Historically, inflation is negatively correlated with stock returns, leading investors to fear inflation. We document using a variety of measures that this association became positive in the U.S. during the 2008-2015 period. We then show how an off-the-shelf New Keynesian model can reproduce this change of association due to the binding zero lower bound (ZLB) on short-term nominal interest rates during this period: in the model, demand shocks become more important when the ZLB binds because the central bank cannot respond as effectively as when interest rates are positive. This changing correlation in turn reduces the term premium, and hence contributes to explaining the decline in long-term interest rates. We use the model to evaluate this mechanism quantitatively. Our results shed light on the validity of the New Keynesian ZLB model, a cornerstone of modern macroeconomic theory.