Looking to expand its wealth management business after a period of corporate turbulence, Merrill Lynch & Co. opened a private banking service in Brazil in November and promoted it with an advertising campaign in the country’s financial media. The firm had high ambitions, given the robust growth of the country’s economy in recent years, but even so executives were struck by the response. Within days of the launch, the firm had dozens of wealthy individuals knocking on its door to become clients — and several private bankers looking for jobs.

“It was very well received,” says Antonio Costa, managing director of Merrill Lynch Wealth Management in Brazil.

Merrill is far from alone. Brazil’s economic transformation over the past decade has created an explosion of wealth, and most of the world’s leading private banks and wealth managers are scrambling for a piece of the action....