Jackie Bugnion is an American citizen who has lived in Switzerland for 45 years. She had two securities accounts in her adopted country but in the spring she was told that she should find another home for her money. This summer those accounts were moved into SEC-regulated subsidiaries. "I call them the 'American ghettos'," she says. These subsidiaries are subject to higher fees and higher minimum investments than normal accounts. "It makes you feel toxic when this happens to you after you have been the client of a bank for years," says Ms. Bugnion.

American...