The Misbehavior of Markets: A Fractal View of Financial Turbulence

335 Pages·2006·3.6 MB·English

by  Benoit Mandelbrot

Table of Contents

ALSO BY BENOIT B. MANDELBROT
Title Page
TO THE SCIENTIFIC READER: AN ABSTRACT
Dedication
Acknowledgements
PRELUDE

PART ONE - The Old Way
CHAPTER I - Risk, Ruin, and Reward
The Study of Risk
The Power of Power Laws
A Game of Chance
CHAPTER II - By the Toss of a Coin or the Flight of an Arrow?
Chance in Finance
Chance, Simple or Complex
The “Mild” Form of Chance
The Blindfolded Archer’s Score
Back to Finance
CHAPTER III - Bachelier and His Legacy
“Not an Eagle”
The Coin-Tossing View of Finance
The Efficient Market
CHAPTER IV - The House of Modern Finance
Markowitz: What Is Risk?
Sharpe: What Is an Asset Worth?
Black-Scholes: What Is Risk Worth?
Spreading the Word on Wall Street
CHAPTER V - The Case Against the Modern Theory of Finance
Shaky Assumptions
Pictorial Essay: Images of the Abnormal
The Evidence
But Does It Work?
The Persistence of Error

PART TWO - The New Way
CHAPTER VI - Turbulent Markets: A Preview
Turbulent Trading
Looney ’Toons for Brown-Bachelier
Preview of More Close-Fitting Cartoons
CHAPTER VII - Studies in Roughness: A Fractal Primer
The Rules of Roughness
A Dimension to Measure Roughness
Pictorial Essay: A Fractal Gallery
CHAPTER VIII - The Mystery of Cotton
Clue No. 1: A Power Law Out of the Blue
Clue No. 2: Early Power Laws in Economics
Clue No. 3: The Laws of Exceptional Chance
The Cotton Case: Basically Closed
The Dénouement
The Meaning of Cotton
Coda: Looney ’Toons, Reprised for Long Tails
CHAPTER IX - Long Memory, from the Nile to the Marketplace
Abu Nil
Father Time
A Random Run
The Selling of H
Coda: Looney ’Toons of Long Dependence
CHAPTER X - Noah, Joseph, and Market Bubbles
An Alien Plays the Market
Two Dual Forms of Wild Variability
A Good Reason for “Bubbles”
CHAPTER XI - The Multifractal Nature of Trading Time
Looney ’Toons for the Last Time
Multifractal Time
Beyond Cartoons: The Multifractal Model with No Grids
Putting the Model to Work

PART THREE - The Way Ahead
CHAPTER XII - Ten Heresies of Finance
1. Markets Are Turbulent.
2. Markets Are Very, Very Risky—More Risky Than the Standard Theories
Imagine.
3. Market “Timing” Matters Greatly. Big Gains and Losses Concentrate into
Small ...
4. Prices Often Leap, Not Glide. That Adds to the Risk.
5. In Markets, Time Is Flexible.
6. Markets in All Places and Ages Work Alike.
7. Markets Are Inherently Uncertain, and Bubbles Are Inevitable.
8. Markets Are Deceptive.
9. Forecasting Prices May Be Perilous, but You Can Estimate the Odds of
Future Volatility.
10. In Financial Markets, the Idea of “Value” Has Limited Value.
CHAPTER XIII - In the Lab
Problem 1: Analyzing Investments
Problem 2: Building Portfolios
Problem 3: Valuing Options
Problem 4: Managing Risk
Aux Armes!

Notes
Bibliography
Index
Copyright Page
ALSO BY BENOIT B. MANDELBROT
Les objets fractals: forme, hasard et dimension
(1975, 1984, 1989, 1995)
Fractals: Form, Chance and Dimension
(1977)
The Fractal Geometry of Nature
(1982)
Fractals and Scaling in Finance:
Discontinuity, Concentration, Risk
(1997)
Fractales, hasard et finance (1959–1997)
(1997)
Multifracals and 1/f Noise: Wild Self-Affinity in Physics
(1999)
Gaussian Self-Affinity and Fractals:
Globality, the Earth, 1/f, and R/S
(2002)
Fractals, Graphics, and Mathematics Education
(With M. L. Frame)
(2002)
Fractals and Chaos:
The Mandelbrot Set and Beyond
(2004)

TO THE SCIENTIFIC READER: AN ABSTRACT
Three states of matter—solid, liquid, and gas—have long been known. An
analogous distinction between three states of randomness—mild, slow, and wild
—arises from the mathematics of fractal geometry. Conventional financial
theory assumes that variation of prices can be modeled by random processes
that, in effect, follow the simplest “mild” pattern, as if each uptick or downtick
were determined by the toss of a coin. What fractals show, and this book
describes, is that by that standard, real prices “misbehave” very badly. A more
accurate, multifractal model of wild price variation paves the way for a new,
more reliable type of financial theory.

Understanding fractally wild randomness, also exemplified by such diverse
phenomena as turbulent flow, electrical “flicker” noise, and the track of a stock
or bond price, will not bring personal wealth. But the fractal view of the market
is alone in facing the high odds of catastrophic price changes. This book presents
this view in a highly personal style, with many pictures and no mathematical
formula in the main text.