We study how monetary policy affects the cross-section of expected stock returns. For this purpose, we create a parsimonious monetary policy exposure (MPE) index based on observable firm characteristics that are theoretically linked to how firms react to monetary policy. We find that stocks whose prices react more positively to expansionary monetary policy surprises earn lower average returns. This finding is consistent with the intuition that monetary policy is expansionary in bad economic times when the marginal value of wealth is high, and thus high MPE stocks serve as a hedge against bad times. A long-short trading strategy designed to exploit this effect achieves an annualized value-weighted return of 9.96 percent with an associated Sharpe Ratio of 0.93 between 1975 and 2015. This return premium cannot be explained by standard factor models and survives a battery of robustness tests.