REUTERS/Aly Song
Investors took the news well after the announcement on Thursday, and the stock surged by up to 7% in after-hours trading.
In pre-market trading on Friday, Twitter's stock rose by as much as 5%.
But research notes out Friday suggest that Wall Street analysts are not expecting a drastic turnaround in the company's performance under the new leadership.
Morgan Stanley analysts view the stock as "Attractive," and they note that Twitter is unrivaled in providing real-time news and information. However, they add, "even without Dick Costolo in the CEO seat, uncertainty around improving user growth and engagement and advertiser Return On Investment still remain."
Macquarie analysts have never recommended that investors buy Twitter shares, which are flat year-to-date, and up 7% over the past 12 months.
In their note Friday, they write that Thursday's news changes nothing, and CEOs don't resign when everything is going well:
"The bottom line is that, as Jack Dorsey stated, TWTR has unmet potential. And the surprise timing of this announcement, combined with the "steady-as-she-goes" tone of the executives on the conference call, indicate to us that TWTR will continue to underperform until it can either a) significantly improve its execution against its current strategy, or b) institute a new vision."
Wells Fargo analysts note that there's been a high turnover of the CEO position; Jack Dorsey will be Twitter's fourth chief executive in nine years.
"By reaffirming strategy and keeping Costolo on the board, could Twitter's board be sending a signal that no changes are likely? We believe Twitter is an invaluable and incomparable source for real time news, but we continue to believe that its product and positioning remain confusing and ill-defined for those not counted among its core enthusiast user base."
The firm, however, is "Overweight" the stock.
Twitter's rally after-hours is a sign that investors are at least satisfied that the status quo has changed, the analysts wrote. "We believe the key question remains whether TWTR will make necessary changes to lure back the roughly 700MM+ users we believe use the service infrequently, or have left altogether."
In an interview with Business Insider on Thursday, Costolo said it's beneficial that Dorsey, who's already very active and familiar with the company, is taking over.
But that may be the problem.