Benoit B. MandelbrotRezensionen

There is a huge problem with the book, it is way to fun to read. This book is a different way of thinking about finance. The depth and breath of finance that Mandelbrot explains without simplifying the subject is almost unbelievable. This book starts with what the world of finance looks like, and then a way to fix it. Fractals are a very dynamic and simple way of modeling many different forms of turbulence from nature to finance. From dependence to power laws, fractals can provide a more realistic view of how markets behave.

Everyone should carefully read this text, the significance of Mandelbrot's points remains unfortunately as important as ever and still largely ignored by the average person.
Many aspects which we believe to be true measures or robust facts are actually, under the surface, ruled by distributions that can fluctuate wildly. What does an average price index of a stock mean, if the underlying distribution doesn't really have a mean?

Excellently written though poorly on-topic. Only the last four chapters (of 11 or so) had anything novel than a history of the industry. The meatiest two of these four chapters were difficult to follow, so poor marks there.

Ultimately, the points are depressing: 1) markets are riskier and more volatile than standard methods suggest, 2) (intrinsic) "value" is not really useful and 3) the reiteration that despite 150 years of research so far, we don't seem to know much more than that we don't know much.

A bit disappointing, but probably one of those books that is a victim of its own success. Perhaps when it was originally written, the views were considered more heretical than they are now. I would recommend that a close reader of taleb's anti-fragile and/or the black swan skip this book since taleb's works rehash the main thesis of Misbehavior (down to the self-aggrandizement, almost every time Fama is mentioned, Mandelbrot claims him as his doctoral student, and Mandelbrot spends a fair amount of time praising his own work/ describing his maverickiness [though to be fair, I suppose that's fair for a mathematician of his status]). In Misbehavior, Mandelbrot lays out the case against the foundational assumptions of modern portfolio theory, mainly its reliance on the gaussian distributions. Mandelbrot makes the simple observation that many of the observed drops in the markets should not have occurred under standard assumptions (technically the standard bell curve allows the possibility, but the chances are so remote that such events should not be observable in several billion lifetimes, let alone recurring several times in a few hundred years). Mandelbrot attacks the assumptions of normal distribution, independence of events, and constant volatility. Mandelbrot shows that the data just does not bear out the milder swings the normal distribution anticipates (that actual price data exhibit fatter tails than the normal distribution). Mandelbrot argues that analysis shows a long term dependence, that prices exhibit a certain type of memory that is endogenous but also moves are clustered. He develops a measure H, to show the persistence of momentum or anti-momentum as opposed to the standard random walk (which incidentally has an H of 0.5). Mandelbrot criticizes methods such as GARCH as building on a flawed foundation in fixing changing volatility. Instead Mandelbrot advocates the use of power laws, so-called Cauchy-levy functions and fractals in creating models. He claims that fractals, especially ones that accounting for trading time that stretch or compress can model price movements in a more accurate way. The work seems pretty technical, and Mandelbrot admits freely that research in using multi-fractal models is only developing. More interestingly (at least in my opinion) is the crash course lesson in fractals (the three steps to form a complex pattern, initiator, generator and rule of recursion) and measures of roughness. Mandelbrot believes fractals can be used to explain many naturally occurring phenomenon as well as complex systems as the economy.

On the whole, the book is written for a non-technical audience. Mandelbrot helpfully summarizes basic modern portfolio theory (from Bachelier's thesis on bonds, to Markowitz, CAPM (Sharpe), finally to Black Scholes). That portion was relatively well done, I thought it was a fair and accurate representation of what I had learned in basic finance in college. Mandelbrot also convincingly shows that the normal curve is not a good assumption, and that reliance on it can lead to blow ups. However, Mandelbrot is not as convincing when it comes to proposing fractals as a solution. Perhaps it's the limits of my technical knowledge, but it just did not seem convincing. On many parts of Mandelbrot's analysis, I just had to take him at his word that a certain analysis produced the conclusion he claims, despite his admissions at the end that scholars disagree over metrics like H. An interesting read, but it lacked the scholarly rigor to convince me that his solution could be the new foundation for risk analysis. The ideas seem to move and jump, seeming more like an interesting collection of Mandelbrot's works and thoughts rather than a coherent rigorous argument. On the other hand, I might not be able to understand a comprehensive scholarly defense without a deeper mathematical background. I suppose we'll never know.

