In late 2011, business was bleak for Fort Worth, Texas-based American Airlines, which had filed for bankruptcy after its fourth straight year of annual losses. Since 2007, American had posted only one profitable quarter, and had suffered losses just shy of $5 billion over a three-year span.

Today, American Airlines Group Inc. (NASDAQ: AAL) is the largest airline in the world, measured by passengers carried, fleet size, or passenger miles flown. It’s buying back stock, returning more than $9.6…