By Anora Mahmudova and Barbara Kollmeyer, MarketWatch

NEW YORK (MarketWatch) -- U.S. stocks rose sharply on Tuesday morning, boosted by upbeat earnings from Apple, Inc. as well as hopes of further stimulus from the European Central Bank.

A big jump in Apple shares, the heaviest weighted component on the Nasdaq Composite and the S&P 500, helped the benchmarks in early trade.

The S&P 500 (SPX) gained 16 points, or 0.8%, to 1,919.84. The Dow Jones Industrial Average (DJI) rose 80 points, or 0.5%, to 16,577. The Nasdaq Composite (RIXF) jumped 48 points, or 1.1%, to 4,364.08.

Shares of Apple Inc. (AAPL) rose 3%, after the company reported a 13% rise in profit, boosted by strong demand for its new, bigger-screen iPhones and blowing out Wall Street estimates.

Morgan Stanley lifted its price target on Apple to $115 from $110, and analysts at the investment bank said strong iPhone demand and gross margin expansion will help drive upside for shares. Also read: How you could have seen Apple's beat coming

Ahead of the market open, a news report suggested the ECB is considering buying corporate bonds on the secondary markets as it attempts to fight deflationary pressures and revitalize the economy.

Even as the ECB played down the news story about its plans to embark upon a bond-buying stimulus plan, investors took it as a good news.

"ECB (reports) and corporate earnings are propelling stocks higher, but I think here in the U.S., basically the market has hit a bottom and earnings are paving the way for a year-end rally which will take us to new records highs," said Peter Cardillo, chief market economist at Rockwell Global Capital, who said he's looking at the S&P 500 to hit 2,075 by year end.

Economists expect existing-home sales crept higher in September to an annual rate of 5.10 million from 5.05 million in August. That data is due at 10 a.m. Eastern. See the daily data preview

Earnings: Shares of Travelers Cos. (TRV) and United Technologies (UTX) both rose after results.

But McDonald's (MCD) shares inched lower after the fast-food restaurant chain's profit dropped by 30% in the third quarter.

Coca-Cola (KO) shares fell 5.7% after the company's revenue slipped, while it lowered its long-term revenue target and warned it did not expect to meet its earnings view.

Yahoo Inc. (YHOO) will report after the close.

Chipotle Mexican Grill Inc. (CMG) shares fell 4% after it warned sales growth may slow, even as it reported stronger-than-expected earnings late Monday. Follow more of the day's big movers here.

ECB cheer: The euro (EURUSD) fell and European stocks rallied on a Reuters report that the ECB may be investing in the corporate bond market.

China growth slows: The Nikkei 225 index fell 2% on Tuesday, which gave the yen (USDJPY) a boost across the board, while China's Shanghai Composite Index fell 0.7% after data showed China's economy grew in the third quarter at the slowest pace in five years. Europe stocks soared on those ECB reports. and a round of solid earnings.

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