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Market Efficiency and the Risks and Returns of Dynamic Trading Strategies with Commodity Futures

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This paper investigates relationships between profits from dynamic trading strategies, risk premium, convenience yields, and net hedging pressures for commodity futures. The term structure of oil, gold, copper and soybeans futures markets contains predictive power for the corresponding term premium. However, only oil futures and soybean futures lead their spot premia. Significant momentum profits are identified in both outright futures and spread trading strategies when the spot premium and the term premium are used to form winner and loser portfolios. Profits from active strategies based on winner and loser portfolios are conditioned on market structure and net hedging pressure effects. Dynamic trading strategies based on contracts with extreme backwardation, extreme contango, and extreme hedging pressures are also tested. On average, spread trading outperforms outright futures trading in capturing the term structure risk and hedging pressure risk. Amongst such strategies, a long-short position in the long-term spread offers the greatest and most significant return and it offers the only exploitable trading profits conditional on past hedging pressure.
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Market Efficiency and the Risks and Returns of Dynamic Trading
Strategies with Commodity Futures
December 2008
Lorne N. Switzer and Hui Jiang*
ABSTRACT
This paper investigates relationships between profits from dynamic trading strategies,
risk premium, convenience yields, and net hedging pressures for commodity futures. The
term structure of oil, gold, copper and soybeans futures markets contains predictive
power for the corresponding term premium. However, only oil futures and soybean
futures lead their spot premia. Significant momentum profits are identified in both
outright futures and spread trading strategies when the spot premium and the term
premium are used to form winner and loser portfolios. Profits from active strategies based
on winner and loser portfolios are conditioned on market structure and net hedging
pressure effects. Dynamic trading strategies based on contracts with extreme
backwardation, extreme contango, and extreme hedging pressures are also tested. On
average, spread trading outperforms outright futures trading in capturing the term
structure risk and hedging pressure risk. Amongst such strategies, a long-short position in
the long-term spread offers the greatest and most significant return and it offers the only
exploitable trading profits conditional on past hedging pressure.
Keywords: commodity futures; market efficiency; dynamic trading strategies
JEL Codes: G13, G14.
_____________________________________________________
* Finance Department, Concordia University. Financial support from the SSHRC to Switzer is gratefully
acknowledged. Please address all correspondence to Dr. Lorne N. Switzer, Associate Dean, Research and
Van Berkom Endowed Chair of Small Cap Equities, Finance Department, John Molson School of Business,
Concordia University, 1455 De Maisonneuve Blvd. W., Montreal, Quebec, CANADA H3G 1M8; tel.: 514-
848-2960, x2960 (o); 514-481-4561 (home and FAX); E-mail: switz@jmsb.concordia.ca.
1
1. Introduction
In recent years, commodity market booms and busts have inspired significant
interest in this asset class amongst academics and practitioners. As an individual asset
class, commodities show several features that distinguish themselves from financial
assets, including:
(1) Commodities are real assets that can be used for consumption. They can be packaged
as derivative securities for generating returns for investors and for transferring real
consumption risk. Therefore, their performance is subject to more factors than
financial assets, including but not limited to business cycles, local and global supply-
and-demand, technology development, substitute and complementary products.
(2) Based on economic theory, commodity returns in the absence of shocks should mean-
revert to the equilibrium marginal rate of production.
(3) Unlike financial assets that are cash-settled at expiration, commodity futures need to
be settled by physical delivery; this entails unique storage and shipping costs. For
those who want to avoid physical exposure at expiry, contract roll-over is essential.
According to Feldman and Till (2006), this roll yield drives the overall yield over the
long-term horizon.
(4) Each commodity should be treated as an individual asset class instead of one asset
class for all. Erb and Harvey (2006) associate commodity index performance with the
performance of its components.
(5) The equilibrium CAPM model does not work well for the commodity markets
because some of its critical assumptions are violated: such as an insufficiently
2
diversifiable base of participants in the commodity markets pointed out by Hirshleifer
(1988) and the exclusion from capital assets by Erb and Harvey (2006).
