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The normal backwardation of Keynes and Hicks in Crude Oil Futures

Ronald D. Ripple

Mervin Bovaird Professor of Energy Business and Finance

School of Energy Economics, Policy, and Commerce

Collins College of Business

The University of Tulsa

Tulsa, Oklahoma, USA

Extended Abstract

The concepts of normal backwardation and normal contango are presented in terms of theory developed by Keynes (1930) and Hicks

(1946) and compared to current usage for backwardation and contango. The evolution of the forward curves for crude oil futures over

the 1995-2015 period is evaluated against the expectations of the relationships between hedgers’ net short positions and corresponding

risk premia. A series of error correction models based on autoregressive distributed lag (ARDL) specifications are estimated to

evaluate the relationships between the percent of open interest represented by net short hedgers and the slope of the forward curve,

which proxies risk premium. A significant long-run positive relationship is found. Support is also found for Samuelson’s (1965)

prediction that near-maturity futures prices will be more volatile than more distant maturities based on the speed of adjustment

coefficient estimates of the error correction specifications.

Keywords: normal backwardation, normal contango, autoregressive distributed lag, error correction, oil futures, forward curves.

Introduction

Keynes (A Treatise on Money, 1930) is credited with introducing the concept of backwardation into the economist’s lexicon, and

Hicks (Value and Capital, 1946) provides additional clarity. The form of backwardation put forward by these two influential writers is

often referred to as normal backwardation, and this may be distinguished from the current common usage of the stand-alone term,

backwardation.

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Normal backwardation refers to the relationship between the current futures price for a commodity to be delivered at some future

time, T, and the current expectation for the future spot price at T. This is distinct from the current usage of backwardation which

relates the current futures price for a commodity to be delivered anytime in the future to the current spot price or nearer maturity

futures price.1

The current common usage of the terms backwardation and contango may be represented as backwardation holding when ,t t T

S F and

contango holding when ,t t T

S F , where S is the current spot price, F is the futures price, t is the present time period, and T is the future

date at which the futures contract matures. These relationships imply that the forward curve of futures prices will be downward

sloping for backwardation and upward sloping for contango. Alternatively, normal backwardation and normal contango require these

slope conditions but require further that , ,t T t T

ES F holds for both, where ,t T

ES is the expectation at time t for the future spot price at

date T. Therefore, normal backwardation requires ,t t T

S F and , ,t T t T

ES F , while normal contango requires ,t t T

S F and , ,t T t T

ES F .

Therefore, normal backwardation/contango provides for an explicit representation of a risk premium (or insurance, in the words of

Keynes), while the current usage does not.

Keynes’ theory of normal backwardation relates hedgers’ futures positions to the risk premium (insurance) necessary to attract

sufficient speculative activity to support risk mitigation demand. The fundamental assumption is that hedgers are typically net short in

the futures contract for their commodity and speculators are therefore net long. Being net long, it is argued that the current futures

price for delivery at time T will be below the spot price expected to hold at time T, so that the speculators who are providing a risk

mitigation service may expect to earn a positive return. Moreover, there is a positive relationship between hedgers’ net short positions

and the necessary risk premium.

The current paper diverges from the typical literature related to backwardation,2 and its alternative contango, and seeks to determine

whether or not this fundamental condition and its relationship to normal backwardation and normal contango, as stated by Keynes and

Hicks, does or does not hold. That is, the paper examines the relationships between hedgers’ net short positions and the slopes of

forward curves, and tests for the posited relationships between net short positions and required risk premium.

The specific commodity to be examined is crude oil, and the forward curves to be examined are those for the futures contracts traded

on the New York Mercantile Exchange (NYMEX). The data to be employed for this analysis are drawn from both NYMEX futures

1 This distinction also holds when one constructs a discounted forward curve, taking into consideration the time value of money over the term structure. The

relationship between the discounted forward curve and the current spot price falls into the same category as the current interpretation of backwardation, since the

spot price of interest is the current spot rather than the expected future spot. 2 See for example, Considine and Larson (2001) and Charupat and Deaves (2002).

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price data and the Commitment of Traders (COT) database collected and published by the Commodity Futures Trading Commission

(CFTC). The COT database contains information on the open interest (OI) positions of large traders, which have been partitioned into

commercial and non-commercial trader categories. The CFTC data are reported weekly, and they are date-matched to the forward

curves for each of the NYMEX crude oil futures contracts. The analysis evaluates the relationship between the net short open interest

positions of the large commercials (hedgers) and the shape of the forward curve over the period from January 1995 through December

2015. This commodity represents a significant input into global economic activity, the futures contract for crude oil is the most heavily

trade commodity contract globally, and it provides a challenging testing ground for this theory given the swings from contango to

backwardation (in current usage), and back, over the period.

The paper examines the net short positions of hedgers, as characterized by those large traders with a commercial interest in the traded

commodity, to determine both whether or not the fundamental assumption held by Keynes and Hicks has been met over the 1995-

2015 period and how the distributions of open interest positions relates to the observed evolving shapes of the forward curves for

crude oil.

The paper proceeds by presenting the theory of normal backwardation and contango of Keynes and Hicks. This is followed by a

discussion of the empirical model and testing procedures. The data used are then presented, and this is followed by the empirical

results. The paper closes with a summary and conclusions.

