German shares hit a fresh record high on Tuesday, supported by gains in industrial stocks and insurers, while data showed a services sector downturn in the euro zone's largest economy eased in November. Germany's DAX climbed 0.8%, propelled by strong gains in Allianz and Daimler Truck Holding, while the STOXX 600 index closed 0.4% higher. The German index is up nearly 18.7% so far this year, outperforming the 10% gains on the pan-European STOXX 600 index. Business activity in Germany and the overall euro zone declined in November, although at a slower rate than in the previous month, surveys showed....