Trade patterns predict financial earthquakes - Stock Market

USA Today (Society for the Advancement of Education), August, 2003

The stock market has its share of shakeups, but who would guess that large movements in this man-made system adhere to a similar pattern of predictability as earthquake magnitudes? After analyzing four years of data from the world financial markets, an interdisciplinary team comprised of an economist at the Massachusetts Institute of Technology, Cambridge, Mass., and physicists from Boston (Mass.) University discovered that large-scale events in the stock market adhere to distinct patterns. They believe that market analysts could use these findings to predict--at least partially--the chance of a market crash.

"The frequency of crashes such as those in 1987 and 1929 follow these patterns," explains Xavier Gabaix, assistant professor of economics at MIT. "But that doesn't mean we'll be able to predict with certainty when a change will occur or which direction the change will go."

The patterns found by the scientists are power laws, which describe mathematical relationships between the frequency of large and small events. In short, the scientists have shown that stock markets have a mathematical elegance frequently found in natural systems. One such power law is used to forecast the chances that an earthquake of a given magnitude will occur.

"We have found the artificial world of the financial markets follows a pattern similar to one found in our natural world," notes Gabaix. "Trading on the stock market has a lot of randomness, but at the end of the day you find that a pattern emerges that matches power-law patterns found empirically in data from systems as diverse as earthquakes and human language."

"We want to understand financial earthquakes in order to protect people like you and me, whose retirement is tied up in the markets," says H. Eugene Stanley, director of the Center for Polymer Studies at Boston University. "Fortunately, in Tokyo, they build buildings so that they don't succumb to earthquakes. We need to do the same thing in economics."

However, research suggests that the forces that give rise to the power laws of stock market fluctuations are extremely robust. Consequently, such crashes would be difficult to prevent. "If you put an extremely large amount of friction--in the form of regulations--into the system, you could prevent the crashes. But moderate amounts of frictions will make no difference," adds Gabaix. "In any case, before we can give advice on policy, we need more research...."

The scientists show that--for the market as a whole and for an individual stock--the daily volume of stocks traded, number of trades, and price fluctuations follow power laws. For example, the number of days when a particular stock price moves by one percent will be eight times the number of days when that stock moves by two percent, which in turn will be eight times the number of days when that stock moves by four percent, and so on.

The same relationship (called the inverse cubic pattern) characterizes the number of daily trades. A similar power law (the inverse half-cubic pattern) describes the number of shares traded each day. For instance, if 100,000 shares of a certain stock were traded on 512 days during a specific period, then you can predict that there would be 64 days when 400,000 shares of that stock were traded, and eight days when 1,600,000 shares were traded, and one day when 6,400,000 shares were traded.

To understand these patterns, the researchers looked at the size of large traders, such as mutual funds with more than $100,000,000 in assets. They found that their size also follows a power law. The number of funds that manage $1,000,000,000 is twice the number of funds with $2,000,000,000, which in turn is twice the number of funds with $4,000,000,000, and so on. (This pattern is called Zipf's Law, named after linguist George Kingsley Zipf, who in the 1930s found the statistical pattern in the frequency of word use in languages.)

The scientists prove that the patterns in daily trades, returns, and volume are generated by the actions of large market participants when they trade stock under time pressure. Stocks traded under time pressure by mutual funds cause stock prices to change; these actions are enough to generate specific patterns.

Hence, a lot of the large movements of the market, such as the days of small "crashes" when prices seem to move for no good reason, ultimately can be traced back to the behavior of some very large players.