The theory

The general backwardation or contango character of the forward curve is often related to the balance of current demand and supply

relative to that expected in the future. If supply is relatively limited currently, spot prices will tend to be higher than those expected to

hold in the future, and backwardation will be expected. The reverse holds for current surplus of supply, leading to contango. However,

normal backwardation, according to Keynes and Hicks, is driven by one fundamental relationship; the normality of hedgers being net

short in their commodity contracts. This sense of normal activity in the market for commodities drives the expected relationship

between the forward/futures price for delivery date T and the spot price expected to hold at that date. Since the commercial

participants in the commodity market, with market risk exposure, will normally be out of balance in terms of the desired levels of long

and short hedging positions, speculators must be attracted to the market. Such speculators are said to be attracted to the market by an

expectation of profit just sufficient to provide “fill the gap” between long and short hedgers. The expectation of profit is determined by

the relationship between the current market price for the futures contract for delivery at date T and the speculators’ (and perhaps the

entire market’s) expectation for the spot price that will hold at time T.

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Also, Keynes (1930, p. 143) states, “[b]ut it is not necessary that there should be an abnormal shortage of supply in order that a

backwardation should be established. If supply and demand are balanced, the spot price must exceed the forward price by the amount

which the producer is ready to sacrifice in order to ‘hedge’ himself, i.e. to avoid the risk of price fluctuations during his production

period. Thus in normal conditions the spot price exceeds the forward price, i.e. there is backwardation.”3

The relationship also must hold between the futures price and the associated expected future spot price for an observed contango to be

termed a normal contango. Indeed, Keynes (1930, p. 144) states, “[b]ut the existence of a contango does not mean that a producer can

hedge himself without paying the usual insurance against price changes. On the contrary, the additional element of uncertainty

introduced by the existence of stocks and the additional supply of risk-bearing which they require mean that he must pay more than

usual. In other words, the quoted forward price, though above the present spot price, must fall below the anticipated future spot price

by at least the amount of normal backwardation; and the present spot price, since it is lower than the quoted forward price, must be

much lower than the anticipated future spot price.”4

Keynes implies that hedgers will be net short in their forward markets, as is evident from the requirement to attract speculators by

“paying the usual insurance”. Hicks (1946, p. 137) provides more context for this situation to be deemed normal by noting, “[n]ow

there are quite sufficient technical rigidities in the process of production to make it certain that a number of entrepreneurs will want to

hedge their sales for this reason…But although the same thing sometimes happens with planned purchases as well, it is almost

inevitably rarer…” In other words, we expect short hedgers to dominate long hedgers, creating a void to be filled by speculators.

Hicks (1946, p. 138) states further that “[b]ut for this very reason forward markets rarely consist entirely of hedgers.”

Moreover, speculators are expected to reduce the divergence between the expected future spot price and the futures price for the same

future date. In the absence of speculators, the larger the initial imbalance between short and long hedgers, the larger will be this

divergence. Since in futures markets there cannot exist an imbalance between short and long positions, the futures price that could be

asked by short hedgers, for any given expected spot price, will have to fall to attract sufficient long hedgers, who according to Hicks

are less motivated to hedge. Effectively, supply (of futures positions) is initially exceeding demand, so the futures price must fall to

reach equilibrium. In terms of hedging services, this situation implies that the demand (coming from shorts) for risk mitigation

services exceeds the supply (coming from longs), again in the absence of speculators, so the price paid for risk mitigation services will

3 It is occasionally noted that Keynes frequently requires some careful interpretation; a role that Hicks played on many occasions. Here some clarity also must be

introduced, given the distinctions between normal backwardation and the current backwardation usage, and for consistency across Keynes discussions of these

topics. When Keynes says “backwardation” he means his normal backwardation. And when he says supply and demand are balanced he is talking about the

supply and demand for futures/forward positions (longs = shorts). And, when he says “the spot price” must exceed the forward price, he is talking about the

expected spot price at the maturity date of the forward, which is central to his normal backwardation. 4 This is contrary to the popular interpretation reflected in Hull (2002, p. 28): “…when the futures price is above the expected future spot price, the situation is

known as contango. (Bold emphasis added.)

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be pushed upward, i.e., there will be a larger risk premium as captured by the difference between the expected future spot price and

the futures price for that date.

However, if speculators may enter the market to fill this initial void, they will bid up the price of the futures, or bid down the risk

premium, associated with a given expected future spot price. This may be viewed as either the speculators increase the demand for the

commodity or increase the supply of risk mitigation services.5 An alternative way to think about these relationships is that we typically

expect speculators to be less risk averse than hedgers, which would imply that speculators will be willing to enter the market for a

lower risk premium than will long hedgers. Therefore, the divergence between the expected future spot price and the futures price will

tend to be less when speculators are present. This conclusion follows from Hicks (1946, p. 138) where he states that, “…their

[speculators] action tends to raise the futures price to a more reasonable level.”

Nevertheless, while the introduction of speculators will tend to reduce the risk premium that would otherwise hold, it will still be

necessary for hedgers to increase the risk premium to attract more speculative activity to the market to provide more risk mitigation

service. That is, an increased demand for risk mitigation services will only be satisfied if there is a willingness to pay a higher risk

premium.

As a result, it should be expected that the larger the proportion of the total market that is represented by net-short hedgers, i.e., the

greater the hedging pressure, the larger the insurance that must be paid to attract the required speculators. An increase in the share of

the open interest attributed to net short hedgers implies an increase in the demand for the supply of risk mitigation services provided

by speculators, and this should only be expected to be provided at a price, i.e., an increase in the aforementioned differential, albeit at

a lower price than by long hedgers alone.

The model developed here is informed by these relationship expectations put forward by Keynes and Hicks, and also elaborated on by

Kaldor (1939, where references to Hicks are in the context of Hicks’ first edition, 1939, of Value and Capital). In brief, the normal

economic relationship that underpins the concepts of normal backwardation and normal contango is the tendency for hedgers in the

forward/futures markets for commodities to be net short. Moreover, the larger the proportion of the futures market represented by net

short positions by hedgers the larger should be the expected differential between the futures price for delivery at time T and the

expected future spot price at time T. For a given expected future spot price, this will result in steeper backwardation or flatter

contango.

