Une approche fractale des marchés : Risquer, perdre et gagner (original 2004; edition 2009)

Just a few bits about those wonderful fractals and an interesting lot about Mandelbrot's demolition of many financial market theories. ( )

In these turbulent economy we seem to be victims of the financial markets. Benoit Mandelbrot, famous mathematician and inventor of fractal geometry, joined forces with Richard Hudson, to write a book about financial theory. “The (Mis)behavior of Markets” falls in the popular science genre. It is low on formulas, instead you can find lots of historical anecdotes and opinions.

1. Risk, Ruin and Reward

We start with a brief history of finance. The author asks us to play a game. Out of 4 charts we need to select the ones that are real and the ones that are fake.

2. By the Toss of a Coin or the Flight of an Arrow?

Chance is important in finance. There is the mild form of chance, described by the bell curve. On the other hand, there is the more extreme Cauchy probability distribution. Financial theory follows the mild path, but Mandelbrot is convinced that this is wrong and a more wild variability is to be expected.

3. Bachelier and His Legacy

The third chapter is about Bachelier and his coin-tossing view of finance. His work led to the theory of the efficient market. According to this theory, the market is so efficient that all information is directly reflected in the price of financial assets.

4. The House of Modern Finance

People who helped build the house of modern finance and their theories are mentioned – Markowitz, Sharpe, Black and Scholes. Even though some received Nobel Prizes, they still lost a lot of money in the markets.

5. The Case Against the Modern Theory of Finance

Mandelbrot tries to demolish the house of modern finance starting with shaky assumptions. He tries to disprove these assumptions. More evidence is presented, such as the low price earnings and price book anomalies. These anomalies are in direct conflict with current theory.

6. Turbulent Markets: A Preview

Turbulence is a nice metaphor for trading. Mandelbrot tries to convince us, that we should be thinking of fractals, when we look at stock charts. He uses cartoons of stock charts to achieve that.

7. Studies in Roughness: A Fractal Primer

Fractal geometry deals with roughness. It introduces a measure called fractal dimension, which is similar to the normal dimension in geometry, but is not an integer.

8. The Mystery of Cotton

This chapter describes a research project of Mandelbrot, when he worked at an IBM laboratory. He discovered a power law in the log returns of cotton prices. The evidence pointed at a L-stable probability distribution with features somewhere between a normal and Cauchy distribution.

9. Long Memory, from the Nile to the Marketplace

Hurst, a famous hydrologist, faced the challenge of figuring out a pattern to the Nile river. Hurst discovered a long term dependence in his data set. It is suggested, that the so called Hurst exponent could be a new yardstick, that would explain better long memory effects in financial markets.

10. Noah, Joseph, and Market Bubbles

The author refers to characters in the Bible to describe different forms of wild variability. For people familiar with the Bible this is a good example. In my opinion we can call it a shaky assumption at best.

11. The Multifractal Nature of Trading Time

Some days are slow, some days just fly by. Apparently this applies to trading too and it is due to the multifractal nature of time.

12. Ten Heresies of Finance

A list of ten big errors in financial theory. Markets are riskier, than we thought. Timing matters. Prices often leap.

13. In the Lab

Mandelbrot warns us that fractal finance is not mature yet. However, it is superior to the mainstream theories, since they dangerously underestimate risk.

The book ends with notes containing formulas and bibliography listing scientific articles. A thrilling book, that I could not put down, until I read it cover to cover. It is the finance equivalent of “A Brief History of Time”. I give it 5 stars out of 5. ( )

This book offers some key points on fractals, by the pen of it's creator (the person that formalized it into a theory, more correctly), it offers a fruitful introduction to the topic, and what it lacks in rigor, it makes up in relating theory to events in the real world. ( )

A good explanation of the mathematics behind markets, and how the current models get it wrong. ( )

Mandelbrot is too happy to have met himself. Lacking scientific humility, the I and the my get on the way of the reading. The style is however quite plastic.