“Because of the low interest rate level, we note increasing demand for insurance solutions for the storage of cash,” said Philipp Surholt at Zurich Insurance Group AG, among underwriters reporting a surge in such requests. “We’re seeing demand for coverage for sums ranging from 100 million to 500 million francs.”

For now, the SNB says it hasn’t seen evidence of widespread cash hoarding in Switzerland.

When investors all decide to stampede into the same asset, there's always the worry that the fast money in will be just as fast on the way out.

Investors have largely ignored this concern over the past few months and piled in developing-market bonds, especially those denominated in dollars. This debt has posted huge returns, dwarfing gains on U.S. government bonds and stocks. The nations benefiting the most have often been among the weakest, including Venezuela, Brazil and Sri Lanka.

The largest exchange-traded fund that focuses on this debt -- the iShares J.P. Morgan USD Emerging Markets Bond ETF -- just posted a record one-day withdrawal. That's a marked reversal for an ETF that has received more than $4 billion of deposits so far this year.