Using odds to beat the market
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, either; ex-practitioners of chicken-bone charms are more than welcome to try out magic crystals. 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, wobbling up and down in search of a new equilibrium. For years, it gave people the impression that their portfolios had grown thanks to their particular investment savvy. A lucrative industry touted specialist advice on how to gain wealth beyond the dreams of avarice by flipping your properties or snapping up credit derivatives. But, deep within the wealth machine, the hidden engine was actually 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, and suddenly we don’t feel quite so clever. 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?
As it happens, 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.
First, some setup.
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% 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, to inveigle the unwary. You usually get to toss a coin that favors you (giving you about a 75% 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% of the time. Over the long run, this more than balances out the advantage from the favorable coin.
Game B is as much a mug’s game as Game A -- and in real life it resembles the more volatile corners of the investment world, such as junk bonds.
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 permanently down the pit. Parrondo’s Game A is a platform: It’s motionless. His Game B is the ladder -- but, crucially, it has a jerky engine with a slow upstroke and a sudden down stroke, so a miner who switches to it, even randomly, even blindfolded, will spend more time going up than down.
Ingenious people are trying to find ways to apply this strategy to financial markets, switching assets, say, between high-volatility shares and cash. But problems remain. The biggest, of course, is us. 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.
