand the application of fractal geometry， left me wanting more + clear！！ （really difficult subject matter communicated extremely well）， economic nuance is not lost despite being written by a journalist， puts arguments from different eras in conversation with each other - I didn't quite understand the application of fractal geometry， left me wanting more 。。。more
Ayoub Makroz
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Very interesting ！
Shankar P S
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I first heard about this book referenced in author Nassim Taleb's books。 This book explains a new dimension of the financial market - volatility - which is usually underestimated by classical economics and financial journals。 The author has made great effort to explain the concept of fractals， volatility and power laws。 It is surprisingly simple to read， considering the complex topic。 It would benefit all investors to read and understand this brilliant book。 I first heard about this book referenced in author Nassim Taleb's books。 This book explains a new dimension of the financial market - volatility - which is usually underestimated by classical economics and financial journals。 The author has made great effort to explain the concept of fractals， volatility and power laws。 It is surprisingly simple to read， considering the complex topic。 It would benefit all investors to read and understand this brilliant book。 。。。more
Andrew
，