American Express, whose Platinum card was once an undisputed must-have for premium travellers, is having to launch a costly fightback against Chase, which launched its Sapphire Reserve card this year with eye-popping sign-up bonuses and extensive rewards on spending. Chase attracted so much interest that its supplier ran out of the metal to make the Reserve card and the bank had to issue plastic ones instead. Now it must convince investors that these excited new customers will stick around long enough - and spend and borrow enough - to justify the costs of luring them over.
It is possible to declare one winner of the rewards war already: consumers. "It is an amazing time to be a consumer," says Mr Kelly. "Sign-up bonuses of 100,000 points on the Sapphire Reserve, up to 250,000 points on small-business cards from Amex, and more and more. Miles and points are cash, that's what we teach people, and it's certainly nice when the credit card companies are giving you $1,000, $1,500, $2,000 for getting a single credit card."
Issuers are also trying to persuade customers to put more on their particular card by offering extra rewards across a range of purchases. After Chase offered triple points on restaurant spending on the Sapphire Reserve, Amex responded by saying flights purchased with its Platinum card would earn five times the points. These accumulated rewards points can be converted into more flights, upgrades and other travel perks, such as access to plush airport lounges and free hotel stays - all paid for by the card providers. There are other offers and rebates; both Amex and Chase return some portion of the annual card fee to customers to spend on travel, and Chase has wooed millennial customers by expanding that rebate to cover Uber rides.
Between 2010 and the end of 2015, the six largest US card issuers paid more than $100bn in credit card rewards, according to the research firm Instinet, and this year has witnessed the fastest growth so far. The six issuers - which also include Capital One, Citigroup, Bank of America and Discover - are on course to pay $22.6bn in rewards this year, 18 per cent higher than in 2015 and more than twice the sum they paid out as recently as 2010. Amex, with an estimated $6.8bn in rewards costs, remains the most generous, but at $6.6bn, Chase has almost closed the gap.
Bill Carcache and Steven Chubak, the analysts behind the Instinet report, say that while the bank issuers have all at least doubled their rewards expenses in the past six years, Amex's payouts have grown only 36 per cent. When it comes to premium customers, the company may be paying out less than half the rewards of its rivals. It will have to be more generous, they said, "particularly in a market where heightened transparency exists round the value of rewards and consumers have no tolerance for being short-changed".
Gary Leff, who writes View From The Wing, a travel blog, says consumers are becoming savvier at comparing rewards offers. "Not all points are equally valuable, since you have all these proprietary currencies that do not equate one to one," he says. "Consumers have come to understand them better - not perfectly, but enough that programmes have to adapt and stay competitive."
Mr Leff and Mr Kelly agree that the comparison websites should not take all the credit for the rewards war. Perhaps the biggest factor is the regulatory changes wrought in the US by the Dodd-Frank Wall Street reform. While more esoteric forms of lending and market activity have been penalised, big banks have found that standard credit card lending to consumers is more lucrative, hence the dash to grab market share.
The bank issuers and Amex have taken different approaches to making money from credit cards. Amex has traditionally earned the bulk of its revenue from the fees that merchants pay on each transaction, while banks collect more from interest on customers' balances. In the jargon, Amex has a "spend-centric" model, while banks are "lend-centric". That means Amex and banks are trying to encourage different patterns of use by their cardholders.
The existence of the comparison sites raises the possibility that customers will prove less loyal and predictable than in the past. While Chase and Amex splurge on advertising their offers on these sites, analysts are worried about the efficacy of the strategy.
"We are reluctant to count too heavily on loyalty in today's rewards environment," Messrs Carcache and Chubak wrote. "We believe sites like these tend to attract high-risk customers who are prone to accepting an offer with the end goal of earning reward points after achieving a minimum spending target within a present timeframe, only to turn around and stuff the card in a shoe box after receiving the welcome offer."
This is a concern at Amex, too. Ken Chenault, the company's chief executive for the past 15 years, said it would not be chasing new customers and new customer spending at any cost. "We are not interested in chasing short-term market share," he said at a Goldman Sachs conference this month. "The focus is not just on promotions. That's really not why they get a Platinum card. They get a Platinum card based on the services that we provide. The Centurion lounges [at airports], the concierge services, the Transportation Security Administration Global Entry fee, all of those features are very important."
Concerns notwithstanding, Amex has been unable to avoid the fray. It has told investors to expect "significantly higher" marketing and promotional spending in the fourth quarter, so that the full-year total will be about 10 per cent more than last year's $3.1bn. This spending includes the costs of sign-up bonuses, such as the 40,000 membership rewards points it offers new Platinum customers.
At the same time, it has told investors that it will also be more generous with rewards on spending in 2017 - although rarely has a multimillion-dollar giveaway been promised in such dry language. "You will see a reversal of the trend we have seen the last few quarters where neutral rewards have been growing a little bit more slowly than billings," Jeff Campbell, Amex chief financial officer, said on the company's most recent earnings call in October.
The promise of extra spending on rewards and promotions comes after a period of cost-cutting by Amex, its earlier response to the decline in market share and profitability. The company's shares, which fell 25 per cent in 2015, have risen 8 per cent this year but they lag the S&P 500's 11 per cent gain.
ValueAct, the activist hedge fund that targets companies in need of a big strategic overhaul, sniffed around the company last year, taking a $1bn stake but then selling out without making a public case for change. Concern over the company even surfaced at Berkshire Hathaway's annual meeting this year. Berkshire, run by the legendary investor Warren Buffett, is Amex's largest shareholder, with a 16 per cent stake, and Amex is one of Berkshire's "big four" publicly traded investments.
"I still feel good about owning American Express," Mr Buffett said at the Berkshire meeting in April. "Their position . . . will continue to be under attack. It's too big a business . . . for people to ignore it."
Mr Chenault has taken a similar line with critics, pointing out that despite the fierce competition from Chase Sapphire Reserve in the premium market, the company has increased its customer base and income from card fees, such as the $450-a-year Platinum fee.
"Most of the competitors are copying us," he told the Goldman Sachs audience. "Clearly, the environment we're in is very intense competitively. But the reality is that we've been dealing with competition for decades. If someone takes the position that all customers are the same, and they will react only to promotional offers or something that's free, and they discount the elements of value, we wouldn't have been in business over the last 50 years."
Mr Leff says that while Chase has won market share for its Sapphire Reserve card with offers such as triple points on restaurant spending, Amex may be more subtle.
"Amex uses a lot more targeted offers than Chase does, and they think they have got better at figuring which customers they are trying to acquire. There are lots of things that they try to do to make their portfolios better when they acquire those customers, giving them bonuses for different kind of spending."
For the savviest consumers, this means more potential travel perks and freebies, and as trailblazers like Mr Kelly have shown, it can bring a big lifestyle upgrade. A recent holiday was paid for with the piles of rewards currencies he has accumulated across his 30 personal and business credit cards. It is some boast: first class to the Maldives, via JFK, Frankfurt and Singapore, for 221,000 KrisFlyer points and 170.80 Singapore dollars instead of a $10,616 cash outlay; a five-night stay at the St Regis Maldives for 130,000 Starpoints instead of $11,655 out of pocket.
"It is just a shame Miles the dog has to stay home," he adds.
Consumers may be winning the rewards wars, but that does not mean that Amex, Chase, Citi and the rest will ultimately be losers. In fact, there can be many winners, Mr Kelly says.
"Airlines have gotten billions of dollars from the credit card companies. The card companies are getting even more billions from merchants to process credit cards. So, that's what I like about it. When consumers are educated, too, everyone can make out."
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Copyright The Financial Times Limited 2016