Benoit Mandelbrot and Richard L. Hudson spend good amount of time for making it understandable in the book “The (Mis)Behavior of Markets”
“Markets are much riskier than we have been led to believe. They are prone to violent, unpredictable swings, and these swings are not mere anomalies but part of the natural order of things.”
This quote highlights Mandelbrot’s critique of traditional models that underestimate market risk and fail to account for extreme events.
“The bell curve might be fine for professors of statistics, but it is a lousy tool for describing market behavior,” is one of the book’s most direct critiques of traditional financial modeling. Here’s a deeper dive into its implications:
What is the Bell Curve?
The bell curve, or normal distribution, is a statistical model that assumes most data points cluster around a mean, with fewer occurrences as you move farther from the center. It’s used extensively in finance to model price movements, risk, and return. The curve assumes:
- Symmetry: Price changes are equally likely to be positive or negative.
- Tails decay quickly: Extreme changes (very large losses or gains) are exceedingly rare.
- Independent events: Today’s price movement doesn’t depend on yesterday’s.
Why Does Mandelbrot Critique It?
Mandelbrot argues that the bell curve is a poor fit for financial markets because:
- Markets Have “Fat Tails”:
- In real-world markets, extreme events (e.g., crashes or massive rallies) occur far more frequently than the bell curve predicts.
- For example, the bell curve would consider events like the 1987 stock market crash or the 2008 financial crisis as “near-impossible,” yet such events happen relatively often.
- Volatility Clusters:
- Market movements are not independent; they exhibit patterns where periods of high volatility cluster together. The bell curve assumes no such clustering.
- Skewness in Returns:
- Market returns often show asymmetry, with more extreme negative events (crashes) than extreme positive ones. The bell curve’s symmetry assumption fails to capture this.
- Real Market Data Deviates:
- Empirical evidence shows that financial markets follow distributions closer to Mandelbrot’s fractal models, which feature “fat tails” and long-term dependencies.
What’s the Alternative?
Mandelbrot proposes using fractal geometry and power-law distributions to model financial markets. These models:
- Account for extreme events as intrinsic to market dynamics rather than anomalies.
- Recognize self-similar patterns in price movements, meaning trends appear on both short and long timescales.
- Accept that risk is far greater than traditional models predict.
Fat Tail Fat Tail Fat Tail… If you do not know what fat tail represents for markets please re-consider what you know about market and life it self…