MIT economics professor Xavier Gabaix, along with a team of physicists from Boston University, has discovered that the ups and downs of the stock market follow a mathematical pattern of frequency similar to that of earthquakes. The findings could help future traders protect their investments by suggesting periods when market fluctuations are likely to be significant — and when risk, therefore, is likely to be high.

“The frequency of crashes such as those in 1987 and 1929 follow patterns,” says Gabaix. “Although that doesn’t mean we’ll be able to predict with certainty when movement will occur, or in which direction it will go, we can still predict — better than with other methods — whether it will be a big move or a small one. And that information can be useful.”

For example, he says, the model could benefit those of us whose retirement savings are invested in the stock market because it helps the managers of large pension funds. “Knowing how volatile the market might be in the short term will decrease the probability that fund managers will suffer extremely large negative returns.”

The patterns that suggest stock market, as well as earthquake, movements are known as power laws. Power laws define mathematical relationships between the frequency of large and small events: the larger the effect, the less frequently it occurs. Much of the importance of power laws lies in the mathematically elegant ways they describe artificial as well as natural systems.

In a paper published in the May 15, 2003 issue of Nature, Gabaix’s research team describes how power laws influence both the volume of stocks traded and the number of trades during a given period. Their work also reveals how even slight movements of the largest mutual funds — those with $500 million or more in assets — can move the market, sometimes in big ways, and again with a frequency of occurrence that appears to imitate that of earthquakes and other natural phenomena.

Precise Social Science

That Xavier Gabaix is focused on world financial markets is not surprising. Growing up in Paris, he and his parents had many discussions about economic policies and social programs. “They told me, ‘Because you are a citizen, you need to develop opinions about how society should work.’” Often, he says, his parents would ask: “What should we do about this economic issue? How could we have prevented that crisis?”

These conversations of his youth shaped his thinking. Although he was drawn intellectually to math and physics — which he studied at Ecole Normale Supérieure, an elite school for science in Paris — something in those disciplines was missing. “I loved the fact that math and physics are so rational, but they’re also very dry,” Gabaix says, adding that somehow he also needed to give voice to his social conscience. Economics intrigued him.

“At first,” he says, “we had fairly crude theories in economics: What makes people trade? If I see other people making trades, will I trade more? Less? What are the consequences when people trade recklessly?

“Actually,” he continues, “although people do things that superficially don’t always make sense, I wondered if there couldn’t be some systematic structure underlying their ‘folly.’”

Eager to apply the precise thinking of theoretical math and physics to the less empirical realm of economics, Gabaix stumbled upon the concept of power laws while a Ph.D. student at Harvard. He says the idea of focusing on the stock market was based, to a degree, on convenience. “It is the social system on which we have the best available data — hundreds of millions of transactions. And we can do very precise research on that.”

The Big Question

The million-dollar question is, of course, Can these studies help predict or, better yet, stave off, market crashes? Gabaix explains that although the findings can predict with some certainty that a 25 percent movement in the market will occur roughly every 50 years, what can’t be foretold is whether that movement will be up or down.

“If there were some magic formula on how to predict the direction of market moves in the short term, people would always trade on this, and the regularity would just disappear,” he explains.

For now, Gabaix says he’ll be happy if his ongoing research serves one day to put economics on a firmer empirical foundation, perhaps solving a few mysteries of economic behavior along the way.

“There are few economists like me who find it interesting to apply physical science algorithms to economic data. But I like the idea that we can think about a social domain like the financial markets in a precise, analytical way. That appeals to me.”