If it can be assumed that in the mutual fund business bigger is usually better, then last year appears to have been pretty good for banks that manage their own funds.

Total assets in bank-managed mutual funds rose 42% to $305.5 billion, according to Lipper Analytical Services Inc., a Summit, N.J., research firm.

Not bad, given that total mutual fund assets rose only 4% last year, to $2.16 trillion. This means that banks control more than $1 out of every $7 in mutual funds.

But look closer, and the picture isn't so rosy.

Strip out Mellon Bank Corp.'s acquisition of the $67.5 billion Dreyfus family, First Union Corp.'s purchase of the $3.1 billion Evergreen funds, and Fleet Financial Group Inc.'s purchase of the $639 million IBM funds, and bank-managed mutual fund assets grew very little in 1994.

Go further, and exclude so-called trust fund conversions - in which pooled trust investment funds are merged into mutual funds - and bank- managed fund assets were actually flat to slightly down, said A. Michael Lipper, president of the research firm.

Admittedly, last year was not the best of times for mutual funds.

According to the Investment Company Institute, while sales of stock funds rose a healthy $144 billion in 1994, bond fund sales shriveled to a mere $15.4 billion, stunned by rising interest rates.

Bank-managed mutual funds shared in these capital flows, according to Strategic Insight, a New York research firm.

The only major difference was in money market funds, where bank funds fared worse than the industry, stung by redemptions by institutional investors.

Mr. Lipper said he reads in the data signs that banks are finding it difficult to attract new investors and to keep them.

"I think they have to do a better job of the quality of their sales, so they keep assets on the books longer," he said.

But many of the bankers involved in running mutual funds say they see nothing but potential.

Among them is Joseph C. Penko, a vice president with Cleveland-based National City Corp.

National City's NCC Funds, which Mr. Penko administers, last year gained $330 million of assets, according to Lipper. Mr. Penko said about $300 million of this came from trust fund conversions, which means that new sales were modest.

But Mr. Penko explained that National City is doing the yeoman's work of making the NCC funds available through its trust units.

Once a retail sales push through National City's brokerage affiliate begins in the second quarter, the NCC funds could become sizable asset gatherers, Mr. Penko said.

The trick is convincing mutual fund investors that National City's trust-related investing expertise is transferable to mutual funds.

"The competition for assets is pretty fierce," Mr. Penko acknowledged.

"But we've been one of the premier trust banking organizations for a long time," he added.

Even officials at Mellon, the banking industry's largest mutual fund manager, say they are optimistic. They stick to this belief even though the combined mutual fund assets of Mellon and Dreyfus finished the year $10 billion below 1993's levels, the banking company has been criticized in some quarters for paying too much for Dreyfus, and some key officials have left amid rumors of a culture clash.

"We're very pleased with where we stand," said Steven Elliott, a Mellon vice chairman and chief financial officer.

He argued that the Mellon and Dreyfus cultures actually meshed well, and that the loss of assets was due to market vagaries, not management problems.

"From all my experience in M&A, this is by far one of the smoothest ones I've been in," he said.

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