5 It should be emphasized that speculators do not come to the futures markets for the purpose of providing insurance services to hedgers. They come to these

market with the expectation/hope of making a profit, and it is purely an ancillary benefit to the hedgers that there is sufficient interest from speculators to be on

the opposite side of the deals where they are looking to hedge.

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Normal backwardation/contango is therefore a function of the net short positions of hedgers. And, the degree of normal

backwardation/contango is a function of the proportion of the futures market represented by net-short hedgers. The “degree” of normal

backwardation/contango should be understood to mean the relative divergence between the expected future spot price and the lower

futures price, which, ceteris paribus, may be captured as the steepness of the slope of the futures-price forward curve.

According to the theory, hedgers being net short is consistent with both normal backwardation and normal contango, so a relationship

must be identified that relates the hedgers’ net positions to the slope of the forward curve that captures the theoretical link between net

short hedging and unobserved risk premium.

Assume a risk premium exists, such that 𝐸𝑅𝑃𝑡𝑇 = ln(𝐸𝑆𝑡

𝑇) − ln(𝐹𝑡𝑇) > 0. For ∆𝐸𝑅𝑃𝑡

𝑇 > 0, we will have ∆[ln(𝐸𝑆𝑡𝑇) − ln(𝐹𝑡

𝑇) > 0,

which can occur under five conditions:

(a) ∆𝐸𝑆𝑡𝑇 > 0 and ∆𝐹𝑡

𝑇 < 0,

(b) ∆𝐸𝑆𝑡𝑇 > 0 and ∆𝐹𝑡

𝑇 = 0,

(c) ∆𝐸𝑆𝑡𝑇 > 0 and ∆𝐹𝑡

𝑇 > 0, with ∆𝐸𝑆𝑡𝑇 > ∆𝐹𝑡

𝑇,

(d) ∆𝐸𝑆𝑡𝑇 = 0 and ∆𝐹𝑡

𝑇 < 0, and

(e) ∆𝐸𝑆𝑡𝑇 < 0 and ∆𝐹𝑡

𝑇 < 0, with |∆𝐸𝑆𝑡𝑇| < |∆𝐹𝑡

𝑇|

Only condition (e) is likely to be relevant to an increase in the net short positions of hedgers. To see this, consider the following.

Assume the market is in equilibrium such that the risk premium being charged/earned clears the market for hedging services. Now, if

hedgers increase their net short positions, they are effectively bringing more of the commodity onto the market for sale in period T,

which will tend to decrease the expected future spot price. However, the act of shorting more futures contracts requires that more

speculators (and/or long hedgers) be attracted to take the matching long positions, and this will occur only if the equilibrium risk

premium is increased. Therefore, both the expected future spot price and the futures price will fall. However, since the risk premium

must increase to attract more long-position takers, the futures price will have to fall by more than the expected future spot price.

What market conditions are likely to stimulate an increase in net short positions, relative to long positions, by hedgers? First, the

market may conclude that the expected future spot price will decline because of either expected demand declines or supply increases.

So, the short hedgers are faced with changed market expectations that have a negative impact on their expected future profits, and they

react by acquiring more insurance, that is, they short more contracts.6 Alternatively, but likely inter-connectedly, producers find they

will be able to bring more commodity to market than previously thought, and they seek to increasing their hedging operations

6 This is because they may have limited ability to reduce output.

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accordingly. A third possible driver is a change in hedging preferences, which could be tied to greater comfort with the use of these

derivatives instruments for risk mitigation. So, whether the increase in hedgers’ net short positions is the result of a changed

expectation for future spot prices or changed hedging preferences, the result will be the same.

On the other hand, it is difficult to conceive of a circumstance when we would have both an increase in hedgers’ net short positions

and an increase in the expected future spot price. If hedgers were pure hedgers, those who are insensitive to expectations on future

spot prices, they will only change their hedging position to match their actual change in exposure, and perhaps a change in hedging

preferences. If hedgers’ net positions become more short as a result of pure hedging pressures, this will be most likely associated with

a decline in the expected future spot price, because it implies that more supplies of the commodity will be being delivered to the

market at time T. And, if hedgers do actively consider the expected future spot price when making their hedging decisions, an

expectation of increasing future spot prices will not be associated an increase in short hedging; these hedgers will withhold some share

of their exposure to take advantage of the expected rise in the price of the commodity to be sold. Therefore, conditions, (a), (b), and

(c) are quite unlikely to apply to an analysis of a market where hedgers’ net short positions are increasing.

Finally, condition (d) is also unlikely to be applicable. Pure hedgers will not pay attention to expected future spot price, but if they do

bring more supplies to market, the most likely effect will be for expectations of declining future spot prices. And, if the hedgers do pay

attention to expected future spot prices, the lack of change in expectations will not provide any basis for them to change their hedging

positions from the existing equilibrium levels.

A similar set of five conditions may be developed with reversals in direction or inequality of relative change for a ∆𝐸𝑅𝑃𝑡𝑇 < 0. The

equivalent condition to (e), for a decrease in hedgers’ net short positions7, is: (e´) ∆𝐸𝑆𝑡𝑇 > 0 and ∆𝐹𝑡

𝑇 > 0, with ∆𝐸𝑆𝑡𝑇 < ∆𝐹𝑡

𝑇.

The expected risk premium is assumed to be time sensitive, in that it is expected that 𝐸𝑅𝑃𝑡𝑚 > 𝐸𝑅𝑃𝑡

𝑛 for 𝑚 > 𝑛, where m and n

indicate maturity dates. It is also expected that for a given change in hedging pressure (represented below as the percentage of open

interested account for by net short positions, phns) ∆𝐸𝑅𝑃𝑡𝑚 > ∆𝐸𝑅𝑃𝑡

𝑛 for 𝑚 > 𝑛. Following from these conditions, it is expected that

an increase in the unobserved ERP will tend to lead to a steepening of the forward curve.

