BlackRock's assets under management hit a new high in the second quarter as global markets rallied, but its shares tumbled as much as 7% after a large Asian institutional client pulled money from an index strategy.

BlackRock reported second-quarter net income of $1.59 billion, up 7% from a year ago on a GAAP basis, the firm said Tuesday. That amounted to earnings per share of $10.19, topping the $10.06 expected by analysts.