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...