On April 1, 2018, Tesla Inc.’s founder and CEO Elon Musk tweeted a series of jokes. The funniest one? Tesla had gone bankrupt after failing to raise money. “So bankrupt, you can’t believe it,” he wrote. So funny the company’s stock fell about 5% the next day.

This year, Mr. Musk played it safe and avoided market-moving jokes. Instead, he dropped a rap song. Tesla didn’t respond to a request for comment.

The...