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Despite consistently high jet fuel prices, the airlines have continued to see their stocks go even higher. When you take a look at what they charge for everything from extra luggage to ticket changes, to food on flights, it is no wonder they are piling up huge profits. A new in-depth research report from Deutsche Bank examines everything related to shifts in market share (as measured by seats and total capacity) at major airline hubs for the six largest airlines. Those numbers are growing rapidly in some of the hot markets.

With the busy summer travel season right around the corner, the Deutsche Bank team is very bullish on the major airlines. They have five stocks rated Buy, and one stock rated Sell.

Alaska Airlines Group Inc. (NYSE: ALK) is rated Sell and is one of the names that could just be a straight valuation call. The stock is up right at 100% from this time last year, and now trades at a pricey, at least for some airlines, 12.45 current earnings. Investors are paid a 1% dividend. The Deutsche Bank price target for the stock is $85, and the consensus target is even higher at $106.63. The stock closed Tuesday at $99.89 a share.

American Airlines Group Inc. (NYSE: AAL) leads off the list of stocks to buy and Deutsche Bank, and has been absolutely on fire this year, up over 50%. The company is the holding company for American Airlines and U.S. Airways. Together with wholly owned and third-party regional carriers operating as American Eagle and U.S. Airways Express, the airlines operate an average of nearly 6,700 flights per day to 339 destinations in 54 countries. Despite high fuel prices and the cost of the merger and emerging from the bankruptcy, the stock continues to draw followers. Deutsche Bank has a $45 price target. The consensus target for the stock is $46.31. Shares closed trading on Tuesday at $41.44.

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Delta Air Lines Inc. (NYSE: DAL) has a history of beating earnings estimates, and many of the Wall Street analysts think this quarter it could happen again. In fact, the firm has seen solid earnings estimate revision activity from around Wall Street over the past month, suggesting that other analysts are also becoming a bit more bullish on the firm’s prospects in both the short and long term. Trading at an incredibly low 3.27 times current earnings, Delta could have serious upside. Investors are paid a 0.6% dividend. The Deutsche Bank price target is $40, while the consensus target is much higher at $45.53. Delta closed Tuesday at $41.15

JetBlue Airways Corp. (NASDAQ: JBLU) may be a touch richer than the other top stocks, but it also may have big upside. The company has a very high short interest at almost 21% of the free float. JetBlue is also adding high dollar premium seating to long-haul flights, including New York to Los Angeles and San Francisco routes. Importantly, the company trade at a low 0.6 price-to-earnings growth number, implying good corporate growth ahead. The Deutsche Bank price target is set at $13, and the consensus target is $10. JetBlue closed Tuesday at $10.05.

Southwest Airlines Co. (NYSE: LUV) has gone from industry underdog to an industry leader, and it is another of the high conviction calls in the group. With the domestic market showing good strength, and the pricing environment looking very solid for the second quarter and the busy summer travel season, Southwest is busy expanding routes and adding new gates at key airports. Investors receive a small 0.9% dividend. The Deutsche Bank price target for Southwest is $30, and the consensus target is $27.27. The stock closed Wednesday at $27.20.

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United Continental Holdings Inc. (NYSE: UAL) has been a show-me story for many investors as the merger with Continental has not been smooth, and customers have experienced numerous computer glitches that have snarled traffic over the past two years. With some of the problems starting to recede, the company does have earnings growth prospects that could outshine some of its major competition. Increased Asian traffic could be the wildcard for the stock. The Deutsche Bank price target is $50, and the consensus target is $50.59. Shares closed Tuesday at $47.51

The airline stocks have been top performers this year, and from an overall stock market view, that is extremely positive. Transports are expected to be market leaders so the broad market can trend higher. The reason for that is transports serve as an important proxy for the economy. If they do well, often the economy follows. With the economy expected to improve in the second half of the year, the airlines may continue their ascent.