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Bats Global Markets and Direct Edge Holdings have agreed to merge, uniting two of the biggest American stock exchange operators to form the second biggest market, amid a four-year decline in volume.

The third- and fourth-largest equity market owners said the transaction will close in the first half of 2014. Joe Ratterman, chief executive officer of Bats, will keep that role at the combined firm, while Direct Edge CEO William O’Brien will be president. Financial details weren’t disclosed.

Formed by some of the fastest traders on Wall Street, the closely held companies have watched volume dry up in the U.S., cutting profits at the proprietary trading firms they count among their biggest customers. Shares changing hands on all U.S. exchanges have fallen 36 percent since 2009 to 6.3 billion shares a day in 2013, and profits for high-frequency traders slipped 80 percent, according to data compiled by Bloomberg and Rosenblatt Securities Inc.

“Volume is weak,” said Dan Veru, the chief investment officer who helps oversee $4.5 billion at Palisade Capital Management. “That’s been the trend going on for quite some time. So unless you have real scale, it’s difficult to compete. Mergers like this probably create some scale.”

The companies’ four exchanges will keep operating, using Bats’ technology, according to a statement. The combination will be based near Kansas City, Mo. Bats is based in Lenexa, Kansas.

Bats, an acronym for Better Alternative Trading System, started trading in 2006, aiming to match the existing exchanges on speed and beat them on prices. Seven years later, the firm’s daily average U.S. equity market share is about 10 percent, according to data from Tabb Group. That compares with averages of 23 percent at NYSE Euronext and 18 percent at Nasdaq OMX Group Inc. Direct Edge has about 11 percent, Tabb said.

The deal comes as IntercontinentalExchange Inc. prepares to complete the acquisition of NYSE Euronext, which owns the New York Stock Exchange, the oldest U.S. bourse.

Combining Bats and Direct Edge, based in Jersey City, N.J., would make them the second-biggest market by volume.

Bats, which tried and failed to go public last year, was founded in 2005 by high-frequency trader Dave Cummings of Tradebot Systems. Along with Direct Edge, Bats helped dismantle the duopoly on American stocks that was enjoyed by the New York Stock Exchange and the Nasdaq Stock Market.

“When Cummings set up Bats, it was really in response to the New York and Nasdaq having a dominant stranglehold on the equity trading market,” said Larry Tabb, chief executive officer of the Tabb Group in New York. “But time moves on, order flows declined; it’s gotten much more competitive.”