Twitter's stock pop on Musk's big investment is an overreaction from people who think a sale could be possible, Bernstein says

• After Elon Musk disclosed a 9% stake in Twitter, shares of the social media company rallied 25%.
• Bernstein analysts, however, say the price spike is an overreaction to speculation that Twitter could be sold.

Twitter stock's price spike on Monday from Elon Musk's newly disclosed stake is an overreaction to speculation that the social media company could be bought, Bernstein analysts said in a note.

An SEC filing showed the Tesla CEO bought 73.5 million shares, representing a 9% stake in Twitter that's worth more than $3 billion. The stock jumped 27%.

"The magnitude of the pre-market stock move speaks volumes of an investor base eager for any positive jolt, as the stock was previously around IPO levels," according to Bernstein analysts led by Mark Shmulik. "Some investors are certainly hoping for a sale, but we believe the stock move is likely an overreaction for this broadly speculative possibility."

What Musk intends to do with his Twitter stake remains uncertain. Bernstein said it's possible that he does nothing, inserts himself into leadership, or takes Twitter private.

The analysts assume his interest in Twitter is "mainly personal," pointing out that other billionaires have some ownership in media properties, such as Jeff Bezos and the Washington Post.

"We view the interest as a potential distraction for Musk and TSLA shareholders, given that Musk is arguably already overcommitted, and his fervor for the topic of censorship/free speech is high," Bernstein warned.

His history related to Twitter is complicated. He has amassed 80.2 million followers but has had past run-ins with the SEC over his market-moving tweets.

Musk recently criticized Twitter for pitfalls surrounding free speech and censorship, and hinted that he may create a social media company of his own.

In his poll to his Twitter followers regarding free speech, he asked users to vote carefully as "the consequences of this poll will be important."

Meanwhile, not much has changed at Twitter, Bernstein pointed out.

"The investor reaction to the news seems a bit extreme to us," analysts wrote. "We believe the fundamentals and challenges with Twitter remain broadly the same."