Stumpf said Wells Fargo had room to expand its wealth business, noting that the bank has about 11 percent of U.S. deposits, but just 1 to 2 percent of the wealth.

"It's not like the business is not great; it just could be a whole lot bigger," Stumpf said.

Wells Fargo's ability to sell several products to the same customer is one reason investors value it more generously than banks like J.P. Morgan Chase & Co, Citigroup Inc. and Goldman Sachs Group Inc. But investors are typically reluctant to part with their wealth advisors.

"A lot of the clients don't view it as going with the brand: they trust their individual advisor," said Michael Mattioli, portfolio manager at Manulife Asset Management who owns Wells Fargo shares on behalf of clients.

Recruiting Battle

CFO John Shrewsberry said Wells Fargo is better than peers at selling wealth management products to retail customers.

"We have been recording more than $1 billion per month of closed investment referrals out of the community bank into the wealth and financial advisory business for a couple of years now," he said in an interview on Friday.

Wells is not relying on internal referrals alone. It struck a deal in October with Credit Suisse Group AG, which is winding down its U.S. private banking business, hoping to gain a leg up on rivals in recruiting financial advisers.

However, rivals like UBS and Morgan Stanley have lured away nearly a third of the 270 Credit Suisse brokers despite Wells' effort to offer generous incentive packages, according to press reports.