BENGALURU/SYDNEY (Reuters) – The global economy finished last year on a fragile footing, with factory activity in China shrinking for the 10th month running in December while a pick-up in the euro zone was tepid, suggesting more policy stimulus may be in the pipeline. Coming on a day of turmoil in Asian stock markets after China’s central bank fixed the yuan (CNY=) at a 4-1/2 year low, the data point to a further dose of the sluggish growth and inflation, weak demand and jittery financial markets that characterised 2015.