The world's leading central banks have opened a fresh phase of interest rate cuts, spurred by a softening in inflation across advanced economies.

With inflation sliding closer to target levels, policymakers are keen to unwind some of the policy restrictiveness that's become a drag on growth.

But a significant outlier on the global monetary scene is raising eyebrows—and concerns—for an interest-rate-fueled rally in the stock market.

On Thursday, the European Central Bank (ECB) took its turn, delivering a second 25 basis point rate cut following a similar move in June.

While ECB PresidentChristine Lagarde...