FHFA Principal Reduction Pilot Program. A bill filed by Sen. Robert Menendez, D-NJ, before Congress left town last month would create a shared-appreciation mortgage program in which banks would reduce the mortgage principal for eligible underwater homeowners. Under the Preserving American Homeownership Act, S. 2854, the pilot programs – to be established by the Federal Housing Finance Agency and the FHA – would entitle banks to a portion of the increased value of the home when the market improves.