CAMBRIDGE, Mass.--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 comprising an economist at MIT and physicists from Boston University discovered that large-scale events in the stock market adhere to distinct patterns. They believe that market analysts could use these new findings to partially predict the chance of a market crash, although prevention is not possible.
"The frequency of crashes such as those in 1987 and 1929 follow these patterns," said Xavier Gabaix, assistant professor of economics at MIT and lead author of the paper describing this research, which is appearing in the May 15 issue of Nature. "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. One such power law is used to forecast the chances that an earthquake of a given magnitude will occur.
In short, the scientists have shown that stock markets have a mathematical elegance frequently found in natural systems.
"We have found that the artificial world of the financial markets follows a pattern similar to one found in our natural world," said 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."
The team also found that the actions of large market participants, like mutual funds, produce this power-law behavior when they trade stock under time pressure.
"We want to understand financial earthquakes in order to protect people like you and me, whose retirement is tied up in the markets," said Professor H. Eugene Stanley, director of the Center for Polymer Studies at BU and a co-author of the paper. "Fortunately in Tokyo they build buildings so that they don't succumb to earthquakes. We need to do the same thing in economics." BU physicists Dr. Parameswaran Gopikrishnan and Dr. Vasiliki Plerou are also co-authors.
"But our research suggests that the forces that give rise to the power laws of stock market fluctuations are extremely robust," said Gabaix. "So unfortunately, such crashes would be very, very hard 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," he added. "In any case, before we can give advice on policy, we need more research to better understand all those regularities in the stock market."
When applied to a precise computer model, the power laws might allow market analysts to predict a crash, but not necessarily prevent it.
"We believe that the computer model presently used by most analysts undercounts the number of large, rare events. That is what we're looking at next," said Gabaix. "If we combine physics methods and economic reasoning, we may be on the right track."
Emerging Patterns
In their paper, 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 1 percent will be eight times the number of days when that stock moves by 2 percent, which will in turn be eight times the number of days when that stock moves by 4 percent, which will in turn be eight times the number of days that stock moves by 8 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 Apple stock were traded on 512 days during a certain period, then you can predict that there would be 64 days when 400,000 shares of Apple stock were traded, and eight days when 1,600,000 shares of Apple stock were traded, and one day when 6,400,000 shares of Apple stock were traded.
To understand these patterns, the scientists looked at the size of large traders, such as mutual funds with more than $100 million in assets. They found that their size also follows a power law. The number of funds that manage $1 billion is twice the number of funds with $2 billion, which in turn is twice the number of funds with $4 billion, 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 these 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, can ultimately be traced back to the behavior of some very large players.
Markets Offer Mountains of Data
Physicists Stanley, Gopikrishnan and Plerou had previously described the power law in stock price fluctuations in a paper published four years ago. Gabaix, an economist whose research focuses on power laws and irrational behavior, teamed up with them to apply the laws to stock volume and number of trades, and to find an explanation for the patterns.
"We did not expect our findings to be of this magnitude. Usually in physics your research fine-tunes someone else's findings; you don't find something totally new," said Stanley, whose own research focuses on complex systems in nature, including medical problems like Alzheimer's. He said the physicists began looking at the stock market data because it was there.
"For most science, you have to create the data. But here was a complex system where the data was just sitting there," he said.
Gabaix and the BU research team analyzed about 100 million transactions from the world financial markets--all the transactions from 1994-96--and discovered the mathematical pattern hidden in the data.
The National Science Foundation and the Russell Sage Foundation funded the research.
