Fannie Mae (FNMA) and Freddie Mac (FMCC) shares each jumped 43% Wednesday, the most in three years, after President-elect Donald Trump's nominee for Treasury secretary, Steven Mnuchin, said the two government-backed mortgage-finance companies should be privatized.

Fannie surged to $4.39 in the biggest increase since 2013, while Freddie climbed to $4.29.

Mnuchin, a former Goldman Sachs partner who was one of Trump's most vocal supporters during the campaign, told Fox Business Wednesday that the two companies displace private lenders in the mortgage market and should be restructured so they're not wards of the government but still strong enough to avoid future bailouts. The plan is among the incoming Trump administration's top 10 priorities and will be done "reasonably fast," Mnuchin said.

"We've got to get Fannie and Freddie out of government ownership," Mnuchin said. "It makes no sense that these are owned by the government and have been controlled by the government for as long as they have."

Regulators took control of the two mortgage-finance companies in 2008, when the souring housing market saddled them with steep losses, rattling investor confidence. In 2012, the companies were directed to pay essentially all of their net income to the Treasury Department, instead of the fixed-rate 10% dividend stipulated originally.

"We will make sure that when they are restructured, they are absolutely safe and don't get taken over again," Mnuchin said.

The plan could put the Trump administration at odds with many Republican lawmakers, including representatives on the influential House Financial Services Committee, who have opposed privatizing the companies. Concerns include the possibility that 30-year fixed-rate mortgages, popular with home buyers, might become unaffordable.

"We have trouble seeing the new White House wanting to get into such an ideological fight with its own party," Jaret Seiberg, an analyst at Cowen Washington Research Group. "This would suggest to us that a quick deal for Fannie and Freddie is unlikely."

Even conservative analysts who favor reducing the role of Fannie and Freddie acknowledge Trump would face bipartisan opposition to privatization. 

"Members of Congress are cowards and they have a heavy bias for the status quo," Mark Calabria, director of financial research at the Cato institute. "I think the fears are unfounded but they believe those fears are real."

Budget overseers also may be reluctant to forgo the revenue they get from the mortgage companies, said Don Lamson, a former regulator at the Office of the Comptroller of the Currency. He doesn't expect Fannie Mae and Freddie Mac to be privatized anytime soon.

"Unless and until they start losing money for the government, it is not going to happen," Lamson said. "They are money makers for the government."

Under some scenarios, Fannie could be worth at least $10 a share as an independent company, almost triple the current level, according to Richard Bove, an analyst at Rafferty Capital Markets.

That's assuming the U.S. government determines it has been fully paid back on its $117 billion investment in the company, Bove said. He estimates that the Treasury has already received $154 billion in dividends and other payments, in addition to holding stock warrants in the company currently worth $18 billion to $19 billion.

The government could keep about half of the profit and still leave Fannie with about $25 billion of capital, enough to support itself as a stand-alone company, Bove said.

"You're looking at the government walking away with the biggest profit on anything it's every done," Bove said.

As a private company, Fannie would have earnings of about $1.60 a share, Bove estimated. Assuming a price-to-earnings multiple of seven or eight, the shares should be worth at least $10 each, he said.

"There are 95 different ways to go about doing this," Bove said. "So I'm not going to tell you that's the be-all, end-all solution, but that's one way of thinking about why this thing is so valuable."