Futures basis, scarcity and commodity price volatility: An empirical analysis

Transcription

1 Futures basis, scarcity and commodity price volatility: An empirical analysis Chris Brooks ICMA Centre, University of Reading Emese Lazar ICMA Centre, University of Reading Marcel Prokopczuk ICMA Centre, University of Reading Lazaros Symeonidis ICMA Centre, University of Reading October 2011 ICMA Centre Discussion Papers in Finance DP Copyright 2011 Brooks, Lazar, Prokopczuk and Symeonidis. All rights reserved. ICMA Centre University of Reading Whiteknights PO Box 242 Reading RG6 6BA UK Tel: +44 (0) Fax: +44 (0) Web: Director: Professor John Board, Chair in Finance The ICMA Centre is supported by the International Capital Market Association

2 Futures basis, scarcity and commodity price volatility: An empirical analysis Chris Brooks, Emese Lazar, Marcel Prokopczuk and Lazaros Symeonidis October 25, 2011 Abstract The theory of storage has major implications for the role of inventory in determining commodity prices and their volatility. Most previous research employs indirect proxies for inventory, such as the sign of the futures basis. Instead, we employ a large dataset of physical inventory data on 20 different commodities for the period and find two main results. First, we show that scarcity, defined as the inverse of inventory, is informative about the shape of the forward curve. High (low) scarcity is associated with forward curves in backwardation (contango), as the theory of storage predicts. Second, we show that price volatility is an increasing linear function of scarcity for the majority of commodities in our sample. Our findings are robust with respect to alternative inventory measures and over sub-periods of the full sample. JEL classification: C22, C58, G00, G13 Keywords: Forward curves, scarcity, commodity price volatility, theory of storage, convenience yield. We are grateful to Carol Alexander, George Dotsis, Roland Füss and Apostolos Kourtis for useful comments. ICMA Centre, Henley Business School, University of Reading, Whiteknights, Reading, RG6 6BA, United Kingdom. The authors can be reached at: c.brooks@icmacentre.ac.uk (Chris Brooks), e.lazar@icmacentre.ac.uk (Emese Lazar), m.prokopczuk@icmacentre.ac.uk (Marcel Prokopczuk) and l.symeonidis@icmacentre.ac.uk (Lazaros Symeonidis).

3 1. Introduction Over the past few years, the flow of funds to commodities has increased substantially, primarily through investments in exchange-traded funds (ETFs) and commodity indices. 1 The widespread interest in commodity investments is partly associated with the view of commodities as a good diversification tool, since their correlations with stocks and bonds have been low or negative (Gorton and Rouwenhorst, 2006; Buyuksahin et al., 2010). It is also a common belief that commodities provide a good hedge against inflation (Bodie, 1983; Edwards and Park, 1996). Moreover, recent evidence suggests that momentum strategies in commodities can generate significant profits (Miffre and Rallis, 2007). The behaviour of commodity prices is strikingly different from that of stocks and bonds. For instance, such factors as seasonal supply and demand, weather conditions, storage and transportation costs, are specific to commodities and do not affect, or at least not directly, the prices of stocks and bonds. In the light of these stylized facts, understanding the determinants of commodity prices and their volatility is an issue of great importance. The mainstream theory in commodity pricing, namely the theory of storage, explains the behavior of commodity prices based on economic fundamentals. Furthermore, it has major implications for the volatility of commodity prices. Since its introduction, the theory of storage has been the central topic of many theoretical and empirical papers in the economics literature. Nevertheless, most of these papers employ proxies for inventory, such as the sign of the futures basis (e.g., Fama and French, 1988), thus providing only indirect evidence on the effect of inventory on commodity prices and their volatility. In this paper, we use real inventory data to examine the impact of inventory on the slope of the forward curve and on the price volatility for a wide spectrum of 20 commodities. The theory of storage provides the appropriate economic framework for our purpose. If inventory indeed has a significant effect on the shape of the forward curve ( contango vs backwardation ), then it 1 The Financial Times characteristically reports:... inflows into the sector reached a new high of $7.9bn in October 2010, taking total investor commodity holdings to a record $340bn. 1

