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Quantitative dynamic stochastic general equilibrium (DSGE) models often admit that the zero bound on nominal interest rates does not constrain (optimal) monetary policy. Recent economic events, however, have reinforced the relevance of the zero bound. This paper sheds some light on this disconnect by studying a broad range of shocks within a standard DSGE model. In contrast to earlier studies, we find that risk premium shocks are key to building quantitative models where the zero bound is relevant for monetary policy design. Other commonly included shocks, such as productivity, government spending, and money demand shocks, are unable to push nominal rates close to zero.