(Adds detail and context) By Pete Schroeder WASHINGTON, Feb 3 () – The U.S. housing finance regulator has selected investment bank Houlihan Lokey Capital Inc as its financial adviser for a potential overhaul of Fannie Mae and Freddie Mac. The Federal Housing Finance Agency said in a statement Monday that Houlihan Lokey will advise on how the mortgage finance giants could be rebuilt into fully private companies. The firm will be paid up to $45 million in fees over 5.5 years. Houlihan Lokey will advise on “business and capital structures, market impacts and timing, and available capital raising alternatives,” the FHFA said. The selection of a financial adviser was seen as a critical step in any effort to return Fannie and Freddie to the private market, after operating under a government conservatorship since being bailed out in 2008. The FHFA’s director, Mark Calabria, previously had said he wanted the FHFA to hire an adviser before Fannie and Freddie hired their own to avoid a conflict. The Trump administration has said it is a priority to recapitalize the pair, which guarantee over half of the nation’s mortgages, and remove them from their government lifeline. Calabria said in a statement that he planned to release a new capital rule for the companies in the “near future.” The regulator will pay Houlihan $9 million for the first year of work, with options to extend the relationship for four and a half more years and up to $45 million more in fees. (Reporting by Pete Schroeder Editing by Chris Reese and Leslie Adler)Our Standards:The Thomson Trust Principles.