When Uncertainty and Volatility Are Disconnected: Implications for Asset Pricing and Portfolio Performance

We analyze an environment where the uncertainty in the equity market return and its volatility are both stochastic, generating situations where they can move in tandem as one might expect, but also situations where they are disconnected. We solve in closed form a representative investor's optimal asset allocation and derive the resulting conditional equity premium and risk-free rate in equilibrium. Empirically, we find that equity returns respond negatively to contemporaneous volatility (consistent with the prevalence of the leverage effect in the data), but respond positively, and consistently across horizons, to the uncertainty component in the model. Our results therefore show that the equity premium appears to be earned for facing uncertainty, especially high uncertainty that is disconnected from low volatility, rather than for facing volatility as traditionally assumed. Incorporating the possibility of a disconnect between volatility and uncertainty significantly improves portfolio performance, over and above the performance obtained by conditioning on volatility only.