Volatility Bounds and Preferences: An Analytical Approach

This paper proposes a parametric implementation of the Hansen and Jagannathan (1991) volatility bounds based on log-normal distributions. We obtain analytical expressions for the bounds as well as stochastic discount factors. Using this framework we analyze the role of preferences in determining risk premia. We show that neither risk aversion nor in general determine the elasticity of intertemporal substitution. Instead the elasticity of the stochastic discount factor with respect to the innovation in consumption alone determines the slope of the capital market line. We relate this parameter to more conventional preference parameters like risk aversion. We also show how the Hansen-Jagannathan bounds can be interpreted in the standard finance mean-standard deviation diagram. Preferences and consumption determine the position of the capital market line while the dividend process determines the position of specific assets on or below the capital market line. Using these insights we decomp..