Comovement in the commodity futures markets: An analysis of the energy, grains, and livestock sectors

Journal of Commodity Markets xxx (xxxx) xxx

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Comovement in the commodity futures markets: An analysis of the energy, grains, and livestock sectors Ramesh Adhikari a, Kyle J. Putnam b, * a b

School of Business, Humboldt State University, USA Business Department, Linfield College, USA

A R T I C L E I N F O

A B S T R A C T

JEL classification: G11 G12 G13

We examine the excess comovement of commodity futures returns. We contend that commodities categorized in the same sector possess fundamental price linkages; thus, measures of excess comovement "within-sectors" are much higher relative to "across-sector" measures. Consistent with this premise we find that all copula model dependence measures used in the study capture this feature of the commodity markets. Further, we test the relevance of two new "cross-market" factors related to changes in inventory and open interest as determinants of commodity futures returns. We find a strong positive relationship between changes in cross-market open interest and futures returns to the energy and livestock markets. In contrast, the impact of changes in crossmarket inventory on futures returns to the energy and grains sectors is very minor.

Keywords: Commodities Commodity futures Comovement Dependence

1. Introduction The mid-2000s saw a large rise in the popularity of commodity futures investment. This in turn increased attention to the asset class among regulators and academics who began to study the dynamics of commodity prices. One particular thread of literature examines commodity price comovement among various markets (Chng, 2009; Tang and Xiong, 2012; Dorfman and Karali, 2013; Le Pen and Sevi, 2018), and another strand analyzes the factors that help to explain commodity returns (Hirshleifer, 1990; De Roon et al., 2000; Hong and Yogo, 2012; Acharya et al., 2013; Gorton et al., 2013; Daskalaki et al., 2014). We examine both the comovement of commodity prices and the potential risk factors that explain their returns. Specifically, this paper measures the degree of excess comovement in the commodity futures markets and tests whether the characteristics of closely related commodities—those with high measures of excess comovement—impact futures returns. We examine the energy (WTI crude oil, heating oil #2, unleaded gasoline, natural gas), grains (corn, oats, soybeans, wheat), and livestock (live cattle, feeder cattle, lean hogs) sectors. Using weekly data, we utilize a subset of copula models to measure the excess comovement between 11 different commodities coming from these three different groups, where excess comovement is defined as the bivariate dependence measure of commodity prices after adjusting for the impact of common macroeconomic and commodity market factors. Comovement is examined through the lens of copula models, rather than the often implemented correlation coefficient, because copulas provide a more robust measure of dependence and relax the stringent assumptions inherent in the correlation coefficient. Moreover, copulas can capture asymmetric and non-linear dependence while the correlation coefficient is only a measure of linear association. The traditional correlation coefficient is an exhaustive measure of comovement when the joint distribution of two variables is multivariate normal; however, this assumption is frequently violated by the distribution(s) of financial asset returns which are commonly fat-tailed and * Corresponding author. E-mail address: kputnam@linfield.edu (K.J. Putnam). https://doi.org/10.1016/j.jcomm.2019.04.002 Received 1 August 2018; Received in revised form 15 January 2019; Accepted 9 April 2019 Available online xxxx 2405-8513/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Adhikari, R., Putnam, K.J., Comovement in the commodity futures markets: An analysis of the energy, grains, and livestock sectors, Journal of Commodity Markets, https://doi.org/10.1016/j.jcomm.2019.04.002

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skewed. To this end, we utilize four different copulas in our assessment: normal, Student's t, Clayton, and Gumbel. We contend, and results confirm, that the futures prices of commodities categorized in the same sector (i.e. "within-sector" commodities) exhibit much higher dependence, and hence greater excess comovement, amongst each other than with the prices of commodities categorized in a different sector (i.e. "across-sector" commodities); common factors alone do not explain this variation in comovement.1 These results hold regardless of the distributional lens that the residuals are viewed through, suggesting that the elevated levels of dependence are not a mere artifact of econometric modeling. Such evidence of excess comovement has strong implications for portfolio management, as the residual dependence may limit the potential for diversification among the various commodities within a given sector. This is particularly important for passive investors who are seeking commodity exposure for diversification benefits. Excess comovement is also indicative of inadequate supply and demand models of commodity futures returns. As a result, other pertinent pricing characteristics must be uncovered as the decisions of suppliers, producers, hedgers, and forecasters may be impeded (Pindyck and Rotemberg, 1990). Additionally, active traders in these contracts can use the observed dependence structure to identify directional relationships, of varying magnitudes, among futures contracts and implement trading strategies based on deviations from these documented statistical averages. This is quite valuable for spread options traders and hedgers alike. We hypothesize that the observed excess comovement is due in large part to the fundamental economic linkages that commodities categorized within the same sector possess, though the strength of the dependence inherently varies with each sector. The factors that drive commodity prices (e.g. production, consumption, weather, inventory, and geopolitical conditions) are distinct not only from those of traditional asset classes, but also from each other. Yet, some commodities, despite appearing to be unrelated, possess a substitution or complementary relationship in their utilization process that drives an interdependence between them. In an effort to capture the impact of these relationships and identify other relevant pricing factors, we construct two commodity-specific “cross-market” variables related to changes in inventory and open interest and test their importance as priced risk factors in a linear framework while controlling for common macroeconomic, commodity market, and commodity-specific factors.2 The two cross-market variables are constructed as the week to week change in aggregated inventory and open interest data, respectively, of N-1 constituents in a given sector, where N represents the number of commodities in that sector. The commodity whose inventory/open interest data is excluded from the variable construction is the asset whose return vector is the dependent variable in the regression. We find that changes in cross-market open interest has the most prominent impact of the two cross-market factors examined, particularly in the energy and livestock sectors. In contrast, changes in cross-market inventory plays a very minor role as a determinant in futures returns to the energy and grains sectors. Overall, the majority of cross-market factors are insignificant in the grains markets. In all, the risk factor examination does not provide a consistent result across all sectors despite the observation of high within-sector excess comovement. We believe this is partially due to the inability of a linear factor model to fully capture the nature of the relationships among commodities. Nonetheless, our results suggest that cross-market characteristics of closely related commodities matter, particularly open interest for the energy or livestock markets. This paper adds value to the existing literature in two key ways. First, we document that economically related commodities (based on sector groupings) have higher excess comovement as compared to commodities that are not directly related. This result differs from most prior work which typically examines samples of commodities that are diverse and completely unrelated through any production and/or consumption mechanism (Pindyck and Rotemberg, 1990; De Roon et al., 2000; Le Pen and Sevi, 2018) and only control for macroeconomic factors. We construct two commodity market controls (momentum and term structure), in addition to the macroeconomic controls, to better disentangle the impact of common factors on commodity prices. Our findings are consistent with Casassus et al. (2013); however, we extend the empirical number of commodities included in our sample and use weekly—not monthly—returns because the higher frequency data provides more relevant results for portfolio managers, active traders, and other active market participants. We also measure both linear symmetrical dependence and non-linear tail dependence using copulas to ensure that the results are not a modeling issue. Second, we show that the characteristics of closely related commodities are instructive and help to explain the price dynamics of their sector constituents. Although changes in physical cross-inventory is not particularly informative, changes in cross-open interest is a significant determinant of returns to the energy and livestock sectors. This result, in particular, is an extension of the literature strand that explores commodity factor pricing. The remainder of this paper is organized as follows. Section 2 provides a review of the pertinent literature and emphasizes our contribution. Section 3 describes the nature of the economic linkages between the commodities within each sector. Section 4 discusses the dataset. Section 5 describes the methodology and empirical results. Finally, Section 6 offers concluding remarks. 2. Literature and contribution Early work by Pindyck and Rotemberg (1990) pioneered the concept of excess comovement among commodity prices. They examine the cash prices of seven seemingly unrelated commodities (wheat, cotton, copper, gold, crude oil, lumber, and cocoa) that theoretically should be uncorrelated because of a lack of underlying economic linkages. However, they discover that the regression residuals, after controlling for macroeconomic conditions, are highly correlated. This finding led to their well-known excess comovement hypothesis where standard supply and demand models may not explain commodity prices due to significant price comovement in excess of

1 For example, corn and wheat futures are both components of the grains sector and hence defined as within-sector commodities. Corn and natural gas futures are part of the grains and energy sectors, respectively, and would be designated as across-sector commodities. 2 Inventory has relevant information about its state built into futures returns (Gorton et al., 2013; Symeonidis et al., 2012) and open interest has found support as a pro-cyclical predictor of broad asset class returns (Hong and Yogo, 2012).

