Having spent millions of dollars to launch mutual funds, bankers are beginning to ask how much they have to bring in to make the business pay off.

One thing is clear, according to industry experts: only a few banks have reached the turning point, known as "critical mass," at which mutual funds can become profitable.

Neil Bathon, president of Chicago-based Financial Research Corp. estimates that of the 115 banks and thrifts that now manage proprietary funds, only about 20% are in the black.

But defining critical mass is another matter entirely.

An influential study last year by Goldman Sachs & Co. concluded that it takes $10 billion of assets for a mutual fund family to turn a profit. Mr. Bathon and other consultants peg the figure at $1 billion. Still other analysts say the answer lies somewhere in between.

Why are the estimates all over the lot? For on thing, Mr. Bathon says, much depends on how a bank positions its funds.

"I don't feel you need to have $10 billion in assets to be profitable, unless your marketing focus is that you're playing with the big boys," he explained. At that point, a bank would have to spend more on advertising, marketing, and distribution to compete with major mutual fund companies, he said.

Nevertheless, some bankers suspect the threshold is creeping higher all the time.

Chase Manhattan Corp.'s Vista funds "turned the corner on profit in the summer of 1993; we reached $4 billion," said Jeffrey S. Hartman, financial controller for Vista Capital Management.

Since then, though, the industry has changed, he said, and now banks need to offer more bells and whistles, such as ways to pay sales loads, to compete. That has boosted the profitability point closer to $6 billion, he said.

"Each time you add a share class, it raises your costs $45,000 to $50,000 per fund, per year - in pure expenses," Mr. Hartman said.

Between the increases in audit staffs to deal with compliance issues, printing costs, and marketing costs, "it's becoming a very expensive business," said Debra McGinty-Poteet, managing director of Bank of America Funds Management, a unit of San Francisco-based BankAmerica Corp.

Most bankers reject simple formulas for profitability.

For Bank of Boston, "getting to $1 billion was the magic number," said Allen W. Croessmann, the bank's mutual funds director.

But breaking into the black also meant "making sure our money market funds were in the $200-million-to-$250-million range, our stock funds were in the $35-million-to-$50-million range, and bond funds were in the $70- million-to-$75-million range," he said.

Even on this score, however, the consultants disagree.

For instance, while Mr. Bathon believes bond mutual funds need at least $75 million to break out of the red, Kurt Cerulli, principal of Cerulli Associates in Boston, puts the figure at $150 million. And while Mr. Bathon said money market funds can be run profitably at $50 million, Mr. Cerulli sees the break-even point at $300 million.

Many bankers think they can reach critical mass at a lower point than mutual fund companies, because some costs of running fund complexes are already covered.

For example, "Banks don't have a high cost of distribution," since they sell funds through branches, said Eric M. Rubin, managing director for mutual funds at Columbus, Ohio-based Banc One Corp.'s Investment Advisors unit.

Another key factor is a bank's ability to provide trust, custody, administration, and other services for its own funds.

Banks that handle such tasks themselves, "can make money with a couple of billion in assets" in a fund complex, said BankAmerica's Ms. McGinty- Poteet.

Whether managing a fund family makes sense depends on what a bank is trying to achieve, said Ronald M. Petnuch, director of bank proprietary funds management for Federated Investors, Pittsburgh. Banks that want to compete on a national scale need their fund complex to have several billion dollars to compete, he said.

Nevertheless, Mr. Petnuch said, many of Federated's customers "are making money and don't have $10 billion."

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