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NEW YORK — After a string of disappointing debuts, the IPO market showed signs of life last week, with shares of four newly public companies each shooting up more than 20 percent in their first day of trading.

All of the companies — Realogy, the owner of realty firms Century 21, Coldwell Banker and Corcoran Group; online stock-photo provider Shutterstock; Kythera, a developer of shots to treat double chins; and Intercept Pharmaceuticals, which develops drugs for liver diseases — garnered strong demand from investors in their debuts Thursday.

The companies raised more money in their initial public-stock offerings than they had predicted, an unusual occurrence over the past few months.

The companies’ stock performance bodes well for the IPO market overall, said Thomas Murphy, head of securities and capital markets for the law firm McDermott Will & Emery.

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“Whether the market has fully recovered, it’s too early to say,” Murphy said. “There’s always some kind of a tipping point where things start to be in vogue and start to get going again. I hope that’s what we’re seeing here.”

The flop of Facebook’s IPO in May had weighed on the amount of money companies were able to raise throughout summer. And about 70 percent of companies that had gone public since late July have priced at the bottom or below the levels they had expected, according to IPO investment and research firm Renaissance Capital.

Other prominent IPOs were canceled, including arcade and restaurant chain Dave & Buster’s Entertainment earlier this month and CKE, the owner of the Carl’s Jr. fast-food chain, in August.

Companies may have had more success last week because they kept their expectations low, pricing shares less aggressively, Murphy said.

The largest IPO Thursday was Realogy Holdings. The Parsippany, N.J., realty firm raised $1.08 billion from its offering.

That was the third-largest U.S. IPO of the year, according to Renaissance Capital.

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