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“They’re very dangerous for the Swiss government, because they’re so big,” said Jacob Funk Kirkegaard, research fellow at the Peterson Institute for International Economics. “If their banks go broke, the government goes broke, as well. So they have to hold much higher captial than banks elsewhere, and that makes it difficult for them to compete in investment banking.”

But UBS and Credit Suisse being the only major Swiss players in investment banking doesn’t mean the smaller banks won’t face their own problems. At the same time, Swiss banks are also losing their reputation for banking secrecy, as governments pressure them to release the names of their customers.

“They’ve lost the ability to hide money,” Ms. Rehman said. “They’ve lost the ability for secrecy and descretion.”

In fact, the problem is so bad, they turn many potential customers away. “For American customers, Swiss banks pretty much tell you, ‘Listen, don’t come to us unless you have a lot of money,’” she said. “They won’t take you. You’re too much work for them.”

Changes are coming to the industry, and Swiss banks seem to be leading the way.

“They are probably only the first of many banks that are going to go through and decide how to restructure their businesses in the coming years,” said David John, senior research fellow at the Heritage Foundation.