Default Risk, Hedging Demand and Commodity Prices

Transcription

1 Default Risk, Hedging Demand and Commodity Prices Viral V. Acharya, Lars Lochstoer and Tarun Ramadorai November 15, 2007 Abstract Recent literature has argued that commodity producers manage their inventories and hedge with futures contracts in part to mitigate default risk. The empirical work, however, has employed outcomes - such as inventory and hedging demand - rather than the primitive - the default risk itself, in order to explain commodity spot and futures prices. We employ balance-sheet based measures of default risk for commodity producers and relate these to spot and futures commodity prices. We show that while high default risk is associated with high levels of hedging demand in futures markets and predicts higher excess returns on short-term futures contracts, default risk is not much related to contemporaneous convenience yield (measured as the basis between the shortest maturity futures contract and a longer-term one). The convenience yield is instead better explained by inventories of commodity producers. These results are consistent with a model of hedging by commodity producers (especially during inventory stock-outs) that face costs of raising external nance when their default risk is high. Since hedging is likely to be incomplete, we hypothesize that such default risk may in fact be a risk factor a ecting commodity prices. We nd that a measure of default risk of commodity producers as a whole improves the ability of the consumption capital asset-pricing model (CCAPM) to explain the cross-section of expected excess returns on short-term commodity futures contracts. London Business School (Acharya, Lochstoer) and Oxford University (Ramadorai). Correspondence: Lars Lochstoer. llochstoer@london.edu. Mailing address: IFA, 6 Sussex Place Regent s Park, NW1 4SA, London, United Kingdom. We thank Nitiwut Ussivakul and Prilla Chandra for excellent research assistance.

2 1 Introduction Recent literature has argued that commodity producers manage their inventories and hedge with futures contracts in part to mitigate default risk. The empirical work, however, has employed outcomes - such as inventory and hedging demand - rather than the primitive - the default risk itself, in order to explain commodity spot and futures prices. In this paper, we ll this important gap in the literature. Employing balance-sheet based measures of default risk for oil, gas and metal producers, we show that default risk of commodity producers is related to the risk premium on commodity futures contracts. In particular, an increase in the default risk of producers forecasts an increase in excess returns on short-term futures of these commodities. In contrast, default risk of producers does not appear to explain well the contemporaneous convenience yield or basis on the commodity (measured as the basis between the shortest maturity futures contract and a longer-term one). The convenience yield is explained well, however, by inventory positions of producers. This suggests that inventory and futures contracts perform somewhat distinct economic functions for producers, a theme that we elaborate below. Consider the optimization problem of a producer who faces uncertain demand shocks in future as well as costs of raising external nance that increase in its risk of default. External nance being costly potentially limits the producer from exercising its growth options to their fullest potential. Alternatively, default leads to loss of these growth options. The producer can manage inventory and trade in futures contracts in order to smooth cash ows and when faced with these uncertainties. We argue that the primary role of inventories is to smooth cash ows or pro ts across time. To wit, consider a low, transitory demand shock today which lowers spot prices today but raises the expected growth in the spot price between today and tomorrow. Futures contracts are not naturally suited to adjust pro ts to such a demand shock. In contrast, producers can build up inventory optimally to capitalize on higher spot prices tomorrow. Thus, inventory responds to demand shocks, which in turn are primary drivers of spot prices. As a result, an increase in inventory is associated with a lower basis or convenience yield, or in other words, a lower di erence between the spot price and expected spot price in future. In contrast, futures are better suited to hedge against default and help equate the marginal product from growth options across future states. In particular, the producer can reduce the variability of its future cash ows by going short in commodity futures. This represents a transfer of cash ows across future states of the world: In good states, the 1

3 producer will have ex-post regret at having hedged with futures, whereas in bad states, the hedge will help stave o default (some times). Thus, an increase in default risk raises producers propensity to hedge, and, in turn, lowers futures price and raises returns on futures contracts. Before we test this hypothesis on the di erential role of default risk and inventory for commodity producers and for spot and futures prices, it is important to make two observations. First, the intuitive arguments presented above are formally not exact. For example, managing pro ts better through inventory management also serves to hedge against costs of external nance when default risk is high, and through that channel, a ects the extent of hedging and futures prices. However, if inventory is low ( stock-out"), then its exibility in enabling the rm to hedge reduces and the distinct roles of inventory and futures are more likely to manifest. Second, since spot prices are hard to come by for most commodities, empirical work almost exclusively relies on futures prices. For instance, basis or convenience yield is proxied by di erence between shortest maturity futures price (a proxy for spot) and the next maturity futures price. To summarize, there are theoretical as well as empirical factors that potentially intertwine the role of default risk and inventory in predicting spot and futures prices. The burden is thus on data to a large extent to inform us further. In our tests, we focus on eight commodities heating oil, crude oil, gasoline, natural gas and four metals copper, zinc, lead and aluminium. Our choice of these commodities is driven by data requirement that we have at least ten producers in each quarter to produce an average measure of default risk for a given commodity. Our measures of default risk are the Z-score (Altman, 1968) as modi ed by Mackie-Mason (1990) and the Zmijewskiscore (Zmijewski, 1984). These measures are based on balance sheet information obtained from Compustat, for which we have quarterly data available from last quarter of 1969 to The futures data is from Datastream, the hedger and speculator positions are from the Commodity Futures Trading Commission (available to us only for oil and gas futures), while the inventory data is collected from a variety of sources. We nd strong evidence that our measures of default risk predict excess futures returns at the quarterly frequency. In particular, when current default risk is high, next quarter s futures return tends to also be high across all commodities. The e ect is robust to business-cycle conditions and economically signi cant: A one standard deviation increase in the aggregate commodity sector default risk is on average associated with a 3% increase in the respective commodity s futures risk premium. Importantly, the level of default risk is also associated with high hedging demand. When inventory is added as a regressor, it comes 2