Given this background, much of the extant theoretical and empirical research has
looked at commodities apart from financial assets. One strand of literature relates
commodity returns to inventory level storage costs, which affect the state-time
opportunity set for consumption. Another strand focuses on hedging pressures, which
constrain the risk transference function. The purpose of this paper is to synthesize both of
these literatures, and to provide empirical tests that differentiate between them. In
particular, we provide various tests of the models by looking at the determinants of risk
premiums for NYMEX crude oil, COMEX gold, COMEX copper and CBOT soybean
contracts. We also conduct tests based on trading strategies for these contracts.
These four commodity futures contracts are chosen for the following reasons: (i)
their liquidity; (ii) their diverse historical term structure and hedging experience; and (iii)
their different sensitivities to the business cycle.
We find that both the term structure and hedging pressure variables are significant
determinants of commodity returns. In addition they are found to contain information that
can be used to construct profitable trading strategies.
The remainder of the paper is organized as follows. Section 2 provides a review of
the literature. Section 3 provides a description of the data. The methodology for the tests
is provided in section 4. The empirical results follow in Section 5. Section 6 performs
three active trading strategies and specifies results. The paper concludes with a summary
in section 7. For readers unfamiliar with commodities, some terminology is provided in
Appendix 1.
3
2. Literature review
2.1 Theory of storage and theory of inverse carrying charge:
The most well-known benchmark model in commodity futures is the arbitrage-
free cost-of-carry model, the core of theory of storage:
()()
() rscTt
T
t
tSe
F
+
−−
= (1)
where r is interest foregone, s storage cost and c convenience yield. A basic drawback of
this model is the difficulty in obtaining reliable estimates of s and c.
Kaldor (1939) proposes the convenience yield as a measure that captures the
abstract benefit of holding inventory to avoid out-of-stock risk in production process. It is
an indirect measure of inventory scarcity and widely used as a variable of inventory in a
large body of literature. Brennan (1958) and Dincerler, Khokher and Simin (2005)
empirically validate an inverse relationship between inventory and convenience yield in
agriculture, energy, and metal markets. Dincerler et. al. (2005) finds that up to 42% of the
variation in convenience yield can be explained by inventory levels.
Fama and French (1988) develop an indirect test of the theory of storage for metal
markets. Their results are consistent with the theory: when inventory is low (high) futures
prices have less (approximately the same) volatility than (as) spot prices.
Working (1948) extends Kaldor’s theory (1939) into a theory of inverse carrying
charges. In this approach, the carrying charge in the futures market is determined by the
shape of the convenience yield. Simply put, nearby futures price 1P and delayed futures
price 2P are linked by carrying charge
s
Pas follows:
120sPPP+− = (2)
4
so that the change of nearby futures can be explained in terms of the change of carrying
charge and that of distant futures:
12
s
PPP=− (3)
The significance of this theory is two-fold: it clarifies the important role of futures
market in adjusting the carry of stock from one date to another1 and addresses the
correlation between the nearby and distant futures in a clear and concise way. Equation
(3) suggests that (i) common determinants affecting distant futures price 2P tend to affect
nearby futures price 1P to a similar extent and (ii) factors affecting carrying charge
s
P
have an equal but opposite influence on the nearby futures price 1P.
2.2 Net hedging pressure hypothesis
The net hedging pressure hypothesis provides a benchmark for changes in
commodity prices through time. Working (1953) recognizes the significant role of
hedgers in the market for U.S. grain futures. Cootner (1960) introduces hedging
pressures into the theory of storage and proposes trading strategies built on varying
degrees of hedging pressure in seasonal wheat and cotton markets. Sizable correlations
are observed between inventory and hedging pressure during the pre-harvest and harvest
seasons. In the pre-harvest season, inventory is low while the commitment of delivery is
high so that the market is driven by a net long hedging pressure; short hedging pressure is
enhanced with the arrival of new crops. Prices of agricultural commodities remain
depressed until the peak of harvest and then gradually rise as consumption increases.
