Appaloosa Management added new stakes in Apple and State Street in the third quarter while cutting exposure to Facebook and e-commerce hub Alibaba.

Billionaire manager David Tepper's firm had added 100,000 shares of Apple and 1.2 million shares of financial firm State Street by the end of September. Appaloosa cut its position in Facebook by 1.8 million shares, to 3.3 million shares, and more than halved its stake in Bank of America, to 3.4 million shares.

Apple gained 0.6 percent in after hours trading following the release of Appaloosa's filing with the Securities and Exchange Commission.

In mid-September, Tepper told CNBC that Facebook's stock looked inexpensive at its price and that the fund had not reduced its holding.

"It's kinda cheap in this market for the growth rate. So we're still holding on as big as we were," Tepper told CNBC's Scott Wapner on Sept. 13.