4 in insigni cant for excess future returns and has little e ect on both of these results. For the basis, the pattern is the opposite: low inventory is signi cantly associated with high contemporaneous basis for all the commodities, while the measures of default risk in this case do not appear to be an important factor. In this case too, the e ect is economically signi cant: A one standard deviation decrease in the inventory level is on average associated with about a 2% increase in the basis. These results are somewhat di erent from a recent study by Gorton, Hayashi, and Rouwenhorst (2007), who nd that low inventory predicts high excess futures returns. However, they do not consider default risk directly, which we show knocks out the role of inventory as a determinant of futures risk premiums for the commodities in our sample. Identifying and highlighting this role of default risk the primary underlying risk that drives producers to hedge using futures contracts in a ecting commodity futures prices constitutes our most important and novel contribution. Our nal test relates to the role of commodity producers default risk in a traditional cross-sectional asset pricing framework. Since hedging in real world is likely to be incomplete, we hypothesize that such default risk may in fact be a risk factor a ecting commodity prices. We nd that a measure of commodity-sector default risk improves the ability of the consumption capital asset-pricing model (CCAPM) to explain the cross-section of expected excess returns on short-term commodity futures contracts. In ongoing work, we are trying to provide a rmer theoretical foundation to these cross-sectional tests and results. 1.1 Related Literature There are two classic views on the behavior of commodity forward prices. The Theory of Normal Backwardation, put forth by Keynes (1930), states that speculators, who take the long side of a commodity future position, require a risk premium for hedging the spot price exposure of producers. The risk premium on long forward positions is thus increasing in the amount of hedging pressure and should be related to observed hedger versus speculator positions in the commodity forward markets. Bessembinder (1992) and De Roon, Nijman and Veld (2000) empirically link hedging pressure to futures excess returns, basis and the convenience yield and interpret their ndings as consistent with the Theory of Normal Backwardation. The Theory of Storage (e.g., Kaldor, 1936, Working, 1949, and Brennan, 1958), on the other hand, postulates that forward prices are driven by optimal inventory management. In particular, the Theory of Storage introduces the notion of a "convenience" yield 3

5 to explain why anyone would hold inventory in periods of expected decline of spot prices. Tests of the Theory of Storage include Fama and French (1988) and Ng and Pirrong (1994). In more recent work, Routledge, Seppi and Spatt (2000) introduce a forward market in the optimal inventory management model of Deaton and Laroque (1992) and show that timevarying convenience yields, consistent with those observed in the data, can arise even with risk-neutral agents. In this case, of course, the risk premium on the commodity forwards is zero. The convenience yield arises because the holder of the spot also implicitly holds a timing option in terms of taking advantage of temporary spikes in the spot price. The time-variation in the value of this option is re ected in the time-variation in the observed convenience yield. Thus, time-variation in the observed convenience yield need not be due to a time-varying forward risk premium. Note, however, that the two theories are not mutually exclusive. A time-varying risk premium on forwards is consistent with optimal inventory management if producers are not risk-neutral or face, e.g., bankruptcy costs and speculator capital is not unlimited: If producers have a hedging demand, absent from the Routledge, Seppi and Spatt model, speculators will take the opposite long positions given they are awarded a fair risk premium on the position. In the data, hedgers are on average net short forwards, while speculators are on average net long, which indicates that producers indeed have an average hedging demand. Gorton and Rouwenhorst (2006) present evidence that long positions in commodity futures contracts on average have earned a risk premium. It has proved di cult to explain the unconditional risk premium on commodity futures with traditional asset pricing theory (see Jagannathan, 1985, for an earlier e ort). In a recent paper, Gorton, Hayashi, and Rouwenhorst (2007) argue that time-varying futures risk premia are driven by inventory levels and not by net speculator or hedger positions. In particular, they show that various de nitions of hedging pressure do not signi cantly forecast excess long forward returns, although the signs are consistent with Keynes hypothesis. Inventory, on the other hand, forecasts future forward returns with a negative sign in their sample; i.e., when inventory levels are low, the forward risk premium is high. They argue that this evidence is in favor of the Theory of Storage and that hedging pressure is not an important determinant of commodity forward risk premiums. In addition, Gorton, Hayashi, and Rouwenhorst show that the inventory level is negatively related to the basis, spot commodity price and that the relation is nonlinear in that it is stronger the lower the inventory level. This evidence strongly supports the main features of the Theory of Storage. 4

