WASHINGTON - Banks that sell mutual funds through a combination of brokers and licensed branch employees see dramatically better results than banks that rely on a single sales force, a study has found.

On average, investment programs that deploy tandem sales forces earn $586 in profits on fund sales for every $1 million of deposits at the bank, according to preliminary results of the study commissioned by the Consumer Bankers Association.

In contrast, banks that only use brokers book average profits of $324 per $1 million of deposits. And those that rely exclusively on customer service representatives with mutual fund sales licenses stand to earn just $11 per $1 million.

The findings, released at the association's investment products conference here, were based on responses from 60 large and small banks that were polled this year about their investment sales programs.

The banks were asked by Kenneth Kehrer Associates, Princeton, N.J., to supply information on sales in the 12 months through last June.

How best to structure an investment products sales force is a nettlesome issue for banks. Many have relied solely on one group - brokers or licensed customer service representatives - because they feared turf wars erupting between two sales groups, industry analysts said.

First Union Corp., however, was not put off by potential territorial disputes and has been licensing more than 1,000 customer service representatives to work with brokers, said Richard K. Wagoner, executive vice president at the Charlotte, N.C., bank company.

Mr. Wagoner sees the new study as further justification for the bank's efforts to field two sales forces. The licensed branch employees provide "leverage" to the existing brokerage sales effort, he said.

"You'd be surprised at how many of these (customer service people) are finding out they can sell. They're doing a great job."

Not every bank has had that kind of success. First Chicago Corp. recently scrapped its platform sales program after less than a year, said Richard A. Davies, president of the Chicago bank company's brokerage.

The effort, in which 100 customer service representatives supplemented the efforts of 58 brokers, failed primarily because of the market's prolonged slump and internal issues over management of the new sales group, Mr. Davies said.

First Chicago does not envision redeploying customer service employees when the market firms up, Mr. Davies said.

Full-service brokers, with the expertise and hand-holding they provide customers, "will probably better take you through the different market cycles," he said.

The study also found that brokers do better when they are given broad information about other products and services, like loans and deposit accounts, that customers receive from the bank.

Brokers produce $946 in sales for every $1 million in bank retail deposits when this information is supplied, versus $739 in sales when the data is not, the study found.

Brokers are better able to determine customers' needs when they have "a fuller picture" of the customers' financial condition, Mr. Kehrer said.

Conversely, brokers do not sell measurably more when they are given lists of maturing certificates of deposit. Just 14.5% of CD dollars are rolled into mutual funds when the lists are mined, the study said.

The study also found:

*The average bank broker sold $4.5 million of investment products and generated $202,400 of commissions.

*The average customer service representative sold $394,000 of mutual funds.

*77% of banks paid tellers for referrals in 1994, down from 84% in 1993.

*Half of the banks require follow-up with customers to test their understanding of the investment products they purchased. Only 29% of banks had this requirement in 1993.

*The average broker covers five branches, or a retail deposit base of $213 million.

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