The marble halls and frantic pace of the world's stock exchanges are giving way to quietly humming computers. Financial action is increasingly found within electronic stock quotation systems and on the trading desks of individual brokers and investors. Their primary bases: New York, hub of the powerful US economy; Tokyo, capital of an emerging financial superpower; and London, where liberal laws are sparking unprecedented growth for the financial community. THE stock exchange is perhaps the central symbol of capitalism.

It's usually pandemonium. Young men flail their arms and rush around with slips of paper, while coded stock prices roll by on big electronic scoreboards. Phones ring. Papers fly. Traders gather into crowds at one station. Evaporate. Then form at another.

If you haven't done so already, you ought to tour a stock exchange soon. They're colorful and exciting, and they probably won't be around in their current form by the turn of the century.

Look at Tokyo and you'll see why. At the Tokyo Stock Exchange, the pace is much more subdued than it was five years ago. This is because of the activity in a large, low-ceilinged room off to the side of the soaring trading hall.

The side room is filled with somber Japanese men in white shirts and modest ties. They are looking at computer terminals. There's little shouting and hustling. Just quiet analysis and button punching. All but the 250 most active stocks are traded via computer.

As in so many other businesses, the computer is the unglamorous but highly efficient future for stock, bond, and commodity trading. The Hong Kong Stock Exchange is already fully computerized; come 1997, it could be the centerpiece of the Chinese financial system.

The London exchange, like Tokyo, has put the order placing and execution of less-traded stocks onto computers.

In New York, floor traders are still a fixture, and the New York Stock Exchange says that, while new technologies are under study, there are no plans to abolish floor traders. But meanwhile the National Association of Securities Dealers Automated Quotation system (NASDAQ), fully computerized and decentralized, is experiencing extraordinary growth.

At his office in Tokyo's Nihombashi financial district, Yoshio Iwata, senior managing governor of the Tokyo Stock Exchange, considers the pros and cons of human trading vs. computer trading.

``Face to face, you have more turnover,'' Mr. Iwata notes. ``You see the movement of people and whose company they are with and what their faces say. You hear whispers and look at their eyes. You can't do that with a black box.'' LINKING UP

But face-to-face stock trading costs more, and there is a greater possibility of miscommunication than there is with a computer. Moreover, advances such as Reuters Instinet -- which offers up-to-the-second stock quotations -- are taking business away from face-to-face exchanges.

The global stock market competition is among the world's exchanges -- Tokyo, London, New York, etc. -- and it is also between them and the computer-driven information vendors such as Reuters and Dow Jones. Exchanges are exploring links with one another and with information vendors.

So far, at least, the universe of institutional assets has been expanding so rapidly that all the exchanges and all the information services appear to be prospering at once. As long as the world economy continues to grow, technology will probably continue to drive all the players toward computerization, so that the exchanges eventually metamorphose from cacophonous gathering places into quietly humming computer banks.

``What you're seeing,'' says Gordon S. Macklin, president of the National Association of Securities Dealers, ``is an evolution from marble halls to computerized systems. Meeting 196 years ago under a buttonwood tree [to organize the NYSE] was the state of the art in communications at the time.''

In the future, any shouting, if it occurs, will be heard on the trading desks of individual broker-dealers: the big rooms operated by Merrill Lynch, Morgan Stanley, Citicorp's Vickers da Costa, etc. These are where the human component of the financial industry is growing.

Broker-dealers want to be involved, worldwide, in operations across the whole range of financial services, from money management to underwriting to banking. Employment in this field is growing rapidly, and broker-dealers are setting up operations worldwide and seeking seats on stock exchanges around the world.

``You're seeing a financial system where at the top are world-class players who have the management skills, capitalization, distribution capacity, and global reach,'' says John Heimann, vice-chairman of Merrill Lynch Capital Markets.

Merrill Lynch-New York would like, for instance, to be able to snag an institutional order to buy 100,000 shares of, say, Sumitomo Heavy Industries and execute the order in Tokyo without sharing the work with another broker.

This year the Tokyo Stock Exchange granted seats to Merrill Lynch and nine other foreign firms.

Other linkups: The London Stock Exchange now trades stock quotations with the National Association of Securities Dealers in the United States. There are ties between the Chicago Mercantile and Singapore, Philadelphia and London, Boston and Montreal, the American Exchange and Toronto. LONDON'S YEAR

But three global stock market centers are clearly the most important:

New York, with its big banks, brokerages, stock exchanges -- all backed by the massive American economy and the international legal tender, the US dollar. New York is still the biggest stock exchange in the world, comprising about half of the world's $3.5 trillion in equity capital.

