* Dow Chemical jumps on Third Point stake
* Verizon, Travelers and J&J all fall after results
* IBM down, Cree rises in extended trading after results
* Dow off 0.3 pct, S&P up 0.3 pct, Nasdaq up 0.7 pct
By Ryan Vlastelica
NEW YORK, Jan 21 (Reuters) - U.S. stocks mostly rose on Tuesday, with the S&P 500 snapping a two-session decline as the materials sector rallied, though the Dow fell on disappointing earnings by three of its components.
Trading was volatile, with the S&P fluctuating between positive and negative territory throughout the session, while the Dow moved between modest and solid losses and the Nasdaq swung between modest and strong gains.
The S&P materials index rose 0.6 percent as one of the best performing major S&P indexes, led by a 6.6 percent gain in Dow Chemical to $45.93. Activist investor and hedge fund manager Daniel Loeb has taken a stake in the company and wants it to spin off its petrochemical arm.
In addition, Alcoa Inc jumped 6.8 percent to $12.13 following an upgrade to "overweight" from JPMorgan. The firm also lifted its price target on the aluminum company to $15 from $9.
Energy stocks, another group with some correlation to the pace of economic growth, advanced 0.5 percent.
"We still think economically-sensitive stocks have room to run... Those have the potential to be long-term winners," said Jeff Mortimer, director of investment strategy for BNY Mellon Wealth Management in Boston.
The Dow fell as Travelers Cos Inc, Verizon Communications Inc and Johnson & Johnson - all bellwethers for their sectors - tumbled following results.
Travelers fell 1.7 percent to $85 after posting a profit that beat expectations, though investors worried about the insurance provider's margins. Verizon lost 1.3 percent to $47.70, while J&J dropped 1.1 percent to $94.03 after it gave a forecast at the low end of analyst expectations.
According to Thomson Reuters data, earnings for the fourth quarter are expected to grow 7 percent over the prior year. Of the 61 companies in the benchmark S&P index that have reported so far, about 56 percent topped analyst expectations, below the long-term average of 63 percent. About 71 percent have topped revenue forecasts, above the long-term average of 61 percent.
The Dow Jones industrial average was down 44.12 points, or 0.27 percent, at 16,414.44. The Standard & Poor's 500 Index was up 5.10 points, or 0.28 percent, at 1,843.80. The Nasdaq Composite Index was up 28.18 points, or 0.67 percent, at 4,225.76.
As the Federal Reserve has embarked on its plan to reduce stimulus, investors will closely monitor corporate profits for signs of growth. About eight companies have issued negative outlooks for every positive one, which would mark the lowest ratio on record should it continue.
"Results are running light, and negative announcements have been off the hook with very high levels of negative guidance," said Mortimer, who helps oversee about $185 billion in client assets. "The market pays a premium for growth, and the stocks that have rallied and then disappointed are susceptible to large drops almost immediately."
International Business Machines Corp turned lower in after-hours trading. The Dow component reported adjusted fourth-quarter earnings that beat expectations, but revenue was below consensus.
Cree Inc rose 4.2 percent after the market closed after posting second-quarter revenue that topped expectations.
U.S.-listed shares of BlackBerry Ltd were the top boost to the Nasdaq 100, jumping 9.4 percent to $9.93 as short-sellers bailed out of the smartphone maker. The stock is up about 33 percent in 2014.
Delta Air Lines Inc rose 3.3 percent to $32.08 after it reported a higher-than-expected fourth-quarter profit, aided by lower fuel costs.
About 63 percent of companies that trade on the New York Stock Exchange closed higher while 59 percent of Nasdaq-listed names ended in positive territory. About 6.78 billion shares traded on all U.S. platforms, according to BATS exchange data.