Private-equity firms such as Pershing Square Capital Management and Fairholme Funds are gobbling up the common and preferred shares of Fannie Mae and Freddie Mac, a trend that may continue as long as the two stay profitable and Congress dithers with how to end their conservatorships. “There’s some value there,” said Brian Harris, a senior analyst with Moody’s Investors Service. “The hedge funds believe the two will continue to earn money.” Industry observers who closely follow the government-sponsored enterprises predict...