Tesla CEO Elon Musk's plan for a new political party prompted an analyst to recommend Tesla's board board create new "ground rules" to keep Musk focused on Tesla's future.

Mr. Musk’s involvement in politics and his financial support for the president’s campaign were 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.