E' autografato dall'autore, e questo lo rende un po' speciale - anche perché di solito non tengo molto a questo genere di cose.
Sicuramente è fuori dagli schemi e imparo qualcosa di nuovo praticamente ogni paragrafo. Il che è un gran bene.

Clouds are not spheres, mountains are not cones, and lightning does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry. To describe such shapes, this author conceived and developed a new geometry, the geometry of fractal shapes. This book is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations,

It's kind of a popular economics/popular science book about fractals and markets.

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

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

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

4.5 stars out of 5.

fascinating story but a bit much: a more balanced view of his contributions would have been more impressive

Moving autobiography of the unconventional and peripatetic mathematician (pure and applied variants thereof, not to mention physicist, linguist, engineer, and economist) who founded and named fractal geometry. Fellow nonconformists Norbert Wiener and John von Neumann are just two of the startlingly many big-name scientists Mandelbrot (1924-2010) had dealings with at one time or another, right from his difficult early life in Poland and France before and during WWII. "Being ill defined is a feature common to all important concepts." (p 181) "I feel exceptionally privileged that my wanderer's life led me to be the agent of [the Mandelbrot set's] discovery." (p 261)

Just a few bits about those wonderful fractals and an interesting lot about Mandelbrot's demolition of many financial market theories.

In these turbulent economy we seem to be victims of the financial markets. Benoit Mandelbrot, famous mathematician and inventor of fractal geometry, joined forces with Richard Hudson, to write a book about financial theory. “The (Mis)behavior of Markets” falls in the popular science genre. It is low on formulas, instead you can find lots of historical anecdotes and opinions.

1. Risk, Ruin and Reward

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

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

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

3. Bachelier and His Legacy

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

4. The House of Modern Finance

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

5. The Case Against the Modern Theory of Finance

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

6. Turbulent Markets: A Preview

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

7. Studies in Roughness: A Fractal Primer

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

8. The Mystery of Cotton

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

9. Long Memory, from the Nile to the Marketplace

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

10. Noah, Joseph, and Market Bubbles

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

11. The Multifractal Nature of Trading Time

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

12. Ten Heresies of Finance

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

13. In the Lab

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

The book ends with notes containing formulas and bibliography listing scientific articles. A thrilling book, that I could not put down, until I read it cover to cover. It is the finance equivalent of “A Brief History of Time”. I give it 5 stars out of 5.

I read this in high school, and finally picked up a copy many years later when I wandered across it in a used bookstore. To be honest, though, this is one of the books that sits on my shelf because a mathematician has to have a copy of it, not because it is of any interest to me. There's too much fluff and belaboring here, and not enough clear explanation. For example, there is a color plate of a computer-generated planet, but no explanation of how it was created. "We can do this", but not much "here's how this is done." It left me frustrated in high school, and looking through it since then has done nothing to improve my opinion.½

A good explanation of the mathematics behind markets, and how the current models get it wrong.

Mandelbrot is too happy to have met himself. Lacking scientific humility, the I and the my get on the way of the reading. The style is however quite plastic.

Mostly a selection of the author's technical papers from the 1980s. The newly written and more discursive chapters are interesting, but even they show evidence of Mandelbrot's characteristic crypticality.

I understood a lot more of this book than I thought I would... Which is to say, I followed it about 3/4's of the way.

The way that markets work don't follow a "Random Walk" model and their changes do not follow a bell curve. If investors believe either of the above two aren't right, then they're exposing themselves to more risk than they think.½

A Fresh Look at Financial Orthodoxy

This book details one of this generation’s finest mathematical minds offers “obvious” observations he calls his “Ten Heresies of Finance.”