4 should also affect the profitability of various term-structure based investment strategies ( roll-yield ). Furthermore, the results from our research are of substantial academic and practical interest since volatility underlies a variety of key financial decisions such as asset allocation, hedging and derivatives pricing. Our analysis is based on scarcity, defined as the inverse of inventory, in order to capture the decreasing and convex relationship between convenience yield and inventory predicted by the theory of storage French (1986). ways. We extend the empirical literature on the theory of storage in several First, our study is the first to test the impact of scarcity on the slope of the forward curve using inventory data on a wide set of 20 different commodities. 2 Second, we document a significant positive relationship between scarcity and price volatility for the same set of 20 commodities. This gives us the ability to assess the universal impact of scarcity on price volatility, taking into consideration the heterogeneous characteristics of the different commodities. Third, we assess the robustness of the empirical results by dealing with seasonalities observed in inventories, prices and volatilities in several ways. This ensures that results are not sensitive to the selection of a particular method for modelling seasonality. Our analysis provides a number of interesting results. First, using OLS and logit regressions we document a negative relationship between scarcity and the slope of the forward curve, the latter approximated by the 6-month interest-adjusted basis. In particular, higher (lower) scarcity for a commodity is associated with lower (higher) interest-adjusted basis and forward curves in backwardation ( contango ) as the theory of storage predicts. Since the interest-adjusted basis represents storage costs and a convenience yield, our findings also shed light on the relationship between convenience yield and inventory. Specifically, our evidence suggests that the convenience yield is a monotonically increasing function of scarcity for the majority of commodities in our sample. 2 Gorton et al. (2007) also use physical inventory data for a large panel of commodities. However, their study deals with non-linear patterns in the basis-inventory relationship. By considering scarcity in our empirical analysis we implicitly assume a form of non-linearity, since by definition scarcity is a convex function of inventory. 2

5 Second, we empirically show that price volatility is an increasing function of scarcity for the majority of commodities in our sample. We do this by estimating for each commodity univariate regressions of monthly price volatility against the end-of-month scarcity. Monthly price volatility is measured by the standard deviation of the daily nearby futures returns/daily adjusted basis respectively during each month. Our evidence is in line with the implications of existing theoretical studies (Williams and Wright, 1991; Deaton and Laroque, 1992). In addition, we perform a number of robustness tests. In the first test, we assess the stability of the results obtained by repeating the analysis over sub-periods of the entire sample. Second, to make sure that our results are not driven by the functional form of scarcity employed to represent the level of inventories, we re-estimate all models replacing scarcity with logarithmic inventory. Finally, in addition to the 6-month interest-adjusted basis we also consider the 12-month adjusted basis and repeat all relevant estimations. The remainder of the paper is organized as follows. Section 2 briefly discusses the theory of storage and the relevant literature. Section 3 presents the datasets used for the empirical analysis. Section 4 examines the relationship between scarcity and the slope of the forward curve. Section 5 analyzes the relationship between scarcity and price volatility. Section 6 provides the results from various robustness tests. The final section presents concluding remarks. 2. Theoretical background and relevant literature The theory of storage, introduced in the seminal papers of Kaldor (1939), Working (1948), Brennan (1958) and Telser (1958), links the spot price with the contemporaneous futures price through a no-arbitrage relationship known as the cost-of-carry model. This theory is based on the notion of convenience yield, which is associated with the increased utility from holding inventories during periods of scarce supply. 3

6 The classical no-arbitrage relationship between spot and futures prices is given by: F t,t = S t (1 + R t,t ) + w t,t y t,t (1) where F t,t is the price at time t of a futures contract maturing at T, S t is the spot price of the commodity at time t, R t,t is the interest rate for the period from t to T, w t,t is the marginal cost of storage per unit of inventory from t to T, and y t,t is the marginal convenience yield per unit of storage. If the above equation is re-written as [F t,t S t (1 + R t,t )]/S t = (w t,t y t,t )/S t, then the left part represents the interest-adjusted basis as a function of marginal storage costs and the convenience yield. Thus, assuming that storage costs do not vary much over the period (t,t), variations in the interest-adjusted basis are mainly determined by variations in convenience yields. Within the context of the theory of storage, convenience yield can be regarded as an option to sell inventory in the market when prices are high, or to keep it in storage when prices are low. Milonas and Thomadakis (1997) argue that convenience yields exhibit the payoff profile of a call option with a stochastic strike price, which can be priced within the framework of Black s model (Black, 1976). Evidence has also shown that convenience yield is a convex function of the available stocks (Brennan, 1958; French, 1986). A high convenience yield during periods of low inventory drives spot prices to be higher than contemporaneous futures prices and the adjusted basis becomes negative. Specifically, as inventories decrease, the convenience yield increases at a higher rate due to the convex relationship between the two quantities. Equivalently, the higher probability of a stockout increases the value of the timing option embedded in the convenience yield. As a result, a demand shock cannot be absorbed by available inventory and spot prices tend to be higher than futures prices due to a high convenience yield. In contrast, at high levels of inventory, the convenience yield is small and futures prices tend to be higher than contemporaneous spot prices to compensate inventory holders for the costs associated with storage. In sum, as inventory 4

