Banks have some ground to make up in the growing on-line trading business, equity analysts say.

The two banks that have gained market share in securities trading on the Internet-Fleet Financial Group and Toronto-Dominion Bank-have done so only through acquisitions. Banks that have developed Internet brokerage internally barely register on the radar screen, according to two second- quarter reports released last week.

Boston-based Fleet entered the market this year when it bought the discount broker Quick & Reilly; Toronto-Dominion did so in 1996 through its purchase of Waterhouse Investor Services.

The rest of the banking community has been less aggressive.

"A lot of banks are under the impression that they can just set up their on-line site and then they're in business," said Bill Burnham, a senior analyst with Credit Suisse First Boston in San Francisco. But they fail to follow the launch with sufficient advertising, he said.

"The only one that I've ever seeing advertising is Citibank," said Stephen Franco, a senior analyst at Piper Jaffray Inc. in Minneapolis. However, Mr. Franco did not include Citibank or any other retail bank in his second-quarter findings on the on-line industry.

Mr. Burnham did include Citibank, along with First Chicago NBD Corp., among institutions that offer on-line trading service but lack sufficient market share to be singled out. That group constitutes 13.6% of the market.

Mr. Burnham said that for banks to succeed as players, they must go outside for the necessary technology.

"They've got to think about partnering with someone else, like an E- Trade," he said.

The two analysts concurred on Waterhouse's second-quarter performance, but they differed somewhat on the position held by Quick & Reilly.

Both said New York-based Waterhouse held roughly 9% of the on-line market at the end of the second quarter. However, Mr. Franco's study showed Quick & Reilly with 5% of the market after the first half; Mr. Burnham put the figure at 4.2%.

They also differed about whether Quick & Reilly had gained or lost market share in the second quarter. Mr. Franco said it had gained, from 4% in the first quarter, because more of its customers were accessing their accounts over the Internet. But Mr. Burnham saw a decline, from 4.4% in the first quarter.

Both analysts said Quick & Reilly has reduced its marketing expenditure in recent months to promote its affiliate SureTrade, the no-frills deep discounter it launched last November.

"SureTrade is spending something like $20 million on advertising," Mr. Franco said.

He said SureTrade, which averages about 135,000 trades a day-half of them active-controls 3% of the market. Mr. Burnham would not break out numbers for SureTrade, but he described the firm as "a good product" with "good positioning within Quick & Reilly."

SureTrade has received substantial funds in recent months, but the bank is not neglecting Quick & Reilly, said a spokesman for Quick & Reilly/Fleet Securities Inc.

Fleet is working on linking Quick & Reilly's QuickWay Net trading service with Fleet's Internet banking service, launched last month, the spokesman said. That link should be up by the end of the first quarter of 1999, he said.

Both analysts said the industry continues to grow rapidly. Mr. Burnham said total trading volume grew by 17% compared with the first quarter.

Mr. Franco's report said that 22% of all retail trades during the first half were conducted on-line.

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