Short hedging falls after the harvest peak. Cootner (196) exploits seasonality in
1 “Futures markets, through their use for hedging, make the holder of stocks sharply aware of any losses
that must be expected from carrying unnecessary stocks in times of relative shortage of supplies, and
provide assured returns for storage over periods when there is a surplus to be carried.” (Working,1953).
5
agricultural production for devising trading strategies built on: (1) peaks and troughs in
grain supplies; (2) peaks and troughs in hedging positions; (3) fixed calendar spreads
taking advantage of factor (1) and/or (2).
Since Cootner’s pioneering paper, numerous empirical studies have investigated
whether net hedging pressure leads to predictable trends in futures prices (see e.g. Chang
(1985) and Carter, Rausser and Schmitz (1983)). Bessembinder (1992) finds significant
positive mean returns conditional on net short hedging pressure.Roon, Goorbergh and
Nijman (2000) confirm Bessembinder’s findings, and further identify cross-hedging
pressure among futures of related commodities.
More recently, Roon, Goorbergh and Nijman (2004) test a trading strategy based on
hedging pressure to capture spot and term premia across 23 futures markets. Dincerler,
Khokher and Simin (2005) study a inventory-withdrawn trading strategy that is motivated
by the joint force of inventory and hedging pressure in markets. Till and Eagleeye (2007)
assert that the theory of storage and net hedging pressure should jointly affect commodity
markets, depending on the time horizon of investors: with the theory-of-storage (net
hedging pressure) appropriate for long (short) horizon trading. These authors do not
provide empirical tests of the joint influence of these factors on commodity returns. The
objective of this paper is to fill this gap.
The focus of recent empirical work has been on passive vs. active trading strategies.
2.3 Passive trading strategy
Roon, Goorbergh and Nijman (2004) decompose the futures return into the spot
premium (or basis) and the term premium. Hedging pressures are inferred through two
passive trading strategies: (i) long-only the first-nearby futures and (ii) long spread that
6
longs the first -nearby futures and shorts distant futures, across 23 futures markets. The
return decomposition is motivated by the fact that the basis cannot be earned if futures
positions are not held to maturity—which is often the case for commodity investors and
speculators who do not expect physical delivery. Thus, the expected return is influenced
by both spot and term premiums. In fact, except for the first-nearby futures contract, all
delayed futures exhibit significant term premia as critical components of their returns.
Roon et al (2004) find that the past hedging pressure explains more variation in the term
premium than in the spot premium, and influences both premia differently—negative for
the spot premium and positive for the term premium. Therefore long (short) outright
futures positions or short (long) calendar spread positions can be profitable in a net short
(long) hedging market. The active trading results show that the effect of net hedging
pressure can only be inferred through spreads, consistent with Hirshleifer (1988) and
Bessembinder (1992).
2.4 Active trading strategies
The most widely-used active strategy focuses on momentum - trading futures
contracts based on their past performance. Roon et al (2004) find a significant
momentum effect in term premia across time and commodity markets, but identify no
clear directional pattern that supports simple active trading strategies yielding abnormal
profits.
In contrast, Miffre and Rallis (2007) test several momentum strategies that on
average generate annual excess returns of 9.38%. Their contrarian strategies, proposed to
capture the long-term reversal are not successful. They further associate the momentum
7
strategy of buying winners and selling losers with the option of buying backwardated and
selling contangoed markets. However, they do not explicitly test the latter option, which
is a matter that we address, inter alia, in this study.
This paper serves to advance the literature by exploring new tests of market
efficiency from a returns predictability perspective, by testing whether profitable trading
strategies based on both momentum as well as overreaction (based on appropriately
defined winner vs. loser portfolios) conditioned on the term structure can be devised
using commodity futures. Our strategies are based on VAR Granger causality models
that link returns jointly to risk premia, convenience yields and net hedging pressures.
This is the first paper that we are aware of to demonstrates a link between the momentum
effect and backwardation, while exploring alternative strategies based on information
contained in the convenience yield and net hedging pressure in the relevant markets.