Benoit Mandelbrot is known for making mathematical sense of facts everybody accepts but that geometers never assimilated. Clouds are not round. Mountains are not cones. Coastlines are not smooth. Add another: financial markets are not the safe bet your broker claims. In his first general audience book, Mandelbrot, with co-author Richard L. Hudson, reveal today’s assumptions about the behavior of markets simply do not work.

“What passes for orthodoxy in economics and finance,” the authors conclude, “proves on closer examination to be shaky business.”

Among the book’s observations:

1. Markets are turbulent. After spending a lifetime studying wind and ocean currents, he applies his multi-fractal math to analyze financial markets. “The tell-tale traces of turbulence are plainly there, in the price charts,” he writes. The bell curve does not capture its changes.

2. Markets are inherently risky. Turbulence is dangerous. Market swings are wild and sudden. They are difficult to predict, more difficult to hedge and even more difficult from which to profit.

3. Marketing timing matters. Big gains and losses are concentrated into small time periods. News events such as earnings or economic announcements drive stock market prices.

4. Prices leap suddenly. This adds to risk. News announcements compel investors to act simultaneously and instantaneously.

Using his fractal tools, Mandelbrot describes how financial markets work. He describes the volatile, dangerous and in a unique way, strangely beautiful properties that for which few financial experts account.

This book is a must read for any serious investor. By pin-pointing flaws in accepted market wisdom, it provides a platform for a serious re-consideration of finance.

Well, it's a classic -- and Mandelbrot's idea of "fractals" is certainly a powerful one. I just wish he had decided to work with a co-author on this one. James Gleick and Ivars Peterson do a much better job of describing the science of fractals, IMHO. Kudos to Dr. Mandelbrot for discovering this new world, though!

For me, an up-to-date introduction to the financial theory of market behavior. It shows where typical Bell Curve analysis has mislead investors, by not acknowledging the trmendous turbulence markets may have. Dealing with power law distributions must be added into normal statistical analysis to really understand the temendous spikes in prices that sometimes occur and which are not predictable. The book does not give answers for everything.½

According to conventional financial theory, the odds of calamitous events in the market are extremely long. So long they ought not to happen. But as any investor will tell you companies go bust all the time. Markets crash. And products we supposed were safe turn out to be leaky junks sinking into the ocean swell. Mandelbrot has an alternative model, fractals, the geometry he invented to describe coastlines, the inside of your lung and the distribution of earthquakes. It might one day change the way we value investments

Il disordine dei mercati

Non è facile capirci qualcosa nel mondo della finanza. Salite lente e crolli repentini. I mercati sembrano fare di tutto per non farsi capire. Forse esiste un’altra possibilità: studiare l’andamento del mercato con i frattali.

"Se volete capire l’economia, lasciate perdere i libri e le conferenze ed entrate nel mondo del commercio�€?. Parola di Benoit B. Mandelbrot, professore emerito di matematica a Yale e studioso di modelli matematici applicati alla finanza. Secondo Mandelbrot la comprensione dell’economia non deriva da qualche teoria astratta o da quello che la gente desidera che accada, ma dall’osservazione del mercato. Per capirci veramente qualcosa occorre fare esperienza. I prezzi dei prodotti non dipendono solo dalle spese sostenute per realizzarli o trasportarli, bensì dal loro valore. In un qualsiasi testo di economia troviamo che “quel valoreâ€? è rappresentato, nell’andamento del mercato, con un diagramma a campana. Il diagramma sale, più o meno rapidamente, ogni tanto si trovano dei flessi, cioè zone di stasi, e poi scende. Può accadere anche che si verifichino le cosiddette turbolenze, impennate imprevedibili del valore, in un senso (crescita) o nell’altro (decrescita). In generale le turbolenze vengono definite dagli economisti come effetti esogeni, cioè esterni ed estranei al mercato stesso. Per esempio, le condizioni metereologiche influenzano i raccolti e i raccolti influenzano i prezzi, o ancora la distribuzione di risorse nel mondo (petrolio, acqua) influenza l’offerta e quindi l’offerta influenza i prezzi. Da esempi così semplici e quotidiani si arriva a condizioni esogene imprevedibili e talmente remote da trascurarne la prevedibilità, come ad esempio una catastrofe naturale.

