Any effort in the U.S. to ban or limit proprietary trading by big financial firms should be based on the volume of trades, not the motive behind them, a leading Democrat on market regulation said Friday.

Rep. Barney Frank (D., Mass.), chairman of the House of Representatives Financial Services Committee, told CNBC in an interview that the "Volcker rule" should be implemented using a standard contained in the financial-regulatory reform bill the House passed in December. The Senate is considering legislation introduced by Frank's counterpart, Sen. Christopher Dodd (D., Conn.), but it's unclear how restrictions on big firms' trading their own books would be handled.

"When you ban proprietary trading, you're saying that certain activities a bank conducts are OK if they're doing them on behalf of a client, not if they're doing them for their own account," Frank said. "If you are looking at a bank that has a very high volume, or very volatile trades, that's almost certainly not being done for the customers."

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