3. Data
Daily closing prices of NYMEX crude oil, COMEX gold, COMEX copper and
CBOT soybean from January 1, 1990 to December 31, 2006 are obtained from
Bloomberg. Continuous time-series of futures prices are constructed in the order of the
first -nearby futures, second-nearby futures, etc. up to one-year maturity or the last
contract month before the end of a calendar year, such as November for the soybean
contract. The one-year maturity is chosen because it covers a sufficiently long forward
period and also has substantial liquidity to deal with. Table 1 provides some summary
statistics of the four commodity futures contracts.
Please insert Table 1 about here
8
The first-nearby futures contract is constructed from the series of prices of the
next expiring contract until one week prior to the last trading day of it, at which point the
contract is rolled over to the next expiring contract. We adopt the common practice of
treating the first-nearby futures price, as the spot price, since a united spot market for
each commodity does not exist. By extension, the first-nearby futures is literally the
second-nearby futures and by analogy, all the next nearby futures contracts are mapped to
their subsequent one interval lagged contracts.
For calendar spreads, only the first-nearby futures and futures maturing in six
months and in one year are considered because these contracts usually have the longest
trading life, normally available for trading 18 months before maturity. These are the most
widely used contracts for spreads by practitioners.
Figure 1 shows the term structures of four commodities based on the average
futures prices across maturities.
Please insert Figure 1 about here
Generally speaking, oil and copper markets are in backwardation on average over
the period of the sample. In contrast, the gold market is characterized by contango; the
and soybean market is also generally in contango with its sharpest slope appearing in the
pre-harvest third quarter—from July to September.
Table 2 provides descriptive statistics of the daily returns based on the spot price
and the first-nearby futures price. All returns are calculated against the one-day price lag
of the same time series and not across contracts with different maturities. Returns of the
CRB index (the oldest tradable as well as the most comprehensive commodity index), the
Russell 3000 index (a proxy for the U.S. listed equity market portfolio) and the 10-year
9
U.S. Treasury bond (the industry norm of measuring long-term interest rate) are also
shown as benchmarks of commodity indices vs. financial asset returns.2
Please insert Table 2 about here
All commodity returns show significant departures from the normal distribution, based
on the Jarque-Bera estimates. Oil and copper futures exhibit the highest returns, Among
commodities, oil futures exhibit the highest volatility while gold futures exhibit the least
volatility which is only marginally higher than that of the CRB commodity index.
4. Methodology
4.1 Decomposition of futures returns:
Following Roon, Nijman and Veld’s (1998), we decompose futures returns into spot
premia and term premia by simulating the returns of a the strategy of (1) buying a k-day
contract and (2) buying a k-day contract, selling a n-day contract and holding the spread
for k days (k<n) where k and n represent number of days until maturity of the first-nearby
futures and of distant futures respectively.
From the cost-of-carry model, in a structurally contangoed market, a certain yield
()n
t
y based on futures prices, f and spot prices, s 3 can be locked in by longing an asset in
the spot market and simultaneously shorting it in the futures market to be delivered at
time t+n.
()
()
n
nt
t
t
fs
yn
(4)
2 The annualized standard deviations of commodity returns are possibly elevated since commodity returns
are normally autocorrelated and asymmetrically distributed.
3 The prices are in log form.
10
Similarly, the forward yield (,)kn
t
h can be earned from time t+k to t+n by taking a
long position in the contract to mature at t+k, shorting its equivalent to mature at t+n
(k<n), and holding the spread for k days.
() () () ()
(,)
nk n k
kn tt t t
t
f
fnyky
hnk nk
−−
≡=
−−
(5)
Re-arranging (5) we obtain:
() ()
(,)
() (,)
()
( )
nk
kn
ttt
nk kn
tt
tk
nk ny ky
h
nk
y
E
+
−=
⎡⎤
=− +
Θ
⎣⎦
(6)
1
(,) ( )
0
k
kn n i
tt
i
θ
=
Θ
where (,)kn
t
Θ is the estimate of the term premium and can be rewritten in terms of log spot
price and log futures price as:
(
)
(
)
() ( ) ()
(,) knkn
kn
ttk
ttkt
f
ff
s
++
=−− −
Θ (7)
It is reasonable to assume that a naked long position in the first nearby futures
contract that matures in k days, the term premium ()
,
n
yt
π
is negligible. In this case, the
maturity risk premium is explained by spot premium ,
s
t
π
, which is, by definition, the
expected spot return in excess of the one-period yield.