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anything explained by common effects such as inflation, changes in aggregate demand, interest rates, or exchange rates. In contrast, Deb et al. (1996) find no evidence of excess comovement among unrelated commodities when tests using a multivariate GARCH framework are applied, after again controlling for macroeconomic changes. They contend that this more robust framework addresses multiple issues of misspecification present in the work of Pindyck and Rotemberg (1990). Deb et al. (1996) emphasize that the initial findings of Pindyck and Rotemberg (1990) are sensitive to both neglected conditional heteroscedasticity and a neglected structural shift in the prices of certain commodities occurring in the mid-1970s, thus causing the false presence of excess comovement. More recently, Le Pen and Sevi (2018) revisit the issue of excess comovement for eight unrelated commodities. They use factor analysis and analyze 184 macroeconomic variables as potential controls, but narrow it down to nine common factors to facilitate their study. Their estimates offer some evidence of time-varying excess comovement which is primarily driven by speculative intensive trading. Dorfman and Karali (2013) explore the impact of structural change(s) in the commodity markets on the interdependence among futures prices. They note that prices of commodities are not the same after the mid-2000s when the growth of commodity index funds exploded. While they find strong evidence of positively correlated changes for many pairs (and trios) of futures prices that have seemingly little reason to commove together, the probability of cointegration among the commodities is relatively low. This mixed evidence points towards increased efficiency in the commodity futures markets over time, but this uptick in efficiency did not result in stronger economic linkages among previously unconnected commodity prices. Chng (2009) explores the issue of cross-market trading dynamics of futures contracts for seemingly unrelated commodities for a specific industry—automotive manufacturing. Through the lens of basic economics, he argues that non-trivial cross-elasticities of complementary commodities, serving as production inputs, and slow information flow manifest themselves in cross-market volume-volatility interactions among the commodities for a specific group. Malliaris and Urrutia (1996) examine price comovement by looking at a more focused group of commodities in the agricultural sector. They find evidence of significant long-term price relationships between all of the commodities, supporting the idea of interdependency between the agricultural products based on the economic rationale of substitutability and complementarity in the production and input process. Ai et al. (2006) arrive at an antithetical conclusion in their analysis of agricultural commodities. Using a partial equilibrium model that controls for macroeconomic and commodity-level factors (e.g. inventory, harvest size, yield per acre, and planted acres) they find comovements are not excessive; that is, agricultural commodity price comovement arises from commonalities in supply and demand and nothing more.3 Our research complements this range of literature by analyzing the excess comovement of commodity futures in the context of standard investment professional groupings (i.e. sectors) which are based on the function and physical form of the actual commodity.4 The analysis in this sector-based context is unique and particularly enlightening because the well-documented belief that commodities are broadly uncorrelated with one another (Erb and Harvey, 2006) has been challenged in more recent years as large inflows from commodity index investment have been argued to have altered commodity correlation dynamics. In particular, Tang and Xiong (2012) document that prices of non-energy commodities have become increasingly correlated with oil prices and that the trend is a reflection of a fundamental process known as “financialization,” a term used to describe the increasing role of institutional investors in the commodity markets.5 They highlight that the financialization process has led to more correlated commodity prices that are no longer solely determined by supply and demand characteristics, but are a function of the aggregate risk appetite for financial assets.6 We focus on the long-term price excess comovements of 11 commodities within the energy, grains, and livestock sectors that have identifiable and seemingly strong economic relationships as a result of some substitutability or complementarity link in the utilization process.7 The groups are very diverse in terms of factors of production, seasonality, country of origin, and perishability. We contend that the commodities within the same sector generally have robust functional relationships that make their prices comove more strongly, compared to the price comovement with commodities in other sectors where such relationships are not present. We capture the nature of these dependences using copula models to estimate excess comovement and argue it is an improved and more dynamic methodology to observe bivariate dependence than the traditional correlation coefficient. Research focusing on the nature of the underlying relationships among multiple commodity sectors and what explains the comovements has received relatively scant attention. A notable exception is Casassus et al. (2013) who use a futures price ratio of two related commodities (as a proxy for the relative scarcity of one of the commodities) to theoretically demonstrate that for productive commodities the convenience yield depends not only on its own characteristics (e.g. inventory, prices, etc.) but also on the characteristics of other economically related commodities.8 Their analysis extends the traditional theory of storage (Kaldor, 1939; Working, 1949) to a multi-commodity level and shows the importance of long-term economic relationships in futures pricing. Our approach is complementary to that of Casassus et al. (2013); however, we collect and use real inventory data, as opposed to price ratios, as this

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Ai et al. (2006) is one of the few papers to employ commodity-specific variables in their analysis. The Dow Jones Commodity Index (as of December 20th, 2018) lists five commodity sectors: agriculture, energy, industrial metals, livestock, and precious metals. Agriculture is decomposed into two subsets: grains and softs. Petroleum is listed a subset of energy. The S&P GSCI (as of December 20th, 2018) follows a similar division of commodities into sectors, but only lists grains as a subset of agriculture. 5 The trend of increased correlation is much more pronounced for indexed commodities (i.e. those listed on the two most popular indexes—S&P GSCI and DJ-USBCI) than non-indexed commodities. 6 Basak and Pavlova (2016) provide a detailed theoretical framework regarding the impact of institutional trading on all commodity prices. 7 The individual commodities selected for the study must have weekly futures and inventory data that span the sample period September 30, 1992–December 31, 2017; those commodities that did not meet this criterion were excluded from the study. 8 Their theoretical model is applied to empirical data for WTI crude oil, heating oil, and unleaded gasoline pairs only. 4

