Apple Inc shares were trading at $512 on Tuesday, down sharply from $702.10 in September, on worries that its mobile devices are no longer as popular.

Based on options activity just hours before the announcement, due after the market close, traders were estimating about a 7 percent one-day move after the earnings, which would be a much more volatile outcome than normal for Apple. Such a move could push the shares as low as $465 or as high as $535, depending on how earnings come out.

"Three ingredients make this earnings for Apple especially appetizing for options traders: (CEO) Tim Cook has missed earnings estimates 60 percent of the time over the past five quarters, the stock has crashed almost 30 percent since September, and no stock has as many hedge funds owning it," said Gareth Feighery, a founder of options education firm Markettamer.com in Philadelphia.

"Combine those three factors together and Apple is a fireworks display ready to ignite, which makes it no surprise to see its options building in a move of close to 7 percent post-earnings."

In the previous eight quarters, the average one-day earnings move has been 3.9 percent, according to RiskReversal.com, an options research firm based in New York.

As competition intensifies from Samsung Electronics Co Ltd and others using Google Inc's Android software, investors are wondering if Apple's days of hyper growth are over.

Despite the sharp decline in recent months that cost Apple nearly $190 billion in market capitalization - about equal to the entire value of AT&T - plenty of Apple bulls remain on Wall Street, with about four-fifths of the nearly 60 analysts covering the company rating it "buy" or "strong buy," according to Thomson Reuters data.

The median price target on Wall Street is $745, roughly 50 percent above Apple's current stock price.

Dan Nathan, a co-founder of options research firm RiskReversal.com, expects a bounce in shares after results.

"The sentiment got too negative too fast, and expectations for Q1 and Q2 may be achievable and possibly even too low," he said. Nathan said the stock could rebound to about $550 before running into problems, if Apple can "beat and dispel most of the rumors about either iPhone demand or production issues in the quarter, and guide in-line or a tad higher than Wall Street consensus."

Hedge fund manager David Einhorn said in a letter to investors he bought back shares in Apple.

The shares are trading at 9.8 times estimated forward 12-month earnings, a level that analysts say is unusually inexpensive for a company with its growth profile.

But some were more cautious, given the loss of momentum in the stock that had helped it hit records in September and drive the S&P's rally through the summer.

"While there is a bulk of activity in calls way out-of-the-money in prices like $520 and $550, there is also a lot of buying of the at-the-money puts at around $500," suggesting that the put buyers who are most likely to be Apple stock owners are hedging against an immediate downside risk, said JJ Kinahan, chief derivatives strategist at TD Ameritrade.

Feighery noted that February weekly $510 strike calls expiring on the week of February 22 are cheaper than their equivalent puts, suggesting concerns about whether Apple can "bounce back short-term with conviction and maintain its gains."

Analysts, on average, estimate Apple's fiscal first-quarter earnings per share of $13.41, down slightly from $13.87 in the year-earlier quarter. Revenue is seen up 18 percent at $54.7 billion, according to Thomson Reuters I/B/E/S.

Wall Street estimates Apple sold between 47.5 million and 53 million iPhones, up considerably from the 26.9 million sold in the previous quarter, when the iPhone 5 had not yet made it to all markets. IPad sales are expected at 23 million to 25 million.

The company is expected to continue to post double-digit revenue growth into at least 2015 and a Thomson Reuters StarMine analysis of its expected growth over the next decade puts the stock's intrinsic value at about $708 a share.

(Reporting by Angela Moon in New York and Doris Frankel in Chicago; editing by David Gregorio and Nick Zieminski)

By Angela Moon and Doris Frankel

Stocks treated in this article : Samsung Electronics Co., Ltd., Apple Inc., Google Inc, AT&T Inc.