* Oil prices fall for sixth day in a row
* Apple gives biggest boost to S&P 500, Nasdaq
* Under Armour hit by Morgan Stanley rating cut
* Alcoa to kick off earnings season after close
* Indexes up: Dow 0.44 pct, S&P 0.45 pct, Nasdaq 0.49 pct (Updates to open)
By Abhiram Nandakumar
Jan 11 (Reuters) - U.S. stocks broadly rose on Monday, led by Apple, as they rebounded off their worst-ever start to a year and with the corporate earnings season set to kick off.
All 10 major S&P sectors opened higher, before the energy and materials sectors reversed course, staying under pressure as oil prices fell for the sixth day in a row, hovering near 12-year lows.
Global stocks were mixed as jittery investors looked for stability after a bruising start to the year due to declining oil prices and mounting worries about a China-led slowdown in global economic growth.
The S&P 500 slid 6 percent and the Nasdaq dropped 7.3 percent last week. Not even a surge in U.S. nonfarm payrolls in December stemmed the bleeding.
"A relief rally would be expected at some point during the recent precipitous fall," said Andre Bakhos, managing director at Janlyn Capital LLC in Bernardsville, New Jersey.
Bakhos, however, warned of escalating concerns over the issues such as China and falling oil prices that have plagued the market all of last year.
At 9:37 a.m. ET (1437 GMT), the Dow Jones industrial average was up 72.08 points, or 0.44 percent, at 16,418.53.
The S&P 500 was up 8.66 points, or 0.45 percent, at 1,930.69 and the Nasdaq Composite index was up 22.95 points, or 0.49 percent, at 4,666.58.
The consumer staples sector's 0.72 percent rise led the gainers. The health sector, off 0.56 percent, recorded the smallest drop among the three decliners.
The other two decliners, energy and materials companies, are expected to be main cause behind U.S. corporate earnings moving into a recession - two quarters of falling profits - in the fourth quarter.
Overall, fourth-quarter corporate earnings are expected to decline 4.2 percent, according to Thomson Reuters I/B/E/S.
Alcoa is scheduled to report fourth-quarter results after the close, starting the earnings season. The stock was up 1.4 percent at $8.17.
Apple's shares were up 1.6 percent at $98.48, providing the biggest boost to the S&P 500 and Nasdaq.
The company's music streaming service hit the 10 million-subscriber mark in six months, the Financial Times reported. Mizuho upgraded the stock to "buy".
Macy's was up 4.4 percent at $37.48 after hedge fund Starboard Value urged the department store chain to enter into joint ventures for its stores.
Under Armour was down 4.7 percent to $71.47 after Morgan Stanley cut its rating and price target on the stock.
Advancing issues outnumbered decliners on the NYSE by 1,825 to 820. On the Nasdaq, 1,463 issues rose and 772 fell.
The S&P 500 index showed one new 52-week high and 17 new lows, while the Nasdaq recorded seven new highs and 73 new lows. (Reporting by Abhiram Nandakumar in Bengaluru; Editing by Savio D'Souza)