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allows us to draw more direct inferences. What is more, our focus is also on the empirical explanatory power of commodity-specific cross-market variables (related to changes in inventory and open interest) in a given sector due to the underlying relationship(s) of the commodities. 3. Economic linkages among commodities In this section we describe the economic linkages among the commodities in a particular sector that ostensibly result in high levels of excess comovement relative to comovement with commodities in other sectors. The joint production, consumption, or ability to interchange is detailed to understand the fundamental economic relationship between the actual commodities. While the commodities in a sector such as energy have relatively recognizable relationships because they often serve as inputs in a vertical integration process, the connections between commodities in the grains or livestock sectors are not as apparent. These linkages connect the price dynamics of commodities and any transient deviations from a long-term relation between the commodity prices, due to supply- or demand-side shocks, are corrected over time (Casassus et al., 2013). 3.1. Energy sector The commodities underlying the futures contracts in the energy sector are WTI crude oil, heating oil #2, unleaded gasoline, and natural gas. Crude oil, also called petroleum, is a relatively abundant commodity that is acquired directly from the ground and then through a very specific refining process “cracked” into commonly used (unleaded) gasoline. Moreover, through this process of cracking crude oil to supply gasoline, heating oil is also produced as a by-product. Such a refinement process characterizes a very clear vertical production process between most of the commodities in this group. Natural gas on the other hand is often categorized as a substitute good/input for crude oil in the areas of industrial and electrical generation. Similarly, in residential heating, heating oil and natural gas also pose as substitutes. Many single family, multi-family, and apartment complexes operate with either gas or oil furnaces that can be interchanged, albeit at a cost to the consumer. 3.2. Grains sector The commodities underlying the futures contracts in the grains sector are corn, oats, soybeans, and wheat.9 The prices of these commodities are driven by imbalances in global supply and demand. What is more, agricultural production has historically been very vulnerable to altered weather patterns. Even mild climate changes can increase the susceptibility of crops to infestations and diseases thereby dramatically impacting yields and prices across the sector as shortages and planting diversions abound.10 Yet, despite the technological advances the sector has seen relating to crop yields, the production of food(s) is still highly dependent on climate as temperature, rainfall, and solar radiation are the drivers of growth (Rosenzweig et al., 2001). Though weather is a primary factor in production, the use of the grains plays a large role too. The relationships and categorization among the different commodities included in this group are not always clearly defined and often depend on the context in which they are being analyzed. For instance, there is a substitutability between corn, oats, and to a lesser degree soybeans for the feeder cattle market. Corn is generally considered as energy feed for cattle farmers, but if corn prices increase, farmers may opt to use more oats or soybeans as a substitute feed. Yet, depending on the goals of a cattle farmer, some of these grains may be used in a complementary fashion. For example, if the goal of the cattle farmer is to encourage rapid weight gain of the livestock then the feed mix will include a larger proportion of soybeans as a strong protein supplement in addition to corn and/or oats. In the human provisions market there is substitutability between the two grains, corn and wheat. Both types of grains are interchangeable in many commercial food recipes, particularly baking. Furthermore, cooking oils derived from corn and soybeans are also frequently used as substitutes in food preparation. However, just like in the cattle feed market, complementary relationships also exist among several of the grains depending on the provision goals. For example, large amounts of corn and wheat are often used together in large-scale processed food production. Perhaps the most impactful event on the pricing relationship between grains has been the emergence of biofuels as a significant source of transportation fuel. The U.S. Energy Policy Act of 2005, prompted by rising energy prices and increasing dependence on foreign oil, shifted the trajectory of what was a long-term decline in the real prices of grains (Commodity Research Bureau, 2012). The energy laws, within the 2005 Act, mandated that U.S. gasoline must contain increasing amounts of renewable fuel, such as ethanol and biodiesel, which when combined with gasoline increase octane levels and reduce harmful emissions, such as carbon monoxide and hydrocarbons. The production of ethanol is mainly concentrated in the U.S. and Brazil, whereas biodiesel is mainly focused in Europe. Subsequent to the Act, worldwide ethanol production more than doubled and biodiesel production more than tripled over the period 2006 to 2012 (Bernardina, 2014). Concurrently, corn prices began moving sharply higher since it serves as a primary input for ethanol production in the U.S. (in Europe, wheat and sugar beets are principal). The rally in corn prices also resulted in contemporaneous increases for soybean and wheat prices. The increase in the volume of planting for corn in ethanol production caused a massive diversion

9 The wheat futures contracts used are those of Chicago Soft Red Winter (CSRW). CSRW is one of the two global industry standards for wheat—Kansas City Hard Red Winter is the other; CSRW is the most liquid wheat futures contract in the world. 10 The 1930s saw the drought of the U.S. Southern Great Plains cause a reduction in the yield of wheat and corn of nearly 50%. In 1988, the U.S. Midwest drought led to a reduction of corn on the order of 30%.

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in the planting area for soybeans and wheat thereby reducing aggregate supply.11 This became known as the “ethanol effect” (Commodity Research Bureau, 2012). Biodiesel, on the other hand, is derived from natural oils such as soybean oil, palm oil, and rapeseed oil. In the U.S., as well as Brazil, the biodiesel market is primarily driven by soybeans, whereas in Europe rapeseed is principal (Ravindranath et al., 2011). 3.3. Livestock sector The commodities underlying the futures contracts in the livestock sector are live cattle, feeder cattle, and lean hogs. Live cattle represent cattle which have attained an optimal weight as to be sold to a packer. The packer then slaughters the cattle and sells the meat (beef), almost exclusively for human consumption, at different grades to restaurants, schools, hospitals, and households. On the other hand, feeder cattle, generally, are weaned calves that are sent to feedlots; they effectively represent a latent supply of live cattle. In the feedlots an emphasis is placed on efficient growth and weight gain for the cattle which involves a combination of a high-energy diet and a reduction in energy expended by the animals to find such food. On the surface live/feeder cattle and lean hogs may seem similar in that all are primarily used for human consumption. However, the fundamentals of the markets, which include breeding season, food, and optimal weather, are quite diverse. Lean hogs represent hogs that are of sufficient weight to be brought to market and slaughtered. After a hog is slaughtered, portions are allocated out as ham, pork loins, and bacon. The nature of substitutability and complementarity between beef and pork is not a clearly defined one in the literature. Davis et al. (2008) suggests that the relationship is determined by the difference between compensated and uncompensated demand elasticities of consumers. Specifically, the uncompensated cross-price elasticities for both low and high incomes suggest both substitutionary and complementary relationships, while the compensated price elasticities are dominated primarily by substitutionary relationships. Dong et al. (2015) echo similar results, in some respects, but distinctly point out that beef steak purchases increase the most with income and that specific cuts of pork, in particular pork loins, exhibit price responses that are more sensitive to price changes than other animal meat products. Rodriguez and Eales (2015) employ a novel methodology and find that over the last 50 years, beef (chicken) has become more (less) price flexible. Assuming scale flexibilities are consistent with income elasticities, the results indicate that beef has become a necessity whereas chicken has become a luxury. The authors conclude that, “[i]f greater own-price flexibility is consistent with inelastic demand and lower own-price flexibility consistent with elastic demand, this would indicate that consumers have become less price-sensitive to beef and more price-sensitive to chicken… [contradicting] past research and meat consumption data that suggests the opposite.” Of particular interest is an examination of the effects of female labor participation rates on consumer meat demand. Schroeder et al. (2000) document that when the number of females in the labor force rises in the U.S. there is a strong negative impact on the demand for beef.12 The author suggest the decline in demand is due in part because of “a failure to offer consumers high quality, convenient, easy-to-prepare beef products.” Rodriguez and Eales (2015) report similar findings that show when female participation in the labor force is lower, beef has an inelastic demand relative to chicken and pork, suggesting beef is a necessity relative to chicken and pork. However, when female participation in the labor force is higher, chicken and pork have an inelastic demand relative to beef, suggesting chicken and pork become a relative necessity while beef becomes a luxury. Regardless, an economic relationship between the various livestock markets exists, though it may be conditional and sensitive to specification. 4. Data 4.1. Futures returns We extract daily futures price data for the full sample of commodities from the Commodity Research Bureau (CRB) beginning September 30, 1992 and ending December 31, 2017. Returns for the futures contracts are calculated as follows. Each day we compute the daily return on either the nearest- or next nearest-to-delivery contract. More specifically, the daily return series is constructed using the nearby futures contract of a given commodity until one month prior to the contract's expiration and then rolled over to the nextnearby contract.13 Daily futures returns are computed as follows, using the rolling contract approach: ritþ1;T ¼