A specification for the relationship between hedgers’ net short positions and the slope of the forward curve may be employed to test

the Keynes-Hicks theory with an unambiguous expectation of a positive relationship. This may be represented generally as

7 Remember that a decrease in net short positions implies that less product is being brought to market at time T. Furthermore, the specification of net short

positions is robust to conditions where hedgers are net long; the value of the variable will be negative.

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( )s f phns (1)

where: s is the spread between the near-month futures price and that of a distant maturity

phns is the percentage of open interest implied by hedgers net short positions

For the present date, t, and maturity date, T, ,1 ,

ln( ) ln( )T

t t t Ts F F , phns hns OI , and hns hs hl , where hs and hl are hedgers’

short positions and hedgers’ long positions, respectively. s provides a proxy for the slope of the forward curve. As defined, s>0

implies backwardation, s<0 implies contango, and phns>0 implies hedgers are net short.

A linear representation of this relationship is

T

t ts phns (2)

where: s phns , which is expected to be positive. That is, as the hedgers’ net short positions as a percentage of open interest

increases (i.e., hedging pressure increases), it is expected that the spread, s, will increase, representing the expected increase in risk

premium; i.e., we get a steeper backwardation or flatter contango.

The expectation noted above whereby 𝐸𝑅𝑃𝑡𝑚 > 𝐸𝑅𝑃𝑡

𝑛 for 𝑚 > 𝑛 implies that 𝑠𝑡𝑚 > 𝑠𝑡

𝑛 for 𝑚 > 𝑛 . And further, that ∆𝐸𝑅𝑃𝑡𝑚 >

∆𝐸𝑅𝑃𝑡𝑛 for 𝑚 > 𝑛 implies ∆𝑠𝑡

𝑚 > ∆𝑠𝑡𝑇 for 𝑚 > 𝑛 for a given ∆𝑝ℎ𝑛𝑠. The implication is that a change in hedging pressure is

expected to be revealed by a change in the slope of the forward curve through its effect on the expected risk premium.

The empirical model and testing procedures

A series of error correction models based on autoregressive distributed lag models are specified to test the theoretical relationships

between hedgers’ net short positions and the spreads of the forward curves for different futures maturities. This specification will

provide estimates of both the long-run relationships between the variables and the speed of adjustment of the slope to changes in

hedgers’ net short positions. The models will also allow comparison across maturities.

The relationships between the spread and the proportion of open interest represented by hedgers’ net short positions are modelled as

ARDL(p,q),

0 1( , ) ( , )T

t t tL p s L q phns u (3)

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where L is the lag operator, p and q are the numbers of lags, s is the spread, phns is the percent of open interest accounted for by

hedgers’ net short positions, and u is a disturbance term.

The ARDL approach8 has been shown to produce cointegration vector estimates that are equivalent to those from error correction

models, see Hassler and Wolters (2006). Pesaran et al. (2001) have demonstrated that the ARDL bounds approach may be employed

to test for the existence of a long-run “forcing” relationship between and among variables regardless of whether they are I(0), I(1), or

fractionally integrated. The long-run relationship of the levels variables is tested employing a non-standard F-statistic evaluated

against a band of critical values. If the test statistic exceeds the upper limit of the critical-values band, a long-run relation cannot be

rejected.9 This approach is used here.

Once the existence of a long-run relationship is established the optimal lag lengths, p and q, for the ARDL(p,q) specifications may be

determined.10 The resulting long-run coefficient estimates may then be employed to estimate an error correction model.

The error correction model associated with Equation 3 may be written as follows:

ˆ ˆ1 1

1 01 1

p qT T T

t t t j t j j t j t tj j

s EC phns s phns w u

(4)

where ECt is the error correction term

T T

t t t tEC s phns w

and w are deterministic variables (in this case the intercept, a trend, and three dummies to capture abnormally large spikes in

the slopes in early 2009).

8 The ARDL methodology has a long history of application to a range of economics questions, including the savings-investment relationship, the trade-GDP

relationship, international reserves accumulation and exchange rate intervention, and recent renewed application to energy-related questions. See for example,

Hendry et al. (1984), Bentzen and Engsted (2001), De Vita and Abbott (2002), Pahlavani et al. (2005), Kollias et al. (2006), Vita, Endresen, and Hunt (2006), and

Ramachandran and Srivinsan (2007). 9 While this approach can identify long-run relationships in levels variables, regardless of the degree of integration, to discuss the long-run “forcing” relationship

inn terms of cointegration it is still required that the dependent variable be I(1). In the case of the variables under study in this paper, all series are I(0).

10 Optional tests include an 2R test, the Akaike Information criterion (AIC), the Schwartz Bayesian criterion (SBC), and the Hannan-Quinn criterion (HQC).

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Equation (4) implies that when 0T

tEC the spread (slope) will react by decreasing to return to the equilibrium, long-run relationship,

and vice versa.

The results from these testing procedures will provide estimates of the long-run relationship between s and phns, i.e., estimates of ,

as well as estimates of the error correction coefficient, which provides an estimate of the speed with which the variables return to

equilibrium following a shock. As noted, it is expected that 0 . The magnitude of δ is expected to decrease as the time period

represented by the maturity of the contract increases. This expectation derives from Samuelson (1965) where it is proved that we

expect nearer maturity futures prices to be more volatile relative to more distant maturities. This may be represented in the error

correction representation by differing speeds of adjustment to common shocks, with the speed of adjustment for nearer maturities

being faster. This implies m n for m < n, where m and n represent time to maturity.

