As a boy, John J. Phelan Jr. delivered newspapers in an affluent Long Island community where he learned an early lesson about the risks and rewards of business.

"The bigger the house, the smaller the tip," he recalled with laughter.

As chairman of the New York Stock Exchange, the 53-year-old Phelan still is concerned about risks and rewards -- as they affect the future of the Big Board, competition among the stock exchanges, the practices of the securities industry and protection of the small investor.

But one of his key concerns at the moment, Phelan told Washington Post reporters and editors last week, is the unwarranted investment risk he believes some municipal officials are taking with public funds in their search for high returns.

Phelan was critical of municipal officials who, while unwilling to hire professional money managers, were more than willing to invest their funds with "a firm that nobody in the world had ever heard of before" in return for a "point-and-a-half over prime," he said.

He characterized the actions of the muncipalities as "ineptness" and "lack of professionalism."

Phelan expressed these views against the background of two recent failures of unregulated government securities houses. These firms offer municipalities a chance to improve the yields on their funds through so-called repurchase agreements. The failure of E.S.M. Government Securities Inc. of Fort Lauderdale, for instance, will cost a dozen or so municipalities and five savings and loan associations an estimated $315 million.

One of the losers was Beaumont, Tex., which lost $20 million when it could find no record of the government securities that supposedly served as the collateral for the money it loaned E.S.M. The firm, charged with fraud by the Securities and Exchange Commission, apparently pledged the same securities for loans from several customers.

Phelan's comments came only hours after he received word of the failure of Bevill, Bresler & Schulman Asset Management Corp., of Livingston, N.J., an unregulated government securities firm whose clients may lose as much as $198 million. The firm dealt mainly with savings and loan associations.

In a wide-ranging interview, Phelan also discussed the competitive and technological challenges that confront the Big Board and the events that are transforming the way the 192-year-old institution does business.

Global 24-hour trading, which Phelan said he considers "inevitable," will confront the NYSE with another kind of risk-reward situation, in which the exchange will attempt to forge electronic links with other exchanges around the world without lowering its financial and ethical standards. Phelan, who foresees the linking of three market centers -- New York, London and Tokyo -- thinks that cooperation among the exchanges will ensure NYSE standards.

The exchanges, he said, would have to guarantee the trades within the system and exchange surveillance data.

"I think you can work that out on an international level," he said. "And I think that by providing the mechanisms in which the execution of trades can take place, you've almost got the entire audit trail there." An audit trail provides an electronic record of trading.

The NYSE, Phelan noted, is holding talks with the Pacific Stock Exchange with an eye toward a merger, which might allow the NYSE to extend its trading hours. (The Pacific exchange currently operates from 7 a.m. to 1:30 p.m. or from 10 a.m. to 4:30 p.m. New York time. That is half an hour later than the NYSE.)

The talks, he said, are exploratory but are based on the idea that "the world is changing and is not going to be an old 10-to-4 world. . . . " Phelan said there was doubt about the possible merger because of a "diversity of interests" between the two exchanges, including the fact that the Pacific exchange is controlled by members whose primary interest is options trading.

Phelan noted ruefully that the NYSE had surveyed 4,000 industry, academic and news media people earlier this year to assess their interest in 24-hour trading. When the responses were reviewed, Phelan said, the result was "a unanimity of opinion that says, 'Nonsense. Forget it.' "

And yet, Phelan added, "we do notice that every once in a while when something takes place off hours . . . there are people who are willing to do sizable blocks of stock. . . . So I think despite the fact that everybody said no, that the 24-hour market is more and more creeping into the mentality of the financial world."

"It's there in currencies now. It's there in gold . . . in money trading, and I suspect it's there in Eurobond trading in one form or another. And it's going to be there in stock trading."

Pressure for round-the-clock trading, Phelan anticipates, also will come from investors with personal computers who are plugged into banks and brokerage houses and who now can send orders at night to be stored for execution the next day. "If over the next few years that builds up as a major source," he said, "then those people may want to have some kind of market access up to a certain period of time."

Although Phelan was not specific, other exchange officials said that current thinking is that the NYSE might soon change its hours by opening at 9:30 a.m. instead of 10 a.m. This would create less of a problem for the exchange than remaining open from 4 p.m. to 4:30 p.m. because of end-of-the-day bookkeeping.

The thought given to longer hours, it was said, reflects the NYSE's desire not to lose market share to either the domestic exchanges, including the American Stock Exchange and the burgeoning over-the-counter market operated by the National Association of Securities Dealers, or to overseas exchanges.

Competition between the Big Board and the NASD has been particularly fierce in the last several years, with both exchanges vying for listings. The NYSE appeared to have scored at least some psychological points over the AMEX when Phelan recently hired Robert J. Birnbaum, president and chief operating officer of the AMEX, for a similar job at the Big Board. Birnbaum, 57, is an 18-year veteran of the AMEX. Phelan said there was no plan for a merger of the two exchanges.

Even so, Phelan acknowledged, the heated competition among exchanges has changed the Big Board's outlook on life.

"I think competition in any form makes you better," he said. "We're probably paying more attention to our companies today than we did five, six or seven years ago because they deserve that attention and they have an alternative. You know, when we had the whole ball of wax 15 years ago, you could sit there and take everything in the world for granted. . . . We can't do that today."

One element of the changing scene at the NYSE, an official noted, is the role played by mergers and acquisitions. In 1982, 1983 and 1984, the Big Board added 235 companies to its listings but lost 258 to mergers and acquisitions.

A current challenge faced by the NYSE is the move by corporations -- concerned about the threat of takeovers -- to two classes of stock, typically an A-class stock with a majority of voting power and a B-class stock with limited voting power.

Big Board tradition requires companies to have a single class of common stock, but the exchange is now reconsidering its position. Four firms -- General Cinema, Coastal Corp., Hershey Foods and Dow Jones -- are seeking to remain on the NYSE with two classes of stock, which would violate exchange rules. NYSE action has been suspended pending discussion of a NYSE committee recommendation that the rules be changed.

Phelan has not taken a firm position on the issue, but he has made clear that he thinks the NYSE must adjust to changing circumstances.

"I grew up in a world of one share, one vote," he said, reflecting that the world has changed much in recent years.

Nevertheless, Phelan said, the issue involves far more than merely the one-share, one-vote question.

At what point, he asked, should the exchange tell stockholders what they could do or not do and still remain on the Big Board? Suppose the stockholders of a company decided to omit their annual report or do away with their audit committee, he conjectured. Such are cases in which the exchange might say "Out," he noted.

On the other hand, Phelan said, "There are a lot of other things that come along that I don't think we should play God on and say, 'Yeah, that's okay, and that's not okay. . . . ' "

One other indication of the changing scene at the NYSE, Phelan acknowledged, has been an increase in arbitration cases brought to the exchange. In 1979, there were 311 cases; in 1984, there were 1,008. The cases represent complaints by customers against brokers, firms battling other firms or brokerage firms acting against brokers.

Growth and volume are responsible at least in part, Phelan said.

"In 1975, we had 25 million individual investors; today, we've got 43 or 44 million individual investors. There are more people in the market and more institutions in the market. . . . In 1977, we were doing 20 million shares a day. We're doing over 100 million today on a daily basis. Other kinds of instruments are coming into play -- CMA cash management accounts, limited partnerships, all of those things that weren't in place in 1977. The universe has grown so vast that it's a wonder that the number of cases isn't five times what it is today."

NYSE officials also note that 70 percent of Big Board trading these days is done by institutions, rather than by small investors.