We find that adding a measure of market jump volatility risk to a regression of excess bond returns on the term structure of forward rates nearly doubles the R^2 of the regression. Our market jump volatility measure is based on the realized jumps identified from high-frequency stock market returns using the bi-power variation technique. The significant enhancement of bond return predictability is robust to different forecasting horizons, to using non-overlapping returns and to the choice of different window sizes in computing the jump volatility. This market jump volatility factor also crowds out the price-dividend ratio in explaining much of the countercyclical movement in bond risk premia. We argue that this finding provides support for the unspanned stochastic volatility hypothesis according to which the conditional distribution of excess bond returns is affected by state variables that are not in the span of the term structure of yields and forward rates.