Arbitrage and Its Physical Limits

Transcription

1 Arbitrage and Its Physical Limits Louis H. Ederington Price College of Business, University of Oklahoma Chitru S. Fernando Price College of Business, University of Oklahoma Kateryna V. Holland Krannert School of Management, Purdue University Scott C. Linn Price College of Business, University of Oklahoma January 15, 2017 Abstract We examine how physical constraints limit arbitrage by studying the effect of crude oil storage constraints on arbitrage activity in the U.S. crude oil market. We document both temporary and long-term violations of the no-arbitrage conditions that are robustly attributable to storage capacity constraints. When crude oil storage levels are well below available storage capacity, temporary violations of the upper no-arbitrage bound occur but tend to be eliminated within a few days. However, as the amount of oil in storage approaches the capacity limit, the price adjustment process slows and violations of the upper no-arbitrage limit persist. We find evidence of temporary, but not long-term, violations of the lower no-arbitrage futures pricing bound, with the latter being consistent with our observation that there were no periods of stockout conditions during our sample period. We also find that arbitrage was limited by financial constraints over our sample period. However, the evidence in support of physical constraints impeding arbitrage is independently strong and remains robust when we control for the effect of financial constraints. Our results are also robust to the use of different measures of physical constraints. Our evidence further indicates that arbitrage normally impacts the spot price more than the futures price. Our findings highlight the importance of accounting for physical arbitrage limits in the pricing of commodity futures. We also contribute to the Theory of Storage literature by highlighting the consequences for prices when inventories approach storage capacity limits. JEL Classifications: law of one price, limits to arbitrage, commodity markets, oil futures markets, oil storage, physical constraints, cash-and-carry arbitrage. Keywords: G13, G18, Q41. Author contact information: Ederington: lederington@ou.edu, (405) ; Fernando: cfernando@ou.edu, (405) ; Holland: khollan@purdue.edu; (765) ; Linn: slinn@ou.edu (405) We thank Bruce Bawks, John Conti, Thomas Lee, Yongjia Li, Anthony May, Glen Sweetnam, John Zyren, and seminar participants at the U.S. Energy Information Administration, and the Second IEA IEF OPEC Workshop on the interactions between physical and financial energy markets for valuable discussions and comments. We gratefully acknowledge financial support from the U.S. Department of Energy -- Energy Information Administration and the University of Oklahoma Office of the Vice President for Research. We also thank Moody s Analytics for making the company s EDF (Expected Default Frequency) data available to us and to Sue Zhang and Robert Tran for their gracious help in assembling the data. The views expressed in this paper reflect the opinions of the authors only, and do not necessarily reflect the views of the Energy Information Administration or the U.S. Department of Energy. The authors are solely responsible for all errors and omissions.

2 Arbitrage and Its Physical Limits Abstract We examine how physical constraints limit arbitrage by studying the effect of crude oil storage constraints on arbitrage activity in the U.S. crude oil market. We document both temporary and long-term violations of the no-arbitrage conditions that are robustly attributable to storage capacity constraints. When crude oil storage levels are well below available storage capacity, temporary violations of the upper no-arbitrage bound occur but tend to be eliminated within a few days. However, as the amount of oil in storage approaches the capacity limit, the price adjustment process slows and violations of the upper no-arbitrage limit persist. We find evidence of temporary, but not long-term, violations of the lower noarbitrage futures pricing bound, with the latter being consistent with our observation that there were no periods of stock-out conditions during our sample period. We also find that arbitrage was limited by financial constraints over our sample period. However, the evidence in support of physical constraints impeding arbitrage is independently strong and remains robust when we control for the effect of financial constraints. Our results are also robust to the use of different measures of physical constraints. Our evidence further indicates that arbitrage normally impacts the spot price more than the futures price. Our findings highlight the importance of accounting for physical arbitrage limits in the pricing of commodity futures. We also contribute to the Theory of Storage literature by highlighting the consequences for prices when inventories approach storage capacity limits. JEL Classifications: law of one price, limits to arbitrage, commodity markets, oil futures markets, oil storage, physical constraints, cash-and-carry arbitrage. Keywords: G13, G18, Q41. 2

