The stock market's phenomenal rise is giving some bankers cause for concern over how to keep customers calm when the market eventually dips.

The anxiety comes as many banks have shifted from selling mostly bond mutual funds to the more risky stock funds amid the longest bull market in 30 years.

At a Monday morning session of the Bank Securities Association's annual conference, bankers squirmed when James Shelton, the trade group's executive director, began by saying the Dow Jones industrial average had tumbled 40 points.

The index was down 60 points by the close.

"None of us can predict where the market will go," said Jack L. Kopnisky, president of Key Investments. "Is it cause for concern? It's cause to take notice."

Many bankers here feared a downturn could prompt customers to walk out on them.

"The biggest danger is the damage to our reputation" as a safe haven for savings, said James Litton, president of $40 million-asset First Mineola Corp., Mineola, Tex.

The association's meetings don't normally attract many bank presidents, but the 68-year-old Mr. Litton decided to drop in because he dispenses most of the bank's investment advice himself.

He's particularly worried about younger customers who want to jump into stock mutual funds right now.

"Watch out for the ones who come in when the market is high," he said. "Those are the people you try to have wait."

Mr. Litton is typical of the bank brokerage executives attending the conference, who in the past few months have been preparing themselves - and their customers - for the day stock prices fall.

But some bank brokerage chiefs played down any apprehension about a market correction.

"If the market does turn - and it will- we're prepared," said KeyCorp's Mr. Kopnisky said.

Last November, the Cleveland-based banking company designed an "educational" kit of marketing materials for investment advisers that sell its proprietary Victory Funds.

The kit, entitled Bear Market Strategies, instructs brokers to tell customers to "maintain goals. Take your time, and don't react too strongly one way or another. Maintain a diversified portfolio."

Customers are also given information about past bond and stock market corrections. "Fluctuations are normal - smart investors maintain a long- term investment outlook," the literature says.

Mr. Kopnisky insisted that KeyCorp, like many other banks, has broadened its product line in an effort to retain business even during downswings. In 1994 the bond market soured and scores of investors pulled out of bond funds - the core product of most bank mutual fund programs.

Still, some bankers said they haven't pushed stock funds enough, insisting that traditionally conservative bank customers are missing out on a good thing.

"We're still trying to get to the point of getting our reps to sell more equity" funds, said Deborah Bernot, president of First Nationwide Bank's brokerage unit.

Two-thirds of the West Sacramento, Calif.-based banking company's total mutual fund sales last year were in fixed income funds.

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