6 2 The Commodity Forward Risk Premium In this section, we discuss the Theory of Storage and the Theory of Normal Backwardation in more detail, and then present our theoretical model. We relegate the model details to the Appendix, and instead provide its main predictions as motivation for our empirical analysis. 2.1 General Overview Commodity forward prices are often, with reference to no-arbitrage, written: F t;t = S t e (r+u c)t ; (1) where F t;t is the current, time t forward price of a forward maturing in T periods. S t is the current spot price, r is the continuously compounded risk free rate, u is continuously compounded storage costs, while c is the continuously compounded convenience yield. The latter is necessary to explain downward sloping forward curves (i.e., a plot of forward prices versus maturity), as the risk free rate and storage costs are positive. Equation (1), which relates the forward price to the current spot price, is not necessarily useful for thinking about forward risk premiums. The forward risk premium is a function of the expected future spot price: frp t;t E t [S T ] F t;t ; (2) F t;t and need therefore not be related to the convenience yield extracted from equation (1). For instance, in Routledge, Seppi, and Spatt (2000) agents are risk-neutral, which implies F t;t = E t [S T ], and the explanation for the convenience yield is a pure cash- ow e ect: A low level of inventory is associated with high spot prices and lower expected future spot prices. Holding the spot is valuable as it enables the holder to take advantage of temporary spikes in the spot price if a stock-out should occur. In this case, the holder can provide the commodity when it is most desired and prices are temporarily high. The convenience yield re ects the value of this timing option. This is the Theory of Storage explanation for why anyone would hold a commodity in inventory when spot prices are expected to decline. The convenience yield extracted from equation (1) is in this case a cash ow e ect stemming from mean-reversion in spot prices. The Theory of Storage, pioneered by Kaldor (1936), Working (1949), and Brennan (1958), is therefore in its pure form silent about futures risk premiums. 5

7 The Theory of Normal Backwardation (Keynes, 1930), on the other hand, is directly related to the futures risk premium. Here, risk averse speculators demand a risk premium for taking on the price risk producers wish to hedge against. Therefore, forward prices are lower than expected future spot prices: F t;t = E t [S T ] t;t ; (3) where t;t is the premium required by the speculators for holding F t;t. A high convenience yield is usually associated with a high basis (de ned as the spot price minus the forward price). The basis in the Theory of Normal Backwardation thus has a risk premium component, t;t, in addition to a potential cash- ow component, S t E [S t;t ]: S t F t;t = S t E t [S T ] + t;t : (4) The risk premium component is further associated with the amount of hedging pressure from producers. I.e., the stronger their desire to hedge future spot price uctuations, the higher the risk premium for a given level of speculator risk aversion. 2.2 Forward Risk Premiums and Hedging Demand The two theories are not mutually exclusive. There is no inherent inconsistency in a world where speculators are risk averse and producers have a hedging demand, in addition to optimally managing their inventory. In fact, there is empirical evidence consistent with both as explanations of futures prices. Empirically, investors classi ed as "hedgers" by the Commodity Futures Trading Commission (CFTC) are on average short commodity futures contracts, which indicates that commodity producers on average have a hedging demand. Further, Gorton, Hayashi, and Rouwenhorst (2007) show that average historical returns on long commodity futures are increasing in the average basis of the respective commodity futures. This indicates, consistent with the Theory of Normal Backwardation, that commodity futures risk premia are positively related to the convenience yield. However, Gorton, Hayashi, and Rouwenhorst (2007) present a strong case for the Theory of Storage. First, they provide empirical evidence that commodity futures basis are negatively related to the aggregate level of commodity inventories. Second, they show that for most commodities low inventory levels in the time series are associated with high next quarter futures risk premiums, while the hedger positions from 6

8 CFTC on the other hand are not signi cantly related to futures risk premiums. They conclude from this that hedging pressure is not important for the determination of commodity futures prices. In this paper, we challenge this interpretation by devising a test that focuses directly on primitives of hedging demand; default risk and costs of external nancing. In particular, we investigate the e ect of time-variation in aggregate commodity sector proxies for this friction on the respective commodity sector futures risk premiums and basis. To isolate the e ect of hedging demand, we control for the usual forecasting variables that proxy for some combination of aggregate risk and investor risk aversion. The reasons for focusing on a primitive of hedging demand, instead of relying directly on the CFTC data on hedger positions, are both empirical and theoretical. Empirically, the variable that classi es investors as hedgers or speculators is likely to be quite noisy. For instance, the relative positions are given per commodity, not per contract. Thus, common strategies, for instance the "calendar spread" where one goes long (short) the long term forward and short (long) the short term forward on the same commodity, cannot be identi ed. In addition, the classi cation of who is a hedger and who is a speculator can sometimes be di cult. As an example, many production rms run trading desks as a part of their business. The line between a hedge trade or a speculator trade is therefore blurred. Theoretically, even though rms fundamental hedging demand, that is the rms incentive to decrease the volatility of future pro ts, is high, the equilibrium number of short futures positions may be low. In fact, the relation between futures risk premiums and the number of short futures contracts entered by the rm is complex and depends on the curvature of consumer and speculator demand functions, as well as the nature of the costs of external nancing faced by the rm. 1 In the following, we brie y present our model to convey these intuition and to motivate our subsequent empirical tests. All proofs and a fuller description of the model are given in the Appendix. 2.3 The Model In this section, we model hedging demand as arising from costs of external nancing as in Froot, Scharfstein, and Stein (1993). Otherwise, the model is a two-period version of the 1 These general points were also made by Gorton, Hayashi, and Rouwenhorst (2007), but our conclusions are somewhat di erent. While these authors interpret the negative empirical results with respect to the CFTC hedger positions as evidence against the hedging pressure hypothesis, we interpret such results as a possible equilibrium outcome when producers fundamental hedging demand a ect futures prices. 7

