This paper employs a proprietary data set on commodity producers’ profit margins (PPMG) and establishes a robust positive relationship between commodity producers’ profitability growth and future returns of commodity futures. The spread portfolio that longs top-PPMG futures contracts and shorts bottom-PPMG futures contracts delivers a statistically significant average weekly return of 36 basis points. We further demonstrate that profitability is a strong SDF factor in commodity futures market. We theoretically justify our empirical findings by developing an investment-based pricing model, in which producers optimally adjust their production process by maximizing profits subject to aggregate profitability shocks. The model reproduces key empirical results through calibration and simulation.

We utilize ridge regression to create a novel set of characteristics-based "ridge factors". We propose Bayesian Average Stochastic Discount Factors (SDFs) based on these ridge factors, addressing model uncertainty in line with asset pricing theory. This approach shrinks the relative contribution of low-variance principal portfolios, avoiding model selection and presumption of a "true model". Our results demonstrate that ridge factor principal portfolios can achieve greater sparsity while maintaining prediction accuracy. Additionally, our Bayesian average SDF produces a higher Sharpe ratio for the tangency portfolio compared to other models.

In this paper, we construct a new variance bound on any stochastic discount factor (SDF) of the form m = m(x), where x is a vector of random state variables. In contrast to the well known Hansen-Jagannathan bound that places a lower bound on the variance of m(x), our bound tightens it by a ratio of 1=½2x;m0 where ½x;m0 is the multiple correlation coefficient between x and the standard minimum variance SDF, m0. In many applications, the correlation is small, and hence our bound can be substantially tighter than Hansen-Jagannathan’s. For example, when x is the growth rate of consumption, based on Cochrane’s (2001) estimates of market volatility and ½x;m0 , the new bound is 25 times greater than the Hansen-Jagannathan bound, making it much more difficult to explain the equity-premium puzzle based on existing asset pricing models.