3 Arbitrage and Its Physical Limits contango would have to widen much more to signal real storage distress. Spencer Jakab, Wall Street Journal, December 2, Introduction While the Law of One Price (LOP) is one of the most powerful concepts in the financial economics tool chest, a number of recent papers explore the financial limits to the arbitrage that enforces LOP, and the implications of these limits for asset pricing. 1 Physical limits, specifically limits on the availability of either inventory or storage capacity, are potentially equally important in the arbitrage pricing relationship for financial assets whose value is derived from the value of commodities. 2 While several recent studies have examined the role of financial limits to arbitrage in the pricing of commodity derivatives, 3 the potential effect of physical limits has not been empirically studied. In this paper, we address this gap in the literature by studying the effect of physical storage limits on arbitrage activity in the U.S. crude oil market. We specifically focus on the futures physical delivery hub at Cushing, Oklahoma, which is also the major storage center in the U.S. for crude oil. We draw inferences through an examination of the behavior of the spread between futures and spot prices for West Texas Intermediate (WTI) crude oil. In commodity markets, if the price of a commodity for future delivery exceeds the price for near-term delivery by more than the carrying (including storage) and transaction costs, arbitrageurs should be able to make a riskless profit by simultaneously executing contracts to buy in the spot market and sell in the forward market, while storing the commodity over the interim period. Exploitation of such an arbitrage opportunity, commonly referred to as cash-and-carry arbitrage, results in the now familiar relation between futures and spot prices derived from the Theory of Storage. 4 More precisely, cash-and-carry 1 See, for example, Shleifer and Vishny (1997), Gromb and Vayanos (2002), Mitchell, Pulvino and Stafford (2002), Hong and Stein (2003), Gabaix, Krishnamurthy, and Vigneron (2007), Brunnermeier and Pedersen (2009), Etula (2013), and Acharya, Lochstoer, and Ramadorai (2013). 2 See Routledge, Seppi, and Spatt (2000) and Gorton, Hayashi, and Rouwenhorst (2013). 3 See, for example, Mou (2010), Hong and Yogo (2012), Etula (2013), Acharya, Lochstoer, and Ramadorai (2013), and Cheng, Kirilenko, and Xiong (2015). 4 Kaldor (1939), Working (1949), Brennan (1958), Deaton and Laroque (1992), and Routledge, Seppi, and Spatt (2000). 3

4 arbitrage should place an upper limit on the spread between the price for near-term delivery, the spot price, 5 and the price for longer-term delivery, henceforth the futures price. Likewise, the possibility of reverse cash-and-carry arbitrage, which involves a short sale in the spot market covered by a purchase in the forward market, should set a lower limit on the futures-spot spread. In many commodity markets, however, storage capacity is limited -- especially at the delivery location for the futures contract. Once all available storage facilities are full (or, in the case of reverse cash-and-carry arbitrage, the available inventory is depleted), the corresponding arbitrage described above is no longer possible and the noarbitrage limits on the futures-spot spread should no longer hold. In a classical cash-and-carry arbitrage transaction involving a physical commodity at a spot-futures market hub like the WTI Cushing hub, the arbitrageur will execute three simultaneous transactions: (1) purchase the commodity in the spot market; (2) sell a corresponding quantity of the commodity in the futures market; and (3) contract to store the commodity at the hub until the futures transaction is closed out or settled. The ability to execute this trade depends on the availability of storage space at the hub. 6 If storage capacity or inventory is not immediately available, violations of the no-arbitrage condition may persist until storage becomes available. Storage contracts are typically over-the-counter agreements and thus may require some time to arrange. Moreover, they have elements of counterparty risk, such as force majeure and physical delivery default that are not present in purely financial arbitrage trades. These elements may discourage or delay the actions necessary to implement the arbitrage trades. If delayed, spreads above the no-arbitrage limit may persist until storage can be arranged. Consequently, the physical limits to executing an arbitrage may contribute to the persistence of futures-spot spread no-arbitrage violations above and beyond the limits imposed by financial constraints. 5 As discussed below, contracts in the crude-oil market are normally for delivery over a month since (unlike for commodities like gold) immediate spot delivery of large quantities of oil is very difficult and expensive. For futures contracts held to physical delivery, the CME group allows one calendar month for the oil to be delivered to the Cushing hub. Hence the quoted spot prices are normally forward or futures prices for delivery over the nearest calendar month. Contracts for immediate delivery are rare and typically for small quantities that can be moved by tanker truck. Despite the absence of immediate spot delivery in this market, we keep with convention by using the term spot price to refer to the settlement price for near-term-delivery contracts. 6 In a reverse cash-and-carry arbitrage transaction, the arbitrageur will simultaneously (1) borrow and sell the commodity in the spot market; and (2) purchase a corresponding quantity of the commodity in the futures market. The ability to execute this contract depends on the availability of inventory at the hub that can be borrowed. 4

5 We find evidence of both short- and long-term violations of the no-arbitrage conditions in the U.S. crude oil futures market at the WTI Cushing hub. Consistent with the argument that often storage cannot be arranged immediately, we find evidence of numerous temporary violations of the no-arbitrage upper bound. When storage levels are well below capacity, these temporary violations tend to be eliminated quickly, i.e., within a couple of days. However, as the amount of oil stored approaches the available capacity, the adjustment process takes longer and violations of the upper no-arbitrage limit persist for longer than a few days. In contrast, we observe only temporary violations of the no-arbitrage lower bound indicating the absence of persistent physical limits on reverse cash-and-carry arbitrage. Our finding for reverse cash-and-carry arbitrage is consistent with the absence of any periods of inventory stock-out conditions during our sample period, with crude oil inventory in storage never dropping below 30% of available storage capacity. Our evidence further indicates that the spot price adjusts more than the futures price in bringing the spread back within the noarbitrage bounds, which again points to physical arbitrage limits being a major factor determining the mispricing of the futures-spot spread. Testing for violations of the no-arbitrage conditions is complicated because we are unable to exactly identify the no-arbitrage limits at each point in time since (as discussed below) historical data on storage and transaction costs are not available. Hence, we test for evidence of cash-and-carry and reverse cash-and-carry arbitrage by examining the behavior of the futures-spot spread. We find evidence of both cash-and-carry arbitrage and reverse cash-and-carry arbitrage normally operating to return the futures-spot spread to within noarbitrage bounds. When the futures-spot spread is positive on day t-2 and rises further on day t-1 (and storage capacity is not exhausted), there is a strong tendency for the spread to fall on day t which is what we would expect if the further rise in the spread on day t-1 sets off cashand-carry arbitrage. This reversal tendency is stronger when the spread on day t-2 is high than when it is positive but low. This is again what we would expect since the further rise on day t-1 is more likely to raise the spread above the upper no-arbitrage bound if the spread is already very high. Likewise, if the spread on day t-2 is negative and the spread declines further on day t-1, there is a strong tendency for the spread to rise or reverse on day t. Again, this is what one would expect if the further decline in the spread on day t-1 triggers reverse 5

