Variance risk premia for agricultural commodities

We study the variance risk premium (i.e., the difference between historical realized variance and the variance swap rate) in corn and soybean markets from 2010 through 2016. Variance risk is negatively priced for both commodities, but is more statistically significant for soybean than for corn. There are moderate commonalities in variance within the agricultural sector, but fairly weak commonalities between the agricultural and the equity sectors. Corn and soybean variance risk premia in dollar terms are time-varying and correlated with the variance swap rate. In contrast, agricultural commodity variance risk premia in log return terms are more likely to be constant and less correlated with the log variance swap rate. Variance and price (return) risk premia in agricultural markets are weakly correlated, and the correlation depends on the sign of the returns. The latter finding suggests that the variance risk is unspanned by commodity futures, i.e., it is an independent source of risk. The empirical results also suggest that the implied volatilities in corn and soybean futures market overestimate true expected volatility by approximately 15%. This has implications for derivative products, such as revenue insurance, that use these implied volatilities to calculate fair premia.