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La paradoja de Parrondo II

After a startling run-up, the stocks of Internet and technology companies have suffered a precipitous decline in the past year. A portfolio equally invested in such technology giants as America Online, Dell Computer, Lucent Technologies and Qualcomm, Inc., would have lost half its value between March 1 and December 1, 2000.

But investors can remain fully invested in the market and make money even if they own only poorly performing stocks—provided their portfolio includes several different losers. On the surface, it might seem that if owning one sinking stock were a bad idea, owning several would be insane. Mathematicians, physicists and biologists have proved otherwise.

The key to such a counterintuitive investment strategy is to take advantage of random fluctuations in the prices of the stocks from day to day and from week to week. Even though all the general trends may be downward, the price of virtually any declining stock can also rally briefly if the market momentarily believes the stock is cheap enough to buy. If investors can manage to sell that stock during the brief price uptick that results from such market demand, and then shift those funds to another stock that is in a slump, they can overcome the general losing trends in both stocks. It is not an unproblematic strategy to pull off—transaction fees could gobble up profits, or a crash could drop prices monotonically for every stock in the portfolio. Yet the alternative, holding on to a losing stock as its value progressively slips away, offers no winning possibility at all, and could lead to far greater losses.

No one yet has found a foolproof way to play such odds profitably and reliably with a real losing stock portfolio. But it turns out, in a surprising number of circumstances, that it is quite possible to, in essence, “time the market.” In other words, even when one is faced with a number of scenarios for which the odds of success are unfavorable—whether in games of chance, in choosing between competing political parties or in circumstances involving the second law of thermodynamics—it is possible to play two of the scenarios against each other to create a single winning strategy. The workings of that paradoxical result were elucidated recently by the Spanish physicist Juan M.R. Parrondo of Complutensian University in Madrid. Parrondo showed that what was once an obscure curiosity in physics could be relevant to daily life—and much more besides. Some investigators think Parrondo’s paradox may hold the key to certain biological processes—and perhaps to the development of life itself.


Interestingly, people already exploit switching strategies similar to Parrondo’s in everyday life—though not, of course, because they are applying theoretical insights about Brownian motion. But whenever someone changes jobs to get a salary increase, for instance, or sells peaking stocks and buys slumping ones, Parrondo’s paradox comes into play. Moreover, many ordinary events are governed by random-seeming fluctuations, from the ups and downs of the financial markets to the succession of political parties in power. Economists and mathematicians have begun to ask whether the principles of Parrondo’s paradox could apply to decision making in those realms.

The physicist Sergei Maslov of Brookhaven National Laboratory in New York has shown that principles similar to Parrondo’s paradox can be applied to the stock market. Maslov found a way that the value of a stock portfolio can increase even if all of its stocks decline in the long run: The entire portfolio must be sold periodically—even daily—and the proceeds must be quickly plowed back into repurchasing the stocks in the same proportions as they were in the original portfolio. The net effect of such periodic rebalancing is to apply the gains from stocks that are doing temporarily better than average (and have therefore increased their relative proportion in the portfolio) to buy more stocks that are temporarily underachieving. The beauty of Maslov’s proposal is that one need not know anything about particular stocks; simply sell them all and then buy them back in a rebalanced portfolio. Unless the balance of investments is shifted in that way, the long-term prospects for a portfolio full of duds are “grim indeed,” says Maslov, since all of the stocks tend to decline with time. But Maslov’s tactic can generate better returns than the “buy and hold” policy that is the current favorite of many economists. (It should be noted, however, that the declines in technology stocks mentioned at the beginning of this article might well overcome even Maslov’s strategy.)

Abbott and Parrondo suggest that switching from one option to another could also prove useful in applying government policies to quantities that fluctuate unpredictably; for example, if two policies each cause unemployment to rise, alternating between them might actually create jobs. Furthermore, Abbott notes, citizens could be, in essence, following Parrondo’s principles when they vote political parties alternately into and out of office.

In short, Parrondo’s paradox demonstrates that two wrongs can sometimes make a right—and that a little indecision can be a good thing. “One message of the Parrondian philosophy is to not be a moderate or an extremist, but to maintain a dynamic between positions that may appear to be conflicting,” Abbott notes. “Parrondo gives us permission to be ‘swing voters’ in life’s decisions.”