Bill Ackman’s Pershing Square Capital Management picked up stakes of nearly 10% apiece in the companies, a pair of Friday morning regulatory filings show. Pershing just disclosed a stake of more than 115 million shares in Federal National Mortgage Association(FNMA) and another 63.5 million in Federal Home Loan Mortgage Corp. (FMCC).

This comes two days after Bruce Berkowitz’s Fairholme Capital Management LLC said it would like to buy parts of the bailed-out mortgage-finance giants in a letter to regulators.

The pair of stocks have soared this year: Fannie is ahead by more than 1,200% during 2013 and Freddie by more than 1,100%. The pair are ahead by more than 10% in Friday morning trading.

The WSJ’s look at Fairholme highlighted the difficult road ahead for investors in the companies. “DeMarco” is Edward DeMarco, acting director of the Federal Housing Finance Agency:

The proposal argues that new legislation wouldn’t be needed but would require something else: a partner in the U.S. Treasury and the FHFA. Senior officials at both agencies have said in the past that such a recapitalization is a nonstarter.

Last month, Mr. DeMarco said it would be a mistake to assume that Fannie and Freddie’s recent profitability meant that the problems that resulted in their takeovers have been fixed. “Some people are forgetting a little history,” he told reporters.

Meanwhile, the White House has been working closely in recent months with leaders of the Senate Banking Committee, who are crafting a bill to overhaul the nation’s mortgage market by replacing Fannie and Freddie with new mortgage guarantors.