Stochastic discount factor bounds provide a useful diagnostic tool for testing asset pricing models by specifying a lower bound on the variance of any admissible discount factor. In this paper, we provide a unified derivation of such bounds in the presence of conditioning information, which allows us to compare their theoretical and empirical properties. We find that, while the location of the ‘unconditionally efficient (UE)’ bounds of [Ferson, W., Siegel, A., 2001. The efficient use of conditioning information in portfolios. Journal of Finance 56 (3), 967–982] is statistically indistinguishable from the (theoretically) optimal bounds of [Gallant, R., Hansen, L., Tauchen, G., 1990. Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution. Journal of Econometrics 45 (1), 141–179] (GHT), the former exhibit better sampling properties. We demonstrate that the difference in sampling variability of the UE and GHT bounds is due to the different behavior of the efficient return weights underlying their construction.

We construct long–short factor mimicking portfolios that capture the hedging pressure risk premium of commodity futures. We consider single sorts based on the open interests of hedgers or speculators, as well as double sorts based on both positions. The long–short hedging pressure portfolios are priced cross-sectionally and present Sharpe ratios that systematically exceed those of long-only benchmarks. Further tests show that the hedging pressure risk premiums rise with the volatility of commodity futures markets and that the predictive power of hedging pressure over cross-sectional commodity futures returns is different from the previously documented forecasting power of past returns and the slope of the term structure.