The data

The data used to construct the forward curves for this analysis are the futures prices for NYMEX crude oil contracts from January

1995 through December 2015. For each observation date, the forward curve represents the settlement prices for crude oil for each

contract maturity traded. The data for the percentage of net short open interest held by hedgers is taken from the CFTC database for

large traders; the Commitment of Traders (COT). These data are disaggregated into subsets for commercial, non-commercial, and

non-reporting, where the non-reporting are relatively small traders who are not required to report. As is typical when employing these

data, the positions of the large commercial traders are used to proxy hedger activity.

The frequency of observations is limited by the COT, which is reported on a weekly basis for Tuesday open interest. These data

represent an aggregate value for all contracts traded for a given commodity. Currently for crude oil the open interest associated with

any subset of the COT is for all contracts open for trading from the current March 2016 delivery to the December 2024 expiry, with no

means of disaggregating further to the individual contract level.

The analyses in this paper match the Tuesdays reporting of the CFTC, which provides 1,095 observations over the period. The series

are first “spliced” to provide continuous time series of expiring futures contracts. For crude oil on the NYMEX, the last trading day is

three business days prior to the 25th of the month in the trading month prior to delivery. As the last trading day nears, the volume of

trade and the open interest in the near-month contract wanes quickly, and prices frequently become more volatile. As a result there

may be a considerable disconnection between the price for the near-month contract and that for the rest of the forward curve as the

market shifts its attention to the next-to-near-month contract. The analysis in this paper evaluates the spread (or slope of the forward

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curve) as the relationship between the near-month contract price and successive, later-dated maturities; the spot price is not used, so

the analysis will be sensitive to the unusual volatility on the near-month contract prices.

The splicing method employed aims to produce a series that represents the trading activity of the contract of most market interest on

each reported trading date. The method in this paper incorporates a three-step process. The first step employs an algorithm that shifts

the series from the near-month contract to the next-to-near month contract when both the trading volume and open interest of the next-

to-near month contract exceed those for the near-month. The second step employs an algorithm to determine if there are any instances

of contract reversal; that is once shifting to the next-to-near contract does the first algorithm lead to a return to the near-month

contract. The third step applies only when such a reversal occurs. In such a case, the data are manually inspected to set the roll

between contracts so as to produce a smooth, non-reversing (in the sense of flip-flopping between maturities) series that represents the

contracts upon which the market was focused; this occurred fewer than 20 times over 5,256 daily observations, and only four of these

involved a Tuesday.

The forward curve analysis is conducted for contract maturities of two months, three months, six months, and nine months, i.e., T = 2,

3, 6, and 9. Table 1 shows the concentration of trading activity accounted for by these contracts, along with the near-month contract.

The reported values are averages of the percentage of the daily trading volume and open interest for each grouping. For example, the

value of 0.81 for 3-months (in column 2) under the heading for trading volume implies that on average 81% of all trading volume was

attributable to trades for the nearest three contract maturities.

It is clear that trading volume is more concentrated toward the very near-term contracts than is open interest. Nevertheless, including

in the analysis the first nine traded contracts captures 94% of daily trading volume and nearly 70% of the open interest available for

trading. Another way to think about these results is that the 30% of open interest found in the distant-maturity tail of the forward curve

sees only about 6% of the daily trading activity.

Table 2 reports how frequently the forward curves over the 2-month through 9-month maturities are in backwardation, as defined by

,t t TS F , how frequently hedgers are net short, and how frequently hedgers are net short for the full period, 1995-2004, and 2005-

2015. The Keynes and Hicks assumption that hedgers are typically net short is strongly supported by this evidence, with this class of

trader net short 75 percent of the time.11 Moreover, hedgers are found to be net short under both backwardation and contango

conditions.

11 Crude oil is not unusual in this respect; each of the other four energy futures contracts traded on the NYMEX–gasoline, natural gas, heating oil, and propane–

have hedgers net short over 76% of the time. Many commodities (agricultural and mineral) appear to have hedgers net short well over 50% of the time, while

financial futures are more mixed.

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Figure 1 shows the growth of open interest over the period along with the evolution of the hedgers’ net short positions. Figures 2 and 3

show the percentage of open interest accounted for by hedger net short positions and the four forward curve spreads, respectively, that

are the data for the analyses carried out in this paper.

Empirical results

Four forward curve models are specified, one for each of the more distant maturity futures contracts considered. There is a separate

model for the 2-month, 3-month, 6-month, and 9-month forward curves, with the corresponding spreads designated as s2L, s3L, s6L,

and s9L, respectively. Each s is defined as ,1 ,

ln( ) ln( )T

t t t Ts F F , so, for example, 3

,1 ,3ln( ) ln( )

t t ts F F is a representation of s3 at time

t. And, positive values imply backwardation in the current usage of the term.

The first step of the ARDL bounds approach12 is to estimate an OLS regression of the short-term difference variables and then

perform a non-nested test for the statistical significance of added variables. The initial OLS regression of short-term variables allowed

for a maximum of twelve lags, representing approximately three months of weekly observations, and include an intercept and trend.

These results were tested for stability using the CUSUM and CUSUMSQ tests; all were visually inspected and passed with confidence

bounds at 0.05.

The lagged levels of s and phns are then added to the initial OLS regression, and the statistical significance of these added variables is

tested via an F-statistic. As noted above, the resulting F-statistic is non-standard, so the test statistic is evaluated against the bounds

estimated and reported in Pesaran et al. (2001)13. The F-tests for all four models pass this test. This implies that there is long-run

forcing relationship between the variables, irrespective of their degree of integration, which permits moving on to the ARDL

specification phase and then on to the error correction representation.

