Available online xxxx Using a rational bubble framework, a future spot price bubble can be shown to induce explosive behaviour in current long maturity futures prices under particular conditions. To assess this empirically, we employ a novel test of the unit root null against a mildly explosive alternative to investigate multiple bubbles in the crude oil spot and a range of futures prices along the yield curve employing monthly and weekly data from 1995 to 2013. The results indicate that the series overwhelmingly exhibit significant bubble periods ending in late 2008 even after allowing for an increase in unconditional volatility. Bubbles in the longer-dated contracts emerged as early as 2004 and are longer lasting than those in nearby and spot contracts. The bubble period was characterised by dramatic shifts in the yield curve associated with institutional spread positions that sharply increased futures prices at longer maturities. The results suggest that periods of time series disconnect between the spot and longer dated futures contracts could potentially form an input into early warning systems for macro-prudential policy.

We compare major factor models and find that the Stambaugh and Yuan (2016) 4-factor model is the overall winner in the time-series domain. The Hou, Xue, and Zhang (2015) q-factor model takes second place and the Fama and French (2015) 5-factor model and the Barillas and Shanken (2018) 6-factor model jointly take third place. The pairwise cross-sectional R2 and the multiple model comparison tests show that the Hou et al. (2015) q-factor model, the Fama and French (2015) 5-factor and 4-factor models, and the Barillas and Shanken (2018) 6-factor model take equal first place in the horse race.

and Rouwenhorst (2013), and references therein), we construct two sets of portfolios based on simple momentum strategies. The first set of portfolios comprise futures contracts of all commodities in the sample sorted into quintiles at the end of each month t´1 based on their (monthly) excess returns realized at the end of month t´2 (i.e., ∆f j t´2 ). 1 According to this sorting scheme, portfolio 1 (portfolio 5) contains the 20% of commodity futures with the lowest (highest) excess returns in the preceding month. The second set of momentum portfolios are constructed using all commodity futures contracts sorted into quintiles at the end of each month t´1 based on their average excess returns over the previous 12 months (i.e., ). This results portfolio 1 (portfolio 5) to contain the 20% of commodity futures with the lowest (highest) average excess returns over the preceding 12 months. In both variants of the momentum portfolios, we compute the monthly excess return on a portfolio that is formed at the end of month t´1, but realized at the end of month t as the equally weighted average of excess returns for the constituent futures contracts. The EWA factor is the equally weighted average excess return on a long position in all available commodity futures contracts, while the HML factor is the return difference between the last and first portfolios. We make use of momentum portfolio-specific futures basis as the instrumental variable z k t . Finally, to obtain the unconditional and conditional expectations of the risk factors, we follow similar procedures described in Section 2.1 of the main paper. Value Portfolios:The value portfolios for commodity futures contracts are constructed as per Asness, Moskowitz, and Pedersen (2013), where value is defined as the logarithm of the spot price five years ago (in particular, the average spot price from 4.5 to 5.5 years ago) divided by the most recent spot price. This simple measure of value is essentially the negative of the spot return over the 1 We allow for a one-month lag between exploiting the conditioning signal at the end of the formation period and estimating the excess return over the holding period (in our case, one-month). The rationale for this empirical procedure, standard in the literature, is to avert possible liquidity or microstructure related issues (Grinblatt and Moskowitz (2004) and Asness, Moskowitz, and Pedersen (2013)). 1 past five years. At the end of each month t´1, all commodity futures contracts are sorted into five portfolios based on their values. Portfolio 1 (Portfolio 5) is the portfolio with the lowest (highest) value commodity futures contracts. The monthly excess return on a portfolio constructed at the end of month t´1, but realized at the end of month t is computed as the equally weighted average of excess returns for the constituent contracts. We construct the EWA factor as the equally weighted average excess return on a long position in all futures contracts.The HML factor is created as the return difference between the last and first p...

Expectations about future economic activity should theoretically affect the demand for inventory holdings and therefore commodity spot and futures prices. Consistent with these predictions, we find that news related to future GDP growth is a significant factor that is priced in the cross-section of commodity futures sorted by percentage net basis. The latter is highly correlated with inventories. In particular, it establishes that commodity futures with high inventory levels provide a hedge against risk associated with future GDP growth so that investors are willing to accept lower return. By contrast, those commodity futures with low inventory levels are inversely related to the GDP-related factor so that investors require a higher return. Such results suggest that commodity futures excess returns are a compensation for risk.

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