Rigged, Not Random
Ross M. Miller
Miller Risk Advisors
June 14, 2004
An inordinate amount of academic research examines the
issue of whether investment success can be attributed to the skill of the
money manager or is merely the luck of the draw. With so many people
trying to beat the market, it is tempting to attribute the stunning
success of the few to good fortune or, in academic terms, randomness.
Back when I was an academic, I was a devoted member of
the randomness school of thought. Then, I went into the corporate world.
Now I know better. Now I know that the world isn't random, it's rigged. I
also know better than to cast my finding in academic terms, and so I have
written a novel appropriately titled Rigged
that endeavors to be entertaining and clever yet has a lot going on
beneath the surface. This commentary is not so much a blatant plug for my
online novel as a frontal assault on a new game that the randomness crowd
is playing. That game can be summed up in two words: black swan.
Back in the old days, the randomness crowd used the
normal distribution as the reference point for their work on the random
character of stock and other prices. In fact, the most notable achievement
of that crowd, the Black-Scholes-Merton model, is constructed around a
normal distribution of changes in prices, which makes the distribution of
prices itself lognormal.
The nicest thing about the normal distribution is that
it can be fully characterized by the first two moments—its mean and its
standard deviation (which has come to be known as volatility in the
financial markets.) A not-so-nice thing about the normal distribution is
that it does a poor job of describing most financial time series. The
problem is that the tails of the normal distribution are too thin. One
elegant way to generate a fat-tailed distribution, which is done by
assuming the volatility of the distribution is not a constant, won a Nobel
prize for Robert Engle last year. Another elegant way to create fatter
tails is to consider distributions whose volatility is infinite. The graph
of such a distribution looks almost like a normal distribution (to the
non-statistician, anyway), so it is not obvious that something odd is
Now let's imagine that you knew that the volatility of
the S&P 500 was either infinity or some vastly large number, like
5000%. Well, you would be in luck because the current market assessment is
that the volatility of the S&P 500 is a mere 15% and traders are
willing to sell any number of derivative securities, including a new
futures contract, based on that number. What is wrong with these fools?
Maybe they either don't know or don't care about this mysterious black
Here's the black-swan story in two sentences: Back in
days of old, the only swans that anyone ever saw were white swans and so
people naturally assumed that swans all were white. Then, one day, a black
swan was discovered and that invalidated the theory that all swans were
The black-swan crowd says that the financial markets are
currently in their white-swan period, making the volatility of the S&P
500 and just about everything else in the financial markets absurdly low.
When the black swan, which is supposed to be some event of horrific
proportions, makes the scene, volatility will shoot through the roof and
everyone who laughed at the black-swan people will be sorry.
I have two major issues with the black-swan story.
First, I don't believe that the black swan is out there. Second, even if
there is a black swan, it may be much easier to lose money than make money
on it when it comes to town.
As I see it, the entire black-swan story is built on a
basic logical misconception. I think it is just dandy that someone
discovered not just a single black swan, but a whole species of them. They
did not, however, find a pink elephant, Bigfoot, the Loch Ness monster,
little green men, or tall, thin gray men. One improbable thing showed up,
billions of others didn't. That sounds like really long odds to me.
But let's say, as I am sure the black-swan crowd would
intimate, that I am somehow missing the point--that I just don't get it.
Indeed, it could just be that I've misinterpreted everything in
the paper that I need explicit permission to quote from. Well, I still
have an issue with how I could make money from this black-swan notion.
This issue breaks down into four problems.
First problem: The current 15% volatility in the S&P
500 already reflects the entire history of the U.S. financial markets.
This history includes a civil war, a world war in which chemical weapons
were used on troops, a world war in which nuclear weapons were used on
civilian populations, numerous financial panics, a great depression, two
big stock-market crashes, an oil disruption that quadrupled oil prices,
presidential assassinations and assassination attempts, a giant hole in
the ground near the center of the financial world, scandals galore, and
much more. It is not like things have been dull and without all this
excitement there is a good argument that the volatility of the S&P 500
should be somewhere near 5% based on fundamentals alone. There may well
already be several black ducks in the soup it we make the definition
liberal enough and so it is not clear what difference one black swan would
Second problem: It could take the black swan 87 billion
years (to pick a random number out of a hat) to show up. In fact, if it
only takes a mere 120 years to show, all of us will be dead by then unless
the biotech folks get on the ball. So, we must face the problem of either
running out of capital or running out of life before the dark-winged
waterfowl makes the scene.
Third problem: If the black swan (who we must remember
symbolizes DEATH) brings anything like the end of the world with him,
we're not collecting. As I stated in an earlier commentary, Waiting
for the End of the World, when the world ends, it will take all the
counterparties with it.
Fourth problem: Let's say we get really luck. There is a
black swan, he comes before all our capital vanishes, and the world
doesn't end. But remember, the world is rigged. We are fools if we ignore
the possibility that the appearance of the black swan will change all the
rules of the game and not in our favor. Just ask the Hunt brothers, who
thought they had it made in silver until the margin requirements were
raised sky-high by the Fed. Remember that betting on the black swan is
betting against the "house."
Despite all this, I recognize that the black swan's
number could come up and those who bet on him could be big winners. At
current odds, however, the likely nonexistence of the black swan combined
with the four problems given above make the black swan a real sucker's
And if this is not enough to convince you, one must also
consider that the increasing sophistication of the financial markets
brings with it new ways to hedge risk that significantly reduce
volatility. Betting on the black swan involves betting against a major
long-term trend in the markets. Of course, this reduction in volatility
could all be illusory. With large pools of risk concentrated in the
money-center banks and GSEs, it is possible for the tails to get fatter as
volatility goes down. But this is a bad thing for black swan players in
the market, not a good thing, because it increases the likelihood
that when the black swan comes he takes everything with him.
The black-swan crowd likes to point out the failure of
LTCM as the result of some kind of ten-sigma event. A closer look at the
situation shows that the brokers who pushed LTCM into financial distress
turned out be the big winners after they got together to bail out the firm
under the auspices of the Federal Reserve. That doesn't look random to me—it
If you still want to believe in the black swan, I
suggest that you read Richard Feynman's commencement address entitled Cargo
Cult Science . Let me know who flies in first: the cargo planes or the
Next week, after I pore over all the hate mail, I move
beyond the black swan and into the depths of the human mind with my
commentary, "Three Cheers for the Subconscious."
Copyright 2004 by Miller Risk Advisors. Permission
granted to forward by electronic means and to excerpt or broadcast 250
words or less provided a citation is made to www.millerrisk.com.