Legg Mason Inc., the money manager that has struggled with more than five years of net redemptions, agreed to buy QS Investors, a global quantitative equity firm that split from Deutsche Bank AG in 2010.

Legg Mason affiliates Batterymarch Financial Management and Legg Mason Global Asset Allocation will be integrated into QS Investors, which has $4.1 billion in funds under management and $100 billion in advisory assets, the Baltimore-based firm said today in a statement. The transaction will result in costs of about $35 million to Legg Mason, which didn’t disclose the terms of the purchase.

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