Shares of Fannie and Freddie were down more than 10% in recent action, while the preferred shares were also taking a hit. Representatives for both firms didn't immediately return calls for comment on Monday morning.
"Fannie Mae and Freddie Mac have been at the heart of the U.S. housing boom, bust and recovery," KBW said. "As the mortgage market moves away from crisis mode, the future of the GSEs has to be addressed."
The pair plays a key role in the nation's housing market because they buy mortgages from lenders and bundle them up into securities, and guarantee payment. They also provide liquidity to the secondary mortgage market.
"There have been many recommendations made about potential structures for the GSEs," KBW said.
"The most noteworthy is the Government Accountability Office report which presents options for the companies ranging from becoming full government entities to returning to being stock-holder corporations," the analysts noted. "What all the recommendations to date have not done -- including the ones in the GAO reports -- in our view is address the most crucial issue regarding the agencies: how to recapitalize them."
Fannie and Freddie accounted for 68% of all mortgage originations in 2009 as they stepped in to provide credit during the lending crunch, according to KBW.
Fannie and Freddie are being hit by ongoing mortgage losses and higher borrowing costs during the housing downturn. Fannie reported a second-quarter loss of nearly $15 billion, after it lost more than $20 billion in the first quarter.
"Under such an approach, the banks that originate an agency conforming loan would be required to retain 5% of the loan balance as an equity investment in either Fannie Mae or Freddie Mac," KBW said. "Thus the new agencies would be recapitalized at a solid 5% level of the new expanded balance sheets."
This level of capital "would allow the government to phase out an explicit guarantee of the new agencies' debt over time," George wrote. "We would expect the government to initially guarantee the debt of the new agencies for a period, possibly up to five years, in order to establish the credibility of the new agencies."
In September 2008, Fannie and Freddie were placed into the conservatorship of the Federal Housing Finance Agency. With the financial system seemingly past the worst of the crisis, speculation on what the government should do with the GSEs has been ramping up.
A decline in the preferred stock of Fannie and Freddie would be a blow to banks that hold the shares, and could further stress the banking system.