[
]
[
]
()
,,
k
tstk ttk t st
t
ky
ss
Er E
π
++
=−=+ (8)
Rearrange (8) to get the expression of spot premium:
(
)
()
,
k
st t k t
f
s
π
+
=− (9)
Table 3 provides descriptive statistics for both premia. In most cases, they are found
to be significantly different from zero at conventional levels. Average term premia
11
decline as maturities increase in oil and copper markets and rise in longer-dated gold and
soybean markets, implying backwardation (contango) of oil and copper (gold and
soybean). A structurally backwardated market carrying an inverse-charge from nearby to
distant delivery renders a long spread unprofitable—thus, a positive term premium is
needed for remuneration, vice versa for a contangoed market.
From a volatility perspective, spot price risk is much higher than spread trading
risk. However, spreads in oil and soybean markets are still quite volatile, with annual
term volatilities above 9% and ranging from 7% to 12%, respectively.
Please insert Table 3 about here
4.2 Estimation of the Convenience Yield and Net Hedging Pressure Variables
We estimate the convenience yield proxy using the Fama and French (1988)
approach, as the negative of the interest-adjusted basis.4 Three most widely used
contracts—the 3-month,5 the 6-month and the 12-month futures are used to calculate the
short-, intermediate- and long-term convenience yields for each commodity.
The metric used to capture net hedging pressure, tH, is the difference between the
short and long hedge positions of commercial traders divided by their total hedge
4
[
]
[
]
(, ) () () (, ) (, ) (, ) ()FtT S t St RtT W tT CtT St−−=
where F and S are prices of futures and spot markets, R is interest foregone, W is storage cost and C is
convenience yield. Interest-adjusted basis in the left-hand-side can be expressed as difference between
relative storage cost and relative convenience yield. For a constant storage cost, the variation of relative
convenience yield naturally dominates that of the interest-adjusted basis, so that convenience yield can be
approximately expressed as the negative of the interest-adjusted basis.
5 Since gold futures only mature in even months and soybean futures only in odd months, different
contracts other than the three maturities have to be chosen for both. The 4-month futures is used to
calculate the short-term convenience yield for gold, and the 7-month and 11-month contracts are used to
calculate the intermediate-term and long-term convenience yields for soybean.
12
positions6, with all position’s information from the semi-monthly7 report of Commitments
of Traders in Commodity Futures (“CFTC report” hereafter). A positive tH means a net
short hedging market whereas a negative ratio a net long hedging market.
The convenience yield is calculated as the negative of the interest-adjusted basis.
We provide estimates of the convenience yield i under conditions of adequate (“positive”
column) and inadequate (“negative” column) inventory levels.
Summary statistics of the convenience yield are provided in Table 4
Please insert Table 4 about here
Oil and copper exhibit relatively high average convenience yields, on average. On the
other hand, hedging pressure for oil is less pronounced for oil than for the other
commodities. Oil exhibits the highest unconditional convenience yield and gold the
lowest and least volatile one. Convenience yields across all four futures are negative
when inventory is abundant (“positive” column) and substantially positive when it is
scarce (“negative” column); and convenience yield is more volatile at low inventory
levels than at high inventory levels; its variation does not increase proportionally but at a
decreasing rate with extending term to maturity excluding copper, showing declining
price impact along time as implied by the Samuelson hypothesis.
Sample characteristics of the net hedging pressure variables are provided in Table
5. For the entire observation period, all the four commodity futures are net short hedging
markets, supporting Keynes’ insurance perspective hypothesis. Net hedging pressure
6 short hedge positions - long hedge positions
total hedge positions
tH=
7 This report was released bi-weekly until September 1992. From October 1992 on, was released on a
weekly basis.