9 Deaton and Laroque (1992) model of commodity prices and optimal inventory management. A recent, related model is Gorton, Hayashi, and Rouwenhorst (2007). There are three types of agents in this model: The commodity producers, who maximize expected pro ts through optimal inventory management and hedging using commodity futures, consumers, whose demand for the spot commodity along with the equilibrium supply determine the commodity spot price, and speculators, whose demand for the commodity futures along with the futures hedging demand of producers determine the commodity futures price Consumption, Production and the Spot Price Let the spot price of the commodity be denoted P t. Each period c (P t ) units of the good is consumed. The production schedule is predetermined and production each period is denoted g t. Thus, we have in mind an economy where the time and cost required to adjust production schedules to transitory demand shocks are prohibitively large. 2 The current economy-wide inventory level of the commodity is denoted I t and goods in inventory depreciate at a rate d. Market clearing demands that incoming inventory and current production, g t + (1 d) I t 1, equals current consumption and outgoing inventory, c t + I t. This equality can be rearranged and we get: c (P t ) = g t I t (5) where I t I t (1 d) I t 1. We assume the immediate use demand, c (P t ), is monotone decreasing in the spot price P t and summarize the spot market with an inverse demand function, f: P t = a t f (g t I t ) ; (6) where a t is an i.i.d. demand shock and f is decreasing and convex in the supply, g t I t. We will in the following for simplicity of exposition assume that the per period depreciation rate, d = 0 and interest rate r = Producers Producers are risk-neutral price takers who maximize expected pro ts through optimal inventory management, hedging in futures, and investment. In period 0, the rm stores an amount 2 We will in the empirical section consider the behavior of short-term commodity futures contracts. Arguably, short-term contracts are more in uenced by inventory uctuations than shocks to longer term supply and demand. 8

10 I as inventory from its current supply, g 0, and so period 0 pro ts are simply P 0 (g 0 I). The rm also enters h short futures contracts for delivery in period 1. In period 1, the rm sells its current inventory and production supply, honours its futures contracts and realizes a pro t of P 1 (I + g 1 ) + h (F P 1 ), where F is the forward price of the futures contracts. At the end of period 1, producers can in addition exercise growth options of the rm. In particular, the net present value at time 1 of the output of an investment of size X is g (X) X, where g (X) is a concave increasing function (g 0 > 0; g 00 < 0). Thus, the net present value of investment exhibits decreasing marginal returns to scale. 3 One can think of g (X) as the ex-dividend value of the rm at time 1. At time 1, the producers solve max g (X) X C (e) (7) subject to where X = w + e; (8) w = P 1 (I + g 1 ) + h (F P 1 ) (9) is the internal funds of the producer. The function C (e) is an increasing convex cost function of the amount of external nancing e the rm requires: e = X w. If the rm faces costs of external nance, > 0, and the severity of the costs is increasing in. The maximization can then be written max X and the rst order condition gives g (X) X C (X w) ; (10) g 0 (X) 1 = C 0 (e) : For the constrained rm, the invested amount increases one for one with the amount of internal funds, dx = 1: Since marginal returns to investment are decreasing and since costs dw of external nancing are convex, the rm has a demand for hedging period 1 pro ts (see Froot, Scharfstein, and Stein, 1993). The rm can, in principle, use both short futures positions and increased inventory to alleviate or avoid altogether the nancing constraint. 3 This will be the case if, for instance, there are technological decreasing returns to scale. 9

11 The rms problem can then be stated max P 0 (g 0 I) + E [P 1 (I + g 1 ) + h (F P 1 )] + E [g (X ) X C (X w)] (11) fi;hg subject to I 0; where X denotes the optimal period 1 investment. Note that dx that dx = dx dw = F dh dw dh is a direct way to transfer money from high P 1 states to low P 1 states. It will be useful to de ne di = dx dw dw di = P 1 > 0 and P 1 > 0 if F > P 1 but dx dh < 0 if F < P 1. Thus, short futures contracts ~g (X; ) = g 0 (X ) 1 = C 0 (X w) ; (12) which is the marginal bene t of an additional unit of internal funds, w. If the rm is nancially constrained, this term is positive. If the rm is not nancially constrained, this term is zero Benchmark Case: = 0 When = 0, there are no costs of external nancing and thus no hedging incentive. In this case, the only determinant of futures prices is the non-negativity constraint on the inventory. In particular, the rst order condition with respect to inventory gives: P 0 E [P 1 ] = ; (13) where is the slack inventory constraint. Since the rms are risk-neutral, the rm will only hold inventory if this period s spot price is equal to the next period s expected spot price. If the current demand shock is su ciently high, an inventory stock-out occurs (i.e., > 0), and current spot prices can rise above future expected spot prices. Firms would in this case like to have negative inventory, but cannot. This creates mean-reversion in the spot price and thus an observed convenience yield from holding the spot. This is the Theory of Storage aspect of the model. In a multi-period setting, a convenience yield of holding the spot arises in these models even if there is no actual stock-out, but as long as there is a 10

