William Ackman’s activist hedge fund has built a roughly 1.1% stake in Starbucks Corp. , a so-far friendly bet that the coffee giant will recover from recent stumbles and weather the departure of its longtime leader, Howard Schultz.

Mr. Ackman unveiled Pershing Square Capital Management LP’s investment in the Seattle coffee company during a presentation Tuesday at a conference in New York, his first such appearance in several months. He took the stage with an unsweetened Starbucks ice tea.

Mr. Ackman said he thinks Starbucks shares have slumped recently due to a slowdown in same-store sales growth, a reduction in long-term growth targets and leadership changes. But he predicted the stock could more than double in price over the next three years.

The noted activist investor said management appeared to be taking all the right steps to get the business back on track, though Pershing Square hasn’t yet met with Starbucks executives.

Mr. Ackman said his fund amassed 15.2 million shares at an average of $51 a share over the past few months. That means he already has made a tidy paper profit on the stock, which rose 2.1% Tuesday to $57.71. Even with that gain, its shares are up less than 1% this year, trailing broader markets.