Mean Reversion and the Comovement of Equilibrium Spot and Futures Prices: Implications from Alternative Data‐Generating Processes

The comovements of spot and futures prices are characterized by six binary variables, including the term structure curvature of futures prices. These variables are used to uniquely identify 48 possible comovement patterns. Among them, 24 cases are associated with mean reversion, which is defined as a state when spreads between futures and spot prices are shrinking. These pattern frequencies are then calculated on a daily basis with the futures prices of 10 commodities, including precious metal, agricultural, and financial commodities. The results are further compared to simulation output from three data‐generating processes: a bivariate pure random walk, a mixed random walk with first‐order autoregression (AR(1)), and an error‐correction representation. The mean‐reverting frequencies for all 10 commodities are about 50%. Around half of the time, spot and futures prices are moving toward each other, and the rest of the time they move in the same direction. The symmetry of these results implies that the existence of substantial shocks originated from futures markets; thus, this is consistent with the risk premium view of futures trading. Also, although all simulation models produce similar mean‐reversion frequencies, the patterns of comovements of spot and futures prices are different, and the price dynamics depend heavily on whether the market is dominant contango or backwardation. Furthermore, the error‐correction model outperforms the random‐walk model for agricultural commodities, and the mixed random walk with AR(1) is hardly distinguishable from the pure random walk. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:769–796, 2001