اساس معاملات سلف، موجودی و نوسانات قیمت کالا: تجزیه و تحلیل تجربی

We employ a large dataset of physical inventory data on 21 different commodities for the period 1993–2011 to empirically analyze the behavior of commodity prices and their volatility as predicted by the theory of storage. We examine two main issues. First, we analyze the relationship between inventory and the shape of the forward curve. Low (high) inventory is associated with forward curves in backwardation (contango), as the theory of storage predicts. Second, we show that price volatility is a decreasing function of inventory for the majority of commodities in our sample. This effect is more pronounced in backwardated markets. Our findings are robust with respect to alternative inventory measures and over the recent commodity price boom.

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 This 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 (Buyuksahin et al., 2010; Gorton and Rouwenhorst, 2006). Recently, Daskalaki and Skiadopoulos (2011) point out that these diversification benefits are preserved only during the recent commodity price boom (2003–2008), but in their study vanish in an out-of-sample context. It is also a common belief that commodities provide a good hedge against inflation (Bodie, 1983 and Edwards and Park, 1996). Moreover, recent evidence suggests that momentum and term-structure based strategies in commodities can generate significant profits (Fuertes et al., 2010 and Miffre and Rallis, 2007).2 The behavior of commodity prices is strikingly different from that of stocks and bonds. For instance, such factors as seasonal supply and demand, weather conditions, and 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 volatilities 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 inception, this theory has been the central topic of many theoretical and empirical papers in the economics literature. Nevertheless, most studies 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 volatilities. In this paper, we employ real inventory data to test two of the main predictions of the theory of storage. Specifically, we show how inventory affects the slope of the forward curve (the basis) as well as the price volatility for a wide spectrum of 21 different commodities. Analyzing the relationship between inventory and the term structure of futures prices is important for various reasons. First, if inventory indeed has a significant effect on the shape of the forward curve (“contango” vs “backwardation”), then it should also affect the profitability of various term-structure based investment strategies. Additionally, the strength of this relationship will provide further evidence on whether the basis should be employed as a proxy for inventory in empirical studies. 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 derivative pricing. Our study contributes to the empirical literature on the theory of storage in several ways. Gorton et al. (2012) employ physical inventory data to document a negative non-linear relationship between inventory and the futures basis for a large cross-section of commodities. They do not examine the link between inventory and volatility as we do. Also, Geman and Ohana (2009) examine the relationship between inventory and the adjusted futures spread in the oil and natural gas markets, using end-of-month inventory data. The present paper adds to the evidence of the aforementioned studies by thoroughly analyzing the link between real inventories and the slope of the forward curve at several different maturities whereas previous research has only examined the short end of the curve. Furthermore, the sample used for our analysis includes the recent commodity price boom, which offers a great opportunity to test our hypothesis over varying market conditions (for an analysis of the recent commodity price boom, see Baffes and Haniotis, 2010). Second, and more importantly, using our extensive inventory dataset, we document a negative relationship between inventory and commodity return volatility. We characterize the time series variability of futures returns and spreads with respect to inventory levels for each individual commodity. From this perspective, our analysis is related to Geman and Nguyen (2005), who analyze the relationship between scarcity (inverse of inventory) and return volatility in the soybean market. However, given the heterogeneous nature of commodities as an asset class (Brooks and Prokopczuk, 2011, Daskalaki et al., 2012 and Erb and Harvey, 2006), it is quite intuitive to examine the inventory–volatility relationship for a broader set of commodities. For example, Fama and French (1987) find that the implications of the theory of storage are not empirically supported for certain commodities. Our analysis provides a number of interesting results. First, we find a strong positive relationship between logarithmic inventory and the slope of the forward curve, the latter approximated by the interest-adjusted basis at different maturities. In particular, lower (higher) inventory for a commodity is associated with lower (higher) basis and forward curves in “backwardation”3 (“contango”) as the theory of storage predicts. Since the interest-adjusted basis represents storage costs and convenience yields, our findings provide insights regarding the relationship between convenience yield and inventory. Our research also implicitly builds on the competing “hedging pressure” literature, which is based on the existence of a risk premium earned by investors in futures for bearing the risk of spot price changes. Recent empirical evidence has shown that there exists a link between futures basis and risk premiums (Gorton and Rouwenhorst, 2006). Second, we find that price volatility is a decreasing function of inventory for the majority of commodities in our sample. To do this, we estimate for each commodity univariate regressions of monthly price volatility against end-of-month inventory. Monthly price volatility is measured by the standard deviation of daily nearby futures returns/adjusted basis for each month. The magnitude of the reported relationship appears to be higher for commodities that are more sensitive to fundamental supply and demand factors, which determine storage. Moreover, heterogeneity is a possible explanation for the difference in the sizes of the coefficients across individual commodities. Some commodities are more difficult to store, and some of them are seasonal or perishable, while others are not. Our evidence generally supports the implications of theoretical studies (Deaton and Laroque, 1992 and Williams and Wright, 1991). Lastly, we investigate the hypothesis that the effect of inventory varies across different states of the market. To this end, we estimate OLS regressions of commodity returns/futures basis volatility on the interest-adjusted basis, decomposing the basis into positive and negative values that indicate the state of inventories (positive basis — high inventory and vice versa). In line with the implications of the theory, our estimation results suggest that the relationship between inventory and volatility is stronger in backwardation (low inventory). Furthermore, the results for energy commodities (crude oil and natural gas) lend support for the existence of the asymmetric V-shaped relationship between inventory and volatility reported by previous studies (Kogan et al., 2009). For crude oil (natural gas), positive deviations from the long-run inventory level (positive basis) have larger (smaller) impacts than negative deviations of the same magnitude.

