A fractal view of the markets, Benoit Mandelbrot

In an uncompromising book, Benoit Mandelbrot, French graduate from Ecole Polytechnique, denounces the inconsistency of the orthodox theory of finance and presents his fractal vision of the markets

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If Independence is a virtue, Benoît Mandelbrot is certainly one of the most tangible representation in contemporary scientific landscape, as he will have assailed in all the disciplines that have marked his career, the attitude of his peers.

With nearly half a century of research in the most varied fields, from physics to computer science, from physiology to finance, this 82-year-old French has been throughout his career one of the leading dissidents of the right-thinking in the financial community. As evidenced by his last essay, A fractal view of the markets: Risk, Ruin and Reward, that arises, undoubtedly, as a true indictment against the orthodox theory of finance.

The essay, divided into three main parts, begins with an overview of contemporary financial market; the author working to return to how ideas have changed since the last century, from Louis Bachelier to Black & Scholes. Mandelbrot returns and review step by step, the various methods that have over time helped to capture efficiently the stock markets and better protect against the risks that were inherent. He returns deeply on all "the edifice of modern finance": Bachelier’s theories, fundamental analysis, William Sharpe CAPM, the modern portfolio theory of Harry Markowitz, the Black, Scholes & Merton model. Everything is reviewed. But he does not stop at the history of ideas. He also makes the process dependent. Thus explaining and demonstrating why almost all the traditional tools which are currently used in the financial industry do not work, while denouncing the containment of the debate on the financial markets modeling to "some very limited circle of mathematicians interested in economics, or economists with mathematical inclinations".

Indeed, according to Mandelbrot, the markets being much "more wild and scary" that the theory would suggest, the whole structure of finance is "built on sand". Or, better yet, the assumptions underlying the use of standard financial instruments are, when considered separately, simply "absurd": price changes are not continuous but exhibit jumps so trivial and important, the price changes are neither independent nor stationary, and they do not follow either the proportions of the famous bell curve of normal distribution. Or, that the efficient market hypothesis is incorrect: the markets is not always a fair game in which the sellers balance the buyers.

Even though today we all agree that no financial professional do not call into question the reserves against the orthodox theory of finance, we nevertheless note the may tools that have begun to be developed to overcome these shortcomings and come closer and closer to the reality of the markets. That is what Mandelbrot says that by the way, while noting that the work to be done is still considerable and there is a need for exploring other concepts. In the second part of his book, he opens the way of what is in his view one of the new trends to better understand the markets: the multi fractal analysis.

The rest of this book is of a different ilk. it comes as another world: a world of beauty, forms and turbulences, where complex geometries, which does not always link with finance, take shape. This is normal. It is first here, no question about the markets and prices, but drawings and graphics. Mandelbrot, in a sort of compendium of the various books on the subject, introduces and initiates to the fractals. Fractals in physical science, fractals in biology, fractals in the society. Then, fractals in finance, Mandelbrot exploring what he calls the "new way": The multi fractal model. He explains, introduces. Even if we can blame the lack of mathematical proofs for the presentation of a model to professionals or novices, unaware of almost everything about this subject, and whose the applicability has never been proven, the author has, however, the main merit of engaging in a way that seems bypassing the set of assumptions from the standard theory that are too inaccurate.

From the eyes of the French scholar, fractal model, unlike other financial models requires very little data to provide much information:"it starts from the fundamental and sustainable facts that regulate the markets. it is economical and flexible, and imitates the market". Mandelbrot concludes his book by presenting its "ten heresies" of finance, a summary of the ideas formulated on the financial theory and his divergences, more or less obvious with reality.

Finally, instead of a simple statement of a new theory to better model the current financial markets, the work of Benoit Mandelbrot is primarily a book of popular science to better understand them, while remaining refined from mathematical formulas that often make up the complexity of the specific standards.

It is a book for any curious, keen on mathematical finance, while still worthy of interest to the financial industry professionals looking for new opportunities. For who knows, maybe Mandelbrot is developing there what can be seen as the vanguard of the next financial industry. And even if this not the case, he can at least have the sense of accomplishment: that of having deeply open the debate on the modeling of financial markets and its relation to reality.

Yann Olivier November 2007

Article also available in : English EN | français FR




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