WASHINGTON — The Federal Reserve Board on Tuesday approved the application of the boutique investment firm Friedman, Billings, Ramsey Group Inc. to become a bank holding company with the acquisition of Money Management Associates of Bethesda, Md., and its subsidiary, FBR National Bank.

The Fed approved a simultaneous application by Friedman Billings to become a financial holding company for banks, insurance firms, and securities companies.

The deal for the $26.4 million-asset bank, which is about one-tenth the size of Friedman Billings, furthers the Arlington, Va., firm’s plan to diversify.

In an interview last year, Webb Hayes, head of the private-client group at Friedman Billings, said that achieving a “well rounded” structure at his company would require “commercial banking powers and fiduciary powers.”

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