Federal Reserve Board Chairman Ben Bernanke said that U.S. housing policy, with its reliance on Fannie Mae and Freddie Mac, is "not sustainable."

Today, the two GSEs provide liquidity to 70% of the residential mortgage market with the FHA accounting for most of the balance.

The Fed chief, testifying before the House Financial Services Committee in his second round of hearings this week, said it was crucial to find a solution to the problems of the troubled mortgage giants, which were placed into conservatorship in September 2008.

Both GSEs continue to lose money and have required $140 billion of taxpayer money to keep their capital positions in the black.

Bernanke suggested two ways the Obama administration could unwind the government's commitment to both companies: break up the privatized entities or transform them into government utilities, similar to Ginnie Mae.

As they stand today, Bernanke joked, both companies are "half-fowl, half-horse." He added: "This is something we need to take on soon."

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