Fitþ1;T  Fit;T

(1)

Fit;T

where, Fit;T is the daily futures price of contract i on day t on the nearest-to-delivery contract with expiration date T, and Fitþ1;T is the daily price of the same contract on day tþ1. Weekly return series are attained by compounding daily returns to a weekly frequency ending Tuesday of each week.14 The cut off of Tuesday is done in order to match hedging pressure and open interest data obtained from the

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In 2007, U.S. corn planting increased by approximately 19% while soybean fell by 14%. Over the period 1992–1999 beef demand decreased an average of 1.3% per annum due to increasing female labor participation. 13 Returns are always calculated on the same contract and we do not include the return on collateral associated with the futures contract in the calculation. 14 !   Asness et al. (2013) and Moskowitz et al. (2012) create a monthly series with the same procedure; specifically, to convert the daily returns to Q ri tþ1 þ 1  1 . weekly returns the following formula is applied: Ri wk ¼ 100 12

t2day

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Commitments of Traders (COT) weekly reports published by the Commodity Futures Trading Commission (CFTC).15 Table 1 provides the relevant summary statistics of the (annualized) futures returns for the full sample of commodities.

4.2. Comovement controls Macroeconomic. We utilize two macroeconomic control variables, namely, a trade-weighted U.S. dollar index and a U.S. leading economic index, to adjust for the impact of common macroeconomic shocks in examining excess comovement within- and acrosssectors. The U.S. dollar index (TWUSDI) is based on the trade-weighted average of the foreign exchange value of the U.S. dollar against the currencies of a broad group of major U.S. trading partners.16 Since commodity prices are measured in U.S. dollars, this factor controls for price movement through changes in international exchange rates. We also include the U.S. leading index (USLI) as a leading economic indicator of U.S. business cycle turns.17 Since futures prices are inherently forward looking, the factor provides a reasonable control proxy for changing market conditions as they relate to real production. The economic data is retrieved from the Federal Reserve Bank of St. Louis (FRED). While much of prior literature uses only macroeconomic variables as controls for common movement, we also utilize variables that control for the affinity in supply and demand characteristics of the commodity markets. The breadth of research on commodity futures markets have identified specific factors that are of significant importance when evaluating market pricing dynamics. Thus, we include factors that account for momentum and term structure (Asness et al. (2013); Fuertes et al., 2010). Momentum. One of the most studied capital market phenomenon is the relation between an assets return and its recent relative performance, or “momentum.” The returns to momentum strategies have become a contentious focal point in the asset pricing literature as recent evidence does not favor the notion of efficient markets. Asness et al. (2013) report a consistent premium (alpha) of 11.4% for high minus low momentum portfolios of commodity futures. Similar work by Fuertes et al. (2010) report annualized alphas of 10.14% for momentum portfolios. To control for momentum in returns we follow the format of Asness et al. (2013) and calculate the momentum portfolios (MOM) as follows. Each day we rank all commodity futures returns in descending order based on their 250-day moving average, excluding the most recent 22 days to avoid the one-month reversal in returns which may be due to liquidity and/or microstructure issues.18 The returns are then assigned to portfolio quintiles where the returns are computed as equally-weighted averages of the commodity returns assigned to that particular portfolio. The daily MOM factor is then constructed as a long-short portfolio between the top and bottom quintiles, whereby the top quintile average return is subtracted from the bottom quintile average return. The daily MOM factor is then accumulated into a weekly frequency ending each Tuesday following the same method used for weekly futures returns. Term Structure. While momentum strategies make use of the nearest- or next nearest-to-delivery contracts, the majority of investable futures contracts on the back-end of the futures curve are largely ignored. This collection of futures contracts offers additional information and investment opportunities ranging from attractive roll yields, lower volatility, lower turnover, to an increased opportunity set of investable assets (De Groot et al., 2014).19 Thus, the prices of the nearby contracts react most heavily to supply, demand, and news shocks, while prices further along the curve are influenced significantly less. Fuertes et al. (2010) implement a term structure strategy that buys backwardated contracts and shorts contangoed contacts to earn an average return of 12.66%. They also explore a double-sort strategy involving momentum and term structure which generates returns in excess of 20% per annum. De Groot et al. (2014) find contracts on the futures curve with the largest expected roll yield, or strongest momentum, earn significantly higher risk-adjusted roll yields than a traditional momentum strategy with a net return of 8.42% per annum. Moreover, the strategy of buying contracts further out from maturity reduces turnover, and consequently transaction costs, by more than 50%. To control for the term structure of the futures curve we follow Fuertes et al. (2010) and calculate the term structure portfolios (TS) as follows. Each day we rank all commodity roll yields in descending order. The returns are then assigned to portfolio quintiles based on the following term structure measure: TS½1; 2d ¼ F1d  F2d

(2)

where, F1d is the price of the nearest delivery contract and F2d is the price of the next nearest-to-delivery contract. Daily quintile returns are computed as an equally-weighted average of returns of the commodity returns assigned to that portfolio. The daily TS factor is then constructed as a long-short portfolio between the top and bottom quintiles, whereby the top quintile average return is subtracted from the bottom quintile average return. The daily TS factor is then accumulated into a weekly frequency ending each Tuesday following the same method used for weekly futures returns.

15 Barring major holidays and government shutdowns, the COT reports cover data from the week prior ending on Tuesday and is publicly released on Friday afternoon. 16 This broad currency index includes: Canada, Japan, Mexico, China, Taiwan, South Korea, Singapore, Hong Kong, Malaysia, Brazil, Switzerland, Thailand, Philippines, Australia, Indonesia, India, Israel, Saudi Arabia, Russia, Sweden, Argentina, Venezuela, Chile, Colombia, the U.K., and the Euro areas. 17 The returns to commodity futures portfolios tend to be pro-cyclical (Alquist and Coibion, 2013), so it is natural to control for the evolution of the business cycle. 18 Skipping the most recent month of returns is standard in the momentum literature (Jegadeesh, 1990; Lo and MacKinaly, 1990; Asness, 1994). 19 Portfolios seeking to exploit the term structure of commodity futures are based on the work of Samuelson (1965) who shows that the volatility of returns decreases as the maturity of contracts increases.

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Table 1 Summary statistics of futures returns. Annualized Futures Returns Sector

Commodity

Mean

Std. Dev.

Skewness

Kurtosis

Crude Oil, WTI Unleaded Gasoline Heating Oil #2 Natural Gas

9.60 17.32 9.75 11.54

33.16 32.60 31.11 45.41

0.25 0.14 0.00 0.10

1.73 1.69 1.11 1.03

Corn Oats Soybeans Wheat

3.14 4.55 7.74 7.25

26.58 33.43 22.93 28.78

0.22 0.31 0.12 0.37

2.75 3.63 1.28 1.63

Live Cattle Feeder Cattle Lean Hogs

2.36 2.58 1.51

15.38 15.06 25.27

0.24 0.51 0.06

3.54 4.08 2.57

Energy

Grains

Livestock

Note. This table presents the summary statistics of the annualized futures returns for each commodity in the energy, grains, and livestock sectors. The sample period spans September 30, 1992 to December 31, 2017. All results are reported in percentages.

