"I have no doubt that the financial industry will face a series of Uber moments," he said in the late-November speech in London, referring to the way that Uber and other ride-hailing companies have rapidly unsettled the taxi industry.

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And that's not just the opinion of one well-informed man.

In a recent report, analysts with Citi said they agreed with Jenkins's view that the number of bank branches could be cut in half over the next decade. A separate survey from Accenture, the management consulting company, shows why: Shifting consumer behavior.

"We believe the consumer banks in the US and Europe are at a tipping point," wrote the authors of the Citi report, which was published late last month.

The number of bank branches in the United States — represented by the dashed blue line in the chart below — could shrink by a third within the decade, according to their forecasts.

Branches just don't matter as much to customers

Customer preferences are key to that industry transformation. What they want and expect from banks has changed dramatically in just a few years.

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In 2013, Accenture found that 48 percent of Americans surveyed said they would switch banks if their current provider's local branch closed. In last year's survey, that share shrank to just 19 percent.

In just two years, the local branch went from being a concern of half of banking customers to just a fifth.

Separate data, from industry analysts Mercator Advisory Group and cited by Citi, paints the same picture: The share of customers who reported going to a branch to speak to a teller at least once in the previous year fell from 79 percent to 70 percent from 2011 to 2014. The share that reported visiting a branch to speak with a customer service representative fell from 62 percent to 45 percent.

The rising importance of Internet services

As branches matter less, online banking matters more.

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For the first time in Accenture's research, good online services ranked as the top reason to stick with a bank. Some 38 percent of consumers surveyed last year cited that as a reason to stay with their bank, while just 28 percent cited branch location. Twenty-eight percent also cited low fees.

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That holds true for populations that have long been used to visiting branches, too: Among customers over the age of 55, the preference for online banking leads the desire for convenient branch locations by a similar 10-percentage-point margin.

"This evolution in consumer preference signals a redefinition of banking convenience," the report's authors wrote. "It is no longer always measured in miles to the branch or extra service hours — it is increasingly measured in clicks and apps."

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A deeper dive into the Accenture data, represented in the Citi chart below, shows how little branches factor into most bank interactions.

Overall, customers engage with their banks an average of 17 times a month. Yet only two of those interactions involve human contact. In the United States, only two out of 15 monthly bank interactions involves a branch.

"Banks will follow consumer behavior and close branches as they see their consumers shift away from branches to digital," the authors of the Citi report write.

But geography matters

While Citi expects an industrywide decline, it expects the transformation to play out differently both globally and within countries.

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Generally, developed markets can expect branch numbers to dwindle, while emerging markets can expect the opposite, the authors write. That applies to the United States, too, even though it seems to lag its European and Nordic peers by about five and 10 years, respectively.

While the number of branches per capita remained unchanged in the United States from 2004 to 2014, it dropped 30 percent in Nordic countries, 22 percent in East Asia and the Pacific and 17 percent in the Euro zone, according to World Bank and Citi data. The number of branches per capita rose 26 percent in Latin American and the Caribbean.