Where’s the line between an enticing offer and a money loser for a bank? In the credit card industry, which advertises reward plans marked by dizzying complexity, the economics can be hard to assess.

But in a new report, an analyst at Mercator Advisory Group argues that rewards on certain cards aimed at affluent consumers have become so generous that they are unsustainable.

These cards, which include Chase Sapphire Reserve, Citi Prestige, American Express Platinum and U.S. Bank Altitude, feature big upfront bonuses and hefty annual fees. Ultimately, their financial success will largely be a function of how long the heavily wooed customers stick around.

“The model faces headwinds and many issuers have already pulled back some of the rich features in their offers,” wrote Brian Riley, the report’s author and a former executive at several large credit card issuers.

The war for so-called mass affluent cardholders is being driven by several factors. First is the fact that people who can afford to pay annual fees of several hundred dollars are highly attractive customers. They tend to generate heaps of interchange fee revenue, and banks want to develop broader relationships with them in the hope that they will buy additional products.

Second, merchants pay issuers higher fees on these cards than they do on other, less-upscale cards. Card networks like Visa and Mastercard justify the two-tier pricing structure by noting that the wealthier card customers will spend more money in their stores.

Finally, the banks that issue these premium cards can spread out the financial hit from the sizable upfront bonuses they pay, which makes it easier to justify big cash payouts as part of a long-term strategy.

“The benefit of the card gets booked over seven years,” JPMorgan Chase CEO Jamie Dimon explained in a CNBC interview about the Sapphire Reserve card, which proved to be so popular that the New York bank ran out of the metal it uses to manufacture them.

Chase made a big splash last year by offering 100,000 bonus points — valued at $1,000 — when customers enrolled in Sapphire Reserve. That offer was later reduced to 50,000 points.

Earlier this month, Citi countered by raising the sign-up bonus for its Prestige card to 75,000 points. In order to qualify for the bonus rewards, customers must spend $7,500 within three months, which is a higher threshold than Chase uses.

Both Citi Prestige and Chase Sapphire Reserve carry $450 annual fees. And both offer less lucrative rewards in customers’ second year and beyond, which could potentially test customers' loyalty.

“They’re hoping that customers who get their card will of course stick with their card,” said Julian Keel, a senior writer at The Points Guy, a website for consumers seeking out good deals on credit cards. “And that’s of course where they’ll make their money.”

Card issuers have options to ensure that their cards remain attractive on an ongoing basis, such as offering additional points and credits, but those measures can be costly, Riley wrote.

In an interview, he noted that the ultimate success of these cards will be determined by their attrition rates, and said it is too early to say how long customers will remain loyal.

“What if you have 10% attrition every year?” Riley wondered.

Another risk that Chase and Citi face is that fewer customers will pay less than their full balance each month than the banks had expected. Credit cards tend to generate substantially higher profits when customers pay at least some monthly interest.

But Nick Clements, co-founder of Magnify Money, a comparison-shopping website, noted that even many affluent consumers choose to maintain a balance on their credit cards at certain times.

“I will say it’s hard to lose money on a $450-annual-fee card,” he argued.

Clements, a former Barclays executive, expressed admiration for the way that Chase has generated buzz around the Sapphire Reserve card. Chase had less reason to pay for advertising last year because the outsize reward bonus generated so much news coverage and positive word of mouth.

“That’s every marketer’s dream,” Clements said.

Some big credit card issuers, such as Capital One Financial and Discover Financial Services, have chosen not to offer products that compete directly with Citi Prestige and Chase Sapphire Reserve.

Discover CEO David Nelms said in a recent interview that his firm focuses more on acquiring customers who maintain a balance. But he said that in the battle for big spenders who typically pay off their entire bill each month, competition appears to have leveled off.

“If people are giving 100% of interchange, that kind of puts a natural cap on what they can offer,” Nelms said.

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