7 decreases (increases), the adjusted basis becomes more negative (positive). Recent evidence also suggests that the futures basis and inventory are linked in a non-linear fashion (Gorton et al., 2007). The theory of storage also predicts a negative (positive) relationship between price volatility and the level of inventory (scarcity). In particular, when inventory (scarcity) is low (high), the lower elasticity of supply and the inability to adjust inventories in a timely manner without significant costs (e.g., imports from other locations) make spot and futures prices more volatile. However, futures prices are less volatile than spot prices because agents anticipate a response of production and consumption in the long-run - i.e., they can adjust real variables more easily in the long-run than in the short-run (Ng and Pirrong, 1994). becomes more volatile. As a result, the (adjusted) basis also In contrast, at sufficiently high levels of inventory, supply is more elastic, the convenience yield function is relatively flat, and the available inventory acts to smooth the effects of supply and demand shocks. Thus, spot and futures price volatilities are both low and almost equal. Moreover, such factors as non-continuous production of some commodities (e.g., agricultural), storage costs, and weather conditions exacerbate the effect of demand shocks on current and future prices and thus have a significant impact on price volatility. 3 Fama and French (1987) use a dataset on 21 commodity futures and show that variation in the basis is driven by seasonals in supply and demand, storage costs and interest rates. Fama and French (1988) employ the sign of the interest-adjusted basis as well as the phase of the business cycle as proxies for inventory to analyze the relative variation of spot and futures prices for metals. They find that when inventories are low, the interest-adjusted basis is more volatile and also spot metal prices tend to be more volatile than futures prices in line with the Samuelson hypothesis. The implications of the theory of storage for commodity price volatility have also been the focus of various theoretical studies. In a different version 3 For instance, in agricultural commodities the uncertainty about the future level of stocks shortly before the end of the new harvest, when inventory is usually low, leads to more volatile prices (see Williams and Wright, 1991). Moreover, weather conditions may affect the total level of supply and induce periodicity in the prices of these commodities (Chambers and Bailey, 1996). 5

8 of the theory of storage, Williams and Wright (1991) build a quarterly model with annual production and point out that price volatility is highest shortly before the new harvest when inventories are low. Deaton and Laroque (1992) suggest an equilibrium competitive storage model, and show that conditional volatility is positively correlated with the price level (the inverse leverage effect ). Thus, the higher probability of a stockout when inventories are low leads to higher prices and therefore to higher conditional volatility in the next period. Chan et al. (2004) provide support for the existence of an asymmetric V-shaped relationship between futures returns and volatility in the Chinese futures market. Routledge et al. (2000) develop an equilibrium model for commodity futures prices and show that backwardation, driven by inventory and supply/demand shocks, is positively related to volatility. A number of recent papers report an asymmetric V-shaped relationship between inventory proxies and price volatility, meaning that both high and low levels of inventory induce high price volatility (Lien and Yang, 2008; Kogan et al., 2009). Carbonez et al. (2010) provide contrasting evidence on the existence of a V-shaped relationship between the futures basis and price volatility, documented by previous studies, in the case of agricultural commodities. The majority of the aforementioned studies employ indirect measures for inventory, such as the sign of the (adjusted) futures basis to support their basic arguments. Surprisingly, very few papers in the literature employ observed inventory data. For instance, Geman and Nguyen (2005) construct a sample of US and global inventories for soybeans at various frequencies and show that price volatility is a monotonically increasing function of scarcity, the latter defined as the inverse of inventory. Gorton et al. (2007) employ physical inventory data on a large set of 31 commodities and conclude that the basis is a non-linear, increasing function of inventory. Finally, Geman and Ohana (2009) find that inventory is negatively correlated with crude oil price volatility, whereas the negative relationship for natural gas is only present during periods when inventory falls below its historical average level. Gaining insights on the determinants of commodity prices and their volatility is an issue of paramount importance given the widespread interest 6

9 of academics and practitioners in commodity investing over the last few years. For instance, the issue of whether and under which conditions investors should include commodities in their portfolios still remains an open question. Bodie and Rosansky (1980) argue that including commodities in a portfolio of stocks improves the risk-return profile of a typical investor. Cheung and Miu (2010) analyze the role of commodities as a diversification tool during bull and bear regimes and document significant diversification benefits in the long run. Nevertheless, these benefits are in general absent in bear markets, when they are probably most needed. Daskalaki and Skiadopoulos (2011) cast doubt on the diversification benefits from investing into commodities and find that these benefits exist only during periods of infrequent outbursts in commodity prices. 3. Data and preliminary analysis 3.1. Price data The primary datasets employed in this study consist of daily futures prices with several maturities for a wide spectrum of 20 commodities traded on the major US commodity exchanges (NYMEX, CBOE, CBOT and ICE) and the London Metal Exchange (LME). The full dataset covers the period from January 1, 1993 to December 31, The particular commodities are selected to cover, as far as possible, such major categories as grains, animal, industrials, energy and metals. All price series except for the metals are obtained from the Commodity Research Bureau (CRB), which assembles data from all major commodity exchanges worldwide. The datasets for metals are collected from Bloomberg. All prices are expressed in US dollars. Since our study involves the calculation of the futures basis, we need the prices of futures contracts with different maturities. The number of available maturities varies across the different commodities from four to twelve per year. Table 1 contains an outline of the commodity price data used in our study along with information regarding the exchange where they are traded and the available delivery months per year. 4 We chose our dataset to begin from 1993 because it corresponds to the common starting point of most price and inventory series in our sample. 7

