Hedge-fund managers David Einhorn and George Soros increased their stakes in Apple Inc. (AAPL) during the fourth quarter.

High-flying Apple shares stumbled last quarter, falling 20% amid concerns about the company's momentum and consumer demand for its devices. The stock is down another 12% so far this year, closing regular Thursday trade at $466.59, well off a September peak at $705.07.

Mr. Einhorn's Greenlight Capital (GLCI.XX), which has owned Apple shares since 2010, is currently in a high-profile battle with the technology giant over its proposal to eliminate preferred stock from the company charter. Apple, for its part, has called the battle "a silly sideshow."

Mr. Einhorn increased its Apple holdings by about a fifth, to 1.3 million shares from 1.1 million shares. The filing also showed a position of 275,000 call options. Call options give shareholders the right to buy shares at a set price by a designated date.

Soros Fund Management LLC (SRS.XX), Mr. Soros' company, more than doubled its stake in Apple, adding 99,118 shares of the iPhone and iPad maker. The position, which is now 183,976 shares, was valued at $98 million at the end of the fourth quarter.

Mr. Soros moved away from the social networking space in the fourth quarter, eliminating a 300,000-share stake in Facebook Inc. (FB) and a LinkedIn Corp. (LNKD) holding that had been 1.2 million shares at the end of September.

Mr. Einhorn's firm also showed a new stake in Google Inc. (GOOG), with 63,000 shares. He appeared to have eliminated previously disclosed stakes in Humana Inc. (HUM), WellPoint Inc. (WLP) and others.

The moves were revealed in so-called 13-F filings with the U.S. Securities and Exchange Commission Thursday. Firms that control investment portfolios of more than $100 million are required to report stock holdings 45 days after the end of a given quarter, giving the public its most fresh possible glimpse into the investing decisions of high-profile money managers.

Activist investor William Ackman's fund Pershing Square Capital Management LP (PSCM.XX)reported no stake in Hawaiian commercial property firm Alexander & Baldwin Inc. (ALEX), though his filing did not mention Mr. Ackman's highest-profile wager.

In December, he launched a public campaign against nutritional supplement maker Herbalife Ltd. (HLF), calling the company a pyramid scheme and disclosing he had shorted more than 20 million of Herbalife shares, valued at roughly $1 billion at the time.

Herbalife has denied Mr. Ackman's accusations. Other fund managers have taken the opposite view on Mr. Ackman's thesis, including Carl Icahn, who squared off with Mr. Ackman in a confrontation on CNBC last month. Mr. Icahn on Thursday revealed a 13% stake in Herbalife, though the disclosure wasn't in his 13-F because Mr. Icahn's investment came in January, missing the Dec. 31 deadline for the filing.

Compared to last quarter, the only new holding in Mr. Icahn's filing is Transocean Ltd. (RIG), an offshore drilling company. But Mr. Icahn had already disclosed the stake, which now amounts to about 5.9% of Transocean's outstanding shares, in a separate SEC filing in January.

Mr. Icahn did omit some information on his holdings in the filing, an action some investment managers are permitted by the SEC to take when they're building or eliminating a position. Such "confidential treatment" prevents others from piggy-backing on their investment ideas. Confidential treatment is usually applied to positions being added by managers.

Meanwhile, Mr. Soros's fund boosted its stakes in commercial banking giants Citigroup Inc. (C) and J.P. Morgan Chase & Co. (JPM), while adding a new position in Morgan Stanley (MS).

Mr. Soros, who waded back into bank stocks in the third quarter with the addition of Citi and J.P. Morgan, boosted the two holdings by 6.6 million shares and 1.6 million shares in the fourth quarter, respectively. The firm also has a 1.3 million call option on Citi, according to the filing.

The fund also bought 4.1 million shares of Morgan Stanley, worth $79.2 million at the end of the fourth quarter.

Over the past two months, many analysts have raised their earnings estimates on the big banks and securities firms amid the resolution of the U.S. fiscal cliff and less uncertainty surrounding the European sovereign debt crisis. The financial services industry has also been buoyed by an improvement in capital markets activity.

Financier Nelson Peltz's Trian Fund Management (TRIANFM.XX) reported reduced holdings in custody bank State Street Corp. (STT), owning 3.1 million shares valued at $148 million as of the end of December. Three months prior, Trian reported holding more than 9 million shares valued at $386 million.

Trian also reported no position in the food company formerly known as Kraft Foods Inc. (KRFT) after it previously disclosed holding more than 8 million shares of valued at $336 million.

Kraft changed its name to Mondelez International Inc. (MDLZ) last year after spinning off Northern American grocery operations.

The fund reported a new holding in Richmond, Va.-based packaging company MeadWestvaco Corp. (MWV), which produces packaging for companies in the healthcare, beauty and tobacco industries, among others. Trian reported holding 1.6 million shares in the company with a value of $51 million.

--Brett Philbin, Christian Berthelsen, Annie Gasparro and Andrew R. Johnson contributed to this story

Write to Mia Lamar at mia.lamar@dowjones.com, Paul Ziobro and Liz Moyer

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