We investigate the effect of oil price innovations on the U.S. stock market using a model that nests symmetric and asymmetric responses to positive and negative oil price innovations. We find no evidence of asymmetry for aggregate stock returns, and only very limited evidence for 49 industry-level portfolios. Moreover, these asymmetries do not match up well with conventional views regarding energy-dependent sectors of the economy. Instead, asymmetries are more likely driven by the effect of oil price innovations on expected and/or realized demand. We inquire whether the size of the shock matters in that doubling the size of the shock more (or less) than doubles the size of the response, finding that the effect of a 2.s.d innovation is just about double the magnitude of the impact of a 1.s.d innovation. Furthermore, we find no support for the conjecture that shocks that exceed a threshold have an asymmetric effect on stock returns.