"You're going to see every board member tell people to keep your money in multiple bank accounts," said Wesley Chan, cofounder and managing partner at FPV Ventures.
"I'm not concerned about Bank of America," one business owner said as they left a Bank of America branch on Monday.
Big banks can be less competitive, for example, on interest rates because of the security they offer.
I think you'll see startups, in particular, questioning moving to the big banks given just how much more expensive it is," Matheson added.
"The big banks are in very good shape, and so it probably is a stabilizing decision to move those deposits.