The S&P 500 jumped 2.5 percent to 1,969.28 at 4 p.m. in New York, after the gauge’s second-biggest weekly retreat this year.

“Now that China showed that it was not going to break down further, our market is taking back what it lost on Friday,” said Matt Maley, an equity strategist at Miller Tabak & Co LLC in New York. “The market got hit hard on Friday because people were worried about China.”

Equities around the world climbed today, led by China. A rally in Shanghai in the final hour of trading followed a pattern that has recently suggested state intervention to prop up the nation’s equities. U.S. stocks have turned more volatile in recent weeks amid concerns that a Chinese economic slowdown will weigh on global growth, while investors bet the Federal Reserve is on course this year for its first interest-rate increase since 2006.

The S&P 500 swung up or down an average of 2 percent a day for more than two weeks through Friday, while before Aug. 20, the 2015 average was around 0.6 percent. In 10 of the last 13 days, the benchmark has closed with a move of at least 1.3 percent. The Chicago Board Options Exchange Volatility Index had posted 11 straight sessions above 25, a level that before August it touched on just five days since 2011.

U.S. stocks slumped last week as August payrolls data gave little guidance on interest rates. The S&P 500 lost 3.4 percent, the second-biggest retreat since December behind the 5.8 percent plunge it suffered in the five days through Aug. 21. The Dow Jones Industrial Average has had declines of more than 270 points in five of the last 12 sessions, the biggest cluster of selloffs since the summer of 2011.

Investors remain confident the Fed will raise borrowing costs this year, even as they pare bets on policy makers deciding to do so at a meeting next week. Traders are pricing in a 30 percent chance the central bank will increase rates at this month’s gathering, down from 48 percent before China’s currency devaluation on Aug. 11. Odds of a move at the December meeting are 59 percent, according to data compiled by Bloomberg.

“These next two weeks are very important — the Chinese market has reopened, we have FOMC next week, we may get some guidance from U.S. companies,” said Pierre Mouton, who helps manage $8.3 billion at Notz, Stucki & Cie. in Geneva. “When it comes to the Chinese situation, it’s important that either you’re positive and think the government can handle the situation and everything will come back to normal, or you’re negative and think a downward spiral has started.”

All of the S&P 500’s 10 main industries climbed at least 1.3 percent Tuesday, with industrial, raw-material, health-care and technology companies rising the most, up more than 2.4 percent.

“We’re just enjoying the snapback rally today,” said Walter “Bucky” Hellwig, who helps manage $17 billion as a senior vice president at BB&T Wealth Management in Birmingham, Alabama. “The market was slightly oversold and there was a lack of any bad news from over the weekend.”