LISBON — Only two months after Portugal proudly exited its international bailout program, the financial problems of the country’s most powerful family have given investors an unwelcome reminder of the potential fragility of the Portuguese recovery.

Portugal’s stock market plunged last Thursday, helping drag equities lower around the world, after one of the companies controlled by the powerful Espírito Santo family missed a payment on its short-term debt. The Portuguese market has since recouped some of these losses, and regulators have offered assurances that the cost of any Espírito Santo rescue would not be sufficient to damage Portugal’s public finances.

But the problems of the Espírito Santo empire have exposed a convoluted corporate structure in which industrial assets were propped up by the group’s own bank, Banco Espírito Santo, Portugal’s second-largest bank.

On Monday, Vítor Bento, a banking industry executive, was appointed chief executive of Banco Espírito Santo under a deal brokered by the Portuguese central bank. Mr. Bento replaces Ricardo Espírito Santo Silva Salgado, who was at the bank’s helm for more than two decades and whose influence made him known in Portugal as “Dono disto tudo,” or “Owner of everything.”