6 cash-and-carry arbitrage and this reversal tendency is stronger the more negative is the spread on day t-2. Both of these spread reversal tendencies are stronger when spread volatility is high. In contrast, if the level of the spread on day t-2 and the change on day t-1 are of opposite sign, making it less likely that the change in the spread on day t-1 carried it outside the no-arbitrage bound, the spread changes on days t-1 and t are basically uncorrelated. While normally a further rise in the spread on day t-1 from an already high level on day t-2 tends to be reversed on day t, this is not the case when oil inventories are close to capacity, which indicates that the lack of available storage space hinders the cash-and-carry arbitrage which would normally operate to pull the spread back down on day t. On the other hand, as alluded to previously, we find no evidence that reverse cash-and-carry arbitrage is impeded by low inventories. We also examine possible financial limits to arbitrage in the WTI crude oil market concurrently with measures of physical limits to arbitrage. The importance of financial limits to arbitrage in the oil market is highlighted by Acharya, Lochstoer, and Ramadorai (2013). 7 Those authors document the effect on futures and spot prices when producers hedging demand in the futures market is not fully met due to broker-dealer capital constraints. We also present evidence that arbitrage was restricted by financial constraints over our sample period. However, the evidence in support of physical constraints impeding arbitrage is considerably stronger and remains robust when we control for the effect of the financial constraint measures we examine. While Acharya, Lochstoer, and Ramadorai (2013) emphasize the importance of an inventory stock-out in giving rise to commodity sector default risk, there is no significant oil inventory stock-out that occurs in the period of our study. In contrast, our study highlights the role played by the unavailability of storage capacity due to high inventory levels as the cause of a decoupling between the futures and spot market in oil, an event that occurs several times during our sample period. Therefore, our study builds on the existing literature on the financial limits to arbitrage in commodity markets by also establishing the importance of the physical limits to arbitrage in these markets. We therefore provide a more complete picture of the role that limits to 7 Birge, Hortacsu, and Mercadal (2016) show that financial constraints impede arbitrage in electricity markets. 6

7 arbitrage, both physical limits as well as financial limits, play in the pricing of commodity futures. We contribute to the literature on the Theory of Storage by examining the effect of inventory storage capacity limits. The existing literature has focused on the effect of stockouts when inventories are very low with little or no attention to the possible pricing effects when inventories are very high and storage capacity becomes limited or is exhausted. For instance, Routledge, Seppi, and Spatt (2000), who explore the consequences of the nonnegativity inventory constraint for forward and futures prices, write, Inventory can always be added to keep current spot prices from being too low relative to expected future spot prices. We contribute to this literature by exploring the price consequences when inventories approach storage capacity limits so that additional inventory cannot be added. Modeling inventories as buffers to supply and demand shocks, Deaton and Laroque (1992) show that the increase in the risk of an inventory stock-out when inventories are low carries through to an increase in expected future spot price volatility. Routledge, Seppi, and Spatt (2000) extend the Deaton and Laroque (1992) model by including a forward market and show that inventory stock-outs can break the arbitrage link between the spot and forward markets. Similarly, we show that when storage capacity is limited or exhausted, the commodity s spot price will also be decoupled from the forward price. Therefore, in the case of both inventory stockouts and full storage situations, the arbitrage pricing relation between forward and spot prices will break down. Additionally, consistent with the Theory of Storage, we find that when inventories are neither very high nor very low, arbitrage restores the futures-spot spread to its no-arbitrage bounds following temporary violations. The rest of the paper is structured as follows. In the next section, we discuss arbitrage and storage in the crude oil market and develop our primary hypotheses. The data is described and basic results are presented in section 3, where we test for how the market responds to temporary violations of the no-arbitrage limits and present evidence that violations of the upper limit persist as storage approaches full capacity. In section 4, we explore how reverse cash-and-carry arbitrage enforces the lower no-arbitrage limit on the spread and whether this spread enforcing arbitrage is hindered when available oil inventories are low. In section 5, we expand the analysis to consider financial as well as physical limits 7

