When it comes to credit card profitability, consumer loyalty to a single card may not be such a virtue after all, according to a new study by Oliver Wyman.

In a two-year study of 4,000 U.S. credit card accounts, Oliver Wyman determined that customers who show the least loyalty and flit from one card program to another looking for a better deal can generate about 95% more net revenue than those who stick with one card.

Cards with richer rewards programs had a higher share of switchers, and customers who switched primary cards also tend to be those who use the card often and revolve a balance, and thus generate nearly twice as much net revenue per card, Oliver Wyman found.

Chart: Who's loyal to one credit card?

Card loyalty is up for grabs, said Tony Hayes, a partner at Oliver Wyman and co-author of the study.

Only half of all credit card customers from 2014 to 2015 had a single primary card over two years, while two in five switched their primary card at least once over the time period, and 11%—those most likely to revolve a balance—had no loyalty to a primary card over two years, Oliver Wyman’s study indicated.

Credit card issuers are earning the highest percentage of net revenue from customers who drive interchange income from heavy spending and interest from revolving a balance, even after subtracting the cost of rewards, and those happen to be customers with no loyalty to a particular card, the research suggests.

Of course, there’s a catch—customers who routinely revolve balances and switch cards to get the lowest APRs also tend to carry higher risk and have lower FICO scores, Oliver Wyman noted.

While issuers want to avoid tilting their credit card portfolios into risky territory with too many unsecured receivables from revolvers in the mix, data suggests issuers should rethink their rewards strategies to avoid giving incentives to the wrong customers for the wrong reasons, Hayes said.

“With the rise of digital payments, credit card customers are getting savvier about how to get the best deal, and in the race to be top-of-wallet, issuers need to understand where to compete for a particular transaction to actually make a profit, instead of putting so much focus on loyalty alone,” he said.

For example, credit card issuers offering triple points on travel and rewards could be encouraging customers to cherry-pick rewards in that spending category alone, causing gaps in other lucrative categories. To rebalance the product, the issuer might consider introducing a minimum spending threshold across all spend categories to qualify for the triple points in travel purchases, he suggested.

Any loyalty consumers have to a particular card is poised to change as digital payments evolve, Hayes said.

The internet is already giving consumers more tools to hunt around for the best offers, and although mobile wallet use is still low, a variety of tools including apps, bots and notifications are emerging that will eventually make mobile wallets more useful for consumers looking to decide which card to use at the point of sale, Hayes warned.

“There will be a rebalancing of choices at the point of sale, where consumers have more information and they’ll be more likely to pick one card over another based on a particular purchase at a particular store,” Hayes said.

The upshot is that credit card issuers working to keep up with the evolving landscape of consumer payment choices will need to retool products to be more personalized, and rewards and benefits must be delivered at the transaction level and in real time, he said.

“Issuers will need to participate in mobile wallets, and tailor their incentives to drive specific, profitable transactions,” Hayes said, adding that instant credit-line expansion, promotional APRs, bonus rewards and even product warranties could be part of that mix.

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