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Here is to the crazy ones, the misfits, the rebels, the trouble makers the round pegs in a square hole, the ones who see things differently. They are not fond of rules and they have no respect for the status quo.You can quote them, disagree with them, glorify or vilify them. About the only thing that you can't do is ignore them, because they change things. They push the human race forward, and while some may see them a s crazy ones, we see genius, because the people who are crazy enough to think they can change the world, are the ones who'll do it. 

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The Unknown World-Nassim Nicholas Taleb Interview on Business Week

Wednesday, June 11, 2008

Mandelbrot on Modern Portfolio Theory

Individual investors and professional
stock and currency
traders know better than ever
that prices quoted in any financial market often
change with heart-stopping swiftness. Fortunes are
made and lost in sudden bursts of activity when the market
seems to speed up and the volatility soars. Last September,
for instance, the stock for Alcatel, a French telecommunications
equipment manufacturer, dropped about 40 percent
one day and fell another 6 percent over the next few days. In a
reversal, the stock shot up 10 percent on the fourth day.
The classical financial models used for most of this century
predict that such precipitous events should never happen. A
cornerstone of finance is modern portfolio theory, which tries
to maximize returns for a given level of risk. The mathematics
underlying portfolio theory handles extreme situations with
benign neglect: it regards large market shifts as too unlikely to
matter or as impossible to take into account. It is true that
portfolio theory may account for what occurs 95 percent of
the time in the market. But the picture it presents does not
reflect reality, if one agrees that major events are part of the
remaining 5 percent. An inescapable analogy is that of a sailor
at sea. If the weather is moderate 95 percent of the time, can
the mariner afford to ignore the possibility of a typhoon?
The risk-reducing formulas behind portfolio theory rely on
a number of demanding and ultimately unfounded premises.
First, they suggest that price changes are statistically independent
of one another: for example, that today’s price has no
influence on the changes between the current price and tomorrow’s.
As a result, predictions of future market movements
become impossible. The second presumption is that all
price changes are distributed in a pattern that conforms to
the standard bell curve. The width of the bell shape (as measured
by its sigma, or standard deviation)
depicts how far price changes
diverge from the mean; events at the extremes
are considered extremely rare. Typhoons
are, in effect, defined out of existence.
Do financial data neatly conform to such assumptions?
Of course, they never do. Charts of stock or currency changes
over time do reveal a constant background of small up and
down price movements—but not as uniform as one would
expect if price changes fit the bell curve. These patterns, however,
constitute only one aspect of the graph. A substantial
number of sudden large changes—spikes on the chart that
shoot up and down as with the Alcatel stock—stand out
from the background of more moderate perturbations.
Moreover, the magnitude of price movements (both large
and small) may remain roughly constant for a year, and then
suddenly the variability may increase for an extended period.
Big price jumps become more common as the turbulence of
the market grows—clusters of them appear on the chart.
According to portfolio theory, the probability of these large
fluctuations would be a few millionths of a millionth of a millionth
of a millionth. (The fluctuations are greater than 10
standard deviations.) But in fact, one observes spikes on a regular
basis—as often as every month—and their probability
amounts to a few hundredths. Granted, the bell curve is often
described as normal—or, more precisely, as the normal distribution.
But should financial markets then be described as abnormal?
Of course not—they are what they are, and it is portfolio
theory that is flawed.
Modern portfolio theory poses a danger to those who believe
in it too strongly and is a powerful challenge for the theoretician.
Though sometimes acknowledging faults in the
present body of thinking, its adherents suggest that no other
premises can be handled through mathematical
modeling. This contention leads to the
question of whether a rigorous quantitative description
of at least some features of major financial upheavals can be
developed. The bearish answer is that large market swings
are anomalies, individual “acts of God” that present no conceivable
regularity. Revisionists correct the questionable
premises of modern portfolio theory through small fixes that
lack any guiding principle and do not improve matters
sufficiently. My own work—carried out over many years—
takes a very different and decidedly bullish position.
I claim that variations in financial prices can be accounted
for by a model derived from my work in fractal geometry.
Fractals—or their later elaboration, called multifractals—do
not purport to predict the future with certainty. But they do
create a more realistic picture of market risks. Given the recent
troubles confronting the large investment pools called
hedge funds, it would be foolhardy not to investigate models
providing more accurate estimates of risk.

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