BOSTON - Affiliated Managers Group Inc., an asset management company, announced Tuesday that it had agreed to acquire a 60% share of Welch & Forbes, a wealth management firm, for an undisclosed price.

Both are based in Boston. Welch & Forbes manages $4.2 billion of assets, about 80% of it in equities, for high-net-worth individuals and families. Its average account size is about $2 million.

The cash transaction is expected to close in late October.

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