Model explains market movements

By Eric Smalley and Kimberly Patch, Technology Research News

Researchers from the Massachusetts Institute of Technology and Boston University have developed a mathematical model that explains some well-known fluctuation patterns in the stock market.

The model shows that the trading choices of the largest 500 or so players are responsible for big up and down movements, including extreme swings like the crashes of 1929 and 1987, said Xavier Gabaix, an assistant professor of economics at MIT.

The model also shows that the same forces underlie all types and sizes of markets, including stock markets in different countries, said Gabaix.

It has long been known that stock market fluctuations follow mathematical patterns, known as power laws, that are similar to those of earthquakes, business sizes, city sizes, and Web site popularity.

In all cases there are a few very large examples of this type of activity or entity and many smaller occurrences or examples, said Gabaix. There are only a few very large earthquakes, businesses, cities and very popular Web sites, and there are many more small earthquakes, businesses, cities and less popular Web sites. This relationship follows a precise mathematical graph.

Numbers that describe the relationship between large fluctuations in stock market prices, trading volume and number of trades also follow the same power-law mathematics, Gabaix said.

For example, the number of days a particular stock price moves by one percent will be eight times the number of days it moves by two percent, and the number of days it moves by two percent will be eight times the number of days it moves by four percent, and so on.

A similar power law characterizes the number of daily trades, said Gabaix. "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," he said.

Past postulations about power laws in the stock market have looked at the effects of large collective movements arising when, for example, some type of anxiety snowballs. What has been difficult to explain with this hypothesis, however, are the specific numbers shown by the empirical evidence, said Gabaix. The power law exponents for return and volume in the stock market remain steady at 3 and 1.5 respectively.

The researchers model showed that the behavior of big players is responsible for these numbers.

Certain power laws arise when market participants trade optimally, meaning they carefully trade off the time to execution and the cost of execution, said Gabaix. "If you want to trade a large trade quickly, you'll have a very big price impact, which traders want to avoid. This leaves them to trade more slowly when they have to make a big trade. But they don't want to trade too slowly either, because the opportunity for a good trade may go away," he said.

Big trades beget more trades, and those additional trades are usually in the same direction as the initial trades, according to the model.

When traders follow the optimal strategy, "they appear to generate exactly the power laws we observe empirically -- an exponent of 3 for returns and an exponent of 1.5 for volumes," said Gabaix. "Being smart about how to trade in the short term is part of the basic knowledge that professional traders must have, so we think... optimal execution of trade is a good approximation for the traders' behavior," he said.

The model can help predict the probability of a stock market crash occurring in a given period of time based on past returns and trading activity, said Gabaix. A 30-percent crash, for example, is likely to happen every century, he said.

The model probably won't help much in preventing crashes, however, said Gabaix. This is because preventing crashes would require drastic regulations or taxes to make the market much less liquid. Such drastic measures are "probably not desirable, because it's good to have a liquid market for a host of other reasons," he said.

The model could be used to hedge against large risks or to make money on stock market derivatives, but will not help investors gain better returns on direct stock trades, said Gabaix.

The researchers are currently working on identifying the origin of extreme movements in the stock market, Gabaix said. This may allow for a model that could help in mitigating the extremes, he said.

Gabaix' research colleagues were Parameswaran Gopikrishnan, Vasiliki Plerou, and H. Eugene Stanley of Boston University. The work appeared in the May 15, 2003 issue of Nature. The research was funded by the National Science Foundation and the Russell Sage Foundation.

Timeline:   Now
Funding:   Government, Private
TRN Categories:  Applied Technology; Computers and Society
Story Type:   News
Related Elements:  Technical paper, "A Theory of Power-Law Distributions in Financial Market Fluctuations," Nature, May 15, 2003


May 21/28, 2003

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