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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 going on.

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 swan.

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 white.

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 make.

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 bet.

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 looks rigged.

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 black swan.

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