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 Posted: Tue Sep 29, 2009 9:09 am |
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http://www.forbes.com/2009/09/28/mandelbrot-madoff-math-intelligent-investing-cycles.html
Forbes.com
Intelligent Investing
You Don't Know The Math
Michael Maiello, 09.29.09, 6:00 AM ET
Four years retired from Yale, Benoit Mandelbrot, the inventor of
fractal geometry, is still trying to teach the essential lesson of his
life's work--nature and markets defy easy description. Anyone who
tells you otherwise is either trying to sell you something, doesn't
know the math or both.
Last week, Mandelbrot, 84, spoke to a gathering of diplomats, business
leaders and philanthropists at the Louise Blouin Foundation's Creative
Leadership Summit. Mandelbrot has also served as mentor to economist
Nassim Nicholas Taleb. Mandelbrot's work on fractals and complex
systems is inextricably tied to Taleb's concept of the "Black Swan,"
or those once in a lifetime events that seem to happen far more often
than once in a lifetime.
In 2004, Mandelbrot and Richard L. Hudson wrote The (Mis)behavior of
Markets: A Fractal View Of Financial Turbulence. It was thankfully
reissued with an update about the credit crisis, but it would have
been better had people read and heeded the warnings in the first
edition. Though we often speak about markets reverting to the mean
(and they do) we frequently forget that the road to the mean is quite
chaotic.
For investors, there are two essential insights about Mandelbrot's
work that are important. First, there are no smooth returns in any
complex market. Mandelbrot started out studying cotton prices and
found that the distribution of prices was clumpy and chaotic instead
of uniform. He found the same phenomenon in other assets and in
stocks.
For simplicity's sake (or because they don't know the math), financial
products are generally sold on the premise that returns will grow
steadily over time and that compounding returns over a long period of
time is the sure path to wealth. This is wrong. Returns are lumpy.
There are big booms and big crashes. Miss the best trading days of a
bull market and you might as well have been on the sidelines all year.
"You'll find five events over five years that are more important than
everything else that happened and if you ignore them, you're in
trouble," says Mandelbrot.
The second lesson is that volatility begets volatility. Big rises and
falls in the markets tend to be clumped together. We certainly saw
this with the spike in the volatility index since the credit crisis,
but it goes back much further. Standard and Poor's investment
strategist Sam Stovall has studied big moves in the S&P 500 (which he
defines as an advance or decline of greater than 2%) and found that
the market sometimes goes years without them, but once it happens
once, it tends to happen multiple times in short order. Unfortunately,
there's no magic way to tell how long a high volatility period will
last before it peters out.
The mathematically fluent financial engineers at AIG, Goldman Sachs
and Citigroup mistakenly thought that a diversity of holdings would
protect their complicated mortgage and debt-related securities.
Everything can't default at once, right? An implication of
Mandelbrot's work is that they can and will.
The same would hold true for a retail investment portfolio. In 2008,
none of the traditional hedges worked. Foreign stocks fell along with
U.S. stocks. Commodities spiked but then fell. The stock market's
volatility spread to other markets, proving that they are
interconnected rather than discreet.
Though some have claimed they found ways to practically apply
Mandelbrot's work to the art of stock picking, the professor hasn't
put his name to any of them. He trades for his own account and is
informed by his own theories but that's all very much a work in
progress.
You don't need to be a mathematician to get some benefit from the
master's work. Just be wary, remember that the impossible can and will
happen, and don't count on consistency. A student of fractals would
have seen right through Bernie Madoff's claims. |
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