Private-equity firms, the exclusive money managers overseeing $3 trillion worldwide for the wealthiest investors, are discovering a new type of client: ordinary people.

Carlyle Group, Blackstone Group and KKR & Co., which usually open their doors only to clients willing to commit at least $5 million, are lowering that threshold or offering investments directly to individuals, an effort to attract fresh cash amid lackluster fundraising. Their ultimate goal: a slice of the $3.57 trillion Americans have accumulated in their 401(k) retirement plans.

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