'Power laws' show how big players shake the market

Many stock-market investors may feel they have been shaken by an earthquake in the past few years.

In fact, the market behaves like earthquakes, holds Xavier Gabaix, an economist at Massachusetts Institute of Technology. It bumps up and down in a somewhat predictable pattern, similar to the earth's tremors.

Stock prices may be looking better this year. The Standard & Poor's 500 stock index shot up nearly 15 percent in the quarter just ended.

But because stock-market movements, though man-made, behave with the mathematical elegance frequently found in natural systems, investors can expect another crash ahead like that of 1929 or 1987, or the more recent one.

The problem, notes Mr. Gabaix: You can't predict exactly when it will hit - a decade from now or in 50 years.

Nor can market regulators do much about crashes. Gabaix doubts the "circuit breakers" imposed by major stock exchanges to restrain price movements during a rough day will do the trick. But, he adds, perhaps a major injection of liquidity into the financial markets by the Federal Reserve could limit a crash.

Gabaix's views arise from research he conducted along with H. Eugene Stanley, a Boston University physicist, and two other associates.

They examined more than 100 million stock trades from 1994 through 1996 at the New York Stock Exchange and markets in Britain, Canada, Japan, and seven other nations. Their findings (indecipherable to most) were recenty published in Nature, a science magazine.

The four found that for the market as a whole and for an individual stock, the daily volume of stocks traded, the number of trades, and price fluctuations follow "power laws."

For instance, the number of days when a specific 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 days that stock moves by 8 percent, and so on. The same pattern characterizes the number of daily trades.

An inverse power law describes the number of shares of a specific stock traded each day. For example, if 100,000 shares of IBM stock were traded on 512 days during a certain period, then it could be predicted that there would be 64 days when 400,000 shares of IBM stock were traded, and eight days when 1.6 million traded, and one day when 6.4 million shares traded.

The patterns applied in all the markets they examined, even though national economic systems vary. "It is surprisingly consistent," says Gabaix.

Although the new knowledge may be intriguing, an ordinary investor won't be able to profit from it. It doesn't tell whether a price move will be up or down, only its size. "At this stage, it's largely pure science," says Gabaix. Perhaps those trading in options on stocks could benefit from knowing that price movements tend to move in certain-size jumps and not smoothly, Gabaix speculates.

Stock-market prices and trading volumes are governed by the millions of buy-and-sell decisions made by multitudes of investors acting on their own complex judgments.

This has led to the "efficient markets hypothesis." This academic theory holds that it is extremely difficult for investors to consistently get a return on their portfolios better than that of an appropriate market average. This is popularized as the "random walk" or "dart board" theory - that over time the investors who choose a portfolio of stock by throwing darts at a listing of stocks will do as well on average over time as those carefully selecting a portfolio.

Gabaix figures his "power law" doesn't violate the random walk. But Burton Malkiel, a Princeton University economist who is a major proponent of the random walk, says he's "suspicious" of any finding of regularity in stock-price changes. There is, he says, an infinite variety of variations.

Gabaix attributes the power-law patterns to the major influence on stock markets of large financial institutions, such as mutual funds or hedge funds.

When these institutions, each with more than $100 million in assets, decide, for instance, to dump a stock under time pressure, they move the market. Sometimes their decisions may be based on news about a stock.

Last month, the Internal Revenue Service reported that the nation's Top 400 taxpayers reported a collective income of nearly $70 billion for 2000, with an average of $174 million. They accounted for 1.09 percent of total US adjusted gross income, more than twice the Top 400's share for 1992.

But Gabaix doubts their individual trading power matches that of big institutions.

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