Time-Change Risks and the Aggregate Stock Market Behavior

Abstract

This paper investigates how the investors responses to the evolution of uncertainty affect equilibrium asset returns. I develop a discrete-time real endowment economy where the aggregate economic uncertainty, as detected by a time-change for the endowment process, alters the perceived utility from consumption and drives the state of the economy. The equilibrium pricing kernel reflects both the return on investments - a supply-side effect, as in the standard framework - and the agents' responses - a demand-side effect - which evolve with the arrival of news. Equilibria with both unpredictable and persistent impact of uncertainty are fully characterized: the pricing of supply-side and demand-side time-change risks is discussed. The model calibration shows that many features of financial returns are well described consistently with a low correlation of returns with consumption growth and a low and constant risk aversion. The model captures a high and countercyclical equity premium and Sharpe ratio, a high and clustered volatility, a rich time-variation of returns and a low and little volatile risk-free rate. I empirically verify the designed mechanism for intertemporal decisions by relating the model state-variable to the consumption-wealth ratio.