10 For the purpose of our analysis, the prices of the first nearby futures contract are treated as spot prices, similar to Fama and French (1987). Since futures contracts have fixed maturity months, we need to construct a continuous series of futures prices for each commodity. In order to avoid expiration effects (Samuelson, 1965) and low liquidity effects due to thin trading, we roll over from the closest to maturity to the next closest to maturity contract five trading days before expiration. We follow the same procedure for the futures prices of the second nearest to maturity contract and so on. This rollover strategy represents the return of an investor who closes out his position one week before maturity and immediately after buys the next to maturity contract. 5 each commodity i: We then calculate the logarithmic return at time t on r i,t = ln F i,t,t F i,t 1,T (2) where F i,t,t is the closing price on day t of the futures contract on commodity i maturing at T. Table 2 provides summary statistics for the daily nearby futures returns series of the 20 commodities in our sample. The means and standard deviations of the series are expressed on an annual basis and as percentages. As seen from the table, the returns of all commodities are highly volatile. Among the main drivers of this high price volatility are: the non-continuous production of some commodities (e.g., agricultural), storage costs (Fama and French, 1987), weather conditions (Geman, 2005) especially for the agricultural and energy commodities as well as the uncertainty regarding the future macroeconomic conditions (e.g., changes in inflation, exchange rates fluctuations, etc). comparison with the other commodities, metals exhibit the lowest amount of annual variation. This can be explained by the fact that metals are easier to store and their storage cost is lower relative to their value (Fama and French, 1987). The annualized daily volatility of 55.9% for natural gas is the highest among 5 For a thorough analysis of the various rollover procedures and their implications the interested reader can refer to Ma et al. (1992). In 8

11 all commodities in our sample, followed by 41.6% for coffee and 40.9% for pork bellies. Crude oil and heating oil nearby returns also exhibit significant amounts of variation close to 37%. The high volatility of natural gas returns is mainly associated with the higher uncertainty regarding the future demand and weather conditions shortly before the start of the heating season, when demand reaches its peak. The volatility of coffee returns, on the other hand, is mainly explained by the dependence of supply on weather conditions (Geman, 2005). Perishability is the main cause for the highly volatile prices of animal commodities, since they are essentially non-storable. The sign of skewness is mixed, yet it is different from zero for most commodities in the sample. The kurtosis coefficients are all significantly higher than three, which means that very high and very low returns are more likely to occur than a normal distribution dictates. These non-gaussian features of commodity returns are also confirmed by the Jarque-Bera test statistic, which clearly rejects the null hypothesis of normality in all cases Inventory data Apart from the commodity price data, we also compile a large set of inventory data, using various sources. Most of the datasets correspond to end of month stocks covering the period from December 1992 to December In the cases when inventory level is reported on the first day of a calendar month, we shift to the end of the previous month. For some commodities, inventory data are not available from 1993 and thus we utilize the subsequent date when those became available as the starting point of our series. The data for agricultural and animal products are obtained from the US Department of Agriculture (USDA). For soybeans, corn, oats and wheat, the original datasets are available at a weekly frequency and thus we consider the inventory level of the last week of month as a proxy for the end of month inventory. For the three energy commodities, we gather data from the US Energy Information Administration (EIA). Finally, data for metal stocks stored in the Commodity Exchange (COMEX), for gold, silver and copper, and the London Metal Exchange (LME), for aluminium and tin, are collected from Datastream. 9

12 As discussed in Gorton et al. (2007), the use of inventory data presents some problems. The most important of those concerns the definition of inventory. For example, in a global market, such as that for crude oil, international inventories may provide a better proxy for available supplies compared to inventories stored at the various delivery locations across the US. In a recent study, Geman and Ohana (2009) provide empirical evidence that the use of either domestic US or global petroleum inventories allows for very similar conclusions. 6 Moreover, it can be argued that a proper definition of inventory should take into account all quantities that can be effectively used in case of a shortage, including government stocks or off-exchange stocks. Nevertheless, this information is not always available. Another issue with inventory data is the possibility of measurement errors, which may lead to errors-in-variables biases. 7 To alleviate the first concern, in the case of oil we employ some additional measures for inventory, such as the volumes of all petroleum products in US and OECD countries, respectively. We also consider global inventories for corn, soybeans and wheat in addition to domestic US inventories. Unfortunately, we lack availability of global inventory data for the remaining commodities in our study. Nevertheless, the potential problems analyzed above are not expected to invalidate the overall conclusions from our analysis. Figure 1 plots the inventory series for a subset of commodities. inspection of the graphs and of the inventory datasets shows that the inventories of agricultural and animal commodities, as well as those of natural gas and heating oil, display strong seasonality. An The seasonal variation in natural gas and heating oil stocks is basically determined by the higher demand during heating seasons (cold winter months) combined with capacity constraints of the available systems. Seasonality in the inventories of agricultural commodities is mainly driven by their non-continuous production (crop cycles) and also by exogenous factors, such as weather conditions. Most 6 Geman and Nguyen (2005) also find that the relationship between inventory and spot price volatility for soybeans is significant regardless of whether US or world soybeans inventory is used. However, world stocks offer a higher explanatory power. 7 For a detailed analysis, see Gorton et al. (2007). 10