8 to arbitrage. In section 6, we examine how spot and futures prices change due to arbitrage and ask whether arbitrage impacts primarily the spot price, primarily the futures price, or both. Various robustness checks are presented in section 7, and section 8 concludes. 2. Oil market arbitrage and storage 2.1. No arbitrage spread conditions in the oil market Consider the limits that arbitrage places on the futures-spot and futures-futures spreads at the crude oil futures contract delivery/pricing hub assuming that storage is available for lease at the hub location. 8 Let Pt,t+v designate the price at time t for delivery at time t+v and Pt,t+s represent the time t price for delivery at time t+s where s>v. If t+v is the first available delivery time, Pt,t+v may be referred to as the spot price and Pt,t+s-Pt,t+v as the futures-spot spread. We will follow that convention here. Since large quantities of crude oil cannot be delivered instantaneously, virtually all physical delivery contracts in the crude oil market, including spot contracts, are contracts for delivery over a future period of time generally one month (Kaminski, 2012). For futures contracts held to physical delivery, the CME group allows one calendar month for the oil to be delivered to the Cushing hub. For example, suppose the current month is June. The three-month futures contract will be the contract that, if held to expiration, will result in physical delivery of crude oil commencing September 1 and ending on or before September 30. Similarly, delivery on the two-month futures contract will occur from August In the case of the spot contract traded in the month of June, physical delivery of crude oil will commence July 1 and end on or before July 31. Hence by convention the quoted spot prices in the crude oil market are typically prices for delivery over the nearest forward calendar month. 9 Contracts that stipulate physical delivery over shorter periods, including immediate physical delivery, are rare and typically for small quantities that can be moved by tanker truck. 8 More generally, storage may also be available at remote locations, in which case the availability of such remote storage will be determined by both storage and transportation constraints. 9 The CME group stipulates several methods by which the buyer can opt to receive physical delivery. At the buyer's option, delivery can be made by: (1) by inter-facility transfer ("pumpover") into a designated pipeline or storage facility with access to seller's incoming pipeline or storage facility; (2) by in-line (or in-system) transfer, or book-out of title to the buyer; or (3) if the seller agrees to such transfer and if the facility used by the seller allows for such transfer, without physical movement of product, by in-tank transfer of title to the buyer. Especially with the third option, physical delivery will effectively be instantaneous and subject only to the provision that the buyer has acquired the right to store oil in the tank/s used previously by the seller. 8

9 Let SCt,t+v,t+s represent the present value as of time t of the cost of storing one unit of the commodity from time t+v to t+s including transaction costs on the futures trades. 10 Let CVt,t+v,t+s designate the (assumed known) present value as of time t of the convenience yield from holding physical units of the commodity from time t+v to t+s. If Pt,t+s > [Pt,t+v + SCt,t+v.t+s CVt,t+v,t+s](1+rt,t+v,t+s) where rt,t+v,t+s is the interest rate from t+v to t+s, arbitrageurs can earn a riskless profit by simultaneously: (1) buying the near-term contract Pt,t+v, (2) shorting the longer term contract Pt,t+s, and (3) assuming storage capacity is available, arranging for storage from t+v to t+s. 11 An implicit assumption is that funding of the transaction is not constrained, which we will relax in the analysis presented in section 5. As arbitrageurs transact to capture the riskless profit, Pt,t+v should rise and Pt,t+s fall until Pt,t+s [Pt,t+v + SCt,t+v.t+s CVt,t+v,t+s](1+rt,t+v,t+s). Hence this arbitrage should ensure that: [Pt,t+s -Pt,t+v] [Pt,t+vrt,t+v,t+s + (SCt,t+v.t+s CVt,t+v,t+s)(1+rt,t+v,t+s)] (1) Ederington, Fernando, Holland, Lee, and Linn (2016) provide strong evidence in support of this arbitrage relationship for U.S. crude oil futures at the Cushing delivery point. Assuming trades and storage can be contracted the instant violations of equation 1 are observed, violations of equation 1 should be fleeting and only observable in high frequency data. However, if storage takes time to arrange (as explored in section 2.2 below), violations of equation 1 could arise but be temporary. If storage cannot be arranged immediately, a trader pursuing riskless arbitrage would need to wait to arbitrage the mispricing between the spot and futures contracts until storage becomes available. 12 In the latter case, the spread may continue to exceed the no-arbitrage upper bound in equation 1 until sufficient storage capacity becomes available. Assuming storage can be arranged, any temporary violation of 10 For ease of exposition, we disregard the possibility of storage at a location away from the hub, in which case any transportation costs between the delivery points for the t+v and t+s contracts need to be added to the transaction costs. 11 This trade is not completely riskless if the convenience yield is uncertain. For pedagogical simplicity we allow future storage costs to be uncertain but treat the convenience yield as uncertain but effect of uncertainty regarding either is basically the same. Nonetheless, risk cannot be completely eliminated due to physical and financial performance risk. 12 Speculators could execute a naked speculative transaction involving only the spot and futures trades, hoping that storage can be arranged in the future on terms that would not eliminate arbitrage profit. However, such transactions are not riskless. Ederington et al. (2016) show that most cash-and-carry arbitrage transactions in this market tend to be riskless. 9

