The head of the agency that regulates Fannie Mae and Freddie Mac said Tuesday that interest rates on U.S. mortgages have further to fall and that a reduction of up to 1 percentage point would be reasonable based on historical data.

"Certainly one would think another 50 basis points easily and maybe a hundred," James Lockhart, the director of the Federal Housing Finance Agency, said during an interview on CNBC. Mortgage-backed securities issued by Fannie and Freddie largely determine a mortgage's interest rate. "You could see [those] rates are significantly higher than Treasuries, so … they could come down."

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