13 of the agricultural commodities in the domestic US market are harvested once a year, and thus their inventory level reaches its peak immediately after the harvest and its lowest shortly before the beginning of the new harvest. The seasonality observed in animal inventories is related to their perishability as well as to seasonal variations in slaughter levels. Soybean oil inventory does not exhibit seasonal variation, most likely because of its conversion process from soybeans. In addition, we do not observe clear seasonal patterns in the inventories of coffee, cotton and lumber. For coffee, this can be explained by its long maturing process. For the other two, inventory fluctuations are mostly determined by long-term factors such as industrial demand. Finally, metal stocks are not subject to short-term seasonal variations, since their inventories are primarily determined by investment demand, for the precious metals, and manufacturing demand, for the industrial metals. Finally, crude oil is continuously produced and consumed, and thus its stocks are not subject to seasonal variations. Our subsequent analysis is based on scarcity, defined as the inverse of inventory. By definition, this variable is a decreasing convex function of inventory. Moreover, it reflects the non-linear relationship between inventory and convenience yield/futures basis documented in previous studies (e.g., Telser, 1958; Deaton and Laroque, 1992). In the analysis that follows, we standardize the scarcity variable for each commodity by subtracting its mean and dividing by its standard deviation in order to allow for better comparability of coefficients across the different commodities. 4. Adjusted basis and scarcity Using our extensive inventory dataset, we analyze the relationship between scarcity and the slope of the forward curve individually for each commodity. The forward curve slope is approximated by the 6-month interest-adjusted basis (henceforth, adjusted basis). The theory of storage implies that high (low) scarcity for a commodity is associated with negative (positive) adjusted basis. 11

14 In order to calculate the adjusted basis, we collect daily data on the six-month Treasury-bill (T-bill) from Thomson Reuters Datastream. rate refers to the annualized T-bill yield with six months to maturity. This subsequently define the 6-month adjusted basis (b i,t ) of commodity i on day t, as follows: where F i,t,t1 We b i,t = F i,t,t 2 F i,t,t1 [1 + R f,t δ] F i,t,t1 (3) is the price on day t of the first nearby futures contract maturing in T 1 days, which is used as the spot price in our study. Also, F i,t,t2 is the time t price of a futures contract with T 2 days to maturity (T 2 > T 1 ) and R f,t is the annualized 6-month T-bill rate on day t. δ = T 2 T is the difference between the maturities of the two futures contracts in years. Finally, b i,t is the daily 6-month adjusted basis, which represents the slope of the forward curve on day t. Since daily data are employed for inventory/scarcity in our analysis, we further compute the monthly forward curve slope as the average of the daily 6-month adjusted basis for each month in the sample period. An issue in calculating the basis concerns the fact that futures contracts of different commodities do not expire every month. 8 basis does not always correspond to six months. Thus, the computed daily To alleviate this concern, we take the price of the next futures contract whenever there is no traded contract with six months to maturity. The same applies to the nearby futures price treated as the spot price in our study. For instance, to calculate the 6-month basis of corn on January 15th, we need the price of the February contract, maturing at the end of January, as the spot price, and the August contract, maturing at the end of July, as the 6-month futures price. If there is no February contract for this particular commodity, we consider the next to maturity contract, i.e., the March contract, as the first nearby contract, and therefore the September contract as the 6-month futures contract. Accordingly, if there is no contract maturing in September for the specific commodity, we consider the next to maturity contract (i.e., October) and so on. 8 See Table 1 for details on the available maturities of the commodities considered in the current study. 12

15 4.1. Empirical Evidence Our first objective is to empirically test the relationship between scarcity and the slope of the forward curve (adjusted basis). To this end, we estimate for each commodity i the following regression: bi,τ = α i + β i s i,τ 1 + u i,τ (4) where b i,τ is the deseasonalized forward curve slope of commodity i in month τ, computed as the monthly average of the daily 6-month adjusted basis over each month τ, and of month τ-1. s i,τ is the deseasonalized standardized scarcity at the end To deseasonalize the standardized scarcity and the adjusted basis, we estimate regressions against monthly dummy variables and then take the residuals from these regressions as the deseasonalized adjusted basis ( b i,τ ) and deseasonalized scarcity ( s i,τ 1 ), respectively. 9 A time trend is included in the seasonal regressions of monthly scarcity in case it is both statistically and economically significant. We treat as economically significant any coefficient greater than or equal to 0.1%. The adjustment for seasonality in the basis and scarcity series of each commodity is based on the significance of the F -statistic, which tests the null hypothesis that the coefficients of all monthly dummies, in the seasonal regressions above, are jointly zero. As a result, dummy variables are not included in the equations of metals, crude oil, soybean oil, cotton, coffee and lumber, since there is no indication of annual periodicity in either their adjusted basis or their standardized scarcity. Three unit root tests are performed on the monthly scarcity and adjusted basis of each commodity. These tests are: the Augmented Dickey-Fuller test (ADF, Dickey and Fuller, 1979), the Phillips- Perron test (PP, Phillips and Perron, 1988) and the Elliott, Rothenberg and Stock test (ERS, Elliott et al., 1996). The ERS test is used as a more efficient test, since the ADF and PP unit root tests have low power in rejecting the null hypothesis of a unit root under specific circumstances (DeJong et al., 1992). 9 We also applied two additional methods to remove seasonality from the series: a) a moving average filter and b) fit of sine/cosine functions. All methods gave very similar results. 13

