Understanding the Sources of Risk Underlying the Cross Section of Commodity Returns

Abstract

We show that a model featuring an average commodity factor, a carry factor, and a momentum factor is capable of describing the cross-sectional variation of commodity returns. More parsimonious one-and two-factor models that feature only the average and/or carry factors are rejected. To provide an economic interpretation, we show that innovations in equity volatility can price portfolios formed on carry with a negative risk premium, while innovations in our measure of speculative activity can price portfolios formed on momentum with a positive risk premium. Furthermore, we characterize the relation of the factors with the investment opportunity set.

Basis‐Momentum

“…() includes three factors that we construct from a sort on the basis: (i) the nearby return of the High4‐minus‐Low4 basis portfolio (), (ii) the spreading return on the High4 portfolio (), and (iii) the spreading return of the Low4 portfolio (). The model of Bakshi, Gao, and Rossi () includes three nearby return factors: (i) an average commodity market factor (i.e., the equal‐weighted average return on all commodities, ), (ii) as in Szymanowska et al. (), and (iii) the High4‐minus‐Low4 momentum portfolio ().…”

“…Table IA.VI of the Internet Appendix examines whether the benchmark factors of Szymanowska et al. () and Bakshi, Gao, and Rossi () are subsumed by models that include the basis‐momentum factors. We find that the average and momentum nearby factors provide an alpha relative to a five‐factor model including three basis factors and two basis‐momentum factors.…”

“…() (setting ). The second specification is the model of Bakshi, Gao, and Rossi () (setting ). The third and fourth specifications add the basis‐momentum nearby factor to these first two models.…”

“…This approach follows recent arguments in the literature to run cross‐sectional tests for individual stocks rather than portfolios (see, for example, Lewellen, Nagel and Shanken () and Ang, Liu, and Schwarz ()). Because betas of individual commodities vary dramatically over time (Bakshi, Gao, and Rossi ()), we estimate conditional commodity‐level betas over a one‐year rolling window of daily returns to keep the betas timely . Daskalaki, Kostakis, and Skiadopoulos () find that the cross section of individual commodities is hard to price, so this exercise presents a challenge for any new factor.…”

The skewness of commodity futures returns

“…In these frameworks, skewness 1 The literature on commodity futures pricing has established that a suitable benchmark should include a long-only commodity portfolio as well as long-short portfolios deemed to capture the phases of backwardation and contango (see Bakshi et al, 2017or Fernandez-Perez et al, 2017 for recent references). Acknowledging that backwardation (contango) signals a likely rise (fall) in futures prices, such long-short portfolios buy backwardated commodities described by lower standardized inventories (Fama and French, 1987;Symeonidis et al, 2012;Gorton et al, 2013), downward sloping forward curves (Erb and Harvey, 2006;Gorton and Rouwenhorst, 2006;Szymanowska et al, 2014;Koijen et al, 2017), good past performance (Erb and Harvey, 2006;Miffre and Rallis, 2007;Asness et al, 2013;Gorton et al, 2013), net short hedging and net long speculation (Bessembinder, 1992;Basu and Miffre, 2013;Dewally et al, 2013); they also short contangoed commodities with opposite characteristics.…”