4.3. Regression controls To examine the role of excess comovement as it pertains to the total returns of commodity futures it is necessary to control for commodity-specific variables in addition to macroeconomic (TWUSDI and USLI) and commodity market (MOM and TS) factors. As such, we introduce hedging pressure, changes in inventory, and changes in open interest as additional regression controls for risk premium. We then augment the model with the cross-market commodity-specific variables of interest. Hedging Pressure. The hedging pressure hypothesis, whereby non-participation in the futures markets by speculators influences the risk premium of commodity futures, was developed by Hirshleifer (1990).20 Early tests of the hypothesis confirm the role of own commodity hedging pressure as a determinant of futures prices (Bessembinder, 1992; Cootner, 1960). More recent work notes that for some groups of commodities their returns depend on both their own and cross-market (from within their defined group) hedging pressures.21 Acharya et al. (2013) demonstrate that the interaction of limited speculator capital and producer hedging demand is important for understanding commodity futures risk premiums, especially during periods of financial distress. In order to control for commodity-level hedging pressure we obtain positions of large trader's data from the CFTC COT reports. Large traders are required to report to the CFTC if they take a position in a futures market for speculative or hedging purposes. Given this, the position measures can be used to construct a hedging proxy that shows whether traders are net long or short in a given futures market. Following De Roon et al. (2000), we construct a hedging pressure variable (HP) based on aggregated weekly commercial short and long positions from all the markets that a particular commodity trades. For each futures contract, i, we calculate the control variable as follows: HPi;t ¼

HSi;t  HLi;t

(3)

HSi;t þ HLi;t

where, HSi;t is the aggregate number of commercial short hedge positions for commodity i in week t, and HLi;t is the aggregate number of commercial long hedge positions for commodity i in week t. Inventory. The behavior of commodity inventory is fundamental to the theory of storage. Gorton et al. (2013) demonstrate that futures prices carry pertinent information about the nature and state of inventories (e.g. scarcity). In order to control for changes in the state of commodity-level inventory we collect real physical inventory data for our entire sample of commodities from a variety of sources. We obtain weekly inventory data for the energy sector from the Department of Energy (DOE). The weekly inventory data for grains is taken from the United States Department of Agriculture (USDA).22 Finally, inventory data for livestock is retrievable from the National Agricultural Statistics Service-United States Department of Agriculture (NASS-USDA); however, it is only available in a monthly frequency so we are forced to omit this variable from the livestock sector regression analysis. The inventory of the commodities is tested for seasonality and deseasonalized when necessary. To formally test for seasonality, we regress the inventory of each

20 One of the main contributions of the hypothesis is that it links backwardation to lower levels of hedgers' hedging pressure and contango to higher levels of hedgers' hedging pressure. 21 These futures groups are defined as follows: financial (S&P 500, Value-Line, T-bond, T-bill, and Eurodollar), agricultural (wheat, corn, soybeans, live cattle, and world sugar), mineral (gold, silver, platinum, crude oil, and heating oil), and currency (Deutsche mark, British pound, Japanese yen, Canadian dollar, and Swiss franc). 22 Grains weekly inventory data is available at: https://www.ams.usda.gov/market-news/search-market-news. The publication of the weekly frequency data was discontinued in August 2014. The weekly data is not in a centralized databse and requires that it be hand collected. The data is made available from the authors by request.

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commodity against monthly dummy variables. The resulting F-statistic is used to test the null hypothesis that the coefficients of all the seasonal dummies are equal to 0. Rejection of the null means the inventory of that particular commodity exhibits seasonality, in which case the residuals from the dummies serve as the deseasonalized inventory to facilitate the analysis. Changes in inventory (INV) is measured as the percent change on two consecutive weeks. Open Interest. Recent research contends that open interest in the commodity futures markets is a more powerful predictor of returns than past commodity prices or macroeconomic measures of real economic activity (Hong and Yogo, 2012). The supposition is that transaction quantities contain information that is not fully revealed by transaction prices alone. Thus, open interest is extremely informative about commodity futures returns in the presence of hedging demand and restricted risk absorption in the futures markets. The idea that transaction quantities can be more informative than transaction prices is a relatively new concept which offers a more robust and richer understanding of movements in asset prices. To control for changes in commodity-level open interest (OI) we extract open interest from the weekly CFTC COT reports and measure the percent change on two consecutive weeks. 4.4. Regression variables of interest Much of the prior literature regarding commodity futures has primarily focused on the stochastic behavior of individual commodities, employing commodity-specific factors to test single commodity time-series pricing properties. The fundamental linkages among the commodities within each of the three sectors gives us reason to examine new variables that may capture these dynamics and their impact on returns. Given the importance of the information conveyed by inventory and open interest measures we construct two new commodity factors that account for the influence of within-sector commodities on their constituents' returns. Cross-Inventory and Cross-Open Interest. Both changes in cross-inventory (C_INV) and changes in cross-open interest (C_OI) factors are formed as the week to week percentage change in the aggregate value of the appropriate data for all commodity futures in a given sector excluding the commodity whose futures return properties are being estimated. For instance, to find the changes in cross-open interest factor for corn, we begin by aggregating weekly open interest data for the other constituents of the grains sector (i.e. oats, soybeans, and wheat). Next, we compute the percentage change for this aggregated measure of the grains sector each week, and employ this variable as the cross-open interest factor for corn. In a similar fashion, changes in cross-inventory for corn is computed as the weekly percentage change in the aggregated inventory of oats, soybeans, and wheat. For each sector, this approach is followed to calculate all cross-market factors for each individual commodity. 5. Methodology and empirical results 5.1. Excess comovement and copulas To investigate excess comovement between commodities, we utilize standardized residuals from a linear factor model that filters the returns through the macroeconomic and commodity market controls discussed in section 4.2. The model is estimated via ordinary least squares (OLS) and takes the following form for each commodity: ri;t ¼ αi þ βi TWUSDIt þ βi USLIt þ βi MOMt þ βi TSt þ εi;t

(4)

where, ri,t is the weekly return of commodity i at time t. The simple correlation measure and commonly used dynamic conditional correlation (DCC) measure both impose the assumption of common price dynamics among all assets (Billio et al., 2006). This particular restriction may or may not be true, but the imposition that the correlations of commodity futures are all identical seems somewhat impractical. Ai et al. (2006) remark that the inappropriate assumption of normality in Pindyck and Rotemberg (1990) may induce the manifestation of excess comovement where none truly exists, suggesting that excess comovement findings are nothing more than an econometric modeling problem. In order to alleviate such pitfalls, we apply copula models that provide a dynamic measure of comovement. A copula is a way of creating a joint probability distribution for two variables, or more, while preserving their marginal distributions. The joint probability of the relevant variables is defined implicitly by mapping them to other variables that have a known joint distribution. This method disentangles the unique characteristics of each return series from the dependence structure that links them together and allows for a range of models which can capture different forms of dependence between variables.23 We choose a total of four copula models to measure the bivariate dependence of the standardized residuals in equation (4). These copulas capture such features as upper and lower tail dependence, as well as symmetrical and asymmetrical dependence. Specifically, we utilize (i) the normal (Gaussian) copula to measure symmetrical dependence—a symmetrical and frequent dependence structure that has no tail dependence, (ii) the Student's t copula—a symmetrical but non-zero tail dependence structure which nests the normal copula, (iii) the Clayton copula to capture lower tail dependence, and (iv) the Gumbel copula to capture asymmetric dependence in the upper tail. These copula models allow a good deal of control to be exercised over what part of the distribution the filtered residuals are more strongly associated for analysis. Practically speaking, these copulas also represent the most relevant shapes for finance and are

23 The dependence structure estimated via copula is more robust in the sense that the approach separates the dependence structure from the choice of marginal distributions. Moreover, the copula approach does not require elliptically distributed returns and is invariant with respect to increasing and continuous transformations of the marginal. Manner and Reznikova (2012) provide an extensive survey on copulas and their properties.

