After leaving the White House in 2001, former President Bill Clinton was inundated with business and job offers, from investment-bank partnerships to seats on corporate boards. He turned them all down, with one exception: He agreed to be an adviser to a family of funds run by the Yucaipa Companies, a California private equity firm controlled by one of his best friends, the billionaire Ronald W. Burkle. Mr. Clinton's arrangement with Mr. Burkle is an unusual one for a former president, giving him the potential to make tens of millions of dollars without great effort and at virtually no risk,...
