This study assumes homothetic robust Epstein-Zin utility and analyzes the consumption--investment problem and CAPMs under a quadratic security market model in which interest rates, the market price of risk, the variances and covariances of asset returns, and inflation rates are stochastic. First, we demonstrate that homothetic robust Epstein-Zin utility is interpreted as homothetic stochastic differential utility. Then, we derive a robust version of the two-factor CAPM and show that the CAPM can contribute to solving both the equity premium puzzle and the risk-free rate puzzle.