Fannie Mae and Freddie Mac could be required to maintain nearly $200 billion in capital if they are ever released from the government’s hands, the regulator of the two bailed-out mortgage giants indicated Tuesday.

The Federal Housing Finance Agency, responsible for regulating the two businesses, issued a proposed capital rule that would require Fannie and Freddie to maintain a combined $181 billion in risk-based capital, a buffer that would allow them to sustain losses without becoming insolvent.