In the race to bulk up in mutual funds, a number of banks with midsize fund businesses are having trouble keeping up.

Banks managing $1 billion to $10 billion of mutual funds saw their fund assets increase by an average of just 4.4% in the first three months of this year-far below the 8.3% for banks managing more than $10 billion, according to data provided to American Banker by Lipper Analytical Services.

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