The equity premium puzzle with 2 different rates of return definitions : the stochastic nature of their solutions

Abstract

This paper suggests that the models which try to explain the equity premium puzzle underestimate rare economic events. The stochastic nature of the model increases the probability of far-from the mean output levels. A multiplicative-additive ran- dom walk formulation is considered, consistent with a fat-tail gaussian distribution. Using Barro s (2009) rate of return de nition, the calibrated model yields an equity premium of 5.8% and a risk-free rate of 1.3%. Taking into account the classical de nition, the solutions are 6% and 1.1% respectively. Adopting the utility formu- lation of Epstein and Zin (1989), the coe¢ cient of relative risk aversion that best performs is about 1.8 and the intertemporal elasticity of substitution is roughly 1.1. Finally, there follows a calculation of the average probability of an economic con- traction higher than 15% in the United States during the period between 1954-2004 by using the probability density function calibrated in the last model speci cation mentioned above and yields 0.06%.