We study factor models augmented by observed covariates that have explanatory powers on the unknown factors. In financial factor models, the unknown factors can be reasonably well explained by a few observable proxies, such as the Fama-French factors. In diffusion index forecasts, identified...

This paper proposes an aggregate index of macro tail risk and examines its role in asset pricing. We observe that a positive market risk premium compensated for the downside risk of macro fundamentals; a high tail risk predicts subsequent high returns. This predictability exists both in- and...