Who could be the next permanent CEO?
Peck believes the top candidates include Dorsey, Adam Bain, Twitter's president of global revenue and partnership, and Ross Levinsohn, Yahoo's former interim CEO.
If Twitter shareholders feel downbeat about their investment so far this year, at least they can take heart that they're not putting money to work in LinkedIn.
That stock is down 10 percent this year, and more than 20 percent from its high of $271 on February 26.
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In its most recent earnings report, the professional social network offered weak guidance due in part to its acquisition of Lynda.com.
The team at BGC, however, notes reasons for guarded optimism: Despite the stock slide, the company's value proposition remains intact for its users and customers, they argue. They also said that the stock does tend to perform better in the second half of the year.
Not every social media name is under pressure. Case in point: Facebook, which is up some 10 percent in the first half of 2015.
Bulls maintain that it will move higher from here, pointing to strong engagement, the ramp-up of advertising at Instagram and continued product innovation.
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But even some Facebook fans, such as Raymond James analyst Aaron Kessler, highlight some issues for investors to consider before carving out a stake in the social network.
"We still think ad prices are going up, but we have seen a big increase in pricing over the last year as a lot of advertisers have come onto the platform and realized the value of Facebook," Kessler says, adding, "We would caution investors not to expect the same growth in pricing going forward."
Those caveats don't appear to concern hedge funds, however. In fact, Facebook is one of the top five tech holdings among hedge funds, according to the latest data available from Goldman Sachs.
Facebook declined to comment for this story. None of the other companies replied immediately to requests for comment.