Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets

This paper examines the optimal consumption and portfolio choice problem of long-horizon investors who have access to a riskless asset with constant return and a risky asset (‘stocks’) with constant expected return and time varying precision – the reciprocal of volatility. Markets are incomplete, and investors have recursive preferences defined over intermediate consumption. The paper obtains a solution to this problem that is exact for investors with unit elasticity of intertemporal substitution of consumption, and approximate otherwise. The optimal portfolio demand for stocks includes an intertemporal hedging component that is negative when investors have coefficients of relative risk aversion larger than one, and the instantaneous correlation between volatility and stock returns is negative, as typically estimated from stock return data. Our estimates of the joint process for stock returns and precision (or volatility) using US data confirm this finding. But we also find that stock return volatility does not appear to be variable and persistent enough to generate large intertemporal hedging demands.