Using data from a survey of almost 200,000 consumers in 27 countries, Bain finds that most banks are missing prime opportunities to deepen their existing customer relationships and are ceding new product sales to competitors.

"The 'easy growth' is over for banks, as increased competition worldwide is forcing banks to fight over too few new customers," says Gerard du Toit, a partner in Bain's Global Financial Services Practice in Boston. "But there is a surprisingly large upside with existing customers to increase win rates on new product sales."

He says that two factors stand out in swaying customers to buy: the customer's loyalty to their primary bank and the bank's ability to actively sell to its customers.

According to the study, a bank's relative customer loyalty measure explains roughly half of the variation in its relative win rate, and it additionally finds that approximately one-third of banking products in the US are sold, not bought. That is, customers did not plan to buy a particular product, but they received an offer and then decided to purchase it.

Bain identifies 'digital transformation', in the shape of smart online and mobile banking services, as a key factor in maintaining customer loyalty. Mobile banking in particular was found to deliver a loyalty 'halo effect', as frequent mobile banking users in all countries gave much higher loyalty scores than non-users.

Loyalty on its own is not enough, however, banks also have to make a sound business case for the sale of new products, says du Toit. "The banking math is simple," he says. "Loyal banking customers own more products, and buy more products - but that doesn't mean they're going to make your sales for you."

The study found that few large incumbent banks had made meaningful progress, with JPMorgan Chase standing out as an exception. Such factors as select investments in mobile technology, a concerted effort to improve the customer experience and effective marketing to tell people how the bank can simplify their financial lives combined to help Chase perform "well above average" in winning new relationships and cross-selling to existing customers.