16 That is, they cannot distinguish between very persistent stationary processes (close to I(1)) and non-stationary I(1) processes very well. The unit root test results show that all adjusted basis series are stationary and from the scarcity series, only lumber, orange juice, aluminium and silver are non-stationary. 10 In what follows, we refer to the first differences of these variables. The left panel of Table 3 presents the results from the OLS regressions of equation (4). The results of Table 4 strongly support a negative and significant relationship between scarcity and the slope of the forward curve (adjusted basis). More specifically, using a two-tailed test we conclude that for the 20 commodities considered, 15 (16) coefficients of the scarcity variable are statistically significant at the 5% (10%) level. Moreover, the statistically significant coefficients are negative for all commodities, except lumber. Regarding the magnitude of the coefficients, we observe that energy commodities exhibit the strongest association with scarcity. Overall, the largest in size coefficient is reported for natural gas and is equal to , followed by hogs with This means that a positive shock of one standard deviation from the mean scarcity for natural gas results in a 9.8% decrease in the natural gas adjusted basis. This strong effect for animal commodities is associated with high storage costs and perishability that lead to low levels of inventory relative to demand. Moreover, the large coefficients for energy commodities can be explained by the high storage and transportation costs as well as the capacity constraints of the available systems that deter storage and make prices more sensitive to inventory withdrawals. Apart from the energy and animal commodities, a strong association is also observed for most of the agricultural and soft commodities. Large coefficients for these commodities are mainly related to the fact that most of these commodities are harvested once or twice a year in the domestic US market and the available inventory must satisfy the demand over the whole year. Given that total imports for these commodities represent a very small proportion of the annual production in the US, the prices of agricultural commodities are highly sensitive to the level of available stocks in the domestic 10 We do not report the unit root test results due to space limitations. These are available upon request from the authors. 14

17 US market. Metals, in particular gold, exhibit the lowest correlation with scarcity (coefficient for gold is the lowest overall, equal to ). The low storage costs relative to their value and the sufficiently high inventory level relative to demand, especially for precious metals, are the main reasons for this low correlation. Also, in line with Geman and Ohana (2009), who used a shorter sample period ( ), we find that petroleum stocks in OECD countries is the best measure for oil scarcity in terms of the highest R 2 coefficient (45% against 27% for US inventories). The R 2 coefficient of the US petroleum stocks regression is quite similar (43.1%). The coefficient estimates of global scarcities for corn, soybeans and wheat are all highly significant at the 1% level and their corresponding t-statistics are higher than those of the US scarcities. 11 In order to examine the association between the level of scarcity and the probability that the adjusted basis is positive, we estimate for each commodity i the following logit specification: P rob(b i,τ > 0) = eθ i+ϕ i s i,τ e θ i+ϕ i s i,τ 1 (5) where b i,τ is the adjusted basis of commodity i in month τ (the slope of the forward curve in month τ), and s i,τ 1 is the deseasonalized standardized scarcity of commodity i at the end of month τ-1. The Berndt-Hall-Hall-Hausman (BHHH) optimization algorithm is used for the estimations with Huber-White quasi maximum likelihood robust standard errors and covariances. The right panel of Table 3 reports the results from the logit estimations. The scarcity coefficient (ϕ i ) is negative and statistically significant at the 5% (10%) level for 15 (17) of the 20 commodities. Moreover, all statistically significant coefficients are negative except for lumber. Our evidence supports the predictions of the theory of storage that when a commodity is in high scarcity the adjusted basis tends to be negative. Furthermore, the agreement between the results of the two alternative specifications enhances the robustness of our inference. 11 Estimation results from regressions against world scarcity are not reported in Table 3 to save space, but are available upon request from the authors. 15

18 Overall, our results suggest that scarcity has high explanatory power for the slope of the forward curve. In particular, high (low) scarcity is associated with a negative (high) adjusted basis and backwardated ( contangoed ) forward curves. Evidence from the logit model strongly supports the results from OLS regressions. 5. Scarcity and price volatility This section presents results from estimating the relationship between scarcity and commodity price volatility. Our tests are based on commodity-bycommodity OLS regressions. We distinguish between two alternative cases for price volatility: i) adjusted basis volatility, and ii) volatility of nearby futures returns. To obtain a measure for the adjusted basis volatility, we first compute for each commodity the annualized standard deviation of the daily adjusted basis over each month τ in the sample. Then we estimate the following regression: σ i,τ = α i + γ i s i,τ 1 + ϵ i,τ (6) where σ i,τ is the annualized standard deviation of the daily adjusted basis series of commodity i in month τ, and s i,τ 1 is the standardized scarcity of commodity i at the end of month τ-1. We deseasonalize both the standardized scarcity and the adjusted basis volatility as discussed above. The estimation results of equation (6) are reported in Table 4. The coefficients of the individual regressions indicate a positive relationship between scarcity and adjusted basis volatility. We observe that for the 20 commodities considered, 10 (11) scarcity coefficients are positive and statistically significant at the 5% (10%) level. If we analyze the results across the separate commodity groups, we see that the relationship is particularly strong for most of the agricultural and energy commodities and also for hogs in terms of the size of the regression coefficients. In particular, all coefficients of scarcity are positive and strongly significant at the 5% level in the agricultural commodity group, except for oats. For animal commodities, the coefficient 16