10 equation 1 should be followed by a fall in the spread as arbitrage trades take place. 13 However if storage is at capacity, violations of equation 1 can persist. Our treatment of SCt,t+v.t+s in equation 1 warrants clarification. We recognize that both SCt,t+v.t+s and CVt,t+v,t+s are endogenous. In particular, as discussed below, SCt,t+v.t+s will tend to rise and CVt,t+v,t+s will tend to fall as inventories increase. Thus, it could be argued that if storage cannot be arranged immediately, the cost of storage is effectively infinite so that equation 1 always holds but this is void of any predictive content. To obtain predictive hypotheses, when we refer to equation 1 being violated, we are treating SCt,t+v.t+s as the cost of storage when it can be arranged. We next examine the no-arbitrage lower bound. Consider a trader who holds the commodity in inventory. If Pt,t+s < [Pt,t+v + SCSt,t+v.t+s CVt,t+v,t+s](1+rt,t+v,t+s) where SCSt,t+v,t+s is the saving on storage costs by not storing oil from t+v to t+s minus transaction costs, the trader can profit by simultaneously: (1) selling the oil for delivery at time t+v at Pt,t+v and (2) purchasing for delivery at time t+s for Pt,t+s. This frees up storage from time t+v to t+s. If alternative uses for the storage can be arranged immediately or SCSt,t+v,t+s is known, this arbitrage is riskless and arbitrage should ensure that: [Pt,t+s -Pt,t+v] [Pt,t+vrt,t+v,t+s + (SCSt,t+v.t+s CVt,t+v,t+s)(1+rt,t+v,t+s)] (2) Note that this lower bound on the spread may be either positive or negative. 14 If alternative storage uses cannot be arranged immediately and SCSt,t+v,t+s is uncertain, this trade is risky unless the trades are delayed until alternative uses for the storage have been arranged. Therefore, it is possible that inequality (2) is violated temporarily. If inventories are depleted so that there is no oil to sell for delivery at time t+v, then the violation of equation 2 may persist longer. 13 Additionally, temporary violations of arbitrage bounds could occur because of inattentive traders (Duffie, 2010) or lack of sufficient financial traders in the market, which is also inhabited by physical traders who have traditionally dominated the market. 14 In commodity futures market analyses, it is sometimes assumed that (1) transaction costs are negligible, and (2) any storage costs can be completely recaptured if the storage is not used so that SCS t,t+v,t+s = SC t,t+v,t+s and hence [P t,t+s -P t,t+v] = [P t,t+vr t,t+v,t+s + (SC t,t+v.t+s CV t,t+v,t+s)(1+r t,t+v,t+s)]. However we argue in section 2.2 below that in commodity markets, and crude oil in particular, SCS t,t+v,t+s is generally less than SC t,t+v,t+s either because transaction costs are not negligible or because storage costs cannot be totally recouped if the storage is unused. Hence there is normally a gap between the upper and lower spread limits in equations 1 and 2. 10

11 2.2. Storage and storage costs If oil is purchased for delivery at time t+s and sold for delivery at time t+v in a cashand-carry arbitrage, storage must be arranged for the time period between t+s and t+v. Since the availability and cost of storage are important to our analysis, it is helpful to summarize relevant characteristics of crude oil storage. Once produced, crude oil may be stored in tank farms, underground caverns, refineries, and pipelines, or off-shore in tankers. Particularly important for our purpose are storage levels and costs at the pricing point and delivery hub for the WTI futures contract, which is in Cushing, Oklahoma. Ederington et al. (2016) find that most arbitrage in the WTI crude oil market entails Cushing oil inventories. The U.S. Energy Information Administration (EIA) estimates the working capacity of tank farms in the U.S. at million barrels as of September 2015 of which 73 million barrels, or 18.0%, are at Cushing, making it the largest oil storage facility in the world (EIA, 2015, ). Cushing, labeled the pipeline capital of the world, is connected to crude oil production facilities and oil refineries throughout the United States through an extensive pipeline network. Oil is stored in Cushing for operational, arbitrage, and speculative purposes. While anecdotal and media reports appear from time to time about investment banks and other oil traders leasing storage at Cushing for arbitrage and speculative purposes (see, for example, Leff, 2015), hard data is unavailable. However according to the EIA, in spring 2015 approximately 80% of the storage at Cushing was leased by the owner-operators to others while the percentage leased to others at other tank farms in the U.S. was only about 29%. Storage away from Cushing entails additional transportation costs or additional risk to arbitrage using crude oil futures since the delivery point for the NYMEX oil futures contract is Cushing. 15 This suggests that much of the storage at Cushing is leased for arbitrage or speculative purposes. Storage capacity at Cushing has grown considerably over the last decade. The EIA reports that working capacity increased from 46.0 million barrels in September 2010 to 71.4 million in March Capacity figures prior to 2010 are unavailable but the maximum held in storage prior to January 2006 was only 22.8 million barrels. The business media commonly attribute at least 15 Nonetheless, the press has published articles describing crude oil being stored on floating tankers in conjunction with arbitrage trades (See, for example, Kent and Kantchev, 2015). However, a precise time series of tanker storage data is not available. 11

