David Einhorn is betting against one corporate stalwart and on another.

The head of Greenlight Capital said Wednesday he is short Caterpillar and long GM as the former faces a decline in some of its core businesses and the latter tightens its belt and faces a stronger future.

"While analysts are projecting a recovery in 2017 and 2018, we don't think CAT has yet hit bottom," Einhorn said at the Sohn Investment Conference in New York.

Caterpillar faces challenges from a boom-and-bust cycle in mining as well as a slowdown in China and drop in energy exploration revenues. He said the company also faces a significant sales headwind from idled equipment.

Caterpillar's stock is likely to trade at half its current value as the variables play out.

As for , he said the company has done a solid job in cutting costs and channeling its focus.

"GM is now focused on four brands: Chevy, Cadillac, GMC and Buick, and is financially healthy and thriving," he said.

GM is trading at too low a multiple while Caterpillar is too expensive, Einhorn added.

"The reality is we're at much closer to mid-cycle for both companies than we are a peak or trough, and investors are assigning the wrong multiple to both companies," he said.

Caterpillar was off 1.5 percent in after-hours trading while GM rose 1.3 percent.