Investoid

After reading a book review on Capital Ideas over at Canadian Financial DIY’s site, I decided it would be good to write about one of the books I read last year that had a lasting impact on me.

The (Mis)Behavior of Markets is written by Benoit Mandelbrot, a mathematician who is the inventor of fractal theory. Mandelbrot has been applying fractals to many different areas of application, including finance, for over 40 years. While modern financial theory was being written, Mandelbrot was finding issues with the mathematical models used for the derivations and suggested alternatives. While his work was largely ignored during the explosion of mathematical finance, his views have been gaining momentum over the past 10 years or so.

In this book, Mandelbrot provided a non-technical account of what’s wrong with the basic tenets of modern financial theory, namely:

• Asset returns can be modeled with the normal or log-normal distributions, meaning that:
  • returns from separate time periods are independent (ie. no correlation)
  • the mean return is an important number because it can be used as an expected value for future returns
  • it is very unlikely to have extreme returns (ie. 99% of returns should be within 3 standard deviations of the mean)
• Investors have identical knowledge and goals
• Price changes are nearly continuous (as opposed to sporadic changes that cause the price to ‘jump’)

Mandelbrot uses evidence from various financial situations, not the least of which the 1998-2001 bubble/bust era, to demonstrate how these assumptions rarely hold (if ever). By refuting the models that form the basis of modern financial theory (including the Black-Scholes option pricing formula), Mandelbrot sets the stage to offer his own mathematical models that he believes more accurately depict how financial markets work.

I won’t go into any technical detail about fractals (neither does he in the book), but from his modeling he draws some interesting conclusions:

• Markets are way more risky than financial theory suggests (which most people can appreciate - just look at the huge 8.3% decline in China today).
• Bubbles are apt to happen: due to the long term correlation in pricing with his models as well as empirical evidence that trends occur in stocks, bubbles are not only possible but likely from time to time.
• Value metrics are useless: the only appropriate way of determining stock prices is based on estimating what someone will pay for it later, regardless of what is underlying the asset. Thus all value metrics (P/E, etc.) have no ability to assist with investment decisions.
• Market timing is of high importance. Because of the correlation of returns, you need to be able to follow the trends in order to capitalize on them.

Mandelbrot’s views are a fresh take on financial markets from a mathematical perspective, one that has little vested interest in actual investment outcomes. His theories are self-admittedly early in their development, and many young researchers have begun to expand on his basics to more accurately refine the models and re-develop financial theories regarding risk and portfolio construction using them.

It is important to note that fractals are not the only advanced mathematical theory out there that’s looking to supplant the incumbent theories. Chaos theory and nonlinear filtering are two other types of mathematics that look to explain price movements and take advantage of the current use of traditional pricing methods in the markets.

I don’t agree with all his conclusions, because I don’t think his models completely encapsulate investor behaviour, but they are definitely better than the current status quo. I highly recommend that you pick up his book and read it. It provides great insight into what may very well be the future of portfolio management theory and application.