is a wall full of books on statistics and the history of statistics, books I
never had the fortitude to burn or throw away; though I find them largely
useless outside of their academic applications (Carneades, Cicero, and
Foucher know a lot more about probability than all these pseudosophisticated
volumes). I cannot use them in class because I promised myself never
to teach trash, even if dying of starvation. Why can't I use them? Not one
of these books deals with Extremistan. Not one. The few books that do
are not by statisticians but by statistical physicists. We are teaching people
methods from Mediocristan and turning them loose in Extremistan. It is
like developing a medicine for plants and applying it to humans. It is no
wonder that we run the biggest risk of all: we handle matters that belong
* This is a simple illustration of the general point of this book in finance and economics.
If you do not believe in applying the bell curve to social variables, and if,
like many professionals, you are already convinced that "modern" financial theory
is dangerous junk science, you can safely skip this chapter.
L O C K E ' S MADMEN, OR B E L L CURVES IN T H E WRONG PLACES 2 7 5
to Extremistan, but treated as if they belonged to Mediocristan, as an
"approximation."
Several hundred thousand students in business schools and social science
departments from Singapore to Urbana-Champaign, as well as people
in the business world, continue to study "scientific" methods, all
grounded in the Gaussian, all embedded in the ludic fallacy.
This chapter examines disasters stemming from the application of
phony mathematics to social science. The real topic might be the dangers
to our society brought about by the Swedish academy that awards the
Nobel Prize.
Only Fifty Years
Let us return to the story of my business life. Look at the graph in Figure
14. In the last fifty years, the ten most extreme days in the financial
markets represent half the returns. Ten days in fifty years. Meanwhile, we
are mired in chitchat.
Clearly, anyone who wants more than the high number of six sigma as
proof that markets are from Extremistan needs to have his head examined.
Dozens of papers show the inadequacy of the Gaussian family of distributions
and the scalable nature of markets. Recall that, over the years,
I myself have run statistics backward and forward on 20 million pieces of
data that made me despise anyone talking about markets in Gaussian
terms. But people have a hard time making the leap to the consequences of
this knowledge.
The strangest thing is that people in business usually agree with me
when they listen to me talk or hear me make my case. But when they go to
the office the next day they revert to the Gaussian tools so entrenched in
their habits. Their minds are domain-dependent, so they can exercise critical
thinking at a conference while not doing so in the office. Furthermore,
the Gaussian tools give them numbers, which seem to be "better than
nothing." The resulting measure of future uncertainty satisfies our ingrained
desire to simplify even if that means squeezing into one single
number matters that are too rich to be described that way.
The Clerks' Betrayal
I ended Chapter 1 with the stock market crash of 1987, which allowed me
to aggressively pursue my Black Swan idea. Right after the crash, when I
2 7 6 THOSE GRAY SWANS OF EXTREMISTAN
FIGURE 14
3000 I
2500 I
2000 I
o
Y E A R S
By removing the ten biggest one-day moves from the U.S. stock market over the
past fifty years, we see a huge difference in returns—and yet conventional finance
sees these one-day jumps as mere anomalies. (This is only one of many such tests.
While it is quite convincing on a casual read, there are many more-convincing ones
from a mathematical standpoint, such as-the incidence of 10 sigma events.)
stated that those using sigmas (i.e., standard deviations) as a measure of
the degree of risk and randomness were charlatans, everyone agreed with
me. If the world of finance were Gaussian, an episode such as the crash
(more than twenty standard deviations) would take place every several billion
lifetimes of the universe (look at the height example in Chapter 15).
According to the circumstances of 1987, people accepted that rare events
take place and are the main source of uncertainty. They were just unwilling
to give up on the Gaussian as a central measurement tool—"Hey, we
have nothing else." People want a number to anchor on. Yet the two
methods are logically incompatible.