12 positive probability of a stock-out (see Routledge, Seppi, and Spatt, 2000). 4 The rst order condition with respect to the futures position gives: F = E [P 1 ] : (14) Since the rm is risk-neutral and since there is no bene t to hedging with futures in this case (remember, = 0), the futures risk premium must be zero. The basis is then purely driven by the cash- ow e ects induced by the inventory level: P 0 F = P E [P 1 ] = : (15) In sum, the model without hedging demand predicts zero futures risk premium as futures do not decrease a dead-weight loss due to nancial frictions. Further, the basis is negatively related to the level of inventory Hedging Demand Case: > 0 When > 0, the rm has an incentive to decrease the volatility of future pro ts as this decreases the expected costs of external nancing. We refer to this incentive as the fundamental hedging demand. In this case, the rst order condition of the rm with respect to inventory gives: P 0 E [P 1 ] = E [P 1 ~g (X; )] + : (16) The additional term relative to the benchmark case, E [P 1 ~g (X; )], is due to the hedging bene t from holding inventory. The fundamental hedging demand is given by ~g (X; ), the marginal bene t of additional internal funds in the next period, which is positive when > 0. In fact, ~g (X; ) is increasing in, the severity of the nancing friction (see Appendix). The future spot price, P 1, is the amount of additional internal funds a unit of inventory delivers. Thus, a convenience yield from holding the spot arises from a fundamental hedging demand. This is in addition to the inventory level e ect from the benchmark case given by. The rst order condition with respect to the short futures position yields: E [P 1 ] F = E [(F P 1 ) ~g (X; )] : (17) 4 In terms of intuition with respect to practical application, where a de facto stock-out very rarely occurs, one can think of "stock-outs" in our simple one-period model as an increase in the probability of a stock-out. 11

13 The futures premium, the cost of entering a short futures position, equals the marginal bene t of hedging with a futures contract: The payo of the short futures contract is F P 1, and again ~g (X; ) is the fundamental hedging demand. Before we turn to the speculator demand for futures contracts, we note that the basis can be interpreted as the cost of holding one additional unit of inventory hedged with a short futures position: (P 0 E [P 1 ]) + (E [P 1 ] F ) = E [P 1 ~g (X; )] + E [(F P ) ~g (X; )] + (18) m P 0 F = F E [~g (X; )] + : (19) Thus, the basis is determined by the level of inventory, as in the benchmark case where = 0, as well as by the amount of fundamental hedging demand. The Speculators The Benchmark case highlights the role of inventory as a cash- ow e ect arising from inventory stock-outs. The magnitude of this source of the convenience yield depends on the curvature of the consumers demand function. If a change in the level of inventory has little e ect on prices, the constraint is less severe, and vice versa. In general, the counter-party with respect to inventory decisions are the consumers. For futures hedging, however, the counter-party is the speculators. First, consider the case when speculators are unconstrained and risk-neutral. In this case, it is costless to hedge with futures contracts as the futures risk premium is zero. The rm will be fully hedged and the basis would only re ect cash- ow e ects as in the benchmark case. We will, however, assume that speculator demand is not perfectly elastic with respect to commodity futures, and that they therefore require a risk premium to take on the long futures positions. In particular, we have in mind a demand function for the commodity futures of the form N S = E [P 1] F V ar (P 1 ) : (20) This functional form can be achieved by assuming, e.g., quadratic utility over end of period wealth. Alternatively, one can think of the penalty parameter for volatility,, as a tracking error constraint or a capital constraint with respect to margin requirements. 12

14 Model Predictions We are interested in the model predictions with respect to changes in the level of fundamental hedging demand, given by. Below we summarize the main predictions of the model which we will test in the remainder of the paper. See the Appendix for proofs and further details. 1. The Basis: The futures basis is increasing in fundamental hedging demand and decreasing in inventory. The latter relation arises both because hedging demand is decreasing in inventory and because of the direct e ect of an inventory stock-out. Consider an exogenous demand shock that decreases the level of inventory. In this case, both the fundamental hedging demand and the probability of a stock-out increases. Since the level of inventory is linked to both determinants of the futures basis, the model predicts that inventory is more tightly linked to the basis than hedging demand is. 2. The Futures Risk Premium: In the case of an inventory stock-out, the rm cannot hedge further with inventory. The futures risk premium is then increasing in hedging demand regardless of the preferences of speculators. However, if there is not a stock-out, the rm will use both inventory and futures to hedge future pro ts. In this case, the e ect on the risk premium depends on the relative cost of hedging with futures and with inventory, which in turn depends on the relative curvature of the consumers and speculators demand functions. For instance, if an increase in inventory, arising from an increase in, reduces the variance of future spot prices by more than rms demand for short futures contracts, the risk premium on futures will decrease as per equation (20). Thus, the model predicts that the futures risk premium is increasing in the fundamental hedging demand if inventory levels are low. If we assume speculator demand is not a function of the volatility of spot prices (e.g., risk-neutral speculators with a capital constraint), or that the volatility of the spot price is constant, the model predicts that the futures risk premium is increasing in the fundamental hedging demand also in the case when inventory is high. 3. The Hedger Positions: The CFTC data on hedger positions gives the net number of contracts held by hedgers. In our model, the e ect on this number from an increase in the fundamental hedging demand depends on the curvature of the speculator and 13

