This paper comprehensively examines the existence and significance of a contemporaneous/intertemporal risk-return trade-off for crude oil futures using high-frequency transaction data. The results reveal that the contemporaneous relation between risk (volatility risk, downside risk or jump risk) and return in the crude oil futures market is negative and statistically significant and that the contemporaneous negative relation between downside risk and return is stronger than the two others. However, the intertemporal volatility/jump risk-return relationship is insignificant, and there is weak negative correlation between downside risk and expected return in the crude oil futures market. These findings can be explained by the asymmetric effect of risk on returns. The findings are robust across different samples and different measures of volatility, downside and jump risks. Thus, there is no risk-return trade-off in the crude oil futures market. (C) 2016 Elsevier Ltd. All rights reserved.