SHANGHAI, Nov 3 (Reuters) - China stocks rose on Friday with consumer-related shares leading gains, even as a private survey showed the country's services activity growth was slower-than-expected in October.

Hong Kong stocks also advanced, following a rally overnight in New York.

** China's blue-chip CSI300 Index was up 0.9% by the lunch break, while the Shanghai Composite Index gained 0.8%. Hong Kong benchmark Hang Seng rose 2.1%.

** China's services activity growth in October was slightly better than in the previous month, a private-sector survey showed, though new orders rose at their slowest rate in 10 months with employment stagnating as business confidence waned.

** The pace of expansion disappointed some investors as it remained much slower than the average growth in the first half of the year.

** Still, consumer-related stocks led the gains in China, with liquor shares rising 1.1%.

** Computer stocks also climbed, up 2.1%.

** Market sentiment towards China stocks will stay volatile in the near term unless investors see positive signs such as housing market stabilisation and improvement in Sino-U.S. relationship, analysts at Morgan Stanley said in a note.

** In Hong Kong, the stock rally overnight in New York boosted the sentiment, especially lifting internet stocks.

** Tech stocks rose 2.3%, with Alibaba and Tencent up 1.8% and 3.1%, respectively.

** Shares of China Evergrande opened more than 6% higher before reversing some gains, after news that the troubled developer had proposed a new debt restructuring plan.

** Shares of sportswear group Li Ning jumped 5.8%, after filings showed that Singapore sovereign fund GIC had boosted stake in the company. (Reporting by Shanghai Newsroom Editing by Vinay Dwivedi)