Unbeknownst to me, 1987 was not the first time the idea of the Gaussian
was shown to be lunacy. Mandelbrot proposed the scalable to the economics
establishment around 1960, and showed them how the Gaussian
curve did not fit prices then. But after they got over their excitement, they
realized that they would have to relearn their trade. One of the influential
economists of the day, the late Paul Cootner, wrote, "Mandelbrot, like
Prime Minister Churchill before him, promised us not Utopia, but blood,
sweat, toil, and tears. If he is right, almost all our statistical tools are obsolete
[or] meaningless." I propose two corrections to Cootner's statement.
First, I would replace almost all with all. Second, I disagree with the
blood and sweat business. I find Mandelbrot's randomness considerably
L O C K E ' S MADMEN, OR B E L L CURVES IN T H E WRONG PLACES 2 7 7
easier to understand than the conventional statistics. If you come fresh to
the business, do not rely on the old theoretical tools, and do not have a
high expectation of certainty.
Anyone Can Become President
And now a brief history of the "Nobel" Prize in economics, which was established
by the Bank of Sweden in honor of Alfred Nobel, who may be,
according to his family who wants the prize abolished, now rolling in his
grave with disgust. An activist family member calls the prize a public relations
coup by economists aiming to put their field on a higher footing than
it deserves. True, the prize has gone to some valuable thinkers, such as the
empirical psychologist Daniel Kahneman and the thinking economist
Friedrich Hayek. But the committee has gotten into the habit of handing
out Nobel Prizes to those who "bring rigor" to the process with pseudoscience
and phony mathematics. After the stock market crash, they rewarded
two theoreticians, Harry Markowitz and William Sharpe, who
built beautifully Platonic models on a Gaussian base, contributing to what
is called Modern Portfolio Theory. Simply, if you remove their Gaussian
assumptions and treat prices as scalable, you are left with hot air. The
Nobel Committee could have tested the Sharpe and Markowitz models—
they work like quack remedies sold on the Internet—but nobody in Stockholm
seems to have thought of it. Nor did the committee come to us
practitioners to ask us our opinions; instead it relied on an academic vetting
process that, in some disciplines, can be corrupt all the way to the
marrow. After that award I made a prediction: "In a world in which these
two get the Nobel, anything can happen. Anyone can become president."
So the Bank of Sweden and the Nobel Academy are largely responsible
for giving credence to the use of the Gaussian Modern Portfolio Theory as
institutions have found it a great cover-your-behind approach. Software
vendors have sold "Nobel crowned" methods for millions of dollars. How
could you go wrong using it? Oddly enough, everyone in the business
world initially knew that the idea was a fraud, but people get used to such
methods. Alan Greenspan, the chairman of the Federal Reserve bank, supposedly
blurted out, "I'd rather have the opinion of a trader than a mathematician."
Meanwhile, the Modern Portfolio Theory started spreading. I
will repeat the following until I am hoarse: it is contagion that determines
the fate of a theory in social science, not its validity.
I only realized later that Gaussian-trained finance professors were tak2
7 8 THOSE GRAY SWANS OF E X T R E M I S T AN
ing over business schools, and therefore MBA programs, and producing
close to a hundred thousand students a year in the United States alone, all
brainwashed by a phony portfolio theory. No empirical observation could
halt the epidemic. It seemed better to teach students a theory based on the
Gaussian than to teach them no theory at all. It looked more "scientific"
than giving them what Robert C. Merton (the son of the sociologist
Robert K. Merton we discussed earlier) called the "anecdote." Merton
wrote that before portfolio theory, finance was "a collection of anecdotes,
rules of thumb, and manipulation of accounting data." Portfolio theory
allowed "the subsequent evolution from this conceptual potpourri to a
rigorous economic theory." For a sense of the degree of intellectual seriousness
involved, and to compare neoclassical economics to a more honest
science, consider this statement from the nineteenth-century father of
modern medicine, Claude Bernard: "Facts for now, but with scientific aspirations
for later." You should send economists to medical school.