13
does vary across time and markets. Copper and soybean futures are net short hedging the
majority of time, and oil and gold markets vacillate more often. Net short hedging
pressure characterizes the gold market from 2001 to 2006.
Please insert Table 5 about here
4.3 VAR Granger-Causality Estimates, Weekly Data
Bessembinder (1992) uses the Fama and MacBeth (1973) two step approach to
capture the effect of net hedging pressure on residual risks of commodity futures. We
employ a more direct approach, and estimate a nested Vector Autoregressive (VAR)
system that includes as joint variables the commodity risk premia, convenience yields,
and net hedging pressure. As is shown in Table 6, based on Augmented Dickey-Fuller
(ADF) and Phillips-Perron (PP) unit root tests, the null hypothesis of a unit root is
rejected by all the tested time series under all settings at a significance level of 5%. Since
the spot premium, term premium, convenience yield and net hedging pressure varibles
are stationary in nature, an unrestricted VAR Granger-causality model is appropriate.
Please insert Table 6 about here
The testing period is from the issue of the first weekly CFTC report8 on October 6th 1992
to its last issue in 2006 on December 26th, 2006. The data encompass from 670 to 730
weekly observations across the four markets.
8 The CFTC report was once published every two weeks until the end of September 1992. Ever since
October 1992, this report becomes a weekly issue and has been disclosed on each Wednesday. To keep as
much as information intact, weekly data of risk premiums, net hedging pressure and convenience yield are
re-calculated and used in this test.
14
5. Empirical Results
5.1 Results of VAR Granger causality model
Estimates of the VAR Granger-causality model for of risk premia, convenience yields
(with different maturities) and net hedging pressure in the market, are provided in Table 7
for spot premia across markets.9
Please insert Table 7 about here
5.1.1 Spot premium vs. term structure & net hedging pressure
The most striking result of the estimation is that spot premia serve as leading
(predictor) variables for both convenience yields and net hedging pressure across all
commodities. On the other hand, net hedging pressure does not lead the spot premium in
any market. Convenience yields show market-dependent results. In particular, they lead
spot premiums in the oil and soybean markets. For all the markets excluding copper, the
longest convenience yield has the least effect on the spot premium.
Bi-directional causality is detected between term slopes of different horizons in
all markets, showing that some intertwining of information contained in each part of the
term structure. Causality between the term structure and net hedging pressure is observed
only for the metal markets studied. For gold, net hedging pressure uni-directionally leads
the term structure while for copper, the overall term structure leads net hedging pressure
and net hedging pressure leads the short-term slope only.
9 We use the FPE (final prediction error) criterion, the Akaike information criterion, the Schwarz criterion (SC); and
the Hannan & Quinn (HQ) criterion and in all cases find an the optimal lag lengths of one.
15
5.3.2 Term premium vs. term structure & net hedging pressure:
Estimates of the VAR Granger-causality model for the term premium, the term
structure and net hedging pressure, for the commodities studied are shown in Tables 8-
11.10
Oil Futures
Please insert Table 8 about here
For all three oil spreads, a leading effect from the term premium to the overall
term structure and net hedging pressure appears in the 12th and 13th lags, showing that the
spread premiums contain information that can be used to forecast the term structure and
net hedging pressure in approximately three months away.
The overall term structure improves forecast of term premium across time, but at
slightly different lags. In general, the predictive power of term structure shows up in
various term premia in most cases up to the third month in the future.
Gold and Copper Futures
Please insert Tables 9-10 about here
The same causality effects of term premium on term structure and net hedging
pressure are observed in the gold spread using the 6-month contract and in all the three
copper spreads. Negative (positive) coefficients of gold (copper) spreads can be naturally
associated with its contangoed (backwardated) convenience yield shape. Causality
between the term structure and net hedging pressure is observed in both spread rates
10 The optimal lag lengths, using the criteria of footnote 9, are: thirteen for both oil and soybean spreads
and one lag for gold and copper. To conserve space, we have shown the results including only one lag in
Table 8 and Table 11 for oil and soybean respectively. The complete results are available on request.
