Treasury holds $188.5 billion in senior preferred shares in the two companies, representing the amount of aid they have drawn from taxpayers to stay afloat. The companies have sent back $65.2 billion in dividends, which count as a return on the government’s investment and not as a repayment. Treasury also holds warrants to purchase nearly 80 percent of the companies’ outstanding common stock.

Under the bailout’s terms, there’s no mechanism for the enterprises to exit conservatorship. Neither Fannie Mae nor Freddie Mac can build capital because Treasury takes virtually all of their quarterly profits.

Holders of the rest of the preferred shares as well as common shares were widely presumed to have been wiped out when the government took over. The companies’ return to profitability has created renewed enthusiasm for the enterprises’ securities.

Hedge funds don’t publicly disclose their holdings of Fannie Mae and Freddie Mac securities. Claren Road and Perry Capital hold preferred shares, according to investors in the funds.

Taxpayer Profit

Fannie Mae’s preferred and common shares spiked after the company reported record earnings of $17.2 billion for 2012 on April 2. Common shares closed yesterday at 83 cents, giving the company a market capitalization of $4.8 billion, up from $1.5 billion at the end of 2012, according to data compiled by Bloomberg.

If the housing market continues to improve, and Fannie Mae and Freddie Mac remain in conservatorship for the next 10 years, taxpayers would come out ahead by $50 billion, White House budget analysts have projected.

Hedge fund lobbyists are arriving at Capitol Hill meetings with detailed financial analyses contending that selling off the government’s shares and recapitalizing the companies could make taxpayers an even larger profit, the people said. That also would boost chances that investors in preferred shares would benefit. The funds are making it clear they would be interested in buying the shares now held by Treasury, the people said.

Millstein Plan

The funds’ proposal is similar to one being circulated by James Millstein, the former Treasury official who oversaw the restructuring of bailed-out insurer American International Group. Millstein’s multiple-step blueprint calls for selling off the government’s stake, recapitalizing the two mortgage companies and creating a new U.S. agency to reinsure loans. He said his plan could leave taxpayers with $100 billion to $190 billion in profit.