In this paper, we test the consistency of the $q^5$ 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 $q^5$ 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 $q^5$ model.

在本文中，我们测试了 $q^5$侯等人的模型。（2019，2020）和默顿（1973）的跨期资本资产定价模型（ICAPM）框架。我们发现，除了$q^5$该模型带有明显的正协方差风险价格。但是，盈利率因素对于预期收益的横截面几乎没有解释力。时间序列测试表明，投资因子预测股票市场波动会显着下降，从而与其协方差风险的正价格一致，并满足与ICAPM相关的符号限制。重要的是，被发现有助于描述横截面平均收益的预期增长因素无法以正确的符号预测未来的投资机会，这表明根据ICAPM，这不是有效的风险因素。总体而言，ICAPM不能用作$q^5$ 模型。