Arbitrage and Its Physical Limits

53 Pages·2017·0.75 MB·English

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 stock-
out conditions during our sample period. We also find that arbitrage was limited by financial
constraints over our 2004-2015 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: [email protected], [phone]; Fernando: [email protected],
[phone]; Holland: [email protected]; [phone]; Linn: [email protected] [phone].

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.
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 no-
arbitrage 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 2004-2015 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
Arbitrage and Its Physical Limits
“…contango would have to widen much more to signal real storage distress.”
Spencer Jakab, Wall Street Journal, December 2, 2015

1. 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).
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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 no-
arbitrage 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
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 no-
arbitrage 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 no-
arbitrage 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 cash-
and-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
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 2004-
2015 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 2004-2015
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
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 stock-
outs 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 non-
negativity 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
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 P designate the price at time t for delivery at
t,t+v
time t+v and P represent the time t price for delivery at time t+s where s>v. If t+v is the
t,t+s
first available delivery time, P may be referred to as the spot price and P -P as the
t,t+v t,t+s t,t+v
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 1-31. 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
Let SC represent the present value as of time t of the cost of storing one unit of
t,t+v,t+s
the commodity from time t+v to t+s including transaction costs on the futures trades.10 Let
CV designate the (assumed known) present value as of time t of the convenience yield
t,t+v,t+s
from holding physical units of the commodity from time t+v to t+s. If P > [P +
t,t+s t,t+v
SC – CV ](1+r ) where r is the interest rate from t+v to t+s, arbitrageurs
t,t+v.t+s t,t+v,t+s t,t+v,t+s t,t+v,t+s
can earn a “riskless” profit by simultaneously: (1) buying the near-term contract P (2)
t,t+v,
shorting the longer term contract P, , and (3) assuming storage capacity is available,
t t+s
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, P should rise and P fall until P ≤
t,t+v t,t+s t,t+s
[P + SC – CV ](1+r ). Hence this arbitrage should ensure that:
t,t+v t,t+v.t+s t,t+v,t+s t,t+v,t+s
[P -P ] ≤ [P r + (SC – CV )(1+r )] (1)
t,t+s t,t+v t,t+v t,t+v,t+s t,t+v.t+s t,t+v,t+s t,t+v,t+s
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
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 SC in equation 1 warrants clarification. We recognize that
t,t+v.t+s
both SC and CV are endogenous. In particular, as discussed below, SC will
t,t+v.t+s t,t+v,t+s t,t+v.t+s
tend to rise and CV will tend to fall as inventories increase. Thus, it could be argued
t,t+v,t+s
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 SC as the cost
t,t+v.t+s
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 P < [P + SCS – CV ](1+r ) where SCS,
t,t+s t,t+v t,t+v.t+s t,t+v,t+s t,t+v,t+s t 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 P, and (2)
t t+v
purchasing for delivery at time t+s for P This frees up storage from time t+v to t+s. If
t,t+s.
alternative uses for the storage can be arranged immediately or SCS is known, this
t,t+v,t+s
arbitrage is riskless and arbitrage should ensure that:
[P -P ] ≥ [P r + (SCS – CV )(1+r )] (2)
t,t+s t,t+v t,t+v t,t+v,t+s t,t+v.t+s t,t+v,t+s t,t+v,t+s
Note that this lower bound on the spread may be either positive or negative.14 If alternative
storage uses cannot be arranged immediately and SCS is uncertain, this trade is risky
t,t+v,t+s
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 = SC and
t,t+v,t+s t,t+v,t+s
hence [P -P ] = [P r + (SC – CV )(1+r )]. However we argue in section 2.2 below
t,t+s t,t+v t,t+v t,t+v,t+s t,t+v.t+s t,t+v,t+s t,t+v,t+s
that in commodity markets, and crude oil in particular, SCS is generally less than SC either because
t,t+v,t+s t,t+v,t+s
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