MILAN—Britain’s vote to leave the EU has produced dire predictions for the U.K. economy. The damage to the rest of Europe could be more immediate and potentially more serious. Nowhere is the risk concentrated more heavily than in the Italian banking sector.

In Italy, 17% of banks’ loans are sour. That is nearly 10 times the level in the U.S., where, even at the worst of the 2008-09 financial crisis, it was only 5%. Among publicly traded banks in the eurozone, Italian lenders account for nearly half of total bad loans.

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