Starbucks’ stock has been soaring, its earnings are strong, and it has been expanding rapidly in its fastest-growing major market, China.

Yet as shareholders head toward the company’s annual meeting on March 20, there is a cloud on the horizon: the risk that latte lovers will punish Starbucks because they are turned off by Howard Schultz’s prospective campaign for president.

Mr. Schultz, who presided over Starbucks when it went public in 1992 and dominated it for years, gave up his last operational position at Starbucks in June. Still, the company embodies his taste and vision. What’s more, Mr. Schultz remains Starbucks’ largest individual shareholder, and the current chief executive, Kevin Johnson, is his chosen successor.

In official documents, Starbucks says this is a “pivotal year,” one in which it is making the transition from a “founder-led” to a “founder-inspired” company. That would have been hard enough if Mr. Schultz, 65, had retired quietly, said Nancy F. Koehn, a historian at the Harvard Business School who has studied Mr. Schultz and Starbucks extensively. But his incipient quest for the presidency as a third-party candidate, she said, makes the handover much more difficult.