Why do markets misbehave? How should you measure market risk? And whatâs wrong with academic finance?
These are a few questions that polymath Benoit Mandelbrot addresses in the fascinating book The Misbehavior of Markets: A Fractal View of Financial Turbulence
. Mandelbrot suggests all of these questions can be properly understood by rejecting the standard assumptions of academic finance and instead using a âfractal viewâ 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 heâs 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 itâs 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 chapterâŠ
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.
Second, fractals can help explain why bubbles form and how prices are dependent over time. These are phenomena that every stock trader understands, but amazingly are classified as impossible by standard academic theory. Clearly something is wrong when experience contradicts the sacred cows of the random walk, Efficient Markets, CAPM, and Black Scholes, etc. Although this fractal theory doesnât offer a complete answer yet, it at least allows for a theory consistent with practical experience.
But Mandelbrotâs fractal view has not taken hold in academia, the author explains, and it is this conflict that drives the narrative. The arguments in the book are about the battle between Mandelbrotâs ideas and standard finance. Mandelbrot elaborates on this in many ways, and after reading the book here are some useful comparisons between the two theories:
| 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 dependentâtrouble runs in streaks |
| Markets are computing machines | Markets have personality |
| Bubbles and patterns shouldnât exist | Markets mislead and bubbles are possible |
| Trading time is linear | Trading time is relative with clusters of intense activity |
If you have qualms with academic finance, or agree with even a few of Mandelbrotâs revisions, I think youâll enjoy this book.
There are but two reservations I have to this book. The first is that it touches on a lot of different ideas so it doesnât elaborate on how to put the ideas into practice. Mandelbrot talks about the concepts like alpha (α) for measuring volatility and the H coefficient as an exponent of price dependence, but the book doesnât offer enough for my liking. This appears to be intentional, however, as the authors admit their motives early in the book:
So caveat emptor. This book will not make you richâŠIf it fits any genre, it is that of popular science. It explains a new, and important, way of looking at the world-in this case, the financial world. It attempts to do so using common English, with as few formulae as possible-or at least, with no jargon unexplained. (p 23)
The second reservation is that the Mandelbrot makes everything into a battle between himself and academia. It reminded me a lot of the way Taleb wrote The Black Swan: The Impact of the Highly Improbable.(Though to be honest, as much as it annoyed me, there is something fun about reading someone with so much conviction.)
In short, check this book out and prepare to learn a new way of looking at risk and the markets. At a minimum youâll be more skeptical about the frequently quoted statistics of risk so you can make better investment decisions.
Source: Mind Your Decisions,
http://mindyourdecisions.com/blog/2009/03/31/the-misbehavior-of-markets/
