* SSEC 1.3%, CSI300 1.6%, HSI 1.0% * China November factory activity growth highest in 10 years * Property firms lag as new home price growth eases SHANGHAI, Dec 1 (Reuters) - China stocks rose on Tuesday as fresh factory data underscored the country’s solid economic rebound, even as new home price growth eased and as government officials cautioned against financial risks. ** China’s factory sector activity grew at its fastest pace in a decade in November, a business survey showed on Tuesday, as the world’s second-largest economy rebounds to pre-pandemic levels. ** At the midday break, the Shanghai Composite index was up 1.31% at 3,436.04 points. ** China’s blue-chip CSI300 index was up 1.56%, with its financial sector sub-index higher by 2.15%, the consumer staples sector up 1.17%, and the healthcare sub-index up 2.83%. ** The real estate index lagged broader market moves, gaining just 0.09%. ** Chinese new home prices growth eased slightly in November, weighed by tighter market curbs in larger cities and increased demand weakness in smaller towns, a private survey showed. ** The country’s chief banking regulator said on Monday that China’s property market is the biggest “grey rhino” - a very obvious yet ignored threat - in terms of financial risks, given it is so deeply intertwined with the financial industry. ** Chinese H-shares listed in Hong Kong rose 1.19% to 10,671.98, while the Hang Seng Index was up 0.93% at 26,586.21. ** The smaller Shenzhen index was up 1.1%, the start-up board ChiNext Composite index was higher by 1.9% and Shanghai’s tech-focused STAR50 index rose 1.06%. ** Around the region, MSCI’s Asia ex-Japan stock index was up 1.07% while Japan’s Nikkei index was up 1.55%. ** The yuan was quoted at 6.5768 per U.S. dollar, 0.04% firmer than the previous close of 6.5792. ** So far this year, the Shanghai stock index is up 12.7% and the CSI300 has risen 23%, while China’s H-share index listed in Hong Kong is down 4.4%. Reporting by Andrew Galbraith, Editing by Sherry Jacob-Phillips Our Standards: The Thomson Reuters Trust Principles.