SHANGHAI, Jan 2 (Reuters) - China and Hong Kong stocks fell on their first trading session of 2025, hurt by weaker-than-expected Chinese factory activity data, while investors awaited more policy support.

** China's blue-chip CSI 300 Index .CSI300 dropped 1.4% by the lunch break, while the Shanghai Composite Index .SSEC lost 1.1%. Hong Kong benchmark Hang Seng .HSI was down 1.5%.

** China's factory activity grew in December but at a slower-than-expected pace, missing investors' expectations, as overall sales were dampened by falling export orders amid concerns over the trade outlook, a private-sector survey showed.

** Chinese stocks registered their first annual gain in 2024 following an unprecedented three-year decline, as a package of stimulus policies lifted investor sentiment.

** "The equity market's performance will largely depend on the strength of upcoming policies," said analysts at Huaxi Securities in a note.

** "Uncertainties surrounding potential tariff increases by the Trump administration could affect exports. Boosting domestic demand remains crucial for fundamental recovery."

** Many market participants expect the market will lack clear direction until the National People's Congress in March, where the government's growth target and stimulus measures will be announced.

** China's central bank kicked off a second round of operations this week under a newly-created funding scheme for financial institutions to aid the country's stock market.

** On Thursday, financial .CSIFN and tech .CSIINT shares led the declines, falling 1.8% and 2.6% respectively.

** Real estate stocks .CSI000952 retreated 0.7%, despite prices of new homes in China rising at a slightly faster pace in December.

** Small stock index CSI 2000 .CSI932000 was one of the few bright spots, up 0.6%, as retail investors often favour small stocks for potentially quick gains despite the risks involved.

** Hypermarket chain Sun Art shares 6808.HK were down nearly 17%, after Alibaba 9988.HK said on Wednesday it had agreed to sell its majority stake in the company to Chinese private equity firm DCP Capital. Alibaba stocks slipped 0.7%.

** Tech giants traded in Hong Kong .HSTECH were down 1.5%.

(Reporting by Shanghai Newsroom; Editing by Varun H K)

((li.gu@tr.com))