Tokyo, where the world's bankers and brokers dearly want to be -- mainly to tap the huge savings pools and to participate in the early stages of Japan's financial internationalization. The Japanese Ministry of Finance is liberalizing financial markets and allowing in foreign companies.

``With the yen becoming an international currency, the role of Japanese banks and securities companies inevitably is going to be more international,'' says Takashi Ohta, executive director of the Bank of Japan.

The Tokyo exchange, at $600 billion capitalization, is the second-biggest equity market in the world.

And London, which has perhaps the greatest natural advantage. Geography puts it in roughly the same hemisphere as 13 of the world's 20 biggest exchanges. Geography also allows British brokers to connect with Tokyo, Hong Kong, and New York during different portions of a long workday.

On Oct. 27, a major deregulation package will put London's financial district, the City, on the same footing with New York's Wall Street and Tokyo's Nihombashi. Commissions for broker-dealers will no longer be fixed, so financial intermediaries will be able to attract big clients by lowering their prices. Londoners call this ``the big bang.''

Because of time-zone advantages and Britain's already more liberal banking laws, London is attracting a huge number of international brokers and banks. By operating in London, they can skirt US and Japanese laws that bar banks from underwriting securities.

Salaries for trading specialists in London have zoomed as a result, and a building boom is changing the face of the financial district. Morgan Stanley, for example, is planning a $2.2 billion trading complex east of the City at Canary Wharf; its London staff has risen from 25 to 500 in nine years.

The London Stock Exchange has been setting up overseas trading links, too. In April, for the first time, a selection of stocks from America's NASDAQ became accessible to brokers in Britain; similar British stocks are being listed on NASDAQ screens in the US. London is also discussing links with the NYSE.

Stephen Raven, chairman of the international markets committee of the London Stock Exchange, notes that London already dominates overseas trading of American securities. Mr. Raven feels London will thus become ``the non-American headquarters'' of the global stock market.

``London has always preferred that role,'' a British Treasury official adds, ``and that's one of the reasons we are keen to make sure London is still competitive. Financial services is really the most dynamic sector in the U.K. economy.''

The big bang seems likely to ensure that. HOW YOU FIT IN

Very well. But what do these financial tugs of wars have to do with those of us who aren't financial wizards?

When you put money in your individual retirement account, or send a few hundred dollars off to a mutual fund, or when your company sets money aside for your pension -- all those funds are gathered into massive investment accounts.

This is known as the ``institutionalization'' of investments. Merrill Lynch, Fidelity, Vanguard, Citicorp, or any of a thousand services manage this money. In Japan, West Germany, Britain, and other countries, savings are also aggregated and invested.

Professional money managers are required by law to seek a healthy return on this money without going to imprudent extremes. Money managers figure they can put 5 to 15 percent in any one investment and increase the return without jeopardizing the overall assets.

Since their fees and reputations are based on their performance as money managers, they've been eyeing virtually any opportunity on earth.

In Japan, money managers and wealthy individual investors determined several years ago that one of the best investments on earth was US Treasury bonds. Japanese now hold some $100 billion in Treasuries, which has helped greatly in funding US budget deficits.

British money managers have a century-old tradition of looking abroad for investments. The British domestic market is rather small, so British individuals and financial houses have continually invested overseas. Some 10 percent of British insurance company assets, 13 percent of pension fund assets, and 35 percent of total unit-investment-trust (mutual fund) assets are invested overseas.

And in recent years, American money managers have discovered that despite the four-year-old bull market in the US, foreign stocks have performed exceptionally well. Result: International mutual funds are growing enormously, and pension fund commitment overseas increased from $3.5 billion in 1980 to $27 billion (out of $1 trillion total) last year.

Such investing takes all sorts of brokers and counterparties. Large corporations routinely turn to international financial markets to raise money, issuing Eurobonds, Yankee bonds, Samurai bonds, and a myriad of other debt vehicles.

This is happening with equities, too. When British Telecom went public in 1984, it sold stock in London, Tokyo, and New York. The Anglo-French consortium building the English Channel tunnel plans to raise capital worldwide through debt and equity offerings.

Ownership is becoming global. Your money may one day fund a Thai shirtmaker, an Italian carmaker, or a Greek shipping company.

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