REVIEW: The (Mis)behavior of Markets

I recently read The (Mis)Behaviour of Markets by Benoit Mandelbrot, Richard L. Hudson - the former discovered Fractal Geometry. Mandelbrot's thesis is that the world of financial modeling is based on some questionable concepts and that better models can be made by using fractal geometry. Many of the ideas in the book are similar to those that appear in Nassim Taleb's Fooled by Randomness (Taleb and Mandelbrot have co-authored some papers on the topic). The first half of the book is a convincing attack on the premises of modern finance by focusing on points of chaos in the history of the stock market (the 1987 crash, the 1997 Russian Crisis). The standard model of finance is based on a Gaussian distribution of price changes - a bell curve with a large number of small price changes and a small number of large changes. Most of the time this model works but extrodinary events break the model. Unfortunately, the extrodinary events matter a lot - if you remove the 10 days with the largest price changes in the S&P 500 the current value would be 2x higher. Mandelbrot goes on the discuss different distribution models such as the Cauchy distribution on which the market might be based. He then goes on to dispute another pillar of financial analysis - that yesterdays price change has no effect on today. He makes a convincing case that, at a minimum, price volatility is correlated - big changes yesterday make big changes today more likely. The net effect of this is that the standard financial models underestimate risk and the likelihood that there will be large price corrections. He also attacks the Capital Asset Pricing Model, the Efficient Market Hypothesis and the Black - Scholes Equation which are all based on the same financial underpinnings. The second portion of the book is somewhat weaker. Mandelbrot develops his own financial model based on fractal geometry and fractal time. Like Wolfram's "A New Kind of Science" there is a tendency to generate pretty graphs and then argue that it looks true therefore it is true. To be fair, this book is aimed at a general audience and delving into the analytic and computational process to vet his fractal model is probably beyond the scope. Mandelbrot does do some interesting statistical analysis of the price change distribution to show the failings of the standard model. Needless to say, the fractal model matches the observed data far better. Mandelbrot makes some effort throughout the book to convince people that this is not a "get rich" book - if anything the message is that the market is far riskier than you think. The book made for an entertaining read and did a good job of explaining the current state (and failings) of financial theory.