The Skewness Premium and the Asymmetric Volatility Puzzle

Abstract

This paper uses a general equilibrium model to study the source and reward of asymmetric volatility or skewness of market returns in an exchange economy. In particular, the dividend growth rate is modeled as a stochastic volatility process and the representative agent is characterized by Epstein-Zin preferences. The equilibrium equity premium, risk-free rate, and asymmetric volatility (measured by the negative correlation between the market return and its volatility) are derived endogenously. It is shown that the equity premium has three components: the first two components parallel those in the Intertemporal CAPM, while the last one is 'new'. It reflects the part of excess returns required by investors to take on the asymmetric volatility or negative skewness risk. The paper then uses the Efficient Method of Moments to estimate the stochastic volatility model of the dividend growth rate and uses the estimated process to study the equity premium, the skewness premium, the risk-free rate, and asymmetric volatility under various values of the risk aversion coefficient and elasticity of intertemporal substitution. It is shown that the skewness premium can be as high as 1.2% annually in real terms. However, under conventional levels of risk aversion and elasticity of intertemporal substitution, the asymmetric volatility generated by the model is much smaller than that observed in the data and hence results in the asymmetric volatility 'puzzle'.