Switzerland has long prided itself on being neutral territory. Now its currency is taking its turn as a safe harbor for investors battered by dueling debt crises in the U.S. and Europe.

The Swiss franc has risen by 30% over the past year against the U.S. dollar and by more than 4% so far in July. On Monday the franc hit a record high of $1.2408, up 1.6% from Friday. It is also in record territory against the euro, which is down 15% over the last year against the Swiss currency and off nearly 5% this month.

"People...