TJX Companies, Inc. (TJX) - Get Report , the parent company of TJ Maxx and Marshalls, is one of few retailers to see recent positive store traffic. Even this brick-and-mortar standout, though, is no match for the formidable, Inc. (AMZN) - Get Report .

Out of 28 top retailers, Amazon has the highest and fastest growing rate of customer loyalty, according to a recent survey from Morgan Stanley. The e-commerce giant garnered a 61% net promoter score, a metric of the loyalty a customer has toward a retailer. Its score saw a 14% increase year over year, while TJX, in second place posted, only a 3% increase.

Amazon and TJX are among three other retailers—Victoria's Secret, of L Brands Inc. (LB) - Get Report , Zara of Inditex SA, and Old Navy of Gap Inc. (GPS) - Get Report —to realize store loyalty growth this past year, according to Morgan Stanley's AlphaWise apparel survey, published Tuesday, Oct. 17.

In price satisfaction, TJX has Amazon beat. Nearly 60% of respondents associated TJ Maxx and Marshalls with having the lowest and best prices on clothing, while 46% respondents recognized Amazon for the same. Walmart led the pack in this category, though, with 73% of respondents saying they get their bang for the buck when it comes to apparel.

Everyone wants to be like Jeff these days.

If Amazon can anticipate higher sales to come, TJX is in the same boat. Both retailers received high purchase intention over the next year, according to the survey. For TJ Maxx, 28% of respondents said they expect to shop there more often in the next 12 months, while Amazon posted an even higher rate of 36%. Zara, however, was the champ, with 41% of respondents saying they intend to visit the store more frequently.

TJX was somewhat of an underdog stock this year, with its price dropping 4% since January.

"Yes, Amazon is hurting retail. Everybody knows the big department stores can't compete with Amazon's prices, ease of use, mobile access, but this is exactly why we love TJX," said Jim Cramer in July, when he added the discount retailer stock to his Action Alerts Plus Charitable Trust Portfolio.

If this new data is any indication, Amazon is encroaching on the discounter's territory.

"Amazon is quickly gaining traction at the expense of department stores and select specialty retailers," the Morgan Stanley analysts wrote. Its "share gains could accelerate from here."

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