These results support the primary hypothesis of this paper. An increase in the share of open interest attributable to hedgers is

positively related to the slope of the forward curve for crude oil through the expected risk premium as represented by the spread

between the near-month contract and more distant maturities. An increase in the demand of hedgers for the services of speculators, an

increase in hedging pressure, comes at a price, the expected risk premium, that is revealed as an increase in the spreads; this implies a

steepening forward curve that is in backwardation and a flattening of one that is in contango. The important estimated coefficients that

12 All estimations and tests were conducted in Microfit 5.0 (2009). 13 For this paper, the critical value bounds reported in Pesaran et al. (2001, p.300) in “Table CI(iii) Case III, Unrestricted intercept and no trend” were used. The

applicable critical value bounds are 4.94 – 5.73, for k=1 and confidence level 0.05. These critical values differ slightly from those found in Microfit 5.0, p. 544-

545, due to a larger T and number of repetitions in the stochastic simulations. Nevertheless, the calculated F-statistics exceed the upper bound against both sets of

tables. The results of these tests are available upon request.

13

provides this support is that for phns, which are reported in Table 3. For the four model specifications, each for a progressively more

distant maturity, the estimated coefficients range from 0.1123 to 0.9698, and they are highly statistically significant, with all positive

as expected and with magnitudes increasing with maturity as expected.

Table 4 reports the error correction term estimates. Each estimated coefficient for the four models has the expected negative sign and

is highly statistically significant. The decrease in magnitude of the speed of adjustment estimates, as the maturities constructing the

spreads increase, is also as expected. On the on hand, the relatively small magnitude of the estimates suggests a modest speed of

adjustment to disequilibria, but it also must be recognized that these speed of adjustments are for a week. And even with the modest

magnitudes, the declining characteristic of these results may be interpreted as providing support for Samuelson (1965) in the following

sense. Samuelson (1965) argues that near-term futures prices will be more volatile than those for more distant maturities. The larger

magnitude of the speed of adjustment term for the nearer term contracts suggests that the prices for these contracts will respond more

quickly to divergences from equilibrium, and this response will be observed as greater volatility in those prices. Table 4 shows that for

a given change in the percentage of open interest accounted for by hedgers the speed of adjustment for the spread between the near-

term contract and the next-to-near contract, s2, will be roughly twice as fast as the adjustment of the spread between the near-month

contract and the ninth-month contract, s9. Since both spreads are anchored by the same near-month contract price, the adjustments

must reflect relative changes to the distant month prices. Therefore, for this example, the next-to-near month contract price must adjust

at roughly twice the speed of the ninth-month price, and this will be observed as greater volatility in the nearer contract price.

Table 5 comprise three sections, A, B, and C, and reports a sample the results of the ARDL estimation sequence, in this case for the

s3L variable. Section A provides the estimation results for the ARDL, Section B presents the long-run coefficient estimates (the most

important being that for phns), and Section C reports the error correction estimation results. The results are presented along with the

range of diagnostic test automatically performed within the Microfit software. The estimates for s3L are very representative of those

for the other three, especially in that all estimated coefficients are statistically significant. Moreover, even the short-run dynamics

reflect the posited positive relation between hedgers’ net short positions and the slope of the forward curves, and, hence, the risk

premium. The other results are available upon request.

Summary and conclusions

The paper develops a theoretical framework for the relationship between a measure of hedging pressure (the net short positions of

hedgers) and the backwardation and contango characteristics of futures forward curves. The analysis finds that the expectations of

Keynes and Hicks regarding hedgers normally being net short is revealed in the data for the NYMEX crude oil futures contracts,

14

which could not have pre-conceived. Moreover, hedgers being net short is consistent with both backwardation and contango

conditions, which is also consistent with Keynes’ observations.

Empirical models, based on autoregressive distributed lag, are specified and estimated. The long-run coefficient estimates for the

relationship between hedgers net short positions and the slopes of the forward curve at different maturities are found to be statistically

significant and of the expected positive signs. Thus, increases in hedgers demands for the services of speculators, i.e., increased

hedging pressure, comes at a cost (increased expected risk premium) revealed as an increase in the spreads between the near-month

contract price and those of more distant maturities.

Finally, the speed of adjustment estimates on the error correction term have the expected sign and decrease with more distant maturity.

This result supports the Samuelson position that near-maturity futures prices will be more volatile than more distant maturities.

While we cannot directly observe the relationships between futures prices and their corresponding expected future spot prices, it is

shown that the theoretical basis for normal backwardation and normal contango has the expected influence on the shape of the forward

curve. The results demonstrate that even over the past 21 years, which have exhibited wide ranging shifts in both the physical and

financial markets for crude oil, the Keynes-Hicks theories of normal backwardation linking the demand for risk mitigation services

(hedger net short positions) and the expected risk premium required to attract those services has remained strong.

Future research may evaluate the possibility for asymmetric responses to changes in the percentage of open interest accounted for by

hedger net short positions depending on whether we are in a backwardation or contango environment.

15

References

Bentzen, J. and Engsted, T. 2001. “A revival of the autoregressive distributed lag model in estimating energy demand relationships,”

Energy, vol. 26, pp.45-55.

Charupat N. and Deaves, R. 2002. “Backwardation and normal backwardation in energy futures markets,” ZEW Discussion Paper No.

02-59, pp. 1-19, ftp.zew.de/pub/zew-docs/dp/dp0259.pdf.

Considine, T.J. and Larson, D.F. 2001. “Uncertainty and the convenience yield in crude oil price backwardation,” Energy Economics,

vol. 23, pp. 533-548.

De Vita, G. and Abbott, A. 2002. “Are savings and investment cointegrated? An ARDL bounds testing approach,” Economics Letters,

vol. 77, pp. 293-299.

