Sen. Mike Crapo (R-Idaho), chairman of the Senate Banking Committee, released an outline Friday for restructuring mortgage giants Fannie Mae and Freddie Mac. (Bill O'Leary)

A decade after Fannie Mae and Freddie Mac were placed under government control, a key Senate Republican on Friday proposed allowing them to once again be private companies.

The proposal by Sen. Mike Crapo (R-Idaho), chairman of the Senate Banking Committee, marks a potentially important turning point in the debate about the futures of the housing finance giants. Fannie Mae and Freddie Mac back more than half the country’s mortgages, and lawmakers have been wary of tinkering with their structure, fearful a wrong move could disrupt the housing market and the availability of 30-year mortgages.

The proposal provides a potential windfall for hedge funds and other investors who have spent years lobbying the White House and Capitol Hill to act on the issue. In particular, Wall Street is vexed that both companies, which received billions in taxpayer bailouts, are sending their profits to the U.S. Treasury rather than shareholders.

“There is a hope that since the government got so much back that they will recapitalize Fannie and Freddie and allow the shareholders to receive what they deserve and what every other shareholder in every other financial enterprise has received,” hedge fund billionaire John Paulson said in a rare interview with the “According to Sources” podcast last month. Shareholders in Fannie Mae and Freddie Mac, himself included, have not received a dividend in 10 years, said Paulson, who is best known for making a $15 billion bet against the housing market and is among President Trump’s biggest supporters on Wall Street. “Shareholders have been absolutely destroyed,” he said.

Fannie Mae and Freddie Mac’s stock prices rose more than 5 percent in the minutes after Crapo released his proposal.

“We must expeditiously fix our flawed housing finance system,” Crapo said in a statement. “My priorities are to establish stronger levels of taxpayer protection, preserve the 30-year fixed rate mortgage, increase competition among mortgage guarantors, and promote access to affordable housing.”

The debate comes at a sensitive time in the U.S. housing market. Home prices and sales have largely recovered from the housing bust. But the market has slowed as mortgage rates have started to rise.

President Trump has nominated Mark A. Calabria, the chief economist for Vice President Pence, to run the government agency overseeing the mortgage giants. Calabria has been a critic of the companies and is widely expected to usher in comprehensive changes if confirmed by the Senate.

Crapo’s proposal leaves some questions about Fannie Mae and Freddie Mac unanswered, including how much capital they would have to hold, and needs to be turned into legislative language. It is also unclear whether there is enough political will to tackle such a complicated issue before the 2020 election when so many efforts have failed. In a statement, Sen. Sherrod Brown (Ohio), the ranking Democrat on the Banking Committee, did not address Crapo’s proposal directly but said he “will fight to ensure that any efforts to reform the housing market start by addressing the affordability crisis that is hurting too many renters and homeowners across this country.

The government seized control of both companies in 2008 as the housing market unraveled, and the firms’ losses piled up. Taxpayers pumped billions into the companies, but over the past few years, Fannie Mae and Freddie Mac have been gathering profits that feed into government coffers. The companies buy mortgages from lenders, then package them into securities to sell to investors.

Over the past decade, they have received $191.4 billion from taxpayers and paid back $285.8 billion in dividends to the U.S. Treasury. Ending government control of the companies is among the last parts of unfinished business from the global financial crisis.

Some lawmakers have advocated for abolishing the companies and allowing the banking sector to take their place. Under Crapo’s proposal, Fannie Mae and Freddie would no longer be protected by taxpayers and its regulator, the Federal Housing Finance Agency, would undergo reforms. The companies could face new competition. The proposal also would establish funds to address affordable housing.

“This is an attempt to do structural reform without the average consumer knowing the difference. Nothing changes for consumers when he or she walks into a bank,” said Ed Mills, a Washington-based policy analyst with Raymond James. But if not done correctly, it could disrupt the market, including raising mortgage rates.

“By keeping Fannie and Freddie around, the plan effectively assures there is no disruption in the government’s support for the mortgage and housing markets — something that might not happen if you try to eliminate them overnight,” said Guy Cecala, the publisher of Inside Mortgage Finance.