American International Group Inc., the bailed-out insurer, posted a fourth-quarter profit fueled by a tax benefit and an increase in the value of a stake in Asian insurer AIA Group Ltd.

Net income rose to $19.8 billion, or $10.43 a share, from $11.2 billion, or $16.60, a year earlier, when the insurer booked gains from the sale of businesses, according to a statement Thursday from the New York-based company. Operating income, which excludes some investment results and the tax figure, was 82 cents a share, beating the 59-cent average estimate of 14 analysts surveyed by Bloomberg.

Chief Executive Officer Robert Benmosche, 67, has asked potential investors to focus on property-casualty and life units as he seeks private funds to replace the U.S. Treasury Department’s majority stake. The insurer’s results have been affected by swings in the value of mortgage investments and shares of Hong Kong-based AIA, which climbed 8.7 percent in the fourth quarter. AIG posted a $4.11 billion loss in the three months ended Sept. 30.

The volatility “is something we should expect from AIG for a couple of years until they can divest” or wind down some of these assets, Paul Newsome, an analyst with Sandler O’Neill & Partners LP, said in an interview before the announcement. “The results will swing back-and-forth.” Newsome has a “hold” rating on the stock.

AIG rose 1.2 percent to $27.99 at 4:02 p.m. Thursday in New York before results were announced. The insurer climbed 21 percent this year, after slumping 52 percent in 2011. The Standard & Poor’s 500 Index has jumped 8.4 percent since Dec. 31 and was little changed in 2011.

AIG posted a tax benefit of $17.7 billion. Losses at the insurer and its subsidiaries helped rack up more than $25 billion in deferred tax assets at the end of 2010 that can be used to lower obligations to the government.

AIA Stake

Results included a mark-to-market gain on AIA of about $1 billion. AIG retained a stake in the Asian insurer after divesting two-thirds of the company in 2010 in an initial public offering to raise funds to help pay back its rescue.

An eventual sale of the remaining AIA shares, valued at about $14 billion, could be used to “buy some of the overhang from the U.S. Treasury,” Benmosche said at a conference sponsored by Bank of America Corp. last week. AIG may wait to sell the shares if it can use other funds to repay some obligations to the government, he said. An agreement with underwriters prohibits AIG from selling its entire AIA stake until April.

Property-Casualty Unit

Benmosche named Peter Hancock to lead Chartis, AIG’s property-casualty division, in March after the unit took charges of more than $4 billion in the fourth quarter of 2010 when it determined its reserves were insufficient.

The SunAmerica division, which sells life insurance and retirement products, has gained market share lost after the 2008 bailout. AIG regained its rank as top seller of fixed annuities in the U.S. in the nine months ended Sept. 30, according to data compiled by trade group Limra.

The Treasury reduced its ownership of AIG in May by selling 200 million shares for $29 each in a public offering. The government needs to divest its stake for an average of at least $28.72 a share to recoup its investment. The insurer has closed below that level every trading day since late July.

AIG was rescued in 2008 as bets on the mortgage market soured. The bailout was revised at least four times, swelling to $182.3 billion as the U.S. extended more credit and lowered the interest charged.