De Vita, G., Endresen K., and Hunt, L.C. 2006. “An empirical analysis of energy demand in Namibia,” Energy Policy, vol. 34, pp.

3447-3463.

Hassler, U. and Wolters, J. 2006. “Autoregressive distributed lag models and cointegration,” Allgemeines Statistisches Archiv, vol. 90,

no. 1, 59-74.

Hendry, D.F., Pagan, A.R., and Sargan, J.D. 1984. “Dynamic specification,” in Handbook of Econometrics, Vol. II, eds. Z. Griliches

and M.D. Intriligator, Elsevier, Amsterdam, pp. 1023-1100.

Hicks, J.R. 1946. Value and Captial, 2nd Edition, Oxford University Press, London.

Hull, J.C. 2002. Fundamentals of Futures and Options Markets, 4th edition, Prentice Hall, Upper Saddle River, New Jersey.

Kaldor, N. 1939. “Speculation and economic stability,” The Review of Economic Studies, vol. 7, no. 1, pp. 1-27.

Keynes, J.M. 1930. A Treatise on Money, Vol. II, MacMillan and Co., Ltd, London.

Kollias, C., Mylonidis, N., and Paleologou, S-M. 2006. “The Feldstein-Horioka puzzle across EU members: Evidence from the ARDL

bounds approach and panel data,” International Review of Economics and Finance, Article In Press, December, pp.1-8.

16

Pahlavani, M., Wilson, E., and Worthington, A.C. 2005. “Trade-GDP nexus in Iran: An application of the autoregressive distributed

lag (ARDL) model,” American Journal of Applied Sciences, vol. 2, no. 7, pp. 1158-1165.

Pesaran, H.M. and Pesaran, B. 2003. Microfit 4.0, Oxford University Press, London.

Pesaran, H.M, Shin, Y., and Smith, R.J. 2001. “Bounds testing approaches to the analysis of level relationships,” Journal of Applied

Econometrics, vol. 16, no. 3, pp. 289-326.

Ramachandran, M. and Srivinsan, N. 2007. “Asymmetric exchange rate intervention and international reserve accumulation in India,”

Economics Letters, vol. 94, pp. 259-265.

Samuelson, P. 1965. “Proof that Properly Anticipated Prices Fluctuate Randomly,” Industrial Management Review, 6, 41-49.

17

Figure 1

18

Figure 2

19

Figure 3

20

Table 1: Concentration of trading activity by contract spread period: volume and open

interest – Daily January 1995 – December 2015 (5,256 observations)

Cumulative Percentage of Volume

2-months 3-months 6-months 9-months

0.72 0.81 0.90 0.94

Cumulative Percentage of Open Interest

2-months 3-months 6-months 9-months

0.36 0.45 0.60 0.69

Table 2: Frequency of backwardation and hedgers net short: averages for the period

Backwardation – Full period

2-months 3-months 6-months 9-months HNS

0.40 0.44 0.49 0.52 0.75

Backwardation – 1995-2004

2-months 3-months 6-months 9-months HNS

0.63 0.70 0.77 0.79 0.61

Backwardation – 2005-2015

2-months 3-months 6-months 9-months HNS

0.19 0.20 0.24 0.28 0.88

21

Table 3: Estimated long-run coefficients employing the ARDL(p,q) approach and the

Schwarz Bayesian Criterion (1,086 observations)

Dependent ARDL(p,q) Regressor Coefficient - β Probability

s2 (2,2) phns 0.1123 0.000***

c 0.0153 0.000***

s3 (2,2) phns 0.2396 0.000***

c 0.0316 0.000***

s6 (2,2) phns 0.6148 0.000***

c 0.0776 0.000***

s9 (2,2) phns 0.9698 0.000***

c 0.1176 0.000***

*** represent significance at the 99 percent level.

Table 4: Error correction representation based on the ARDL(p,q) model selection and

Schwarz Bayesian Criterion (1,086 observations)

Dependent ARDL(p,q) ECM - δ Probability R-bar-square

ds2 (2,2) -0.1001 0.000*** 0.3383

ds3 (2,2) -0.0756 0.000*** 0.3035

ds6 (2,2) -0.0470 0.000*** 0.2921

ds9 (2,2) -0.0365 0.000*** 0.2901

*** represents the 99 percent level.

22

Table 5: Estimation results for S3L 5/25/2016 1:42:11 AM

A. Autoregressive Distributed Lag Estimates ARDL(2,2) selected based on Schwarz Bayesian Criterion

*******************************************************************************

Dependent variable is S3L

1084 observations used for estimation from 13 to 1096

*******************************************************************************

Regressor Coefficient Standard Error T-Ratio[Prob]

S3L(-1) .80773 .027893 28.9586[.000]

S3L(-2) .11667 .027347 4.2664[.000]

PHNS .11522 .013222 8.7142[.000]

PHNS(-1) -.13628 .019710 -6.9141[.000]

PHNS(-2) .039174 .013453 2.9118[.004]

INPT .0023924 .7307E-3 3.2742[.001]

TREND -.6182E-5 .1440E-5 -4.2926[.000]

D11309 -.12321 .010671 -11.5458[.000]

D12009 .085904 .011228 7.6506[.000]

D21709 -.10286 .010656 -9.6522[.000]

*******************************************************************************

R-Squared .91558 R-Bar-Squared .91487

S.E. of Regression .010582 F-Stat. F(9,1074) 1294.2[.000]

Mean of Dependent Variable -.0010399 S.D. of Dependent Variable .036269

Residual Sum of Squares .12027 Equation Log-likelihood 3397.6

Akaike Info. Criterion 3387.6 Schwarz Bayesian Criterion 3362.6

DW-statistic 1.8586

*******************************************************************************

Testing for existence of a level relationship among the variables in the ARDL model

*******************************************************************************

F-statistic 95% Lower Bound 95% Upper Bound 90% Lower Bound 90% Upper Bound

25.9998 6.6238 7.3285 5.5918 6.2706

W-statistic 95% Lower Bound 95% Upper Bound 90% Lower Bound 90% Upper Bound

51.9997 13.2476 14.6570 11.1836 12.5413

*******************************************************************************

If the statistic lies between the bounds, the test is inconclusive. If it is

above the upper bound, the null hypothesis of no level effect is rejected. If

it is below the lower bound, the null hypothesis of no level effect can't be

rejected. The critical value bounds are computed by stochastic simulations

using 5000 replications.

