But in recent weeks, unicorn valuations have cooled off. Several funds run by Fidelity, including Contrafund, have cut the valuations of some big private companies, including Snapchat, Zenefits and Delphix Corp. Individual portfolio managers don't set valuations, which at Fidelity are done by a separate investment committee. Contrafund doesn't own Snapchat, which the committee devalued by 25 percent in October, but it does own Delphix, which the committee cut by 43 percent.

Danoff said he feels good about the two dozen or so pre-IPO companies in his portfolio. But even two years ago, when Contrafund made a $159.4 million investment in Pinterest's Series E funding round, Danoff admits to balking at the price.

"I was like, 'My gosh, that's a high valuation,'" Danoff said. But since then, the value of that Series E stake in Pinterest has climbed nearly 150 percent, according to Contrafund disclosures.

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