12 some of this storage construction to demand for storage by WTI futures traders (see, for example, Blas, 2015, and Kaufman, 2015). Storage contracts at Cushing and elsewhere are typically over-the-counter and thus may require some time to arrange. 16 Moreover, they have counterparty risk, force majeure and physical delivery risk elements that are not present in purely financial arbitrage trades, which may discourage or delay the actions necessary to implement the arbitrage trades. If delayed, spreads above the no-arbitrage limit may persist until storage can be arranged. 17 Unfortunately, historical figures for the storage cost measures SCt,t+v,t+s and SCSt,t+v,t+s are unavailable so we cannot directly test for violations of equations 1 and 2. Instead, as explained below, we test for indirect evidence of violations and consequent market corrections by examining changes in the futures-spot spread. Average crude oil storage costs at Cushing are commonly estimated around $0.40 to $0.50 per barrel per month but reportedly vary considerably depending on capacity utilization. 18 If a trader wants to execute an arbitrage transaction but has not yet leased storage capacity, the cost to him is the storage cost per barrel stated in the new lease. If a trader has already leased storage, what matters to him in considering a particular arbitrage possibility is the storage unit s opportunity cost, which will vary with capacity utilization and quite possibly across individual traders. Consider, for instance, a trader who has leased storage capacity for a year at $0.50 a barrel/month. After the lease is signed, the $0.50 becomes a sunk cost and what then matters is the marginal opportunity cost of using the storage capacity. Depending on whether it is possible to re-lease the unused storage capacity, this marginal opportunity cost may vary from zero to the re-lease rate. Moreover the unused storage has an option value. If the trader institutes a cash and carry arbitrage as soon as the spread widens sufficiently to make the arbitrage profitable and hence fills his storage units to capacity, he loses the option to conduct the arbitrage on even more favorable terms in the future if spreads should widen 16 The CME has recently launched an oil storage futures contract at the Louisiana Offshore Port but not as yet for storage at Cushing. 17 Faced with an apparently profitable futures-spot spread that exceeds expected storage costs, some traders may trade the futures and spot immediately. In doing so, they accept the risk that storage cannot be arranged or will be more expensive than anticipated and the trade will remain a speculation unless and until the exposure is covered in the physical market. 18 Private communication with a company specializing in oil and petroleum product storage confirms that the typical price has been about $.50/barrel per month but that the cost increases whenever the market is in contango, suggesting those are periods in which demand for storage capacity is high. 12

13 further. Thus, in this case, SCt,t+v,t+s is hard to measure and may vary across traders but undoubtedly varies positively with capacity utilization. While storage costs likely vary positively with capacity utilization, the convenience yield likely varies inversely as Einloth (2009), Gorton, Hayashi, and Rouwenhorst (2013) and others point out, reinforcing the tendency for the upper no-arbitrage bound in equation 1 to vary positively with capacity utilization levels. Gorton, Hayashi, and Rouwenhorst (2013) argue that the convenience yield in commodity futures should vary inversely with inventory levels since low inventory levels increase price volatility. Consistent with this, using data for 33 commodity markets, they find that: 1) the cash-futures basis is an inverse function of inventory levels, and 2) returns to a strategy of holding long futures positions are positive and inversely correlated with inventory levels. Turning to reverse-cash-and-carry arbitrage, the storage cost savings if the trader draws down his inventory, SCSt,t+v,t+s, depend on whether the storage tank can be re-leased or used for other purposes since he will pay the storage cost per barrel of leased capacity whether he has oil stored or not. If it cannot be re-leased, SCSt,t+v,t+s is zero. Since we hypothesize that arbitrage possibilities are limited by available storage capacity and that storage costs vary directly with capacity utilization, we need measures of both actual storage levels and storage capacity at Cushing. Since the EIA began reporting actual weekly Cushing storage levels in April 2004, our data period begins April 5, The EIA began surveying and reporting storage capacity figures semi-annually in September Since the EIA s capacity figures cover only the latter third of our data period and only estimate shell and working capacity, not effective capacity, we use as our primary proxy for effective capacity a measure based on historical peaks in actual storage. In Figure 1, we chart Cushing estimated working storage capacity levels and actual storage levels from April 2004 to April 2015 on a logarithmic scale. ***Insert Figure 1 about here*** Searching for the lowest number of peaks or inflection points for a linear spline 19 Prior to that time the Cushing figures were lumped into those for the Midwest region. 20 The EIA reports both shell capacity and working capacity where the latter lower figure adjusts for the fact that oil at the bottom of the tank is not obtainable and that the tanks cannot be filled to the very top. Both the EIA and others stress that the unknown effective capacity is less than either figure since some space is required for effective operation. 13

14 function, which bounds all observed storage levels with inflection points at the chosen peaks, yields the linear spline with peaks at 4/18/2005, 2/2/2009, 1/4/2013, and 4/3/2015 shown as the solid blue line in Figure 1 where we also graph actual storage levels. We use this log linear function as our initial and primary proxy for computing effective storage capacity. In section 7, we also use the EIA measures of working capacity for the October 2010 April 2015 sub-period for which these figures are available Storage and spreads Initial evidence According to the analysis in section 2.l, large positive spreads between the prices of contracts for longer-term and near-term delivery should only persist when storage levels approach capacity so that arbitrageurs find it difficult or impossible to arrange storage. Initial evidence on this is presented in Figure 2 where we chart 10-day moving averages of both capacity utilization and the futures-spot spread. ***Insert Figure 2 about here*** Capacity utilization is measured as the ratio of the actual level of crude oil stocks as reported by the EIA to the proxy for effective storage capacity described in section 2.2. The futures-spot spread in Figure 2 is measured as the difference between the price of the second and nearby futures contracts. As predicted, Figure 2 shows that large positive futures-spot spreads are generally associated with high levels of capacity utilization Hypotheses While Figure 2 indicates that high futures-spot spreads are generally associated with high levels of capacity utilization, this does not necessarily indicate that physical limits to arbitrage were a constraint since other factors could account for the correlation in Figure 2. For instance, an unexpected short-term decline in the demand for crude oil which is not expected to persist could lead to both an increase in crude oil inventories and a disproportionate decline in the spot price, and therefore an increase in the spread. For further evidence on the effect of arbitrage and its limits, we analyze the behavior of the futures-spot spread across time. Ideally, if we could observe the storage cost and convenience yield terms, SCt,t+v,t+s, SCSt,t+v,t+s, and CVt,t+v,t+s, in equations 1 and 2, we could 14

