Product Description

This international bestseller, which foreshadowed a market crash, explains why it could happen again if we donÂ’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.

Product Details

• Amazon Sales Rank: #9360 in Books
• Published on: 2008-11-06
• Original language: English
• Binding: Paperback
• 326 pages

Review
"* Mandelbrot is acknowledged as the father of chaos theory... he is, simply, very clever indeed. * The reader gets a clear picture of the history of finance theory... the best financial read * Entertainingly written... this book is a brain-opener that adds hugely to our sum of knowledge."

About the Author
Benoit Mandelbrot is Sterling Professor of Mathematical Sciences at Yale University. Richard L. Hudson is a former managing editor of Wall Street Journal Europe.

Customer Reviews

Necessary evil
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.

This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.

He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).

More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.

Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.

Revolutionary theory, but hard to apply
"This volume," writes Richard Hudson in his introduction to The Misbehavior of Markets, "will not make you richer ... but it may prevent you from getting poorer."

Benoit Mandelbrot is universally familiar as the father of fractal geometry and the discoverer of the eponymous Mandelbrot set - "named after me by my colleagues," as he bashfully admits - and in a long and maverick career has turned his attention to just about every subject from turbulent systems to CGI. Now in this, his latest work, he condenses his economics writings into a highly readable form for the layman. Markets, says Mandelbrot, do not obey the simple Gaussian curve (think of a man tossing a coin over and over, each flip independent of the last) which has provided the basis for the most academically respectable models of the last century. Price changes are not continuous. There is no such thing as objective value. Disastrous, impossible, Rosencrantz-and-Guildenstern type runs can, and do, occur. Charts of price changes over the course of a hundred years look very similar to changes over a day, if you remove the indices; the man who tells you to invest your money long-term with a view to reducing risk is doing you no favours. What's more, fund-managers already tacitly acknowledge some of the truth of this, and although they may learn the theory at business school, nobody rigorously applies it for long in practice.

Where Mandelbrot shines is in making a potentially forbidding subject highly accessible; in his discursive, entertaining style, in his constant use of visuals to elucidate price movements and models and the satisfyingly chewy mathematics of fractal dimension. Where he falls slightly short, I think, is in convincing us that fractals or chaos theory are going to provide a significantly better framework for investors than the present state of affairs. (Actually, Mandelbrot himself abstains from saying that markets are chaotic, but is there, really, a better word than 'nonlinear' to describe the madness of crowds?) To anyone who has dabbled in shares, yes, the Brownian forgery of price movement is obviously unrepresentative; but there is also something faintly (though indefinably) unconvincing about the graph generated by the, presumably state-of-the-art, fractal. And surely calling, as he does, for extra research into fractal economic analysis will simply cause the markets to skew off in totally new and unforeseen directions. It would have been interesting to know, too, the typical lifespan of a listed company, since presumably this imposes just as much of a real-life constraint on the self-scaling properties of a share price as does, say, osmotic pressure on the self-scaling growth of a tree. Not everything stays in demand as long as cotton!

Having said that, this book is far more useful and honest than the innumerable guides promising to tell you how to make your first million on the Stock Exchange, because Mandelbrot is a mathematician, and underlines the implacable maths of investment, which is something that few of the get-rich-quick guides trouble to do. Buy this book, take what the "experts" say with a pinch of salt and don't invest more than you can bear to see utterly annihilated overnight.

...with tangerine trees and marmalade skies...
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.