State Street Corp. may try to expand its private client business by buying one or two smaller players, president and chief executive officer David A. Spina said Tuesday.

Speaking to a group of buy and sell side analysts at the company's yearly presentation in New York, Mr. Spina acknowledged that State Street had been outgunned in the personal trust area by such competitors as Northern Trust Corp. of Chicago. State Street, based in Boston, has focused on institutional asset management.

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