The Fed became one of the world’s largest mortgage investors because no one else was interested. During the fall 2008 financial crisis, investors stopped buying the mortgage securities issued by the housing finance companies Fannie Mae and Freddie Mac. The two companies buy mortgages made by banks and other lenders, providing money for new rounds of lending, then package those loans into securities for sale to investors, replenishing their own coffers.

Two days before Thanksgiving 2008, the Fed announced that it would buy $500 billion in securities issued by the two companies. By the time the program wound down in March 2010, it had spent more than twice that amount. The central bank now owns mortgage securities with a face value of $1.1 trillion.

A wide range of economists say the Fed’s program  so big that purchases outstripped the issuance of new securities in some months  helped to preserve the availability of mortgage loans and helped to hold interest rates near record lows. Rates that exceeded 6 percent in late 2008 remain below 5 percent today.

But the Fed now must deal with the cleanup.

The central bank could hold the securities until the borrowers repaid or refinanced their loans. Brian P. Sack, an executive at the Federal Reserve Bank of New York, estimated in March that borrowers would repay $200 billion by the end of 2011. And in the meantime, the Fed is collecting regular interest payments.

“We’ve been earning a fairly high income from our holdings and remitting that to the Treasury,” Mr. Bernanke told Congress on Wednesday.

But holding the securities could make it harder to control inflation as the economic recovery gains strength, said Vincent Reinhart, the former head of the Fed’s monetary policy division, now a resident scholar at the American Enterprise Institute.

The Fed bought the securities by pumping new money into the economy, stimulating growth. It could be difficult to reverse that effect without draining the money from the economy by selling the securities, Mr. Reinhart said.