In this paper, we test the consistency of the q5 model of Hou et al. (2019, 2020) with Merton’s (1973) intertemporal capital asset pricing model (ICAPM) framework. We find that all but one factors in the q5 model carry significantly positive covariance risk prices. The profitability factor, however, has little explanatory power for the cross-section of expected returns. The time-series tests show that the investment factor predicts a significant decline in stock market volatility, thereby being consistent with its positive price of covariance risk and satisfying the sign restrictions associated with the ICAPM. Importantly, the expected growth factor that is found to be helpful in describing cross-sectional average returns fails to predict future investment opportunities with the correct sign, which indicates that it is not a valid risk factor under the ICAPM. Overall, the ICAPM cannot be used as a theoretical background for the q5 model.