That
Benoit Mandelbrot's latest book, "The (Mis)Behavior of Markets," should be
squirreled away on the Accounting shelf of my local bookstore speaks volumes
about the Yale University mathematician's reach - and his creativity.
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Mandelbrot, 80, is probably best known
for his groundbreaking work on fractal geometry: the cloud formations, wind
tunnel patterns and rocky coastlines by which he has over several decades
illustrated the underlying structural orders within nature's unpredictabilities.
As popularized since his 1982 book, "The Fractal Geometry of Nature," and in
James Gleick's 1987 best seller "Chaos: Making a New Science," fractal geometry
describes complex, irregular phenomena. Seen as patterns whose shapes repeat up
and down many orders of magnitude, from the distribution of galaxies in the
universe to the shapes of cauliflower florets, fractals are modeled by
turbulence and volatility, not by the smooth laws of certainty going back to
17th-century calculus.
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In Mandelbrot's new book, written with
Richard Hudson, a former editor and reporter for The Wall Street Journal, his
skeptical message is aimed at the broad audience of investors and other
participants in the world's securities markets. The same fractal approach that
explains the limits on advance calculation of the path of a hurricane or the
collapse of a species' population also teaches that markets are more risky, more
vulnerable to violent disruptions and less well understood than conventional
wisdom is prepared to understand or acknowledge.
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To back up his assertion that the entire
body of market learning, based on the concept of an efficient market, is elegant
but fundamentally flawed, Mandelbrot observes that conventional theory greatly
understates the likelihood of ruinous events. As evidence, he cites the "Black
Monday" collapse of the Dow Jones industrial average on Oct. 19, 1987; the
meltdown of the Long-Term Capital Management hedge fund in 1998; and, most
ruinously, the calamitous upheavals of Sept. 11, 2001.
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As Mandelbrot puts it, these events
disprove the conventional bell curve of events spread over a smoothly continuous
time distribution. They reveal the entire body of economic model-building - on
which depend modern financial strategies ranging from index funds to the
Black-Scholes formula for stock option pricing - to be as archaic as the
tinkering of geocentric astronomers before Galileo came along.
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Mandelbrot sees the need for a new body
of fractal analysis that would illustrate that stock-price bubbles and market
crashes are inevitable - so long as investors continue to behave as if they can
search out patterns in the markets' patternless behavior.
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In other words, there is great learning
in the truism that as flawed and obsolete as the old methods are, they work well
most of the time - except when they break down and don't work at all, which is
exactly when great fortunes are made but mostly lost.
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Mandelbrot himself has spent a lifetime
surmounting the odds of extreme and unlikely events: He was a wartime refugee
and fugitive in France, an academic survivor as a dropout from that country's
top school, diverted from university life to the labs of IBM.
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This perspective would explain why he
engages in no small amount of ax-grinding over the hostility his views on the
markets have elicited. His well-sharpened tools are on full and genial
display. But by consigning all his mathematics to the book's endnotes,
Mandelbrot asks most readers to take his positions about market behavior on a
combination of faith, persuasion and good graphics.
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As a self-proclaimed seeker of patterns
in a universe governed by rules both simple and elegant, even if their
consequences are turbulent and chaotic, he draws connections from the everyday
vocabulary of common observations: The stock traders' colloquial description of
a "stormy" day in the trading pits is echoed in the swirling turbulence of
swings in commodity pricing. And he finds useful the observation that stock
price charts follow similar shapes, whether scaled by the day, month, year or
decade - just as with other patterns in fractal geometry.
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Mandelbrot has not produced a how-to
manual that can make readers rich. But he does assert that it can help them from
getting poorer - unless readers suspect and act otherwise, in which case the
symmetry of marketplace purchases and sales will lure some to take Mandelbrot as
a guide to taking up risks that others would shun.
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The careful would find inspiration, if not from
the deeply skeptical Mandelbrot himself, in the advice of Shakespeare's Julius
Caesar: that the tide in the affairs of man, if taken at the flood, leads on to
fortune.
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