A proposal by President Donald Trump to privatize Fannie Mae and Freddie Mac after almost two decades under government control has the mortgage companies' stock prices leaping to their highest levels in 16 years.

Shares of Fannie were up 37% at 1:39 p.m. in New York, while Freddie climbed 35%, both on very heavy volume. It was their best performances since December, pushing them higher than they've been since the housing crash in August 2008. Earlier, Fannie peaked at a 46% gain, while Freddie topped out at 34%.

While investors are enthusiastic about the plan, it will be tricky to pull off. Trump floated the idea in his first term, with Treasury Secretary Steven Mnuchin taking the lead, but ran into resistance over fears that any move to change their status as government-sponsored enterprises, or GSEs, would disrupt the mortgage market.