We identify two types of risk premia in commodity futures returns: spot premia related to the risk in the underlying commodity, and term premia related to changes in the basis. Sorting on forecasting variables such as the futures basis, return momentum, volatility, inflation, hedging pressure, and liquidity results in sizable spot premia between 5% and 14% per annum and term premia between 1% and 3% per annum. We show that a single factor, the high‐minus‐low portfolio from basis sorts, explains the cross‐section of spot premia. Two additional basis factors are needed to explain the term premia.

We show that inflation risk is priced in stock returns and that inflation risk premia in the cross-section and the aggregate market vary over time, even changing sign as in the early 2000s. This time variation is due to both price and quantities of inflation risk changing over time. Using a consumption-based asset pricing model, we argue that inflation risk is priced because inflation predicts real consumption growth. The historical changes in this predictability and in stocks’ inflation betas can account for the size, variability, predictability, and sign reversals in inflation risk premia.