Elon Musk, CEO of Tesla and self-proclaimed "First Buddy" of President Donald Trump, has stepped up criticism of the president's massive tax legislation in recent days. Investors are starting to notice.

Tesla shares dropped more than 8% on Thursday on a day otherwise devoid of news for the electric vehicle maker, leading traders to speculate that Musk's increasingly pointed rhetoric suggests strain in the relationship that has benefited his sprawling empire of businesses.