La domanda è “perchéâ€? il prezzo ad esempio di una azione o il valore di una valuta, varia quando accade un evento esterno al mercato? E ancora, il disordine dei mercati è davvero imprevedibile? Se la probabilità che un evento accada è infinitesima, è corretto trascurarla? Secondo la teoria dei frattali, no. Il termine frattale, coniato dallo stesso Mandelbrot, deriva dal latino fractus, che significa spezzato, rotto: immaginate una figura, una foglia per esempio, che si riproduce fino all’infinito, sempre uguale di forma ma sempre più piccola di dimensioni. In questo modo il frattale è utilizzabile nella descrizione della realtà. Quindi la caratteristica fondamentale delle figure frattali è l’autosimilarità: se i dettagli vengono osservati a scale differenti, si nota sempre una certa somiglianza con il frattale originale. La geometria frattale è un mezzo per individuare queste configurazioni, per analizzarle e manipolarle e può essere utilizzata come strumento di analisi e di sintesi. Con i frattali le regole sono precise e il risultato prevedibile. Questo contrasta con la scienza tradizionale che invece annovera gli aspetti irregolari della natura e gli eventi non similari come teoria del caos. E’ teoria del caos una goccia d’acqua che si espande nel mare, o le fibrillazioni cardiache, o ancora gli errori dei computer e le oscillazioni dei prezzi.

Però qualche volta la realtà supera la teoria del caos nel senso che l’imprevedibile si realizza come ad esempio il crollo della borsa nel 1929 o gli infausti eventi finanziari dell’agosto del 1998. Secondo i modelli standard, cioè i modelli studiati dall’economia tradizionale, la sequenza di questi eventi era così improbabile da essere impossibile. Tecnicamente venne chiamato “valore erraticoâ€?, cioè molto, molto lontano dal normale valore atteso nel mondo azionario. Eppure è accaduto. Questo, secondo i frattali, significa che l’economia tradizionale è in errore. I mercati finanziari sono rischiosi, lo sanno tutti, ma uno studio approfondito del rischio, secondo gli applicatori della teoria dei frattali, può offrire una nuova comprensione e si può sperare di averne un controllo quantitativo. L’obiettivo è dunque studiare il rischio, anche se lo stesso Mandelbrot ammette che nulla si può prevedere con precisione. Vero è che osservando il comportamento di chi gioca in borsa c’è qualcosa di illogico. Osserviamo il fenomeno della Borsa: i prezzi sono molto variabili, i movimenti hanno una tendenza irregolare. Coloro i quali scommettono su queste tendenze per ammassare ricchezza, in genere ci rimettono perché le variazioni sono valutate come prive di ordine: i prezzi aumentano poi senza preavviso, questa tendenza si interrompe e si può persino instaurare la tendenza opposta.

Proviamo a ridurre la scala di osservazione e osserviamo il fenomeno applicando una visione frattale. Le tendenze irregolari dell’andamento della borsa sono raggruppate per dimensioni: le grosse variazioni arrivano in rapida successione seguite da sequenze di piccole variazioni. Il comportamento della borsa è quindi una struttura frattale. Allo stesso modo si può procedere nella descrizione delle “bolleâ€? degli investimenti, cioè la dilatazione abnorme di un valore. Le bolle, per quanto possano sembrare calamitose, sono molto frequenti tanto negli indici generali del mercato (esempio il Dow Jones) quanto nelle singole attività. Nonostante questo, i modelli economici tradizionali considerano le bolle delle aberrazioni, delle deviazioni irrazionali della norma, causate per esempio da uno speculatore avido. Perché invece non le si considera come frutto combinato di tante discontinuità? O ancora, perché la finanza tradizionale presuppone che il sistema finanziario sia una macchina lineare e continua anche se ammette l’esistenza delle bolle?
Un esempio può aiutare: in base al modello standard della finanza (la curva a campana dei prezzi) la probabilità della rovina e pari a 1 su dieci miliardi di miliardi, ovvero è più probabile essere centrati da un meteorite che fare bancarotta in un mercato finanziario. Ma se i prezzi hanno variazioni selvagge (è accaduto per il prezzo del cotone ma anche con il petrolio) la probabilità della rovina aumenta vertiginosamente.