15 consumer demand functions in a manner similar to that of the futures risk premium. If inventory is low, however, the relation is positive. In sum, the model shows how both futures and inventory may be used for hedging purposes. However, the inventory level is in addition related to the current and expected future spot prices, as evident also in the benchmark case where = 0 and there are no nancing frictions. Spot prices and inventory levels are thus important for rms expected pro ts above and beyond any deadweight loss arising from nancing frictions. Futures, however, are more directly related to the volatility of the nal period payo. This fundamental di erence between inventory and futures is important for understanding the behavior of futures basis versus futures risk premiums in the model. 3 Data and Summary Statistics We use time-series data on inventory holdings of a broad cross-section of commodities, commodity futures prices, commodity spot prices, hedger demand, speculator demand, and aggregate real per capita consumption growth. In addition, we use measures of default risk obtained from balance sheet data from Compustat. Due to the scarcity of rms in Compustat that can be classi ed as producers for several of the commodities, we focus the default risk analysis on the energy and metals sectors, In particular, we look at Heating Oil, Crude Oil, Gasoline, Natural Gas, Copper, Zinc, Lead and Aluminium. 3.1 Proxies for Fundamental Hedging Demand In Froot, Scharfstein and Stein (1993), agency costs are motivated as monitoring costs that outside investors must incur to curb the agency problems a ecting rms managers and owners. In a large body of nance literature, such costs are larger in an expected sense when rms are closer to defaulting on debt of the rm since the debtholder-equityholder con icts become more severe in such states. The agency problems that kick in could either be the underinvestment problem, as in Myers (1977), or asset-substitution problem, as in Jensen and Meckling (1976). Indeed, costly state veri cation has been one of the economic rationales for debt being the optimal nancing contract (Townsend, 1979, and Gale and Hellwig, 1985), and the equilibrium of these models features costly veri cation of states only in the default states. Of course, in practice, we do see equity issuances by rms as well. 14

16 These are also however associated with signi cant dilution costs, as theoretically motivated by the adverse selection argument of Myers and Majluf (1984). Empirical evidence on costs of external nance is plenty. Direct costs of bond and equity issuance have been carefully examined by Altinkilic and Hansen (2000). They document that these costs are substantial and that over 85% of the total underwriter spread is a variable cost and that the marginal cost of external nance is rising. Importantly, lower quality o erings are at higher underwriter spreads. Choe, Masulis and Nanda (1993) and Bayless and Chaplinsky (1996) document that equity issuance patterns of rms are procyclical consistent with there being greater dilution costs from issuance during economic downturns and recessions, a nding that is consistent with an increase in agency problems and default risk in such times. There is also evidence that many distressed rms nd it di cult to raise external nance, unless their leverage is restructured in some fashion (Franks and Sanzhar, 2006, among others). Finally, it is well-known (though not as well academically documented) that rms nd it extremely di cult to borrow short-term (generally, in the commercial paper market) unless they are investment-grade rated. That is, a deterioration in credit risk forces rms to borrow long-term and su er a higher cost of capital. Given this theoretical and empirical motivation, we employ a measure of default risk as the empirical proxy for cost of external nance. The speci c measure we employ is the Z- score based on Altman (1968) s seminal approach of identifying the rm-level balance-sheet variables that help discriminate" whether a rm is likely to default or not. We employ two variants of this measure, the Altman s original Z-score as modi ed by Mackie-Mason (1990) and the Zmijewski (1984), the former being negatively related to default risk and the latter positively related. 3.2 Default Risk Data The sample period of our analysis runs from the fourth quarter of 1974 until the fourth quarter of 2006, and varies across commodities and measures according to data availability. The measures of default risk that we employ are the Z-score and the Zmijewski score. To create the Z-score and the Zmijewski score, we require balance sheet information for commodity producers, and we obtain this information by rst matching companies with commodities based on their four-digit SIC code; we obtain these SIC codes from Gorton, Hayashi and Rouwenhorst (2007). For Crude Oil, Heating Oil and Gasoline, this is all rms in SIC codes 2910 and 2911, i.e., Petroleum Re ning. For Natural Gas, this is all rms in 15

