Are The Markets Random?

The random walk theory rationalizes its hypothesis with the notion of an underlying efficiency in the markets. It suggests that all known information about a stock/commodity is already factored into its market price; if this is true, no one trader can have an advantage over the rest of the trading/investing world. The conclusion is that since anything that will change the price in the future is unknown at the present and cannot be expected, it is therefore random in nature. The corollary is that prices are continually adjusted as new information becomes available, and that fair value is maintained by the action between the buyers and sellers in the marketplace.

RANDOMNESS OF EVENTS . . .

The most common example of a random and independent process is the coin toss. When you toss a coin in the air, whether it lands heads or tails is determined randomly. It would make sense to expect an approximately even distribution of heads and tails over a long series of throws. The independence that is inherent in the process is that if you toss the coin four times and get four tails, this has no influence on the outcome of the fifth time; the fifth try is as likely to come up heads or tails as the first.

Random walk advocates also describe this example to support their case: Imagine a soldier, fresh out of boot camp, who is quite drunk (say his military graduation celebration got out of hand). He stumbles around on the street and tries to find his way to his bed. Every step he takes while in this stupor is truly random, since he has completely lost access to the faculties that could guide him to the barracks.

One step forward, two steps backward — the soldier's movements play out in an erratic, completely random fashion. A statistician would tell you that after 100 such paces, in all likelihood the soldier would be right back at the point he started from. The reasoning would be that reflective of true randomness, an expectation of clear progress in any given direction simply isn't reasonable, and so the soldier is most likely to be right back at (or quite close to) his original departure point.

. . . AS APPLIED TO THE MARKETS

Does the market behave in such a random fashion?

To find out, I examined the daily data for the Standard & Poor's 500 index going back to December 16, 1982, which is slightly fewer than 4,700 datasets. The average gain on the up days was 0.701% of the underlying; the average loss on the down days was -0.693%. Our random walk adherents would have been beaming as they declared, "Random, totally random!"

But if the prices were truly determined randomly, then we should have about 2,350 wins and a like number of losses, which would be a true 50-50 balancing act. But that wasn't the case. Instead, the lookback revealed that the index was actually up on 53.3% of the days examined. Admittedly, this is a small edge, but it is statistically significant.

THE STATISTICS OF GAMBLING

Having had, at one point in time, an interest in the statistics of gambling, I knew it was just this kind of small edge that keeps casinos thriving. To put it all in perspective, look at Figure 1. It details the house bias on two of the most popular games of chance, craps and American-style roulette, and then compares this to the S&P data.

Figure 1: House bias. Comparing two of the most popular games of chance to S&P data.

Is it possible that there is an inherent bias to the upside, one that makes buying the index tantamount to representing "the house"? Or is the bias merely reflecting the secular bull market that began in 1982?

I knew the answer could be discerned by using more data, so I examined 28,000 daily datasets making up the Dow Jones industrials since January 1, 1900. This made up a relatively fair view, as it was composed of bull markets, bear markets, and trendless periods.

The findings were a real surprise: 52.3% of the days reviewed were to the upside. This was a bias that almost perfectly matched the one enjoyed by American roulette. Then I looked deeper into the data. The mean was 52.1% and the standard deviation was 0.009%. That meant that more than 95% of the time over the last century, the "house" had the clear advantage — and that going long was the way to make use of its edge.

ABSOLUTE EXCESS

The belief that what came before in some way influences the ensuing toss is often referred to as the gambler's paradox, because many gamblers believe that a run of four tails should be more likely to produce a head on the fifth, reasoning that in the long run, the heads and tails balance out, and some balancing is now overdue.

This is plausible. The paradoxical truth is that the probability of getting heads on the fifth toss is still one in two, no matter how logical the gambler's reasoning may be.

At least part of the difficulty in believing this stems from our inability to distinguish between the balancing of the heads and tails in the sense of a ratio, and balance in a more absolute sense. Figure 2 may prove to be helpful.

Figure 2: Heads to tails. As the number of tosses increases, the ratio of heads/tails moves closer to 50%.

You can see that in the fourth column, the ratio of heads/total tosses is moving closer to 50% as the number of tosses increases. And this is how it should be as the expected balancing takes hold. But look at the last column on the right. The absolute excess of heads over tails (the difference between the number of heads tossed and the number of tails, regardless of whether it is positive or negative) actually expands over time. We can therefore assume that if we were to project this table outward to 25,000 trials, the excess of heads to tails would continue to grow by a considerable amount.

As the absolute excess continues to rise, longer strings of wins could occur without interrupting the movement toward balance in the overall trials. So even as the mix in the individual trials moves closer to 50-50, the house — the casino, the S&P 500 — continues to make more and more money.

THE HOUSE WINS

Casinos use these principles to garner huge profits. While at first glance the small percentages might not seem significant, they are compounded constantly as more games — trials — are played. Savvy market participants can profit from the same advantage as casino operators by finding markets that have a clear, discernible bias and positioning themselves to benefit from that house edge.

R.M. Sidewitz is chief executive officer and founder of Qi2 Technologies, LLC, an investment management company, and the managing member of Qi2 Partners LP, a domestic hedge fund. His website is www.cybrlink.com. For additional information on long-term investing, go to www.longterminvestor.org.

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