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The euro fell to 1.20215 Swiss francs on trading platform EBS, its weakest since September 2012.
The SNB has successfully kept a lid on the franc's gains since it introduced the cap and says it has not had to intervene to reinforce it for more than two years.
But with a referendum on Nov. 30 that is aimed at preventing the SNB from offloading its gold holdings and obliging it to hold at least 20 percent of its assets in gold, speculators are targeting the cap, testing the SNB's patience.