We evaluate whether the introduction of pessimistic homogeneous beliefs in the frictionless Lucas-Mehra-Prescott model and the Kehoe-Levine-Alvarez-Jermann model with endogenous borrowing constraints, helps explain the equity premium, the risk-free rate and the equity volatility puzzles as well as the short-term momentum and long-term reversal of excess returns. We calibrate the model to U.S. data as in Alvarez and Jermann [4] and we find that the data does not contradict the qualitative predictions of the models. When the preferences parameters are disciplined to match both the average annual risk-free rate and equity premium, the Lucas-MehraPrescott model gives a more quantitatively accurate explanation for short-term momentum than the Kehoe-Levine-Alvarez-Jermann model but the latter gives a more quantitatively accurate explanation for the equity volatility puzzle. Long-term reversal remains quantitatively unexplained in both models.