17 SIC codes 1310 and 1311, i.e., Crude Petroleum and Gas Extraction. For Copper, this is all rms in SIC codes 1020, 1021 and For Zinc and Lead, it is SIC codes 1030 and For Aluminium, it is all rms in SIC code We then searched the merged CRSP-Compustat quarterly database for all companies matching these four-digit SIC codes, and for each company, computed: Z score = (3:3EBIT +Sales+1:4RetainedEarnings+1:2W orkingcapital)=t otalassets: Zmijewski score = 4:3 4:5 N etincome=t otalassets + 5:7 T otaldebt=t otalassets 0:004 CurrentAssets=CurrentLiabilities: For each period in which there are at least four rms in the data present, we compute the average Z and Zmijewski score across all these rms. In the following, we will denote the Zmijewski score as the Zm-score. [TABLE I ABOUT HERE] Table I shows summary statistics for each of the aggregate default risk measures. The measures of default risk are highly persistent, with quarterly autocorrelations mainly in the range 0:51 to 0:99. Further, the default measures display some skewness, which is inferred here from the di erence between their mean and median values. This is to be expected as default risk captures extreme events. Figure 1 shows the time-series of the normalized measures of default risk for Crude Oil, Heating Oil, and Gasoline, which all have the same default measures due to the data limitations listed above, and Figure 2 shows the same for Natural Gas. First, the series are correlated, but not identical. As expected, the Zm-score and the Z-score move in opposite directions. Second, there is considerable time-variation in measured default risk, which indicates there is economically signi cant time-variation in the fundamental hedging demand of producers in these commodity sectors. [FIGURE 2 ABOUT HERE] [FIGURE 3 ABOUT HERE] 16

18 The extreme persistence of the default risk measures suggests that there may be problems in incorporating these measures into forecasting regressions for commodity futures returns (see Stambaugh (1999) and Lewellen (2004) for the biases inherent in predicting returns with highly persistent nancial ratios). The biases that arise in such predictive regressions are functions of both the persistence of the predictive variables as well as the correlation between the residuals from the predictive regression and the autoregression of the predictor variable. Campbell and Yogo (2005) present a diagnostic test for possible biases in such predictive regressions, relying on tests for unit roots rst developed by Elliott, Rothenberg and Stock (1996). We perform these pre-tests in Table III, and detrend every default risk series for which there is a unit root in the con dence interval for the largest autoregressive root. We use the Hodrick-Prescott lter, and the recommended quarterly smoothing parameter of 1600 to detrend these series. The resulting time-series are our aggregate default risk measures for these variables. For default risk measures that do not contain unit roots, but do fail the diagnostic pre-test of Campbell and Yogo (2005), we use the Bonferroni con dence bands suggested by these authors rather than the standard t-test to ascertain forecasting power in the predictive regressions of futures risk premia using the default risk measures. Note that the Z-score predicts default with a negative sign, while the Zm-score predicts default with a positive sign. 3.3 Basis and Excess Returns Data To create the basis and excess returns measures, we follow the methodology of Gorton, Hayashi and Rouwenhorst (2007), and employ data from Datastream. We constructed rolling commodity futures excess returns at the end of each month as the one-period price di erence in the nearest to maturity contract that would not expire during the next month. That is, the excess return from the end of month t to the next is calculated as: F t+1;t F t;t F t;t ; where F t;t is the futures price at the end of month t on the nearest contract whose expiration date T is after the end of month t + 1, and F t+1;t is the price of the same contract at the end of month t + 1. The quarterly return is constructed as the product of the three monthly returns in the quarter. The futures basis is calculated for each commodity as (F 1=F 2 1)365=(D2 D1), where 17

19 F 1 is the nearest futures contract and F 2 is the next nearest futures contract; D1 and D2 are the number of days until the last trading date of the respective contracts. We account for the seasonality in the basis by including four quarterly dummy variables in all speci cations employed to explain the basis. The statistical properties of our data match up very closely to those employed by Gorton, Hayashi and Rouwenhorst (2007), summary statistics about these quarterly measures are presented in Table II. The basis does not display high autocorrelation, and the average basis is positive for Crude Oil, Heating Oil and Gasoline, while Natural Gas have on average negative basis over the sample period. This indicates that the convenience yield is on average positive for the three rst commodities. Note the relatively high standard deviation of the basis, which indicates that the basis for each of the commodities at times changes sign. Thus, time-varying convenience yields are an important feature of the data. The excess returns are on average positive for all three commodities, ranging from 2:5% to 6:7%, with relatively large standard deviations (overall in excess of 20%). As expected, the sample autocorrelations of excess returns on the futures are close to zero. [TABLE II ABOUT HERE] 3.4 Hedger Positions Data The Hedger Net Positions data are obtained from Pinnacle Inc., which sources data directly from the Commodity Futures Trading Commission (CFTC). Classi cation into Hedgers, Speculators and Small traders is done by the CFTC, and the reported data are the total open positions, both short and long, of each of these trader types across all maturities of futures contracts. We measure Hedger Net Positions as ln(hedger Long Positions)-ln(Hedger Short Positions). Summary statistics on these data are shown in Table II. First, the hedger positions are on average negative, which means investors classi ed as hedgers are on average short the commodity forwards. However, the standard deviations are relatively large, indicating that there are times when hedgers actually are net long whereas speculators are net short. This is a feature of the data we do not capture in our model. The autocorrelation of the hedger positions is positive, but not as persistent as the autocorrelation of the measures of default risk. Thus, the hedging demand, as measured by the number of forward contracts hedgers hold, does not appear one for one with the aggregate default risk in the commodity sector. While we have discussed previously why this may be, it is important to note these 18

