Billionaire Kirk Kerkorian’s investment company Tracinda Corp. brought its stake in General Motors Corp. back to 9.9 percent after reducing it to 7.8 percent in December, according to a regulatory filing on Wednesday.

Kerkorian acquired 5 million shares on the open market on Jan. 23 at an average price of $21.40 a share for a total of $107 million. He also agreed to purchase an additional 7 million shares the next day for $22.25 per share in a private transaction expected to settle on Jan. 27. The 7 million shares totaled $155.8 million.

Beverly Hills-based Tracinda spent about $262.8 million to acquire the shares, bringing its total holdings in GM to 56 million shares, or 9.9 percent of outstanding shares, the filing said.

In December, Kerkorian and his investment arm sold 12 million shares of General Motors for federal and state tax purposes, reducing its shares to 44 million, or a 7.8 percent stake in the automaker. That was down from a 9.9 percent stake with 56 million common shares.

Tracinda, the majority owner of casino and hotel chain MGM Mirage, began its drive to purchase GM shares in May buying 18.9 million shares. Then in mid-October. Kerkorian spent nearly $56.8 million to increase his stake to 9.9 percent from 9.5 percent in September.

Kerkorian’s past purchase of GM shares rallied the market, especially when he first announced his intention to buy shares of the troubled automaker in May. But one day after the initial offer, Standard & Poor’s downgrade to junk status of GM’s immense debt sent the stock backtracking. GM’s stock has teeter-tottered since then, ending up 3.5 percent Wednesday to $23.85, just before Kerkorian’s boosted stake was revealed in an SEC filing after the market closed.