The scientific way to beat the market

March 23, 2007|By Michael Kaplan

The great thing about superstition is that all kinds work equally well. If your lucky socks don't perform today, you can call on your lucky hat tomorrow. There's no sectarianism about it. Best of all, though, is that if you actually do well, you're entirely free to attribute your success to extreme cleverness.

This was the appeal of the great bull market that only began to stumble this month. For years, it gave people the impression that their portfolios had grown thanks to their particular investment savvy. But deep within the wealth machine, the hidden engine was pretty basic: more money chasing less stuff. Because almost all asset prices rose, the only real skill needed to gain from the bull market was to stay on the upward escalator. Clever us.

Well, now the markets have shuddered. Observers are asking whether the global financial system has reached the point where the cost of servicing debt exceeds the new funds made available by rising asset prices. If so, the result - less money chasing more stuff - reverses the escalator.

The worst may not happen, but we can expect a time of greater volatility as waves of doubt pulse through a nervous investment community. This is the time when genuine cleverness would be handy. So is there anything from the secret world of probability that might help us deal with the exciting times to come?

There is. It's called Parrondo's paradox, and it was devised in 1997 by a professor at the Universidad Complutense in Madrid. It shows how you can still win when every game in town is a losing one.

Imagine a game of coin toss in which you win $1 on heads and lose the same amount on tails. The coin is made to be subtly biased against you (life not being fair), so that you have marginally less than a 50 percent chance of winning. Probability is patient and remorseless. Over time, your capital is gradually eroded. In real life, this is rather like keeping your cash in a mattress: Inflation inexorably reduces your cushion. Let's call this Game A.

Game B is more complicated. You usually get to toss a coin that favors you (giving you about a 75 percent chance), but each time your total capital is, say, a multiple of $3, you have to toss the Coin of Doom, on which you lose 90 percent of the time. Over the long run, this more than balances out the advantage from the favorable coin.

Now the paradox comes in. Let's say you can switch from one game to another - at set intervals, or even randomly. Your total capital begins to increase. Why? Because Game B involves winning often but losing big, while Game A involves near-stasis. Being able to duck out of Game B occasionally will greatly increase your chances of missing the obliterating blow when your capital hits a multiple of $3.

The physical equivalent of this is not an escalator but the Cornish "man engine," an old device for getting workers up and down mine shafts. A ladder ran right down the middle of the shaft, pumped up and down in six-foot strokes by a steam engine. To go down, a miner rode the ladder down six feet, then stepped off to wait on one of the platforms fixed at intervals to the shaft wall while the ladder went up, then shifted to the ladder again for another jerk downward. Miners on their way up simply reversed the process. Neither the ladder nor the platforms went anywhere, so staying on either one would leave a miner down the pit.

Parrondo's Game A is a platform: It's motionless. His Game B is the ladder - but it has a jerky engine with a slow upstroke and a sudden downstroke, so a miner who switches to it will spend more time going up than down.

Ingenious people are trying to find ways to apply this strategy to financial markets. But our irrational exuberance and panic remain the market forces that blow well-constructed strategies to smithereens.

If we all were as active as the Cornish miner, really understanding when and how to commit to the oscillating ladder and when to hug the wall, we could all gain - even when the global escalator breaks down. Now that would really be clever.

Michael Kaplan is co-author of "Chances Are ... : Adventures in Probability." This article first appeared in the Los Angeles Times.

Kathleen Parker's column will return next week.

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