23

Diagnostic Tests

*******************************************************************************

* Test Statistics * LM Version * F Version *

*******************************************************************************

* * * *

* A:Serial Correlation*CHSQ(1) = 31.6779[.000]*F(1,1073) = 32.3004[.000]*

* * * *

* B:Functional Form *CHSQ(1) = 18.6694[.000]*F(1,1073) = 18.8038[.000]*

* * * *

* C:Normality *CHSQ(2) = 2131.9[.000]* Not applicable *

* * * *

* D:Heteroscedasticity*CHSQ(1) = 145.0200[.000]*F(1,1082) = 167.1087[.000]*

*******************************************************************************

A:Lagrange multiplier test of residual serial correlation

B:Ramsey's RESET test using the square of the fitted values

C:Based on a test of skewness and kurtosis of residuals

D:Based on the regression of squared residuals on squared fitted values

5/25/2016 1:44:08 AM

B. Estimated Long Run Coefficients using the ARDL Approach ARDL(2,2) selected based on Schwarz Bayesian Criterion

*******************************************************************************

Dependent variable is S3L

1084 observations used for estimation from 13 to 1096

*******************************************************************************

Regressor Coefficient Standard Error T-Ratio[Prob]

PHNS .23960 .060051 3.9900[.000]

INPT .031647 .0088836 3.5624[.000]

TREND -.8178E-4 .1672E-4 -4.8897[.000]

D11309 -1.6298 .25522 -6.3858[.000]

D12009 1.1363 .23770 4.7805[.000]

D21709 -1.3606 .22586 -6.0239[.000]

*******************************************************************************

Testing for existence of a level relationship among the variables in the ARDL model

*******************************************************************************

F-statistic 95% Lower Bound 95% Upper Bound 90% Lower Bound 90% Upper Bound

25.9998 6.6238 7.3285 5.5918 6.2706

W-statistic 95% Lower Bound 95% Upper Bound 90% Lower Bound 90% Upper Bound

51.9997 13.2476 14.6570 11.1836 12.5413

*******************************************************************************

24

If the statistic lies between the bounds, the test is inconclusive. If it is

above the upper bound, the null hypothesis of no level effect is rejected. If

it is below the lower bound, the null hypothesis of no level effect can't be

rejected. The critical value bounds are computed by stochastic simulations

using 5000 replications.

5/25/2016 1:44:54 AM

C. Error Correction Representation for the Selected ARDL Model ARDL(2,2) selected based on Schwarz Bayesian Criterion

*******************************************************************************

Dependent variable is dS3L

1084 observations used for estimation from 13 to 1096

*******************************************************************************

Regressor Coefficient Standard Error T-Ratio[Prob]

dS3L1 -.11667 .027347 -4.2664[.000]

dPHNS .11522 .013222 8.7142[.000]

dPHNS1 -.039174 .013453 -2.9118[.004]

dTREND -.6182E-5 .1440E-5 -4.2926[.000]

dD11309 -.12321 .010671 -11.5458[.000]

dD12009 .085904 .011228 7.6506[.000]

dD21709 -.10286 .010656 -9.6522[.000]

ecm(-1) -.075597 .010684 -7.0758[.000]

*******************************************************************************

List of additional temporary variables created:

dS3L = S3L-S3L(-1)

dS3L1 = S3L(-1)-S3L(-2)

dPHNS = PHNS-PHNS(-1)

dPHNS1 = PHNS(-1)-PHNS(-2)

dTREND = TREND-TREND(-1)

dD11309 = D11309-D11309(-1)

dD12009 = D12009-D12009(-1)

dD21709 = D21709-D21709(-1)

ecm = S3L -.23960*PHNS -.031647*INPT + .8178E-4*TREND + 1.6298*D11309 -

1.1363*D12009 + 1.3606*D21709

*******************************************************************************

R-Squared .30927 R-Bar-Squared .30349

S.E. of Regression .010582 F-Stat. F(8,1075) 60.1107[.000]

Mean of Dependent Variable -.6477E-4 S.D. of Dependent Variable .012680

Residual Sum of Squares .12027 Equation Log-likelihood 3397.6

Akaike Info. Criterion 3387.6 Schwarz Bayesian Criterion 3362.6

DW-statistic 1.8586

*******************************************************************************

R-Squared and R-Bar-Squared measures refer to the dependent variable

25

dS3L and in cases where the error correction model is highly

restricted, these measures could become negative.

Testing for existence of a level relationship among the variables in the ARDL model

*******************************************************************************

F-statistic 95% Lower Bound 95% Upper Bound 90% Lower Bound 90% Upper Bound

25.9998 6.6238 7.3285 5.5918 6.2706

W-statistic 95% Lower Bound 95% Upper Bound 90% Lower Bound 90% Upper Bound

51.9997 13.2476 14.6570 11.1836 12.5413

*******************************************************************************

If the statistic lies between the bounds, the test is inconclusive. If it is

above the upper bound, the null hypothesis of no level effect is rejected. If

it is below the lower bound, the null hypothesis of no level effect can't be

rejected. The critical value bounds are computed by stochastic simulations

using 5000 replications.