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Table 2 Copulas and dependence. Copula Normal

Bivariate Form ¼

R Φ1 ðvÞ R Φ1 ðuÞ ∞

∞

Dependence ϕρ ðx; yÞdy dx

  x2  2 ρxy þ ρ2 exp  is the density function of the bivariate 2 1 2ð1  ρ Þ 2 2π ð1  ρ Þ2 normal distribution with correlation ρ ¼ ρðx; yÞ ε ½  1; 1 R R t1 1 tν ðuÞ ν ðvÞ tν; ρ ðx; yÞds dt ¼ ∞ ∞ νþ2 ν þ 2   Γ Ry Rx s2  2 ρst þ t2 2 2 where, tν;ρ ðx; yÞ ¼ ∞ ∞  ν  p ds dt is the bivariate ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ νð1  ρ2 Þ Γ νπ 1  ρ2 2 Student distribution with ν degrees of freedom and correlation ρ ¼ ρðx; yÞ ε ½  1; 1 1

where, ϕρ ðx; yÞ ¼

Student's t

Clayton

Gumbel

ρ ¼ ρðx;yÞ, which measures linear dependence

1

λ ¼ 2tνþ1



sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! ðν þ 1Þð1  ρÞ , which 1þρ

measures asymptotic dependence in both the upper and lower tail 1

 ¼ ðuθ þ vθ  1Þ =ϑ , where 0 < θ < ∞

λl ¼ 2 =θ , which measures lower tail dependence

8 9 < 1 = ¼ exp  ððlnuÞθ þ ðlnvÞθ Þ =θ , where 1  θ < ∞ : ;

1

λu ¼ 2  2 =θ , which measures upper tail dependence

Note: This table presents the bivariate form and dependence measure of the normal, Student's t, Clayton, and Gumbel copulas.

frequently used in empirical papers (Embrechts et al., 2002; Rosenberg and Schuermann, 2006; Patton, 2009; Chollete et al., 2011; Delatte and Lopez, 2013). Table 2 describes, for all ðu; vÞ 2 ½0; 12 , the two-dimensional copulas and corresponding dependence measures. All copula parameters are estimated using the Canonical Maximum Likelihood (CML) method. First, the standardized residuals are rankðx Þ

transformed to their unit hypercube by the empirical cumulative distribution function (CDF), defined as ui;t ¼ Tþ1i;t , where rank ðxi;t Þ is the ordinal rank of observation t among T observations. The empirical CDF is uniform by construction. Second, the parameters of the copulas are estimated using Maximum Likelihood (ML). Based on the log-likelihood criteria, in most instances, the Student's t copula best fits the commodity data.24 Table 3 displays the results of the various copula models. Panel A summarizes the dependence estimates from the normal and Student's t copulas. The lower triangular elements represent dependence measures estimated from the normal copula. The upper triangular elements represent dependence measures estimated from the Student's t copula. The coefficient of these two dependence measures lies between 1 and 1, where higher values indicate a greater level of dependence between the returns series, similar to the interpretation of the simple correlation measure. Both copula models show that virtually all within-sector dependence measures are greater than any across-sector dependences for all commodity futures, meaning that levels of excess comovement within-sector are much higher than across-sector. The exception is the Student's t copula across-sector dependence measure of soybeans-heating oil at 0.56 which is equivalent to the smallest within-sector dependence measure (across all three groupings) of feeder cattle-lean hogs. The largest reported within-sector measures of excess comovement for the normal (Student's t) copula from the energy, grains, and livestock sectors are heating oil-crude oil at 0.90 (0.84), corn-soybeans at 0.63 (0.69), and live cattle-feeder cattle at 0.77 (0.77), respectively. Panel B of Table 3 shows the tail dependence measures using the Clayton copula, the lower triangular elements, and the Gumbel copula, the upper triangular elements. The value of these coefficients lies between 0 and 1, where 0 implies no dependence between the returns series and 1 indicates very strong dependence. The overall conclusion looking at the dependence structure in both the lower (Clayton) and upper (Gumbel) tails of the distribution is unchanged from that of the symmetrical models of dependence as all withinsector measures are much larger than across-sector. Noticeably, the Clayton copula shows low, or no, statistical measures of excess comovement at the lower tail between many of the across-sector pairings. The within-sector pairings are strikingly higher for all commodities. The Gumbel copula tells a very similar story to the Clayton. However, in contrast to the Clayton, the upper tail measures of excess comovement for across-sector pairings are well above the lower threshold of 0, but still far lower than the within-sector measures. In all, these measures illustrate that in times of financial market distress the excess comovement of across-sector assets tends to stay quite low by historical standards; the same cannot be said for within-sector excess comovement. This corollary is very useful for diversification purposes in portfolio management. The largest reported within-sector measures of excess comovement for the Clayton (Gumbel) copula from the energy, grains, and livestock sectors are heating oil-crude oil at 0.81 (0.77), corn-soybeans at 0.52 (0.51), and live cattle-feeder cattle at 0.68 (0.62), respectively. These pairings are unchanged from Panel A. Taken together these results show the strong presence of excess comovement within-sectors relative to across-sectors, and these findings are not merely an artifact of the econometric estimation technique. This is consistent with the initial proposition that excess comovement is due to the fundamental economic linkages that commodities categorized within the same sector possess, and that despite appearing to be unrelated in some ways, a substitution or complementary relationship in the commodity utilization process results in

24 The tail correlation is higher in a bivariate t distribution compared to the bivariate normal distribution and since correlations between assets generally increase during times of market distress it seems logical that the Student's t copula is a better descriptor of futures returns than a normal copula.

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Table 3 Copula based measures of dependence.

Note. Panel A shows the dependence estimates from the Student's t copula in the upper triangular elements of the matrix and the dependence estimates from the Normal copula in the lower triangular elements of the matrix. Panel B shows the dependence estimates from the Gumbel copula in the upper triangular elements of the matrix and the dependence estimates from the Clayton copula in the lower triangular elements of the matrix. The sample period spans September 30, 1992 to December 31, 2017. Soy represents soybeans, F.C. represents feeder cattle, L.C. represents live cattle, L.H. represents lean hogs, C. Oil represents WTI crude oil, H. Oil represents heating oil #2, N. Gas represents natural gas, and U. Gas represents unleaded gasoline."

high relative levels of residual dependence between them. Overall, these findings support the position of Casassus et al. (2013) that the economic linkages among commodities create a long-term dependence between the futures returns of related commodities. These findings also support to the work of Malliaris and Urrutia (1996). An interesting outcome, or perhaps lack thereof, from the comovement analysis is the low relative measures of excess comovement across the pairings in the energy and grains sectors. As discussed in section 3.2, the Energy Policy Act of 2005 created a direct link between corn, and to a lesser extent wheat, and gasoline through the infusion of ethanol as a renewable fuel source. Further, the use of soybeans as a production input for biodiesel created a similar connection. This policy shift impacting both sectors certainly seems it should increase the levels of excess comovement between the impacted commodities but the results do not bear this out. Since this change occurs in the middle of the sample period we look at the structural impact of the 2005 Act by creating a dummy variable equal to 1 after the 2005 policy change, and 0 otherwise. Using the standardized residuals from this procedure, we fail to observe any significant difference in our major findings. Therefore, we opt not to use the dummy results in the subsequent factor regressions.25 5.2. Factor regressions The evidence of strong excess comovement among within-sector commodities motivates the subsequent investigation into its role in the predictability of returns. That is, we aim to identify pertinent pricing factors that capture these relationships. We use the two macroeconomic variables (TWUSDI and USLI), two commodity market variables (MOM and TS), and three commodity-specific factors (HP, INV, and OI) as controls in the regression. The cross-market variables (C_OI and C_INV) serve as the testable pricing factors. The

25 A formal structural break test of the correlation between the average returns of the energy and grains sectors occurring in 2005–2006 shows no significant change.

