Finance is chaotic and thus difficult to predict. Obvious, right?

Not according to centuries of financial theory. Benoit
Mandelbrot, the inventor of chaos theory, challenges
traditional financial thinking about prediction, risk, and
even description in a book that's both revolutionary to
the theorist and accessible to the layperson. There's not
a single equation, only a few graphs, and a very limited
number of Greek letters. Mandelbrot and co-writer Richard
Hudson, the editor of the Wall Street Journal Europe,
explain modern financial theory from its history through
its current applications in business school and on Wall
Street and make their case against it. Mandelbrot presents
chaos theory as a possible though underdeveloped
alternative.

Louis Bachelier founded modern financial theory. He
assumed prices, and price changes, were independent and
based on a normal distribution (the bell curve). In other
words, the amount a stock rises or falls today has nothing
to do with its rise or fall yesterday, and if you graphed
all the rises and falls over a month or a year, there
would be lots of small changes and not a lot of large
changes. These assumptions are common in all statistics.
They simplify the math; sometimes they're necessary to
make the math even possible.

Does this matter? Mandelbrot simplifies the positivist
reaction to innacuracies in the formulae by saying, "If so
[if the answers are accurate], then stop arguing about
it." But he goes on, "Alas, by that measure..., the
standard tools of finance often fail" (p 100). However,
financial data shows they aren't true. They don't
accurately describe or predict data. Modern financial
theory does not predict risk accurately. It does not tell
investors how to invest. It is worse than useless.

Mandelbrot presents his chaos theory as a possible way to
interpret and predict financial data. Currently, he has
shown a remarkable ability to simulate financial data - he
offers four charts of price data, two real, one created by
traditional theory with independence of change and normal
distribution of price differences, and one created by his
own formula (p 17). The one created by traditional
theory is obviously fake, even to the naked eye of the
uninitiated. The other three are effectively
indistinguishable in terms of realism.

Chaos theory is the theory that everything affects
everything else. A butterfly flapping its wings in Brazil
affects the wind, and New York City sees thunderstorms
instead of sunshine. Often cause and effect are so complex
as to be effectively untraceable. Chaos measures roughness
and turbulence. Geometry, algebra, and their applications
in financial theory assume a "smoothness" that doesn't
seem to exist in nature. Nature is rough and uneven.
Mandelbrot calls for a theory to take this roughness into
account as chaos theory has taken roughness into account
for geometry. Mountains are not smooth pyramids; they have
a rough texture. The increase in price of a stock is not a
smooth line; it is jagged and rough. The data is different,
but the mathematics are the same.

Prices do not move by chance; they react to themselves and
to events outside of the market. Mandelbrot calls for a
better set of statistics that do not require independent,
normally distributed data.

He also calls for more research and for a fraction of the
federal funding that goes to understand the financial
markets to be spent to explore possible applications of
chaos theory.

This is not a "get rich" book; his only financial advice
is to stick with index funds - even the highest-paid
financial analysts can't reliably beat the market. He
provides a wonderful and brief introduction to chaos
theory for those unfamiliar with it. He assumes nothing
from his readers but interest and an open mind. He closes
his book with a summary of "10 Heresies" of finance (p
225), ten applications of chaos theory that serve to
remind the reader what she has just learned: that markets
are turbulent, that markets are risky, that prices leap
instead of moving steadily. All in all, this is a
well-written, well-researched book that anyone interested
in math or finance will be able to understand. A
fascinating, though slow, read, this book should change
the way we look at financial theory in the years to come.