Airlines expect a good summer. But airline stocks don't reflect that rosy outlook.

Among the shares of the nine largest airlines, only Southwest Airlines Co.  (LUV - Get Report)  has outperformed the S&P 500, which has risen 9% as of Tuesday's close.

Southwest shares are up 21%. But American Airlines Group Inc.  (AAL - Get Report) , Delta Air Lines Inc.  (DAL - Get Report) and United Continental Holdings Inc.  (UAL - Get Report) have gains between 3% and 6%; Alaska Air Group Inc. and JetBlue Airways Corp. have gains below 1%, Spirit Airlines Inc. is down 8%, Allegiant Travel Co. is down 14% and Hawaiian Holdings Inc. has fallen nearly 19%.

Falling oil prices ought to help airlines, since fuel is a principal cost component. However, falling oil prices tend to encourage lower ticket prices, which lead to lower passenger revenue per available seat mile or PRASM, a measurement of the revenue generated by one passenger flying one mile.

To the consternation of most airline industry executives, Wall Street likes to focus on PRASM, which may explain why the shares of every major airline declined on Tuesday --- from a 0.97% decline at Southwest to a 3.28% decline at American.

Oil prices were rebounding early Wednesday.

Last week, at American's annual meeting, CEO Doug Parker reiterated his oft-stated belief that Wall Street hasn't yet figured out the value of an airline industry transformed by bankruptcies, consolidation, ancillary fee revenue and share buybacks.

"If you believe the company is going to produce $5 billion on a regular basis, on an average basis the company is undervalued," Parker declared.

Since the start of 2014, American has bought back nearly 35% of its shares; its share count has declined to about 493 million shares from 756 million shares.

Based on $5 billion in pretax earnings, Parker said the price earnings multiple is 8 times, compared with an average P/E multiple of 19.6 times for the S&P 500 since 1990.

Last month, industry trade group Airlines for America projected record summer travel with 234 million passengers flying between June 1 and Aug. 31. "Rising U.S. GDP, a steadily improving economy, all-time high household net worth and low airfares are fueling the expected growth in summer air travel," said John Heimlich, A4A vice president and chief economist. 

In the first quarter, the nine largest carriers reported pretax earnings of $2.4 billion, down from $4.8 billion in the first quarter a year earlier, primarily reflecting higher costs for fuel and labor.

In a report issued Wednesday, Buckingham Research analyst Dan McKenzie said airline booking trends appear strong as the second quarter draws to an end. Additionally, he said, "Booking volumes for 3Q17 travel also look healthy overall," although United may face weakness in Germany and China.

As for oil prices, McKenzie sees a positive impact. "It's too early to adjust full-year estimates today, but if the recent 19% slide in oil holds, we estimate our pretax earnings for the Big 3 could rise 5% for AAL; 10% for DAL and 15% for UAL, implying high-single digit upside to consensus," he wrote.

McKenzie said he values the Big 3 at 11 times to 12 times estimated earnings per share, but they trade at 8.5 times his 2018 outlook.

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.