Starwood Hotels & Resorts Worldwide Inc. may need to accommodate activist shareholders with a merger or buyout.

Starwood, which owns high-end hotel chains such as W and Westin, has one of the worst stock-return and growth outlooks in the industry. It’s also entering the second month of searching for a chief executive officer as pressure builds for the $14 billion company to buy some lower-cost hotel brands to keep up with rivals.