Switzerland is considering capital controls to fight a sharp rise in the Swiss franc in the event of a euro-zone collapse. Dow Jones's Katie Martin explains in the above video why investors run to it in times of trouble and why this is bad news for the Swiss. Below, Eva Szalay shows how the currency stayed firm on Monday.

The scale of Switzerland's task in holding down the franc became even clearer Monday, as the currency held firm even as the Swiss National Bank warned it could introduce capital controls to hold it down if the crisis in the neighboring euro area deteriorated further.

The safe-haven franc -- a magnet to investors in times of stress -- dipped only very slightly after SNB Chairman Thomas Jordan told the local weekend press that the central bank may consider capital controls to fight the inflow of money that would inevitably flood Switzerland in the event of a euro breakup.

The euro climbed only as high as 1.2030 franc -- just a shade above its official 1.20 floor against the franc -- in response to the news, with investors caught between the urge to own super-safe Swiss assets and the threat of sharp losses that many suffered when the central bank set a floor in the euro's value against the franc at 1.20 last September.

Some analysts poured cold water on the notion that even capital controls -- some of the most heavy-handed currency-management tools available to policy makers -- could reverse the flows into francs.