Plenty of investors are still willing to pay extra to have humans look after their wealth.

Just ask Garth Taljard, who runs 50 multi-asset funds for Schroders, the U.K.'s biggest asset manager. As mutual funds lost more than $300 billion in the U.S. since 2014 amid the rush into cheaper passive funds that mimic indexes, he was hiring to keep up with demand that doubled over five years.

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