Risk Premium, Variance Premium and the Maturity Structure of Uncertainty

Abstract

Theoretical risk factors underlying time-variations of risk premium across asset classes are typically unobservable or hard to measure by construction. Important examples include risk factors in Long Run Risk [LRR] structural models (Bansal and Yaron 2004) as well as stochastic volatility or jump intensities in reduced-form affine representations of stock returns (Duffie, Pan, and Singleton 2000). Still, we show that both classes of models predict that the term structure of risk-neutral variance should reveal these risk factors. Empirically, we use model-free measures and construct the ex-ante variance term structure from option prices. This reveals (spans) two risk factors that predict the bond premium and the equity premium, jointly. Moreover, we find that the same risk factors also predict the variance premium. This important contribution is consistent with theory and confirms that a small number of factors underlies common time-variations in the bond premium, the equity premium and the variance premium. Theory predicts that the term structure of higher-order risks can reveal the same factors. This is confirmed in the data. Strikingly, combining the information from the variance, skewness and kurtosis term structure can be summarized by two risk factors and yields similar level of predictability (i.e., R2s). This bodes well for our ability to bridge the gap between the macro-finance literature, which uses very few state variables, and valuations in option markets.