* China factory activity contracts, stoking economic fears
* U.S. shares open lower, European stocks fall
* German and U.S. bonds rally; safe-haven yen, gold rise (Updates to U.S. markets open, changes byline, dateline, previous LONDON)
By April Joyner
NEW YORK, Jan 2 (Reuters) - Stocks around the world treaded water to ring in the new year while safe-haven assets including bonds, gold and the Japanese yen rallied on Wednesday as Chinese and European economic data bolstered concerns of a slowdown in global growth.
In the United States, the benchmark S&P 500 stock index dropped as much as 1 percent after data showed Chinese factory activity contracting for the first time in more than two years, though the index pared losses later in the session.
The data intensified fears that the global economy may be flagging, which contributed to U.S. stocks posting a loss in 2018 for the first time in a decade.
The Purchasing Managers' Index (PMI) for the euro zone also reached its lowest level since February 2016, and France's PMI fell in December for the first time in two years. The pan-European STOXX 600 index fell as much as 1.7 percent but recovered most of its losses and ended down 0.13 percent.
Though U.S. economic data has been relatively strong compared to data from China and Europe, several economic indicators have not been released recently because of the partial U.S. government shutdown. That has left a void of positive data, said Oliver Pursche, chief market strategist at Bruderman Asset Management in New York.
Investors moved into bonds as a result. Yields on U.S. 10-year Treasury notes hit an 11-month low. Earlier, 10-year German Bund yields slumped to 20-month lows in their biggest one-day fall in two years.
Other safe-haven assets benefited as well, with gold reaching six-month highs and the Japanese yen hitting a seven-month high against the dollar.
"It's a global flight to safety," Pursche said. "Given the global macro insecurity out there, people are in risk-off mode."
Yet there was an encouraging sign for investors as U.S. and European stocks bounced off the day's lows, he added.
"I wouldn't be entirely surprised if we ended up flat or even up at the end of market," Pursche said, referring to the S&P 500. "Sentiment is driving the market, and sentiment can change quickly."
The Dow Jones Industrial Average fell 22.79 points, or 0.1 percent, to 23,304.67, the S&P 500 lost 1.41 points, or 0.06 percent, to 2,505.44 and the Nasdaq Composite added 9.97 points, or 0.15 percent, to 6,645.25.
MSCI's gauge of stocks across the globe shed 0.38 percent.
Benchmark 10-year U.S. Treasury notes last rose 6/32 in price to yield 2.6717 percent, from 2.691 percent late on Monday.
The dollar index, which measures the greenback against a basket of six other currencies, rose 0.7 percent as the euro and sterling fell.
Bucking the risk-off trend, oil prices rose as U.S. stocks pared losses. Brent crude futures rose $2.38 to $56.18 a barrel, a 4.4 percent gain. U.S. West Texas Intermediate crude futures rose $2.09 to $47.50 a barrel, a 4.6 percent gain.
Reporting by April Joyner; Additional reporting by Wayne Cole in Sydney and Sujata Rao and Abhinav Ramnarayan in London; Editing by Mark Heinrich and Andrea Ricci