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sample period spans September 30, 1992 to December 31, 2013.26 We use the seemingly unrelated regression (SUR) technique because it uses the correlation among the error terms in each equation to improve the regression estimates; the model assumes that the errors are contemporaneously correlated but not autocorrelated. The regression model is specified in matrix notation for simplicity: 0

y¼Xβþu

(5) 0

where, y ¼ ðy1 ; y2 ; …; ym Þ , yi is a T  1 vector of total futures returns (i.e. futures return plus the risk-free rate), X ¼ diagðX1 ;X2 ; : : : ; 0

0

0

0

Xm Þ, Xi is a T  K matrix of observations of explanatory variables, K is the number of regressors, β ¼ ðβ1 ; β2 ; …; βm Þ , βi is a vector of 0

unknown parameters that need to be estimated, u ¼ ðu1 ; u2 ; …; um Þ ; and ui is a T  1 vector of error terms.27 The SUR model is estimated by using the feasible generalized least squares (FGLS) method.28 The results of the SUR regressions for the energy, grains, and livestock sectors are displayed in Table 4 of Panels A, B, and C, respectively.29 In Panel A, changes in cross-open interest is positive and highly significant for all energy commodities with the exception of natural gas; thus, underscoring the importance of changes in open interest for fundamentally related commodities. For example, in looking at WTI crude oil, a 1% increase in the open interest of crude oil's constituents in the energy sector results in an increase of 0.1848 basis points for crude oil returns. In contrast, changes in cross-inventory is only significant for natural gas and carries a negative coefficient, indicating an increase in aggregate physical inventory for WTI crude oil, heating oil, and unleaded gas of 1% results in a decrease of 0.0042 basis points for natural gas returns. The estimates for Panel B are less significant than the energy sector. Only the cross-factors for oats are significant at conventional levels and take the expected signs. The changes in cross-inventory coefficient is 0.0029 and the changes in cross-open interest coefficient is 0.0835. One of the puzzling aspects of Panel B is the lack of significance on the USLI control for wheat given wheats importance as a global export for the U.S.—nearly 50% of U.S. wheat is exported. While perplexing, this could be because the U.S. only ranks fourth globally in wheat production. Currently, the U.S. ranks first globally in the production of corn and soybeans. In the case of oats, the U.S ranks near sixth in production, but accounts for over 50% of global demand for the product. Panel C estimates of changes in cross-open interest are more supportive of the original hypothesis. All coefficients are positive and significant with values of an order of magnitude similar to that of oats. Feeder cattle, live cattle, and lean hogs have reported coefficients of 0.0486, 0.0255, and 0.0804, respectively. As noted earlier, low frequency (weekly) inventory data does not exist for the livestock sector so INV and C_INV could not be incorporated into the regression analysis. Overall, the impact of changes in cross-market open interest is the most significant in the energy and livestock markets. The magnitude of the coefficients is larger for energy than livestock or grains, but overall the economic significance of the cross-market variable is relatively small. The economic significance of the two relevant coefficients for changes in cross-inventory in the energy and grains sectors is even smaller. Nonetheless, in the same vein as De Roon et al. (2000), the regression results of the energy and livestock sectors show that cross-market characteristics are relevant factors when examining commodity futures returns. 6. Concluding remarks We look at two different, but related, issues of the commodity futures markets. First, we empirically investigate whether the prices of commodities that possess some form of substitution or complementary relationship in their utilization process comove more strongly than the prices of fundamentally unrelated commodities. We categorize our sample of commodities into three groups (energy, grains, and livestock) and use four specific copula models to capture symmetrical, asymmetrical, right-tail, left-tail, and no-tail dependence as measures of bivariate association. Further, we control for macroeconomic and commodity market conditions to filter out the effects of common events on the return series, resulting in our measure of excess comovement. We find that fundamentally related commodities (i.e. those within the same defined sector) have higher excess comovement than unrelated commodities (i.e. those in different sectors). This is true regardless of the distributional lens that the commodity pairs are viewed through. In light of the argument of the financialization of the commodity markets, we find no support for increased dependence among individual unrelated commodities. Second, given the high level of excess comovement observed within each of the three sectors, we test whether the returns of one commodity are affected by the characteristics of its sector constituents. In an effort to identify new relevant pricing factors we construct two commodity-specific cross-market variables related to changes in inventory and open interest. We then test their importance as priced risk factors in a linear framework while controlling for common macroeconomic, commodity market, and commodity-specific effects. Results show that changes in cross-market open interest has the most significant impact of the two cross-market factors examined, specifically in the energy and livestock sectors. In contrast, changes in cross-market inventory is rather muted in its usefulness as a predictor. The grains markets show scant evidence that the cross-market factors play any substantial role as determinants of futures prices. Overall, the risk factor examination is rather inconsistent across all three sectors despite high within-sector excess comovement. Moreover, the economic magnitude of the relevant cross-market coefficients is somewhat small. While we contend that the commodity-

26

Again, for the grains sector, we are only able to collect complete weekly inventory data for the year through December 31, 2013; the reporting of the weekly inventory data frequency was discontinued mid-2014 by the USDA. Due to this constraint the sample period for the regression analysis ends December 31, 2013. 27 The risk-free rate is the 3-Month Treasury Bill Secondary Market Rate and is obtained from FRED: https://fred.stlouisfed.org/series/DTB3. 28 The system is also estimated using general method of moments (GMM), and similar results are obtained. 29 Including a dummy variable for the 2007 global financial crisis does not materially change the results. 11

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Table 4 SUR regression results.

Note. Panel A shows the SUR parameter estimates of the energy sector with corresponding t-statistics and p-values. Panel B shows the SUR parameter estimates of the grains sector with corresponding t-statistics and P-values. Panel C shows the SUR parameter estimates of the livestock sector with corresponding t-statistics and P-values. Estimates are obtained using FGLS. The sample period spans September 30, 1992 to December 31, 2013. CON represents the intercept, TWUSDI represents the trade-weighted U.S. dollar index, USLI represents the U.S. leading index, MOM represents momentum, TS represents term structure, HP represents hedging pressure, INV represents changes in inventory, OI represents changes in open interest, C_INV represents changes in cross-inventory, and C_OI represents changes in cross open interest. All p-values are highlighted that are significant at 10% or less.

specific cross-factors should have a significant effect on all related commodity futures, we recognize that the heterogeneous nature of the commodity sectors may not so easily be embodied in the measures. Overall, our results provide useful insights into the commodity futures markets. The results regarding high relative excess comovement underscore the importance of diversifying within the commodities asset class (and not just a sector) as a whole, as well as insights for active trading strategies involving, but not limited to, spread options. Moreover, we demonstrate that the pricing of certain commodity futures is driven by not only their own characteristics, but also by the characteristics of those commodities with which they share a relationship. It is through their economic linkage with these other commodities that the commodity-specific factors enter into the pricing dynamics of their related counterparts and have an influence. Possible limitations of our factor model approach to fully capture the impact of the cross-factors on returns may include inappropriate factor identification and linear model specification. Currently, there are no known macroeconomic factors that explain the crosssection of returns in the commodity futures markets. Our specification of macroeconomic factors is not complete—one can explore more observable factors or follow an unobserved factor model to improve future findings. Also, a linear model specification may be inappropriate to fully encapsulat non-linear relationships that are present in these markets—one could try to estimate a non-linear model to better examine the impact of cross-market factors on return dynamics.