Allora, come si deve comportare un investitore? Cosa deve valutare? Spesso i broker consigliano la strategia del “buy and holdâ€?, ovvero comprare e tenere concentrandosi sugli aumenti medi. Ma c’è anche chi suggerisce la teoria del “comprare, vendere e pentirsiâ€?, cioè del pentirsi di non aver guadagnato di più. Non sempre tutto è rappresentabile con una formula matematica applicata indistintamente in fisica e in economia. Sovente le formule sono errate e Mandelbrot attribuisce questo errore al fatto che gli sbalzi, i salti di prezzo e gli scatti della borsa appartengono all’economia e non alla fisica. Ecco perché secondo gli studiosi dei frattali, deve esserci un’altra via. Mandelbrot conclude il suo primo saggio sulla teoria dei frattali (Il disordine dei mercati – ed Einaudi) sostenendo che oggi è ancora prematuro sperare di ottenere guadagni importanti dalla finanza dei frattali, però intuisce che la strada da percorrere sia questa, ammettere che il caos ha un suo ordine e una sua prevedibilità. “Ritengo che la teoria finanziaria abbia bisogno di pragmatismo e, come nel giuramento di Ippocrate, non deve nuocereâ€?, precisa il professore emerito. Nel mondo della finanza invece i modelli tradizionali violano tale giuramento e sono pericolosamente sbagliati. Somigliano ad un costruttore navale che, supponendo che le bufere siano rare e gli uragani miti, progetta le imbarcazioni in base a criteri di velocità, capacità e confort, senza curarsi della stabilità. Far attraversare l’oceano ad imbarcazioni simili nella stagione dei tifoni significa provocare gravi danni. I mercati, come le condizioni atmosferiche, possono essere turbolenti. Bisogna imparare a riconoscerli e ad affrontare meglio la situazione.

Elisabetta Paglia
8/1/2006

«Dalla quarta di copertina: "L'indagine della natura ha trovato un nuovo codice interpretativo nella matematica. Mandelbrot ha descritto in termini grafici forme e processi naturali, quantificando il loro grado di "erraticità" attraverso rigorosi metodi matematici. E' nata così quella che lo stesso M. ha chiamato la "geometria dei frattali". A differenza della geometria euclidea , così rigida nel rappresentare il mondo visibile, e così lontana dal poter rappresentare le forme reali, la geometria dei frattali è capace di rappresentare i profili di una montagna o di una costa, le nuvole, le strutture cristalline e molecolari, e addirittura le galassie . La parola frattali definisce una rappresentazione grafica composta di linee spezzate (dal latino "fractus") dall'andamento apparentemente irregolare , che sono in sostanza delle strutture matematiche, capaci di esprimere comportamenti variabili in spazi anche molto piccoli. In questo volume, che si presenta riveduto e aggiornato rispetto alle edizioni originali francesi, è lo stesso M. a presentare la propria teoria, che si è dimostrata così fertile di applicazioni in ogni campo della ricerca scientifica e tecnologica, aprendo tra l'altro nuove frontiere alla computer graphics.
Il volume rappresenta dunque un punto di partenza essenziale tanto per chi vuole accostarsi alla geometria frattale mosso da un interesse prettamente epistemologico, quanto per chi, avendo già una qualche dimestichezza con strutture matematiche "aberranti e curiose", quali la curva di Peano o l'insieme di Cantor , cerchi per esse un'interpretazione semplice e concreta."»

Hudson, R. L. (Author)