(Bloomberg) -- The world’s largest company by market capitalization got a little bit bigger Tuesday.

Apple Inc., which began flirting with a record valuation of $700 billion during midday trading in November, ended the day at $710.7 billion, marking the first time a U.S. company has reached that milestone. Shares rose 1.9 percent to $122.02 at the close in New York.

The iPhone maker is now more than twice as valuable as longtime rival Microsoft Corp. Exxon Mobil Corp., the world’s next-biggest company, has a market capitalization of $385.4 billion. Optimism about Apple has been growing since Chief Executive Officer Tim Cook revealed larger-screened, more expensive iPhones in September, which helped fuel a record profit during the last three months of 2014. China, where revenue rose 70 percent, is helping to fuel the jump in revenue.

“Given Apple’s powerful iPhone cycle, a big 4G ramp in China and the upcoming launch of Apple Watch in April, we believe there is still plenty to look forward to at Apple during this transformational cycle,” Brian White, an analyst at Cantor Fitzgerald, wrote in a note to investors.

Apple is also preparing ship its first new product line to debut under Cook’s leadership -- the Apple Watch, which has further stoked interest in the Cupertino, California-based company.

David Fuller's view

Apple is by far the most iconic share in the world today.  Inevitably, that will not always be the case but its present psychological influence on the market is considerable. 

Today, plenty of people are worried about Wall Street.  This is partly due to the ‘wall of worry’ that accompanies every bull market.  It is also due to the many uncertainties, not least how the experimental policy of QE works out over the longer term.  There are also plenty of hedge fund managers who hope for a big stock market shakeout so that they can improve their performance sufficiently to justify their fees.  People were short 58,991,635 shares of Apple, according to the Nasdaq Short Interest report as of January 30^th, which was released today.

In my opinion, if Apple can now stay above $120, this will be another reason why Wall Street indices will not break down out of their current trading ranges.