Stocks soared at the open on the first trading day of the New Year after a manufacturing report from China lifted optimism about the global economy.

The S&P 500 and the Nasdaq also opened sharply higher. The CBOE Volatility Index, widely considered the best gauge of fear in the market, was trading near 23.

All 10 S&P sectors started off firmly in the black, led by financials and materials.

For 2011, the Dow finished higher, while the S&P erased its gains to close out largely flat and the Nasdaq ended in negative territory.

“Market’s feeling euphoric and focusing on the positives—we’ve had better news out of Asia and Europe,” said Kenny Polcari, managing director of ICAP Equities. “I think the euphoria stays until Jan. 9 when Sarkozy and Merkel meet…and barring an implosion in Europe, we may see a bit of a rally.”

Worries over the European debt crisis, which dictated the wild market swings for most of the year, are expected to continue.

French President Nicolas Sarkozy, German Chancellor Angela Merkel and British Prime Minister David Cameron all warned of a difficult year ahead in their New Year messages to their respective nations. Despite the arrival of 2012 heralding the tenth anniversary of the single currency 's coming into circulation, there were no celebrations to mark the birth of the euro coins and notes.

Meanwhile, euro zone manufacturing activity declined for a fifth consecutive month in December, although at a slightly slower rate than November's 28-month record low, a survey showed on Monday, suggesting the decline would continue in the early months of 2012.