We measure “good” and “bad” variance premia that capture risk compensations for the realized variation in positive and negative market returns, respectively. The two variance premium components jointly predict excess returns over the next 1 and 2 years with statistically significant negative (positive) coefficients on the good (bad) component. The R2 s reach about 10% for aggregate equity and portfolio returns and 20% for corporate bond returns. To explain the new empirical evidence, we develop an economic model which underscores the difference in investors’ risk attitudes towards upside and downside uncertainty risks