Risk Premium, Variance Premium and the Maturity Structure of Uncertainty

Expected returns vary when investors face time-varying investment opportunities. Long-run risk models (Bansal and Yaron 2004) and no-arbitrage affine models (Duffie, Pan, and Singleton 2000) emphasize sources of risk that are not observable to the econometrician. We show that, for both classes of models, the term structure of risk implicit in option prices can reveal these risk factors ex-ante. Empirically, we construct the variance term structure implied in SP500 option prices. The variance term structure reveal two important drivers of the bond premium, the equity premium, and the variance premium, jointly. We also consider the term structure of higher-order risks as measured by skewness and kurtosis and still find that two factors are sufficient to summarize the information content from the term structure of risks. Overall, our results bode well for the ability of structural models to explain risk-returns trade-offs across different markets using only very few sources of risk.