19 of hogs is positive and significant at the 1% level and is also the largest in magnitude across all commodities. From the three energy commodities, the coefficients of crude oil and natural gas are both positive and significant at the 1% level. Finally, the scarcity coefficients of metals are smaller in magnitude compared to the rest of the commodities, while only those of copper and tin are significant. The lower coefficients for metals can be explained by the easier storage and the sufficiently high levels of inventory relative to demand that limit the variation in convenience yields and therefore in the adjusted basis. Turning our focus to spot return volatility, we compute for each commodity the annualized standard deviations of the daily nearby futures returns over each month τ in the sample. The volatility series obtained are then employed as the dependent variables in the following regression: σ i,τ = ω i + ζ i s i,τ 1 + u i,τ (7) where σ i,τ is the annualized standard deviation of the daily nearby futures returns of commodity i over each month τ in the sample and s i,τ 1 is the standardized scarcity of commodity i at the end of month τ-1. Similar to the regressions of the adjusted basis volatility (given in (6)), we deseasonalize scarcity and nearby futures volatility by estimating regressions against monthly seasonal dummies, as discussed above. 12 The estimation results are reported in Table 5. The coefficient of the scarcity variable is statistically significant for 13 out of the 20 commodities at the 5% level. Moreover, all significant coefficients are positive. Regarding the sizes of the scarcity coefficients, we observe that the relationship appears to be stronger for energy and agricultural commodities and also for hogs. The strong relationship for energy commodities is mainly associated with the high storage costs and also with the capacity constraints in production and transmission systems, which increase the sensitivity of prices to supply or demand shocks. For agricultural commodities, the non-continuous production, the significant 12 Again similar to the case of regression (4), we address seasonality in scarcity and nearby volatility using: i) a moving average filter, ii) sine/cosine functions. The results are very similar in all cases. These results are not reported here due to space limitations, but are available upon request from the authors. 17

20 storage costs and the inability to import supplies from other locations during the cycle at a low cost, reduce the elasticity of supply and thus increase the responsiveness of prices to supply and demand shocks. Perishability can explain the high sensitivity of animal commodities to inventory, since they are essentially non-storable and therefore demand shocks cannot easily be absorbed by available supplies. Finally, we observe relatively lower coefficients for metals in comparison with the other commodities. From the group of metals, only copper and silver provide support for a significant relationship with scarcity. 6. Robustness analysis We perform various tests to check the robustness of the results obtained in the previous sections. First, to test whether our results are driven by the use of the inverse inventory form (scarcity) to represent the availability of a particular commodity, we repeat all estimations above replacing scarcity with logarithmic inventory. The logarithmic form reflects the non-linearities in the relationship between inventory and convenience yield/futures basis (French, 1986). 13 The inventory series of many commodities exhibit a trend and/or seasonality. To address these trends and seasonalities in logarithmic inventories, we follow a procedure similar to Gorton et al. (2007). Specifically, we fit a Hodrick-Prescott filter (H-P filter, Hodrick and Prescott, 1997) to decompose the logarithmic inventory series of each commodity into a trend and a cycle. Then to account for the seasonal fluctuations of inventories around their H-P trends, we take the detrended inventory series (H-P cycle) of each commodity and run a regression against monthly dummy variables. The residuals from these seasonal regressions are employed as explanatory variables in our models. 14 in all cases. The overall results and conclusions remain almost the same Second, to check the stability of our results, we repeat our estimations 13 Scarcity and logarithmic inventory have reverse functional shapes. We thus expect the coefficients of logarithmic inventory to have the opposite signs compared to those of scarcity. 14 We omit from seasonal regressions those commodities which do not exhibit seasonality in inventory. For these commodities we simply consider the detrended inventory from the H-P filter. 18

