Risk Premium, Variance Premium and the Maturity Structure of Uncertainty
Bank of Canada
Bank of Canada
Universidad Carlos III de Madrid
ESSEC Business School Paris-Singapore
September 1, 2012
Review of Finance (2014) 18 (1): 219-269.
Expected returns vary when investors face time-varying investment opportunities. In theory, structural 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 the term structure of risk implicit in option prices can reveal these risk factors exante. Empirically, we find that the variance term structure reveals two important drivers of the bond premium, the equity premium and the variance premium, jointly. Similarly, two risk factors are sufficient to capture the predictive content of higher-order uncertainty – skewness and kurtosis – but these do not add to the predictive content of the variance factors. The predicted equity premium is counter-cyclical and our results are robust to the inclusion of other known predictors of returns. Overall, our results bode well for our ability to link risk-return trade-offs across different markets, and across horizons, within a unified theoretical framework.
Number of Pages in PDF File: 44
Keywords: Equity Premium, Variance Premium, Risk-neutral Variance, Term Structure of Variance, Long-Run Risk
JEL Classification: G12, G13.
Date posted: February 15, 2011 ; Last revised: December 17, 2016