Research In Motion Ltd. has doubled in value over the past three months while Apple Inc. shares have slumped, a turnabout that has rewarded investors such as Renaissance Technologies LLC.

Renaissance, the hedge fund of billionaire Jim Simons, bought 9.9 million RIM shares last quarter while selling almost 600,000 Apple shares, according to data compiled by Bloomberg. As the CHART OF THE DAY shows, RIM has become the inverse of Apple this year, turning the two stocks into a mirror image.

RIM investors are betting that BlackBerry 10 phones, due in February, will let the company win back customers from the iPhone and devices running Google Inc.’s Android. Apple, meanwhile, has been dogged by concerns that orders are slowing for its phones and tablets, as well as a flubbed introduction of mapping software. That’s caused some investors to look elsewhere, said Alex Gauna, an analyst at JMP Securities LLC.

“You’ve seen some freeing up of funds from Apple -- sometimes that will find a home in a peer such as Research In Motion,” Gauna, who is based in San Francisco, said in an interview. “I don’t want to go so far as to say that the market has begun to make a massive bet that Apple is in trouble.”

RIM reports its third-quarter results later today, giving investors a view into its comeback efforts. Analysts estimate that sales declined 49 percent to $2.66 billion in the period. They’re projecting a loss of 35 cents a share, excluding some items, which would mark RIM’s third straight quarter in the red.

With BlackBerry 10, RIM has to win back users who have abandoned the once-dominant smartphone during its slump. The company will finish 2012 with 4.7 percent of the market, with Apple and Android taking almost 90 percent, according to IDC.

Renaissance, which manages more than $15 billion in assets, bought at least $62 million in RIM shares last quarter while selling Apple stock worth at least $340 million. The East Setauket, New York-based firm declined to comment on the purchases or their exact timing.

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