So the Gaussian* pervaded our business and scientific cultures, and
terms such as sigma, variance, standard deviation, correlation, R square,
and the eponymous Sharpe ratio, all directly linked to it, pervaded the
lingo. If you read a mutual fund prospectus, or a description of a hedge
fund's exposure, odds are that it will supply you, among other information,
with some quantitative summary claiming to measure "risk." That
measure will be based on one of the above buzzwords derived from the
bell curve and its kin. Today, for instance, pension funds' investment policy
and choice of funds are vetted by "consultants" who rely on portfolio
theory. If there is a problem, they can claim that they relied on standard
scientific method.
More Horror
Things got a lot worse in 1997. The Swedish academy gave another round
of Gaussian-based Nobel Prizes to Myron Scholes and Robert C. Merton,
who had improved on an old mathematical formula and made it compatible
with the existing grand Gaussian general financial equilibrium
* Granted, the Gaussian has been tinkered with, using such methods as complementary
"jumps," stress testing, regime switching, or the elaborate methods known as
GARCH, but while these methods represent a good effort, they fail to address the
bell curve's fundamental flaws. Such methods are not scale-invariant. This, in my
opinion, can explain the failures of sophisticated methods in real life as shown by
the Makridakis competition.
L O C K E ' S MADMEN, OR B E L L CURVES IN T H E WRONG PLACES 2 7 9
theories—hence acceptable to the economics establishment. The formula
was now "useable." It had a list of long forgotten "precursors," among
whom was the mathematician and gambler Ed Thorp, who had authored
the bestselling Beat the Dealer, about how to get ahead in blackjack, but
somehow people believe that Scholes and Merton invented it, when in fact
they just made it acceptable. The formula was my bread and butter.
Traders, bottom-up people, know its wrinkles better than academics by
dint of spending their nights worrying about their risks, except that few of
them could express their ideas in technical terms, so I felt I was representing
them. Scholes and Merton made the formula dependent on the Gaussian,
but their "precursors" subjected it to no such restriction.*
The postcrash years were entertaining for me, intellectually. I attended
conferences in finance and mathematics of uncertainty; not once did I find
a speaker, Nobel or no Nobel, who understood what he was talking about
when it came to probability, so I could freak them out with my questions.
They did "deep work in mathematics," but when you asked them where
they got their probabilities, their explanations made it clear that they had
fallen for the ludic fallacy—there was a strange cohabitation of technical
skills and absence of understanding that you find in idiot savants. Not
once did I get an intelligent answer or one that was not ad hominem. Since
I was questioning their entire business, it was understandable that I drew
all manner of insults: "obsessive," "commercial," "philosophical," "essayist,"
"idle man of leisure," "repetitive," "practitioner" (this is an insult
in academia), "academic" (this is an insult in business). Being on the receiving
end of angry insults is not that bad; you can get quickly used to it
and focus on what is not said. Pit traders are trained to handle angry
rants. If you work in the chaotic pits, someone in a particularly bad mood
from losing money might start cursing at you until he injures his vocal
cords, then forget about it and, an hour later, invite you to his Christmas
party. So you become numb to insults, particularly if you teach yourself to
imagine that the person uttering them is a variant of a noisy ape with little
personal control. Just keep your composure, smile, focus on analyzing
the speaker not the message, and you'll win the argument. An ad hominem
* More technically, remember my career as an option professional. Not ony does an
option on a very long shot benefit from Black Swans, but it benefits disproportionately
from them—something Scholes and Merton's "formula" misses. The option
payoff is so powerful that you do not have to be right on the odds: you can be
wrong on the probability, but get a monstrously large payoff. I've called this the
"double bubble": the rriispricing of the probability and that of the payoff.
2 8 0 THOSE GRAY SWANS OF EXTREMISTAN
attack against an intellectual, not against an idea, is highly flattering. It indicates
that the person does not have anything intelligent to say about
your message.
The psychologist Philip Tetlock (the expert buster in Chapter 10), after