15 explore how they change as storage levels approach capacity and test for violations of equations 1 and 2. However, as explained in section 2.2 those data are unobservable. Consequently, we test for arbitrage and its limits based on the behavior of the futures-spot spread. Consider the implications of the analysis in section 2.1 for the behavior of the futuresspot spread. As long as the futures-spot spread is between the upper bound defined by equation 1 and the lower bound defined by equation 2, arbitrage should not occur. In this case, if markets are weak form efficient and news arrives randomly, the change in the spread one day should be independent of previous spread changes. However, if a change in the spread in period t-1 carries the spread above the no-arbitrage bound, this should set off arbitrage in which arbitrageurs buy for delivery in the near-term and sell for delivery in the longer-term resulting in a decline in the spread in period t. Likewise, a fall in the spread below the no-arbitrage upper bound in period t-1 should set off arbitrage that raises the spread in period t. Thus, we expect successive changes in the spread to be uncorrelated within the upper and lower no-arbitrage bounds and negatively correlated outside the noarbitrage bounds. Testing for evidence of arbitrage based on spread autocorrelations is complicated by the fact that we cannot observe storage costs, transaction costs, the convenience yield, or the storage cost savings when storage levels are reduced, and so we cannot compute the upper and lower no-arbitrage bounds. However, we expect storage costs to vary directly and the convenience yield to vary inversely with storage capacity utilization and thus, the upper bound should rise as capacity utilization rises. In addition, for given values of the noarbitrage bounds, the likelihood that a change in the spread leads to a violation of the upper or lower bounds should depend on the sign and size of both the change in the spread and its 15

16 prior level. 21 For instance, suppose the period t-1 change in the spread is positive. In this case, it is more likely that it crosses the upper bound and thus leads to a fall in the spread in period t if the spread level at the beginning of period t-1 is positive and high than if the spread at the beginning of period t-1 is negative or low. Likewise, a given decline in the spread in period t-1 is more likely to cross the lower bound, and thus lead to a rise in period t, if the spread at the beginning of period t is already negative or low. This leads to our first hypothesis: H1: If there are no limits to arbitrage, an increase (decrease) in the futures-spot spread should be more likely to lead to arbitrage and a subsequent fall (rise) in the spread if the spread is already high (low). It is not clear a priori whether we should observe this predicted autocorrelation pattern in weekly, daily, hourly, or higher frequency data. If the arbitrage can be arranged almost instantaneously, then we should observe these patterns only in high frequency data if at all. However, we have argued above in sections 2.1 and 2.2 that, when the spread rises above the upper bound, risk or the inability to arrange storage may lead arbitrageurs to delay going long in the near-term contract and shorting the longer-term contract until they can contract for storage. Thus it may take hours or days until the spread change reverses. We test for arbitrage patterns in daily data. We have argued above that there are likely physical limits to arbitrage. When storage is near capacity, both storage costs and the lead time required to contract storage will likely increase. Given these difficulties in storage contracting when storage is near capacity, a 21 To see this, suppose the upper bound is fixed and equal to U. Suppose also that at t-1 the actual spread equals A. The distance to U therefore equals U-A. The narrower the gap the smaller is the required change in the spread before the upper bound is breached. Assume arbitrage opportunities arrive randomly (that is the change in the spread arrives randomly each period) and that the size of the change is a drawing from a stationary distribution with mean 0 and constant variance. The probability that U will be breached given U and A equals the probability that the change will exceed U-A. To illustrate, suppose the change in the spread is a drawing 2 U A from a N(0, ) distribution. Therefore, the probability that the change will breach U equals Pr z, which is increasing in A since U is fixed. Conditional on the change equaling an arbitrary value P, the probability evaluated at t-1 equals Pr U A P z 16 which is increasing in P given U and A.

17 spread change reversing arbitrage is less likely, implying lower first-order autocorrelation. This leads to our second hypothesis: H2: When storage levels are at or near capacity, cash-and-carry arbitrage is more costly or difficult, thus if the futures-spot spread is positive and high, a further increase in the spread is less likely to be followed by arbitrage and a reversal in the spread. Similarly, if there is an inventory stockout or if inventories are at the minimum required for operational purposes, reverse cash-and-carry arbitrage, in which arbitrageurs sell from inventory in the spot market, cannot occur, leading to our third hypothesis: H3: When tradeable inventory levels are at or near zero, reverse cash-and-carry arbitrage is more costly or difficult, thus if the futures-spot spread is negative and low, a further decrease in the spread is less likely to be followed by arbitrage and a reversal in the spread. 3. Results 3.1. Data description and initial evidence. While futures and spot price data are available from 1983, our data period begins in April 2004 when the EIA began reporting crude oil stock levels at Cushing. We examine daily prices of NYMEX WTI crude oil futures contracts from April through May 6, 2015 obtained from the website of the Energy Information Administration. Descriptive statistics for the futures-spot spread measured as the difference between the prices of the second and nearby contracts are presented in Table 1 for both the level and daily changes in the spread. ***Insert Table 1 about here*** Interestingly, while Schwartz (1997) and Routledge, Seppi, and Spatt (2000) argue that in this market backwardation should be more common than contango, the market actually tended to be in contango over much of this period with the spread averaging $0.52, as shown in Panel A. The spread was positive on 76.5% of the observed days. With a standard deviation of $0.39, daily changes in the spread were fairly large. 17

