SunTrust Bank does not see the Labor Department's fiduciary rule having a meaningful impact on its wealth management business.

"I think this is in the highly manageable category," the bank's chairman and CEO, William H. Rogers Jr., said during its earnings call on Friday. 

The team has been thinking about the rule for a long time in terms of structural changes and being ready and is now "diving through" the voluminous new order, he said. 

"We've been fiduciaries for over 100 years. It's a concept that we're certainly comfortable with," he said. Rogers described any potential impact of the new rule as marginal and noted that it might also offer opportunity.

"I don't think this is going to be a big story in terms of a change in direction of our private wealth business," he said.

SunTrust's wealth management business has been lagging, according to the bank's latest financial results. First-quarter revenue from both its trust and brokerage services units were down year-over-year, particularly the trust business, which fell 11%. 

The bank's CFO, Aleem Gillani, attributed the weak performance to challenging market conditions. "Our wealth management-related revenue streams have been pressured by market volatility and lower assets under management," he said during the call.

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