I use model-free methods to estimate the term structures of the variance risk premium (VRP) and the skewness risk premium (SRP) derived from dividend futures and options. I find that VRP is on average negative, whereas SRP is on average positive. They have unique characteristics and can hardly be explained by equity risk factors and equity moment risk premia. I present evidence that both dividend moment risk premia contain significant forecasting power for dividend futures returns in- and out-of-sample. Dividend futures returns are predicted by the VRP (SRP) in almost all setups with a negative (positive) sign.