PORTLAND, Ore. — Statistically speaking, size doesn’t matter when a financial bubble bursts.
The big crashes may hurt a lot more, but new analyses of “microbubbles” presented March 15 at a meeting of the American Physical Society find that the same mathematical laws underlying massive economic crises are also at work in tiny fluctuations that occur on the order of milliseconds.
The new understanding of economic fluctuations both big and small doesn’t predict when the next economic meltdown will wreak havoc on retirement accounts, said study coauthor H. Eugene Stanley of Boston University. But the results help describe complex financial fluctuations and reinforce the idea that governments ought to have a contingency plan in place for the calamitous collapses that his research describes as inevitable, Stanley said.
The results are intriguing “because what is causing these big bubbles to collapse are some instabilities that start at the local level of the millisecond time scale of traders,” Stanley said in his presentation.
Earlier studies conducted by Stanley and his colleagues showed that the properties of big economic fluctuations in the S&P 500 stock index didn’t seem to depend on the scale — the big ones had similar properties to the normal-sized ones. In statistical parlance, this means that the trades follow a power law. Similar power laws describe the distributions of natural events, such as the number of big and small earthquakes that occur over time on a particular fault.
To see just how far down the time and dollar scales their economic power law applied, Stanley and his team acquired detailed trading information for the DAX, a German analog of the Dow Jones industrial average. The researchers analyzed 14 million trades during a nine-month window. During this time, every trade was recorded with millisecond accuracy. “This makes me salivate, because here is a wealth of data on the microscopic level — the millisecond scale — that we can now analyze,” Stanley said.
When the value of the DAX hit lots of minimums and maximums — lots of bubbles forming and bursting — the time between trades decreased, the researchers found. Conversely, when the DAX’s price was relatively stable, the rate of trading slowed. Stanley proposed that this likely reflects traders’ penchant to let things ride if the price is stable, but to launch into frenzied trading when the price rises or drops suddenly. The volume of DAX shares also aligned with the number of bubbles forming and bursting. As more bubbles formed and burst, the volume of trading increased.
The distributions of both trading speed and share volume remained the same regardless of bubble size, the team found. This means that one mathematical law describes events that occur over 10 orders of magnitude — from milliseconds to hundreds of days, Stanley said. The same is true of earthquakes: There is a mathematical relationship between size and frequency that encompasses everything from imperceptible daily tremors to massive once-in-a-lifetime catastrophes.
Although the researchers don’t yet understand the details of bubble formation and bursting, the work shows that large financial collapses, although infrequent, are bound to happen, said Stanley. The results “tell us that the really big crashes or bubbles that burst have something to do with the medium-sized and the small-sized ones,” he said. “Had this law been known earlier and appreciated by governments, governments would have probably taken steps to make plans for what to do if one of these big shocks occurs.”
Physicist John W. Clark of Washington University in St. Louis, who organized the session in which Stanley spoke, said that understanding complex networks like this can “sometimes give us fair warnings of disasters that may befall us before they become inevitable.”