We propose an intertemporal asset pricing model that incorporates both preference for higherorder moments and stochastic investment opportunities, extending traditional theories based exclusively on mean and variance of asset returns. Our model encompasses a wide range of existing models, including the three-moment static CAPM. We also provide empirical evidence to support our theory that systematic skewness is negatively priced in the crosssection of U.S. stock returns, indicating a risk-return-skewness trade-off. In addition, we show that an extra return premium is required for accepting the higher systematic risk associated with a rise in risk aversion. Our findings suggest that asset pricing anomalies such as value, momentum, and failure probability puzzles can be partially explained by our model.