The world's wealthiest people are returning to the private banks of some of the world's largest banking institutions, a welcome turnaround from the depressed numbers private bankers have seen since the financial crisis. Competition is fierce, and as more moneyed customers are settling on just one bank for all of their banking needs, big banks are pulling in more clients.

According to a new ranking by London-based wealth management watcher Scorpio Partnership, three U.S. banks made the list of the top private banks in the world, with Bank of America (NYSE:BAC) in second place, Wells Fargo taking third, and Morgan Stanley (NYSE:MS) residing at No. 4.

Great news, indeed. For Bank of America, however, the announcement is less than joyful -- since it points out the fact that Swiss bank UBS (NYSE:UBS) now has the No. 1 spot, formerly occupied by B of A.

Private banking picks up steam
The study represents a stunning reversal for scandal-prone UBS, which posted a fourth-quarter loss in 2012 after a particularly bumpy year. The bank's downsizing of its investment banking arm and concentration on its private banking section has paid off, though: UBS clocked 9.7% in asset growth last year, compared with Bank of America's 5.6%.

Banks tailored for the super-rich have been ramping up lately as the ranks of the wealthy swell and private banks focus on managing this segment's assets on a global basis. Citigroup (NYSE:C), for instance, is bolstering its own presence in Asia and Latin America, and currently boasts a client list that includes 33% of the world's billionaires.

Here at home, Morgan Stanley has been courting well-heeled customers in upscale areas of states like in New York and Texas, bestowing jumbo mortgage loans and raking in big deposits through its Private Wealth Management arm.

Profits need a boost
Unfortunately, all of this activity hasn't translated into more profits for these banks. Scorpio noted that profits climbed, on average, only 9.8% last year, versus 12.3% in 2011. Much of this is due to rising costs, according to the consulting firm. Both UBS and Bank of America have been concentrating on trimming expenses lately, and the study notes that diversified banks have done a better job at keeping costs down for banks that specialize in wealth management alone.

But emerging markets have represented fertile hunting grounds for private banks, which may explain why B of A has slipped. While wealth inflows from North America, Europe, and Japan increased in 2012 by 5.9%, emerging markets saw growth of 12.9%, according to Bloomberg. Bank of America has sold its non-U.S. wealth management operations to Julius Baer, choosing to concentrate on the domestic front rather than try to boost the underperforming units.

B of A: too much shrinking and not enough expansion?
Will this recent development prompt Bank of America to rethink wealth operations outside of the U.S.? Time will tell, but the big bank seems to be aware of the situation. A recent report by its Merrill Lynch and U.S. Trust units noted that global growth is steadily being influenced by an emerging newly affluent middle class in China and elsewhere, while global economics are tilting less toward the U.S. consumer.

Maybe B of A will learn a timely lesson from UBS: Cost containment is important, but so is expansion into profitable markets. If UBS can do both simultaneously, there's no reason Bank of American can't do the same.

Fool contributor Amanda Alix has no position in any stocks mentioned. The Motley Fool recommends Bank of America and Wells Fargo. The Motley Fool owns shares of Bank of America, Citigroup, and Wells Fargo. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.