Sage issues a warning on prophets

If there is one message I would wish to survive this book, it is this: finance must abandon its bad habits and adopt a scientific method.

I do not claim to have the answers. I know a few things, gleaned by long research and free thought. Interest in my hypotheses has waxed and waned over the years."

This comment pretty much sums this book up. It is written in the first person by Benoit Mandelbrot, although co-authored by Richard Hudson, formerly managing editor of The Wall Street Journal . It is a strangely cohesive first person, made up of Mandelbrot's academic persona and rightful lack of modesty for his intellectual achievements, his naive, almost childish, enthusiasm and Hudson's superb skills of mass communication.

Mandelbrot is Sterling professor of mathematical sciences at Yale University and the father of fractal geometry. And he is no longer a young man. I do not know who convinced him to write this book with Hudson, but it was a splendid idea.

His voyage through the world of economics and quantitative finance and then on to econophysics sounds very familiar. I went through the same journey the hard way, learning mathematics as I went along. He dashed through it on the wings of his master's knowledge of maths and geometry, detouring into other sciences' territories whenever it took his fancy. He and I even spent time with the same visionaries, such as Richard Olsen in Zurich, a researcher in high-frequency financial data, and we landed on the same shores, such as behavioural finance.

The difference between us is that the theories that he rightly takes apart, the CAPM (capital asset pricing model) or the Black-Scholes formula, were proposed either by students of his or by researchers who followed him, whereas for me these researchers were the priests of finance one was supposed to look up to.

When Mandelbrot makes light fun of the economists' utility curve, I feel a deep sense of brotherhood across the age and intellectual divide. Whereas physicists dreamt up dark matter when the figures would otherwise not add up, economists created fictional totems on which they dare to base a reassuringly quantitative construction. One tries to fill the picture, the other just inserts faces and landscapes on a totally arbitrary abstract painting.

The naked conclusion of this book is that there is too little skewness and too much kurtosis in financial markets - that is, the odds are worse and the risk is higher than standard financial literature would have us believe. I could not agree more. I have always thought that those bank boards were deluding themselves when, having introduced "value at risk", they believed they could forecast their maximum potential losses.

The consequence of what Mandelbrot is saying and Hudson is communicating so well is that a lot of commonly practised asset-management styles are uni-dimensional in a fractal world of dimension higher than 1. It is clear that one or both of the authors have not only read the academic texts and the peer-reviewed papers of modern finance, but that they have also read the published works of the practitioners of modern finance.

They stop short, however, of giving those practitioners any credit. Indeed they seem to point to foreign-exchange traders' "chartism" as one of the voodoo practices of finance. A more charitable view is that practitioners contributed to the calibration of models, without which many of the models still used by financial institutions would have caused much more damage.

Mandelbrot and Hudson skate over the Garch (generalised autoregressive conditional heteroskedastic) family of models, though a more detailed review on their part would have been useful to the reader.

More culpably, they sail through the Long-Term Capital Management debacle at speed, whereas no other contemporary live example would have been more useful to illustrate Mandelbrot's case against financial paradigms still too influenced by shaky economics and unreliable econometrics rather than by physical-type models.

Mandelbrot is a troublemaker; he loves to stir up controversy and to set himself up as the target of dissent. He destroys icons from the height of a long life in academic research, of interdisciplinary co-operation and deep understanding of those who came before him. The historical perspective, his insight into the work of younger but already acclaimed contemporaries, and the freshness of his questioning of fashionable fads is unique and make this book precious.

It might have been the intention of the publisher just to cash in on the appeal of Mandelbrot's reputation with a book that was accessible to the finance world's unwashed. The end product is much more than that: a book that lets itself be read as a crime story but that teaches and forces the reader to think. Anyone with a reasonable cultural background can read it and profit from it. They will at least be more restrained in how to invest the family's savings, or, if not, they will know that what they are doing is gambling.

Watch the tails of the distribution curve. If they look fat, they are fat.

Pretending that they are normal and that the curve is a Gaussian one is not an approximation - it is a delusion.

Rudi Bogni, a former banker, is a corporate director and foundations trustee.