When American Airlines Group Inc. exited bankruptcy in 2013, its new boss vowed to trounce rivals within a few years. These days, those competitors are delivering the beating.

American is underperforming Delta Air Lines Inc. and United Airlines Holdings Inc. on profit margins and on-time arrivals. Investors are punishing American’s stock, sending the shares to the biggest decline this year among U.S. transportation companies. And to add insult to injury, a plague of summertime flight cancellations has angered passengers and sullied American’s brand.

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