In late 2011, business was bleak for Fort Worth-based American Airlines, which had filed for bankruptcy after its fourth straight year of annual losses.

Since 2007, American (Nasdaq: AAL) had posted only one profitable quarter, and had suffered losses just shy of $5 billion over a three-year span.

Today, American Airlines 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 billion to stockholders…