Federal Reserve officials are starting to wonder whether a tranquillity that has descended on financial markets is a sign that investors have become unafraid of the type of risk that could lead to bubbles and volatility.

The Dow Jones Industrial Average, up a steady if unspectacular 1% since the beginning of the year, has consolidated big gains registered last year. The VIX, a measure of expected stock-market fluctuations based on options trading, has gone 74 straight weeks below its long-run average—a string of steadiness not seen since 2006 and 2007, before the financial crisis and recession.

Moreover, the extra return that bond investors demand on investment-grade corporate debt over low-risk Treasury bonds, at one percentage point, hasn't been this low since July 2007. The lower this "spread," the less risk-averse are bond investors.

The Fed's growing worry—which could influence future interest rate decisions—is that if investors start taking undue risk it could lead to economic turbulence down the road.

"Volatility in the markets is unusually low," William Dudley, president of the Federal Reserve Bank of New York and a member of chairwoman Janet Yellen's inner circle, said after a speech last week. "I am a little bit nervous that people are taking too much comfort in this low-volatility period. As a consequence, they'll take more risk than really what's appropriate."