Thirteen of the nation's largest banks have agreed to pay a combined $337 million to settle a lawsuit by the Pennsylvania Treasury Department and a contingent of government agencies and pensions funds claiming that they had conspired to fix the price of bonds issued by Fannie Mae, Freddie Mac and other government-sponsored entities.

If approved, it would bring total settlements in the private antitrust litigation to $386.5 million, following previous agreements with three other banks.

On Tuesday, Pennsylvania Treasurer Joe Torsella announced the proposed settlement, which has been filed in the U.S. District Court for the Southern District of New York. Under the terms of two separate agreements, Barclays Capital Inc., which underwrote most of the Fannie Mae and Freddie Mac bonds, would pay $87 million, and the remaining 12 defendants agreed to a $250 million payment to the plaintiffs.

All 13 banks, Torsella said, had also agreed to a series of antitrust reforms, including enhanced training, oversight and a compliance program subject to periodic assessment by the state treasury department.

"In addition to a financial recovery, my focus in this case has been and remains reforming the government-sponsored entity bond market, to which most public investors are exposed, so that this conduct is not only corrected, but that it is prevented," Torsella said in a statement.

"As a result, some of the largest banks in the nation—for the first time—will implement strong antitrust compliance measures to do just that."

The proposed settlement must still be approved by U.S. District Judge Jed. S. Rakoff, who has been overseeing the case in Manhattan.

Filed in March, the lawsuit accused 16 prominent financial institutions of colluding to fix prices of Fannie Mae and Freddie Mac bonds between 2009 and 2016, and cited more than a dozen online chatrooms traders used to set artificial prices before bringing the bonds to market.

Torsella, who was named class representative earlier this year, also decried a pervasive lack of oversight at the financial institutions, which allowed for violations of U.S. antitrust law. In addition to monetary recovery, Torsella sought structural reforms to prevent anti-competitive conduct in the future.

"The allegations in this case were preventable from the start. If the proper safeguards were in place at these banks, we wouldn't need to be here knocking the door down on behalf of investors who were harmed by the banks' conduct," he said.

In a court filing late Monday, Torsella said the preliminary settlement was in line with earlier court-approved agreements to resolve claims against Deutsche Bank, FTN and Goldman Sachs. Each of the 13 banks would be required to implement compliance programs consistent with principles drafted by the Pennsylvania Treasury, and would have to meet annually with department officials, starting two years after the settlement goes into effect.

The banks have all denied any wrongdoing.

The 12 banks responsible for the $250 million payment under the proposed settlements include BNP Paribas, Cantor Fitzgerald, Citigroup, Credit Suisse, HSBC, JPMorgan, Merrill Lynch, Pierce, Fenner & Smith, Morgan Stanley, Nomura, Societe Generale, TD Securities and UBS.

The case is captioned In re GSE Bonds Antitrust Litigation.

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