Risk Attitude Optimization and Heterogeneous Stock Market Participation

Abstract

This paper studies equilibrium portfolio choice and asset returns using a new model of recursive preferences called optimal risk attitude utility. Our model is an extension of recursive expected utility that allows an individual to optimally select her risk aversion parameter in response to the uncertainty that she faces. Choosing a lower level of risk aversion comes at a cognitive cost, and therefore is only undertaken in response to sufficiently large risk exposure. In addition to separating risk aversion from the elasticity of intertemporal substitution, our model can also separate risk attitudes toward small and large risks. We solve the dynamic stochastic general equilibrium of a calibrated economy and show that optimal risk attitude utility can provide a partial resolution to both the stock market participation puzzle and the equity premium puzzle. Our model generates a moderate premium for equity as well as endogenous heterogeneity in risk exposure, with one segment of the population holding minimal risk while the other holds a disproportionate share of aggregate risk, even when consumers have identical preferences and even among wealthy households. Using simple binary gambles as a rationality check for our model, we demonstrate that the preference parameters used in our calibration exhibit descriptively accurate levels of risk aversion for gambles ranging from one hundred dollars up to ten percent of wealth.

Keywords: optimal risk attitude, stock market participation puzzle, equity premium puzzle