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The Actuary The magazine of the Institute & Faculty of Actuaries

Book review: The (Mis)Behaviour of Markets

The standard models for calculating risk are flawed. Benoit Mandelbrot has a new approach to these calculations. There are therefore conclusions to be reached.

This is the framework for this attempt by Mandelbrot and Hudson to convince the world’s financial markets to re-evaluate how they mathematically model themselves. Yet for a slim book, the authors cover a fair amount of peripheral ground.

The book is organised into three parts. The first deals with the older theories of finance. The second proposes Mandelbrot’s view of how the markets behave. The third attempts a conclusion based on Mandelbrot’s views.

In the first section, market theories currently in use, like the Black Scholes model, Capital Asset Pricing Model and Efficient Market Hypothesis, are shown to be mostly based on an assumption that market prices follow a normal distribution curve and that prices are independent of each other. Mandelbrot makes his case that the distribution follows a Cauchy distribution, and therefore has fatter tails. This infers that catastrophes will occur more often than with current models. He goes on to argue that, even if prices are not correlated, their volatility is correlated over time.

In part two, Mandelbrot proposes his view of how the markets behave, suggesting a multi-fractal approach as a substitute for present methods. He proposes new parameters to defi ne how fat the tails of the price change curve are. He then recommends methods to measure the dependence of price changes upon past changes.

The third part is probably the weakest in the book in terms of making Mandelbrot’s case. After an entertaining run through some insights Mandelbrot has gained, it ends on an advertorial note for his methods, alluding to several methods already in use.

If the book has a weakness it is that, while enjoyable — the authors have successfully adopted a light anecdotal style — and including a fair amount of welcome history, it ignores points made in defence of current models. Many economists would say that these models are not supposed to be of reality, but simplify the maths of fi nancial theory. The point is that, despite known weaknesses, they work. In effect, his argument against these models has been made but he offers no concrete replacement, merely a call-to-arms.

While Mandelbrot’s original research launched new fields of study in science and engineering, I am not convinced he is about to do the same for finance. Nevertheless, for the non-mathematician, this is an interesting run-through of the subject.

Paul Robertson is the editor of Cover magazine.