Product Description

Fractal geometry is the mathmatics of roughness: how to reduce the outline of a jagged leaf, a rocky coastline or static in a computer connection to mathmatical properties- to make the complex simple. With his fractal tools, Benoit Mandelbrot has got to the bottom of how financial markets really work. Flying in the face of conventional wisdom, he shows how the complex gyrations of IBM's stock price, the FTSE 100, cotton trading and exchange rates can be reduced to a straightforward formulae that yield a much more accurate description of the risks involved.

Product Details

• Amazon Sales Rank: #6806 in Books
• Published on: 2005-07-21
• Original language: English
• Binding: Paperback
• 288 pages

Synopsis
Fractal geometry is the mathematics of roughness: how to reduce the outline of a jagged leaf, a rocky coastline or a static in a computer connection to a few simple mathematical properties - to make the complex simple. With his fractal tools, Benoit Mandelbrot has got to the bottom of how financial markets really work. He finds they have a shifting sense of time, a unique dimension and a wild kind of behaviour that makes them volatile, dangerous - and also beautiful. In Mandelbrot's fractal models, the complex gyrations of IBM's stock price, the FTSE 100 cotton trading and exchange rates can be reduced to straightforward formulae that yield a much more accurate description of the risks involved.

About the Author
Benoit Mandelbrot invented fractal geometry. The Mandelbrot Set, replicated on millions of posters, t-shirts, and record albums, is named after him, and he was a central figure in James Gleick's 'Chaos'. He is Sterling Professor of Mathmatical Sciences at Yale University. Richard L. Hudson is a former managing editor of 'Wall Street Journal Europe'

Customer Reviews

Tilting at windmills
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.

Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.

The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.

The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.

In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.

...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.

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.