"We just don't sleep well unless we owe people a lot of money," said a smiling and relaxed William Salomon, who last Friday stepped down as the managing partner of Salomon Brothers after 15 years at the helm of Wall Street's largest and most profitable privately held securities firm.

Salomon, 64, was referring to his firm's reputation as The Street's preeminent trader - always willing to step up and take a position, regardless of risk, buying and selling from its huge, mainly bank-financed inventory of stocks and bonds that daily averages in the billions of dollars.

Under Salomon - son of one of the three founding brothers - the firm has meanwhile transcended its reputation as a trader and primarily a "bond house," and has moved aggressively to the forefront of the securities business in a variety of other areas, from international finance to corporate underwritings.

"You have nothing to sell unless you buy something," said Salomon, explaining the firm's philosophy." So we're always desirous to be in there, even if the issue turns out to be a dud. You still maintain contact with your customers. You might lose out on the one hand, but you make it up on the other hand."

In fact, Salomon for the first six months of this year led all firms in domestic securities underwritings, according to the tabulation by Institutional Investor Magazine, edging out arch rivals Morgan Stanley and Merrill Lynch for the first time.

In the international arena, it competes on the same plane as the very largest European and U.S. banks. And it is among a handful of firms that advises the Saudi Arabian monetary agency.

Dealing exclusively with institutional customers, corporations and governments, Salomon is unique in many ways among Wall Street firms.

It recognized early the benefit of strong capitalization, keeping extremely strict rules on with drawal of capital from the firm. This has allowed it to grow rapidly without the need for the big mergers that have characterized The Street in the last decade.

Today, Salomon's partner capital of about $200 million puts it second only to Merrill Lynch, which is publicly owned and has huge equity base exceeding $600 million.

Salomon's profitability is also legendary, with only one loss year since 1960, despite some miserable years for the markets. Last year pretax profits came to $53 million. For the fiscal year just ended on September 30, profits are expected to be down because of higher interest rates and carrying charges.

But what perhaps characterizes Salomon more distinctly than any other quality is its willingness to take risks on behalf of customers, to do the difficult and what sometimes seems the impossible, and to not only carry it off successfully, but to profit handsomely in the process.

Salomon, who almost everyone calls Billy, said the firm's ability to pursue such an aggressive policy without at the same time occasionally courting disaster results from the fact "the professionals in the firm have great judgment about values and reading the future of the market."

John Gutfreund, 48, who succeeds Salomon as the firm's managing partner, recalled one particularly memorable situation when he was manager of the syndicate department.

It was in November 1962, and the day after the U.S. and the Soviet Union went almost to the brink of nuclear war over Cuban nissile crisis.

American Telephone and Telegraph Co. was coming to market with a $250 million bond offering - huge at that time - and the markets were still extremely nervous and uncertain. There was talk about whether a competitive offering was even possible.

"Being the pragmatists and realists that we are, we decided that if the world was going to continue as we knew it, AT and T and its securities would probably be fundible," said Gutfruend.

"And because of the extreme uncertainties in the market, it was an opportunity to buy these bonds a little cheaper than one might. So we took $25 million, which for us at the time was an outsize commitment and a forceful posture, feeling this was a very prudent opportunity." Which is exactly what it turned out to be.

More recently, Salomon had proven its mettle by sticking with New York's Municipal Assistance Corp. after all other underwriters deserted it. The form helped the State of Massachusetts pull off a $500 million debt refinancing that saved it from fiscal chaos. And it single-handedly helped Geico recapitalize itself when the Washington-based insurance company was teetering on the brink of bankruptcy.

This year, Salomon represented the Hong Kong and Shanghai Banking Corp., helping it to gain its 51 percent stake in Marine Midland, in one of the most dramatic financial investments of 1978.

The firm started in 1910 when Arthur, Herbert and Percy Salomon left their father's money-brokerage business and combined with Morton Hutzler, a member of the New York Stock Exchange, to form Solomon Brothers & Hutzler. By the late 1920s, Salomon had already become a prominent bond house.

In the 1930s the firm found a big opportunity when other Wall Street investment bankers protested the Securities Act of 1933 with what was in effect an underwriters strike. And Salomon moved into the vaccuum.

In the 1950s, the firm had its only serious brush with financial difficulties. After the head of the firm, Rudolf Smutny, had locked the firm into portfolio of hard-to trade foreign securities, drastically reducing the firm's capital, he was thrown out in a palace revolt.

Salomon (son of Percy) who started with firm straight out of prep school and took over as the managing partner in 1963, said that the firm's policy since that incident has been to stick to liquid securities. And it follows an extremely conservative policy in valuing its inventory, estimating it at liquidation value so it always knows where its stands.

"Any change in the market, and we mark everything down to where we think we can sell it, or just down to the market price," said Salomon.

As for the future, Salomon, who will remain as a limited partner with the firm, feels that it can thrive under almost any market environment.

"We think that with the team that we have, and the capital that we've accumulated, that we will not only be able to be competitive, but we'll be able to survive and prosper under any circumstances, short of a cessation of trading because of a war," he said.