## The Misbehavior of Markets

**Article Introduction (Via Mind Your Decisions)**

Why do markets misbehave? How should you measure market risk? And what’s wrong with academic finance?

These are a few questions that polymath Benoit Mandelbrot addresses in the fascinating book The Misbehavior of Markets. Mandelbrot suggests all of these questions can be properly understood by rejecting the standard assumptions of academic finance and instead using a “fractal view” of risk and markets.

Fractals are at the heart of this book. Fractal geometry is a form of mathematics developed by Mandelbrot that deals with rough but highly self-similar structures like trees, coastlines, and mountains. Fractals have helped explain a wide range of natural phenomena and revolutionized computer graphics, influencing movies like

Star Wars Episode III. There is room for more applications in this early science, and fractals may help explain the jagged but predictably irrational patterns in the stock market, claims Mandelbrot.In this book, Mandelbrot contends that fractals are the key to modeling the market. The interesting part is that Mandelbrot does not merely explain why he’s right but he goes to great length to explain why others-those using the standard theories of academic finance-are wrong. Mandelbrot offers interesting history, anecdotes, trivia, and beautiful illustrations to make his case. The stock market does not act like a random walk, he says, but rather it’s like the flight of an arrow down an infinite hallway. It sounds a bit abstract at first, but this is exactly where the book shines. There are stories and illustrations that make such abstract concepts easily understandable. I literally felt smarter after reading each chapter…

**Additional Excerpts (Via Mind Your Decisions)**

But back to the subject at hand. What do fractals offer to finance? First, fractal math can help generate realistic stock price series. Mandelbrot graphically illustrates that his fractal-generated prices resemble actual price data more closely than the standard (geometric Brownian-motion) generated prices. Not only will this help for valuation and understanding risk, but it could also help one estimate damages in securities fraud cases.

5 tenets of academic finance |
Revisions by Mandelbrot |

Markets are risky like coin flips (random walk) | Markets are risky like earthquakes (power distribution) |

Price changes are independent over time | Prices changes are dependent–trouble runs in streaks |

Markets are computing machines | Markets have personality |

Bubbles and patterns shouldn’t exist | Markets mislead and bubbles are possible |

Trading time is linear | Trading time is relative with clusters of intense activity |

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