The Misbehavior of Markets
Summary
Mandelbrot, who developed fractal geometry, argues that the standard models of finance are built on assumptions that the data contradicts, and that markets are far riskier than those models imply. The book is written with Richard Hudson for a general audience.
His attack concentrates on two assumptions. Price changes are assumed to be independent, which means past movements carry no information, and they are assumed to follow a normal distribution. Mandelbrot shows that neither holds. Price changes cluster, so large movements are followed by large movements, which he calls long memory or the Joseph effect. And the distribution has far heavier tails than the normal, so extreme events occur orders of magnitude more often than the models predict, which he calls the Noah effect. He documents specific cases where a movement that the standard model treats as effectively impossible occurred within a period of a few years.
His positive proposal is the use of fractal and multifractal models, which reproduce both the clustering and the heavy tails by construction, and which he had applied to cotton prices as early as 1963. He attacks the entire structure built on the standard assumptions, including the capital asset pricing model, modern portfolio theory and the Black-Scholes option pricing formula, arguing that all three understate risk systematically.
The critique is stronger than the alternative. Mandelbrot's models describe the observed behaviour better than the standard ones without providing the tractable pricing and hedging results that made the standard models useful. Practitioners have largely responded by keeping the standard models and adjusting for tails rather than replacing them. The critique remains correct.
Key takeaways 8
- Price changes are not independent, since large movements cluster together, which invalidates the assumption underlying most financial models.
- Return distributions have far heavier tails than the normal distribution, so extreme events occur orders of magnitude more often than models predict.
- Movements that standard models treat as occurring once in millions of years have occurred repeatedly within single decades.
- Volatility itself varies over time and clusters, which means a single volatility parameter cannot describe a market.
- Portfolio theory, the capital asset pricing model and Black-Scholes all rest on the same contradicted assumptions and understate risk systematically.
- Fractal and multifractal models reproduce both the clustering and the heavy tails by construction, which the standard models cannot.
- Timing rather than average return determines outcomes, since a small number of days account for most of the cumulative movement.
- The critique is stronger than the proposed alternative, since fractal models describe behaviour better without providing tractable pricing results.
Who should read it
Investors and risk managers who want the mathematical case against the assumptions underlying standard risk models, from the person who first documented the problem.
Who recommended it 3 · 1 direct
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