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Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jcomm.2019.04.002.

References Acharya, V., Lochstoer, L., Ramadorai, T., 2013. Limits to arbitrage and hedging: evidence from commodity markets. J. Financ. Econ. 2, 441-365. Ai, C., Chatrath, A., Song, F., 2006. On the comovement of commodity prices. Am. J. Agric. Econ. 88, 574–588. Alquist, R., Coibion, O., 2013. The Comovement in Commodity Prices: Sources and Implications. IMF Working Paper. Asness, C., 1994. Variables that Explain Stock Returns. Ph.D. Dissertation. University of Chicago Working Paper. Asness, C.S., Moskowitz, T.J., Pedersen, L.H., 2013. Value and momentum everywhere. J. Financ. 68, 929–985. Basak, S., Pavlova, A., 2016. A model of financialization of commodities. J. Financ. 71, 1511–1555. Bernardina, A., 2014. The Influence of Biofuels, Economic and Financial Factors on Daily Returns of Commodity Futures Prices. ZEF-Discussion Papers on Development Policy No. 187. Bessembinder, H., 1992. Systematic risk, hedging pressure, and risk premiums in futures markets. Rev. Financ. Stud. 5, 637–667. Billio, M., Caporin, M., Gobbo, M., 2006. Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation. Appl. Financ. Econ. Lett. 2, 123–130. Casassus, J., Liu, P., Tang, K., 2013. Economic linkages, relative scarcity, and commodity futures returns. Rev. Financ. Stud. 26, 1324–1362. Chng, M.T., 2009. Economic linkages across commodity futures: hedging and trading implications. J. Bank. Financ. 33, 958–970. Chollete, L., de la Pena, V., Lu, C.C., 2011. International diversification: a copula approach. J. Bank. Financ. 35, 403–417. Commodity Research Bureau, 2012. CRB Commodity Yearbook. Commodity Research Bureau, pp. 1–316. Cootner, P.H., 1960. Returns to speculators: Telser versus Keynes. J. Political Econ. 68, 396–404. Daskalaki, C., Kostakis, A., Skiadopoulos, G., 2014. Are there common factors in individual commodity futures returns? J. Bank. Financ. 40, 346–363. Davis, C., Stefanova, S., Hahn, W., Yen, S., 2008. Complements and meat demand in the U.S.. In: American Agricultural Economics Association Annual Meeting. De Groot, W., Karstanje, D., Zhou, W., 2014. Exploiting commodity momentum along the futures curve. J. Bank. Financ. 48, 79–93. De Roon, F., Nijman, T., Veld, C., 2000. Hedging pressure effects in futures markets. J. Financ. 55, 1437–1456. Deb, P., Trivedi, P.K., Varangis, P., 1996. The excess comovement of commodity prices reconsidered. J. Appl. Econom. 11, 275–291. Delatte, A., Lopez, C., 2013. Commodity and equity markets: some stylized facts from a copula approach. J. Bank. Financ. 37, 5346–5356. Dong, D., Davis, C.G., Stewart, H., 2015. The quantity and variety of households' meat purchases: a censored demand system approach. Agric. Econ. 46, 99–112. Dorfman, J., Karali, B., 2013. The pattern of price linkages among commodities. J. Futures Mark. 00, 1–15. Embrechts, P., McNeil, A., Straumann, D., 2002. Correlation and dependence in risk management: properties and pitfalls. In: Dempster, M. (Ed.), Risk Management: Value at Risk and Beyond. Cambridge University Press, Cambridge, UK, pp. 176–223. Erb, C., Harvey, C., 2006. The strategic and dynamic value of commodity futures. Financ. Anal. J. 62, 69–97. Fuertes, A.M., Miffre, J., Rallis, G., 2010. Dynamic allocation in commodity futures markets: combining momentum and term structure signals. J. Bank. Financ. 34, 2350–2548. Gorton, G., Hayashi, F., Rouwenhorst, G., 2013. The fundamentals of commodity futures returns. Rev. Finance 17, 35–105. Hirshleifer, D., 1990. Hedging pressure and futures price movements in a general equilibrium model. Econometrica 58, 411–428. Hong, H., Yogo, M., 2012. What does future market tell us about the macroeconomy and asset prices? J. Financ. Econ. 105, 473–490. Jegadeesh, N., 1990. Evidence of predictable behavior of security returns. J. Financ. 45, 881–898. Kaldor, N., 1939. Speculation and economic stability. Rev. Econ. Stud. 7, 1–27. Le Pen, Y., Sevi, B., 2018. Futures trading and the excess Co-movement of commodity prices. Rev. Finance 22, 381–418. Lo, A.W., MacKinaly, C.A., 1990. When are contrarian profits due to stock market overreaction? Rev. Financ. Stud. 3, 175–205. Malliaris, A., Urrutia, J., 1996. Linkages between agricultural commodity futures contracts. J. Futures Mark. 16, 595–609. Moskowitz, T.J., Ooi, Y.H., Pedersen, L.H., 2012. Time series momentum. J. Financ. Econ. 104, 228–250. Manner, H., Reznikova, O., 2012. A survey on time-varying copulas: specification, simulations, and application. Econom. Rev. 31, 654–687. Patton, A., 2009. Copula-based models for financial time series. In: Andersen, T., Davies, R., Kreiss, J., Mikosch, T. (Eds.), Handbook of Financial Time Series. Springer, New York, pp. 767–785. Pindyck, R.S., Rotemberg, J.J., 1990. The excess Co-movement of commodity prices. Econ. J. 100, 1173–1189. Ravindranath, N.H., Lakshmi, C.S., Manuvie, R., Balachandra, P., 2011. Biofuel production and implications for land use, food production and environment in India. Energy Policy 39, 5737–5745. Rodriguez, N.M., Eales, J., 2015. Structural Change via Threshold EffectL Estimating U.S. Meat Demand Using Smooth Transition Functions and the Effects of More Women in the Labor Force. U.S. Department of Agriculture Working Paper. Rosenberg, J., Schuermann, T., 2006. A general approach to integrated risk management with skewed, fat-tailed risks. J. Financ. Econ. 79, 569–614. Rosenzweig, C., Iglesias, A., Yan, X.B., Epstein, P.R., Chivian, E., 2001. Climate change and extreme weather events: implications for food production, plant diseases, and pests. Glob. Chang. Hum. Health 2, 90–104. Samuelson, P.A., 1965. Proof that properly anticipated prices fluctuate randomly. Ind. Manag. Rev. IMR 6, 41–49. Schroeder, T.C., Marsh, T.L., Mintert, J., 2000. Beef Demand Determinants. Report prepared for the Beef Board Joint Evaluation Advisory Committee. Symeonidis, L., Prokopczuk, M., Brooks, C., Emese, L., 2012. Futures basis, inventory and commodity price volatility: an empirical analysis. Econ. Modell. 29, 2651–2663. Tang, K., Xiong, W., 2012. Index investing and the financialization of commodities. Financ. Anal. J. 5, 54–74. Working, H., 1949. The theory of price of storage. Am. Econ. Rev. 39, 1254–1262.

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