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I compare the five-factor model of Fama and French (2015) and the q5-factor model of Hou et al. (2018a) and find that the five-factor model outperforms the q5-factor model in terms of having closer-to-zero estimated error terms, time-series and cross-sectional covariance-to-variance ratios, and time-series variance of coefficient in most of the cases. The results thus suggest that the explanatory variables of the five-factor model are more accurate proxies of the factors stock returns depend on.

This paper reports implications from an assumption that total value of equity regresses toward total value of debt and loan liabilities over time. I show that, for example, change in value of equity markets equals change of total value of debt and regression factor determined ten years earlier plus change of value of residual factor and that residual factor explains short and mid-term variance of value of equity markets. Furthermore, I show that expected change in value of equity markets equals constant changes of total value of debt and regression factor and expected change of residual factor and that the constant changes drive the outperformance of equity markets over government bond yields.