18 Partial autocorrelations out to a four-day lag are reported in Panel B for both the spread and its components. Several patterns are worth noting. First, consistent with our arbitrage argument, there is evidence of fairly strong mean reversion with a first order autocorrelation of between changes on successive days. Clearly, there is a tendency for increases and decreases in the spread to be partially reversed on subsequent days. In the absence of arbitrage, this would seem to violate weak-form efficiency. Second, the spread displays considerably more mean reversion than either of its two components. The first order autocorrelation for the futures and spot price changes are only and respectively. This indicates that the mean reversion of the spread is not simply a reflection of mean reversion in the spot and futures prices due to some other cause such as bid-ask bounce. Third, while the first-order autocorrelation in spread changes is clearly the largest, there is also evidence of negative partial correlation at lags of two and three days. As we discussed above, it is unclear a priori how long it would take arbitrageurs to contract storage and thus how quickly arbitrage should reverse violations of the no-arbitrage bounds. If indeed the mean reversion observed in the spread is due to arbitrage, this indicates that most of the reversal takes place in one day but that full reversal may take several days Testing for evidence of arbitrage activity and physical limits to arbitrage According to the arbitrage hypothesis, mean reversion in the spread should be observed only when the change in the spread crosses the no-arbitrage bounds and then only if arranging the arbitrage transactions occurs with a lag. As long as the spread is fluctuating within the no-arbitrage bounds, weak form efficiency implies that there should be little, if any, autocorrelation. As discussed above, testing is complicated by the difficulty in measuring the no-arbitrage bounds. However, as we argued in section 2.4 and H1, an increase in the spread in period t-1 is more likely to cross the no-arbitrage upper bound, and thus lead to mean reversion in period t, if the spread is already positive and high than if it is negative or low. Likewise, a negative change in the spread is more likely to cross the noarbitrage lower bound leading to mean reversion if the spread is already low. To test this, we examine variations of a simple regression ΔSPt = β0 + β1δspt-1+et, The estimated β 1 = which is significant at the 1% level based on Newey-West standard errors. 18

19 where ΔSPt = SPt SPt-1 and SPt = Ft St with Ft being the futures price on day t and St being the spot price. We consider several variations. First, we divide the sample into (1) cases when the change in the spread and the beginning spread have the same sign and (2) cases when they have different signs. We define DSamet-1 =1 if ΔSPt-1*SPt-2 >0 and =0 otherwise. Thus DSamet-1 =1 if a positive spread at time t-2 is followed by a further increase in the spread at time t-1 or if a negative spread at time t-2 is followed by a further decrease at time t-1, i.e. if the spread at time t-2 and the change in day t-1 have the same sign. We define DDifft-1 =1-DSamet-1. Thus DDifft-1=1 if ΔSPt-1*SPt-2 <=0, i.e., if the spread change on day t- 1 is opposite in sign to the spread on day t-2. As reported in Table 2 DDifft-1=1 is slightly more common than DSamet-1=1 since it includes the cases when ΔSPt-1 or SPt-2 are zero. ***Insert Table 2 about here*** Second, we separate those cases when the change in the spread (at time t-1) and the beginning spread (at time t-2) have the same sign into two groups: contango, where both signs are positive (so that the upper bound might be violated) and backwardations, where both signs are negative (or zero) (so that the lower bound might be violated). DPost-1=1 if SPt-2>0 and ΔSPt-1>0 and zero otherwise and DNegt-1=1 if SPt-2<0 and ΔSPt-1<0 and zero otherwise. Table 2 shows that during our sample period DPos is more common than DNeg. Third, given that the spread is positive and in contango for 76.5% of the observations in our sample, we further divide the set when a positive spread is followed by a further increase in the spread into: (1) those cases when the time t-2 spread is positive but less than $0.50 and (2) those cases when the time t-2 spread is positive and greater than $0.50. We choose $0.50 since this is a common estimate of storage costs and since the median spread is $0.45. Specifically, we take cases where the spread is positive (SPt-2>0) and the change in spread is positive (ΔSPt-1>0) and define DPosLowt-1=1 if the spread is between 0 and $0.50, 0<SPt-2<=0.50, and zero otherwise and DPosHight-1=1 if the spread is above $0.5 (SPt-2>0.5) and zero otherwise. Fourth, we consider instances of contango where the spread is more likely to provide opportunities for arbitrage (positive, increasing and above $0.50) but storage capacity is exhausted. To test this, we define the dummy variable DCap_Utilt=1 if the ratio of actual Cushing storage levels announced by the EIA for that week divided by our estimate of 19