This paper analyzes the fundamental role of inventory in explaining commodity futures prices and their volatilities within the economic framework of the theory of storage. Using an extensive dataset of monthly inventories for 21 different commodities for the period from 1993 to 2011, we empirically test two of the main predictions of the theory of storage. First, we document a negative relationship between inventory and the slope of the forward curve. The latter is approximated by the interest adjusted basis at different maturities, namely 2, 6, 10 and 12 months, respectively. In particular, lower inventories are associated with wider and more negative futures basis and therefore more backwardated forward curves. This result also implies that the convenience yield is an increasing function of inventory. Moreover, our evidence suggests that (adjusted) basis can serve as a sufficiently good proxy for inventory in empirical studies. These results also provide further support to those in Gorton et al. (2012). Second, in line with the implications of the theory of storage, we find that inventory is negatively related to commodity price volatility. More specifically, price volatility is a decreasing function of inventory. The documented relationship appears to be stronger for energy, animal and agricultural commodities and weaker for metals, and especially for precious metals. Furthermore, conditioning our analysis on market states (contango vs backwardation) we observe that a negative basis (low inventory) has a more pronounced impact on volatility than a positive basis (high inventory). Also, for energy commodities we document a V-shaped relationship between volatility and the slope of the forward curve, consistent with previous empirical studies (see, Kogan et al., 2009). These findings are preserved during the recent commodity price boom (2003–2008). Our purpose for this study is to test the theoretical considerations relating to the theory of storage in a more direct way than in many existing studies using real inventories. Nevertheless, the current study is not attempting to suggest using physical inventories instead of proxies, such as the futures basis. Inventory data still exhibit problems, such as measurement errors or sometimes unavailability at higher frequencies, such as daily. Instead, our main purpose was concentrated in two main directions: first, to test the validity of these inventory proxies and second, to provide useful evidence on the fundamental relationships the theory predicts using any useful part of information contained in inventory datasets. Our main conclusions offer additional support for the evidence of Ng and Pirrong (1994) that fundamentals drive commodity prices and their volatilities. From a practical point of view, our results have important implications for derivative pricing, asset allocation and hedging. For instance, Geman and Nguyen (2005) find that including scarcity (the inverse of inventory) as an additional factor in a state-variables model significantly improves the pricing performance for soybean futures. Our evidence suggests that this can possibly be extended to other commodities. However, due to the heterogeneity of individual commodities, universal findings cannot be extracted.