21 using sub-samples. Given the limited sample size from the use of monthly observations, we divide the entire sample of each commodity in two equal sub-samples. The availability of monthly data for our analysis restricts our ability to separate the data into sub-samples according to a different criterion, such as the effect of the recent financial crisis (2007 and after), because this would make our estimates sensitive to small sample biases (only 24 observations for the period ). Overall our results are robust across the sub-periods considered. Finally, we test the relationship between scarcity and the slope of the forward curve using the 12-month adjusted basis as a proxy for the slope of the forward curve. We compute the 12-month basis from equation (3) setting the difference between the maturities of the futures contracts equal to 1 year and also considering the price of the year ahead futures contract as the futures price. The 12-month basis has the advantage that it implicitly takes seasonality into account, since taking the difference between the nearby and the year ahead futures prices is similar to applying seasonal differences. Overall, our estimation results strongly support those obtained for the 6-month adjusted basis. 7. Conclusions This paper analyzes the fundamental role of inventory in explaining commodity futures prices and volatility within the economic framework of the theory of storage. Using an extensive dataset of monthly inventories for 20 different commodities and for the period from 1993 to 2009, we obtain a number of empirical results. First, we document a negative relationship between scarcity, defined as the inverse inventory and the slope of the forward curve. The latter is approximated by the 6-month and 12-month adjusted basis, respectively. In particular, high scarcity is associated with negative futures basis and forward curves in backwardation. This result also implies that convenience yield is an increasing function of scarcity. Moreover, our evidence supports the use of the (adjusted) basis as a good proxy for inventory. 19

22 Second, in line with the implications of the theory of storage, we find that scarcity is positively associated with commodity price volatility. More specifically, price volatility is a monotonically increasing linear function of scarcity. The documented relationship appears to be stronger for energy, animal and agricultural commodities and weaker for metals, especially for precious metals. Furthermore, the general conclusions are not specific to sub-periods of the full sample or to the particular method used to address seasonality in prices and volatility. Our results also offer additional support for the evidence of Ng and Pirrong (1994) that fundamentals drive commodity prices and volatility. From a practical point of view, our results have important implications for derivatives pricing, hedging, trading, and risk management. For instance, Geman and Nguyen (2005) find that including scarcity as an additional factor in a state-variables model significantly improves the pricing performance for soybean futures. Our evidence suggests that this can possibly extend to a wider range of commodities. Moreover, since inventory provides important information on the shape of the forward curve (contango versus backwardation) it should be taken into account when designing simple rollover investment strategies. 20

23 References Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics 3 (1-2), Bodie, Z. (1983). Commodity futures as a hedge against inflation. Journal of Portfolio Management 9 (3), Bodie, Z. and V. Rosansky (1980). Risk and return in commodity futures. Financial Analysts Journal 36 (3), Brennan, M. (1958). The supply of storage. American Economic Review 48 (1), Buyuksahin, B., M. Haigh, and M. Robe (2010). Commodities and equities: Ever a market of one? Journal of Alternative Investments 12 (3), Carbonez, K., T. Nguyen, and P. Sercu (2010). The asymmetric effects of scarcity and abundance on storable commodity price dynamics and hedge ratios. Working paper. Katholieke Universiteit Leuven. Chambers, M. and R. Bailey (1996). A theory of commodity price fluctuations. Journal of Political Economy 104 (5), Chan, K., H. Fung, and W. Leung (2004). Daily volatility behavior in chinese futures markets. Journal of International Financial Markets, Institutions and Money 14 (5), Cheung, C. and P. Miu (2010). Diversification benefits of commodity futures. Journal of International Financial Markets, Institutions and Money 20 (5), Daskalaki, C. and G. Skiadopoulos (2011). Should investors include commodities in their portfolios after all? New evidence. Journal of Banking and Finance 35 (10), Deaton, A. and G. Laroque (1992). On the behaviour of commodity prices. Review of Economic Studies 59 (1), DeJong, D., J. Nankervis, N. Savin, and C. Whiteman (1992). Integration versus trend stationary in time series. Econometrica 60 (2),

24 Dickey, D. and W. Fuller (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74 (366), Edwards, F. and J. Park (1996). Do managed futures make good investments? Journal of Futures Markets 16 (5), Elliott, G., T. Rothenberg, and J. Stock (1996). Efficient tests for an autoregressive unit root. Econometrica 64 (4), Fama, E. and K. French (1987). Commodity futures prices: Some evidence on forecast power, premiums, and the theory of storage. Journal of Business 60 (1), Fama, E. and K. French (1988). Business cycles and the behavior of metals prices. Journal of Finance 43 (5), French, K. (1986). Detecting spot price forecasts in futures prices. Journal of Business 59 (2), Geman, H. (2005). Commodities and commodity derivatives. Wiley. England. Geman, H. and V. Nguyen (2005). Soybean inventory and forward curve dynamics. Management Science 51 (7), Geman, H. and S. Ohana (2009). Forward curves, scarcity and price volatility in oil and natural gas markets. Energy Economics 31 (4), Gorton, G., F. Hayashi, and K. Rouwenhorst (2007). The fundamentals of commodity futures returns. Working paper. NBER. Gorton, G. and K. Rouwenhorst (2006). Facts and fantasies about commodity futures. Financial Analysts Journal 62 (2), Hodrick, R. and E. Prescott (1997). Postwar us business cycles: An empirical investigation. Journal of Money, Credit and Banking 29 (1), Kaldor, N. (1939). Speculation and economic stability. Review of Economic Studies 7 (1),