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Cheaper airline tickets is folly: Analyst

Airline investors pocketing fuel savings: Analyst

Airline companies have been benefiting from cheaper oil but that doesn't mean it will translate into cheaper flight tickets, said Jamie Baker, JPMorgan airline analyst. In an interview with CNBC's "Squawk on the Street " on Thursday, Baker said that "100 percent of the fuel savings are being retained."

"It's the owners of these stocks that are reaping the direct benefits," he said. "Passengers will enjoy indirect benefits such as newer airplanes and onboard WiFi."

Airline stocks rallied Thursday morning with Southwest taking the lead. Baker's top picks are Delta, United and American Airlines.

Southwest's monumental Q4

Southwest Airlines CEO Gary Kelly also joined the show earlier on Thursday. His company had the best-performing stock in the S&P 500 in 2014. He said that lower gas costs are a huge boost for Southwest's performance.

"I think on a net basis you have consumers that have a lot of cash in their pockets and they will likely be traveling more than they would have," he said. "My best guess is that it nets out systemwide for us in a big positive and, of course, it's a much less input cost for us."

Gary Kelly, CEO of Southwest Airlines
Jason Janik | Bloomberg | Getty Images

He added that, "because we are a low-cost producer, it is a significant competitive advantage for us to have lower energy prices because it enhances the rest of our cost structure."

Read MoreSouthwest Airlines beats expectations for 4th qtr, expects big fuel savings