American Airlines Group (NASDAQ:AAL) on Thursday provided some of the clearest evidence yet that travel demand is beginning to recover off the bottom, and investors stampeded into the shares as a result.

American said that it plans to fly about 55% of its 2019 domestic capacity this July -- a significant boost after flying just 20% of its schedule in May -- and will reopen some of its airport lounges closed after travel demand evaporated due to the COVID-19 pandemic.

Airlines slashed flights and scrambled to cut costs as the pandemic spread globally, and shares of American and other carriers lost more than half of their value beginning in February on fears of widespread bankruptcies in the sector. American shares were hit particularly hard because the airline has the most debt among major U.S. carriers, and the company was seen as being particularly vulnerable to an extended downturn.

But there is growing evidence that demand might have bottomed out in April, and the early stages of a recovery are at hand.

An American Airlines Boeing 737 in flight over the clouds.

Image source: American Airlines.

American said it averaged 110,330 passengers per day in the last week of May, more than triple the 32,154 daily passenger average for April.

We're still a long way from normal. At most American will fly 4,000 flights per day in July, compared to about 6,800 daily departures prior to the pandemic. International capacity remains well below domestic, and will remain so for some time. And American is taking steps including removing change fees and awarding double frequent flier miles to try to entice travelers.

Even after the rally, American trades at less than 0.2 times trailing twelve-month sales. The company has been busy adding to its cash position and expects to have $11 billion in total liquidity by the end of 2020, enough to weather the crisis. But risks, including a second wave of the pandemic, remain, and the sooner traffic returns the less chance there is of a failure.

The airline's shares soared Thursday on volume more than four times average, which could imply a mix of people betting on a recovery and shorts giving up on bets American would end up in bankruptcy. Other carriers also rallied on American's news, with shares of Spirit Airlines (NYSE:SAVE) closing up nearly 20%.

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