UBS beat expectations with its first quarter net profit, which came in at 1.05 billion Swiss francs ($1.2 billion), as the bank continues to focus on building out its wealth management and private banking business while trimming back its investment bank.
The world's top 25 private banks by assets experienced average growth of 11.3 percent in 2013. Together, the firms manage over 78 percent of the wealth management industry's assets, up 1 percent from last year, Scorpio said.
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Bank of America Merrill Lynch (BofA ML) maintained second position on the Global Private Banking Benchmark, as assets under management (AUM) grew 12.5 percent last year to $1.86 trillion. Morgan Stanley is ranked third, with 17.5 percent growth in AUM of to $1.45 trillion.
BofA ML's decision to sell its international wealth management arm in 2012 to Julius Baer, which helped to boost the Swiss private bank's assets by 40 percent, is just one example of U.S. firms choosing to focus on their home market, Scorpio said.
BNP Paribas and Deutsche Bank both crept up one position on the benchmark, while HSBC slipped from sixth to eight place, due to its strategy to pull out of non-core markets.
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"This year's results highlight major structural changes taking place in global wealth management," Seb Dovey, managing partner of Scorpio partnership, said in a statement. "The findings demonstrate that the international wealth management secotr is acclimatising to a 'new normal'. Strong growth figures are commonplace, but so too are rising costs as the recovery is accompanied by increased regulation."
—By CNBC's Jenny Cosgrave: Follow her on Twitter