Elon Musk says he has formed a new political party called the America Party. But it remains unclear what formal steps, if any, he has taken to establish it.

Mr. Musk’s involvement in politics and his financial support for the president’s campaign was once seen by investors as a benefit to Tesla, fueling a steep rise in company shares after the election last year. That association has now turned into a liability. Tesla shares are down 40 percent from their peak in December.