Shares of American Airlines (NASDAQ:AAL), Delta Air Lines (NYSE:DAL), Southwest Airlines (NYSE:LUV), and United Continental (NYSE:UAL) all took off last month. The biggest gain went to Southwest, which rose more than 21%, while Delta brought up the rear with an increase of "only" 13% during October.

Airline October Stock Performances, data by YCharts.

The airlines clearly fed off of each other's performances last month. However, each one had good news of its own to report. Let's take a look at what each airline did to please investors.

American Airlines completes a major task -- and buys back tons of stock
American Airlines stock spent most of the summer in the doldrums around $40. Last month, the company revealed that it had taken this opportunity to repurchase a stunning $1.56 billion of stock in Q3 -- about 6% of its shares. American Airlines plans to keep the buybacks coming; the board authorized another $2 billion program to be completed by the end of 2016.

This huge share repurchase showed that American's management has a ton of confidence in the company's long-term prospects. But ultimately, confidence only goes so far -- you also have to deliver results.

American Airlines did just that, pulling off a virtually seamless reservations system integration in mid-October. While major integration tasks like this are prone to huge technology failures, everything went as planned for the American Airlines-US Airways integration. In the minds of investors, these positive developments outweighed CEO Doug Parker's prediction that airline profit margins could narrow next year.

Delta Air Lines projects more strong earnings growth
During October, Delta reported that earnings growth accelerated in the third quarter, as its adjusted operating margin rose to 21% from 15.8% a year earlier. This was largely due to Delta finally capturing the full benefit of lower oil prices. (In the first half of 2015, it absorbed big hedging losses.) Delta projected that fuel would remain a tailwind for the next few quarters.

Low fuel prices drove strong earnings growth at Delta in Q3.Shares of the Top 4 U.S. Airlines Soared in October: Here's Why

Investors were also pleased by Delta Air Lines' commitment to capacity discipline. The company has cut service in a number of weaker international markets this fall, holding total capacity flat year over year in Q4. It then plans modest 0%-2% capacity growth for 2016.

This is already starting to have a positive impact on Delta's results. Delta's unit revenue is still declining, but at a slower rate than in Q2 and Q3, and it could start to grow again within the next few quarters. This solid outlook led analysts to revise their 2016 earnings estimates higher by about 3% on average during October.

Southwest Airlines returns to unit revenue growth
Southwest Airlines put together the biggest gain among the top four airlines last month, and for good reason. Southwest confirmed that its unit revenue decline moderated to just 0.4% in Q3, allowing it to post 71% year-over-year growth in adjusted EPS.

Southwest Airlines is returning to unit revenue growth this quarter.

Even more importantly, Southwest Airlines projected that unit revenue will rise 1% in Q4, making it the first of the "Big Four" airlines to return to unit revenue growth. Unit revenue gains could accelerate next year as the carrier's new routes in Dallas start to mature. That should allow Southwest to continue its stellar margin performance in 2016.

United Continental posts rapid margin expansion
Finally, United Continental also had lots of good news for investors last month. Unit revenue came in at the favorable end of the company's original guidance, while unit costs were lower than expected due to falling oil prices and the impact of the strong dollar on costs outside the U.S.

As a result, the company's adjusted pre-tax margin reached 16.6%, well above the 13.5%-15.5% guidance range provided in July. Like Delta, United Continental expects an ongoing tailwind from lower hedging losses in the next few quarters.

United's strong results could have justified an even bigger share price gain in October. However, recently installed CEO Oscar Munoz suffered a heart attack last month, adding a lot of uncertainty for investors. Fortunately, he is now on the road to recovery, and plans to return in a few months. In the meantime, the rest of the management team seems to be maintaining its focus.

Clearly, October was a great month to own airline stocks. With fuel prices likely to remain low for the foreseeable future, and airline management teams working hard to get unit revenue back on a growth trajectory, shares of all four airlines could still have room to run.

Adam Levine-Weinberg owns shares of United Continental Holdings, and is long November 2015 $40 calls on American Airlines Group and long January 2017 $40 calls on Delta Air Lines, The Motley Fool is long January 2017 $35 calls on American Airlines Group. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.