James Coulter speaking at the 2017 Delivering Alpha conference in New York on Sept. 12, 2017.

Even though public U.S. stock markets are at all time highs, the era of private markets is fast approaching, according to James Coulter, the co-founder of private equity firm TPG, which owns a stake in the high-profile, but privately held Uber.

Coulter was delivering the luncheon keynote speech at the Delivering Alpha conference on Tuesday in New York.

Companies like the fast-growing ride hailing service Uber are choosing to stay private for longer, Coulter said, because of the difficulty of making a public stock debut.

Two recent high-profile stumbles underscore his point. Blue Apron and Snap did IPOs this year that largely flopped.

Coulter said instead companies like Instagram are selling to much larger public companies like Facebook or they are waiting longer to become public companies themselves. "We're going into the era of the private markets," Coulter said.

Companies have plenty of time to work out their growing pains when they are not subject to the daily scrutiny of public shareholders. Uber recently went through a board upheaval and the naming of a new chief executive officer. Fellow TPG partner David Bonderman quit Uber's board in July after taking heat for a sexist remark. The ride-hailing company has been under investigation for its workplace culture.

That said, Uber's new CEO, Dara Khosrowshahi, said recently that an IPO is not far down the road, perhaps as early as 2019.

Asked whether he would sell some of TPG's stake in Uber, Coulter said "We're happy with our position in the company. It's been an interesting ride."

The conference is presented by CNBC and Institutional Investor.