20 empirical di erences as they help explain why hedger demand does not signi cantly forecast forward risk premiums, while measures of default risk do. 3.5 Inventory Data Aggregate inventories are created as per the speci cations in Gorton, Hayashi and Rouwenhorst (2007). For all four energy commodities, these are obtained from the Department of Energy s Monthly Energy Review. For Crude Oil, we use the item: U.S. crude oil ending stocks non-spr, thousands of barrels. For Heating Oil, we use the item: U.S. total distillate stocks. For Gasoline, we use: U.S. total motor gasoline ending stocks, thousands of barrels. Finally, for Natural Gas, we use: U.S. total natural gas in underground storage (working gas), millions of cubic feet. Following Gorton, Hayashi and Rouwenhorst (2007), we compute a measure of the shock to aggregate inventory by subtracting tted trend inventory from the quarterly realized inventory. Quarterly trend inventory is created using a Hodrick-Prescott lter with the recommended smoothing parameter. In all speci cations employing inventories, we either employ quarterly dummy variables, or rst regress the inventory shock on these quarterly dummy variables and use the residual from this regression. We do so in order to control for the strong seasonality present in inventories. The nal panel in Table II shows summary statistics of the inventory "shocks", i.e., the cyclical component of inventory stocks, for the commodities. The means are all zero - a feature of the smoothing lter - and the autocorrelation is positive. 4 Empirical Results This section presents our empirical results. The novel predictions of our model are the following. Aggregate commodity sector fundamental hedging demand should be positively related to the respective commodity s futures risk premium. We have argued that fundamental drivers of hedging demand is linked to measures of default risk. In particular, high default risk on average leads to higher hedging demand. Further, the relation between basis and default risk is likely to be overall positive, but not as strong as the relation between inventory levels and the basis. In particular, demand shock driven inventory stock-outs generate cash ow e ects in the basis due to time-varying expected growth in spot prices that may be unrelated to default risk. Thus, consistent with the standard Theory of Storage argument, inventory levels are negatively related to the basis (convenience yield). Our novel prediction 19

21 is that inventory should be more important than default risk for the dynamic behaviour of the basis. Finally, in the excess returns forecasting regressions we control for inventory levels and standard business cycle variables that have been shown to forecast excess returns in other settings. Our measures of default risk are the Z-score (Altman, 1968) and the Zm-score (Zmijewski, 1984), which are both based on balance-sheet information. The Z-score is de ned such that it is negatively related to default risk, while the Zm-score is positively related to default risk. 4.1 The Futures Risk Premium and Default Risk To evaluate whether the measures of commodity sector default risk are important for explaining futures risk premiums, we run standard forecasting regressions. In particular, we regress quarterly (excess) futures returns on one quarter lagged measures of default risk (DefRisk): ExcessReturns i;t+1 = + i DefRisk i;t + u i;t+1 ; (21) where i denotes the commodity and t denotes time measured in quarters. There are eight commodities considered: Crude Oil, Heating Oil, Gasoline, Natural Gas, Copper, Zinc, Lead, and Aluminum. The measures for aggregate commodity sector default risk have been created as explained in the previous section. Table IV shows the results of this regression across the eight commodities considered. [TABLE IV ABOUT HERE] First, we note that in all cases, the regression coe cients have the predicted sign; an increase in default risk forecasts higher futures returns over the next quarter. For the Z- and Zm-scores, the regression coe cients are signi cant at the 10% level or more, using Newey- West t-statistics with 3 lags, in 11 out of 16 regressions. The insigni cant coe cients have the right sign and t-statistics above 1. The strongest evidence is for Crude Oil and Heating Oil, which are the two commodities which have the longest return series available (91 and 108 quarters, respectively). The statistical signi cance is lowest for the Metals using the Zm-score. Note, however, that the metals have a shorter time series of observations (53 to 71 quarters). The same is true for Natural Gas (64 observations) which regression coe cient 20

22 when using the Zm-score is also insigni cant. Given the availability of data, we interpret these results as strong evidence that our measures of default risk are positively correlated with the risk premium in our sample. The adjusted R 2 s range between 0:7% and 13:5% in the regressions with signi cant coe cients, with an overall average around 5%. A one standard deviation increase in default risk is on average associated with approximately a 3% increase in expected futures returns. Thus, we uncover both economically and statistically signi cant variation in the commodity futures risk premiums when using the Z- and Zm-scores as measures of default risk. In sum, the evidence in Table IV supports the hypothesis that a fundamental driver of hedging demand, default risk, is an important determinant for commodity futures risk premiums. This evidence is thus consistent with the hypothesis that fundamental hedging demand is an important determinant of commodity futures risk premiums. Figures 3, 4, 5, and 6, show visually the negative relation between default risk and the Z-score for the four Energy commodities. [FIGURE 3 ABOUT HERE] [FIGURE 4 ABOUT HERE] [FIGURE 5 ABOUT HERE] [FIGURE 6 ABOUT HERE] Inventory versus Default Risk Next, we investigate whether uctuations in inventory levels also capture time-varying expected returns in the commodity futures by running the following regression: ExcessReturns i;t+1 = + i DefRisk i;t + (Inv i;t T rendinv i;t ) + u i;t+1 ; (22) where Inv i;t T rendinv i;t is the cyclical component of the inventory level of commodity i. [TABLE V ABOUT HERE] Our model predicts that inventory is negatively linked to the futures risk premium, but that cash ow e ects stemming from the risk of a stock-out obscure this relation. Consistent 21