Mandelbrot's The Misbehaviour of Markets

I had high expectations of Benoit Mandelbrot's The (Mis)behaviour of Markets — simply because of Mandelbrot's stature as a mathematician. I was initially disappointed by the start of the book, but the latter parts of the book are fascinating.

The problem is that the book starts with criticisms of financial theory that financial theory has long evolved beyond. The first few pages start with an account of the crash of 1998 that implies that everyone was still naively assuming that returns followed a normal distribution. In 1998 I started an MSc in finance, and the existence of fat-tailed (i.e., with a higher risk of extreme outcomes) distributions was very much part of what was taught — bear in mind that a mere MSc is far less than the qualifications required of the quants who run banks' risk management.

It is true, as Mandelbrot says, that simpler models are taught in business schools. Business schools need to stick to simple models (good enough for many purposes) that can be taught to generalists, and in economics departments the simple models are taught first, and more sophisticated models later: just as many people learn Newtonian mechanics, but only a small proportion go on to learn relativity.

The fact that fat-tailed distributions, changing volatilities and many of Mandelbrot's other criticism have long been incorporated into financial theory becomes clearer later in the book. As he explains it, the strength of Mandelbrot's fractal alternative also becomes clear.

The most attractive thing about Mandelbrot's fractal models is that they are conceptually simpler than the very complex alternatives (such as GARCH models — which, personally, I find make my head hurt) that are usually used. The claim is that realistic behaviour emerges from a simple model, whereas a more conventional approach would require lots of tinkering and many more parameters.

I do not know enough fractal maths to be able to decide much for myself, but I now wish I did: it certainly has a higher priority than improving my knowledge of the conventional models. The fact that this particular book does not contain much maths made it easy to read, but it also meant that I do not feel that I more than a superficial understanding of the theories.

My impression is that fractal models probably hold the key to much better approaches to risk, to portfolio theory, to options valuation, and to valuation in general. At any rate, I am going to have to lean something about this.

Comments

Hi Graeme. You've inspired me to read it again. And when you've learned more about fractal maths, perhaps you can explain it to me :-)

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