For more and more of the world's stocks, the trading never stops

The sun never sets on trading in Broken Hill Proprietary stock. And that will be the case for many other stocks in the future. The world's stock markets are being integrated with astonishing speed.

It's a ''24-hour market'' for the shares of Australia's largest corporation and a number of other companies, notes Ian Salter, a member of the London Stock Exchange and a director of Strauss Turnball & Co., a British brokerage house.

For BHP, trading starts the day in Sydney and Melbourne. Toward the close of trading ''down under,'' London's top-hatted stock dealers will have arrived at work and the stock of the steel and mining company will begin changing hands on the London Stock Exchange.

Indeed, during a booming time for Australian shares, more BHP stock could change hands in London than in Australia. Later, before the London market closes , trading in BHP will start up in New York.

Of course, some foreign-company shares have been listed on foreign markets for many decades. But in the last few years, the trend has accelerated enormously.

''Competition among marketplaces is becoming increasingly international,'' comments Gordon S. Macklin, president of the National Association of Securities Dealers (NASD), the self-regulatory association of the over-the-counter market in the United States.

Around the world, he says, government officials and operators of securities markets ''are pondering how to position their markets and their countries in a rapidly increasing 24-hour security trading environment. You can see this whole trend pick up as communications techniques improve and communications costs decline.''

He added in a telephone interview from his Washington base: ''We are neatly along the road to a global securities market.''

Here in London, the securities industry felt it was lagging somewhat in this world competition. To meet the challenge, the industry has launched what may fairly be described as a ''revolution,'' a that is word sometimes misused to describe even minor change.

Before December 1986, the London securities industry will move from fixed to competitive commissions on stock transactions. Brokers here speak of this forthcoming event as the ''day of the big bang.'' It is expected to occur in approximately 18 months, though the actual date has not yet been fixed. A similar shift was made in the United States in 1971, prompting dramatic changes in the American securities industry.

At about the same time as the ''big bang,'' the industry will drop its century-old division between brokers (those who take stock orders from the public) and jobbers (those who buy and sell stocks to the brokers on the exchange floor, never dealing with the public). In the US securities industry, a brokerage house does both jobs, with the exchanges and regulatory bodies watching carefully for abuses where this dual function of trading for both the public and the brokerage house itself produces conflicts of interest.

Electronically, the London exchange will switch at that time to a system somewhat similar to the one the NASD set up in 1971 in the US for over-the-counter stocks, known as the NASDAQ (Automated Quotation system). Competing dealers list prices at which they will sell or buy a certain number of shares of a specific stock. These prices are entered and constantly updated in a computer memory and are immediately available at terminals in the offices of brokers and others. Deals are usually made over the telephone with this information.

Referring to the months ahead, a London Stock Exchange official commented: ''It is going to be a very interesting time indeed.''

Already, the City (London's financial district) has witnessed a rush of mergers and aquisitions as financial firms attempt to enlarge their capability to face an uncertain, changing future.

Essentially, the London market will try to accomplish in two years what has taken 15 or so years to accomplish in New York.

Noted the London Stock Exchange's governing body July 17 in a paper announcing its decision to dismantle its ''single capacity'' broker-jobber system: ''There is growing recognition and acceptance of the fact that if The Stock Exchange is to play a significant role in the international securities market our dealing practices must be reconciled with most of the rest of the world.''

Speaking of the radical reshaping of Britain's securities industry, the London Economist stated: ''At stake is whether British financial houses, mostly tiny by world standards, will be competing worldwide in 10 years time; whether London will remain one of the world's top three financial centers; and - just possibly - whether the vanishing British private investor can be lured back into the marketplace.''

After World War II, the ''internationalization'' of the world's economy moved ahead speedily. Multinational corporations spread their branches and offices around the globe. Trade between countries usually grew faster than commerce within nations. The Eurocurrency and Eurobond markets sprang up to deal in issues of short- or longer-term debts denominated in foreign currencies, such as the US dollar or West German mark. Similar international capital markets developed in such places as the Bahamas and Singapore and Hong Kong.

However, trading in stock - the actual ownership of companies - was somewhat slower in becoming an international market in a big way.

One reason for this happening now is the growth of non-US companies. From 1969 to the end of 1983, the total value of US stocks about doubled to $2.2 trillion. (It would be approximately the same today.) In the same time frame, the value of equities on the world's major markets outside the US about tripled to $1.3 trillion.

As a result, US stocks comprise about 63 percent of the value of global equities today, compared with 75 percent in 1969.

Japan, notes the NASD's Mr. Macklin, has enjoyed a particularly dramatic increase in equity values.

One estimate is that by the year 2000, the size of equity markets outside the US may reach $4 trillion.

New York, as well as London, wants to share in the servicing of that world market. NASDAQ already lists 289 foreign issues, the largest number on any stock market in the United States. There were only 86 issues listed in 1978.

''We see foreign-issue additions to NASDAQ and increased trading in these issues as a primary growth area for our marketplace,'' says NASD's Mr. Macklin. In 1983, foreign-issue volume on NASDAQ rose 96 percent to 1,147 million shares worth $11.4 billion. The Netherlands' Philips Industries, N. V., Britain's Glaxo Holdings, Japan's Fuji Photo Film, Sweden's L. M. Ericsson, and South Africa's Vaal Reef Exploration are among the more active of all NASDAQ issues.

The New York Stock Exchange, facing increased rivalry from NASDAQ for corporate stock listings, lists 2.2 billion shares of about 50 major foreign companies with a total market value of $62 billion.

Looking at the London market, Macklin commented: ''They are putting together a network of significantly stronger, world-class companies. They are doing a wonderful job.''

One example is that of Akroyd & Smithers, London's largest jobber firm. It has strengthened its capital position by selling 29.9 percent (the maximum allowed) to a British merchant bank, S. G. Warburg (which failed to make a link with the Wall Street firm of A. G. Becker work). The jobber firm also has a deal with Mullens & Co., a London company specializing in ''gilt-edged securities'' (the British equivalent of US Treasury securities).

Further, when the rules change, Akroyd & Smithers plans to merge with a major London brokerage house, Rowe & Pitman, which has offices in Boston, San Francisco, New York, Hong Kong, Tokyo, Singapore, and Johannesburg. S. G. Warburg has offices in Switzerland and West Germany.

''We want to have the facility as a firm to keep ourselves informed of price movements in all these time zones,'' said Stephen Raven, director of overseas operations of Akroyd & Smithers.