16
similar to that which obtains in spot returns: Net hedging pressure uni-directionally drives
gold’s term structure while the term structure leads copper’s net hedging pressure.
Perhaps the most important finding in the spread market in these metal markets
comes from the significant leading effect of the entire term structure on the term
premium. In contrast, no significant relationship between the term structure and the
corresponding spot premium. This result is consistent with Roon, Goorbergh and
Nijman’s (2004) who conclude that the term premium should reflect term structure risks.
Similar to the spot premium, variation of the term premium explained by term structure
decreases with the contract horizon. Hence, the latest short-term convenience yield
contains the most relevant information for predicting future term premiums.
Soybean Futures
To conserve space, in Table 11 we report results for the second soybean spread.11
All three term premia clearly lead the term structure by one week, one month and three
months ahead, respectively.
Please insert Table 11 about here
.
In sum, both premia Granger-cause the overall term structure and net hedging
pressure, While the term structure contains information useful in predicting spot premia
in oil and soybean markets, it does demonstrate predictive power with respect to term
premiums in all four of the commodity markets studied. This result demonstrates that the
term structure risk should be better captured by the term premium than by the spot
11 The reason to display results of the second soybean spread is that the term structure effect is supposed to
be most significant in term slope derived from the July contract, since it is the only contract that expires
just prior to the upcoming harvest season starting in September. Test results show that it is the case.
17
premium. No significant causality from net hedging pressure to either premium is
observed.12
6. Returns from Active Trading Strategies
In this section, we use the findings of the previous section on the predictive power
of the term structure and hedging pressure variables to construct active trading strategies,
as tests of market efficiency from a returns predictability perspective (Fama (1991))..
Three active trading strategies are introduced: the momentum/contrarian strategy, the
convenience yield strategy, and the net hedging pressure strategy.
6.1 Momentum/contrarian strategies
6.1.1 Portfolio construction
We create momentum/contrarian portfolios using bi-weekly data from January 1990
to December 2006. To construct the portfolios, at the end of each period, we rank past
spot premia and term premia for all four commodity futures. Based on these rankings,
we go long (and short) futures or futures spreads in those commodities categorized as
“winners” (“losers”) with the highest (lowest) premium. After a designated period of
time, we rebalance or unwind the positions. We continue the process of enter-hold-exit
during the testing period. To facilitate presentation, each strategy is named after its
12 As a robustness test, we have also performed the VAR Granger Causality tests using bi-weekly and
monthly data. These results are qualitatively similar to those reported here. They are available on request.
18
ranking (R) and holding (H) periods as the R–H strategy, with ranking and holding
periods set as one month, three months, six months and twelve months. 13
Miffre and Rallis (2007) build momentum portfolios using an overlapping trading
strategy, following Moskowitz and Grinblatt (1999) and Jegadeesh and Titman (2001).
Our approach extends this strategy, with some notable differences. First, rather than
performing the rankings based on returns (i.e. changes in the log settlement prices), we
perform our rankings using the spot and term premia, as defined in section 4.1. Hence,
we extend both the Roon et al calendar spread strategies as well as the Miffe and Rallis
(2007) long-only strategy. In addition, Miffre and Rallis (2007) form equally-weighted
portfolios. Our study uses a value weighted approach: of investing one dollar in both
winner and loser portfolios in each period. This method avoids capital-allocation risk
introduced by large differences in unit contract prices across commodity markets.
Finally, in this study, returns of winner or loser portfolios are based on the
holding-period returns of taking long positions in the corresponding portfolios. The
momentum (contrarian) trading return is defined simply as the difference between the
winner (loser) portfolio return and loser (winner) portfolio return.
13 It should be noted that rading results are comparable only between outright futures strategies or spread
strategies but not across both groups, since negligible costs are incurred when initiating spreads. Spread
returns are calculated as:
()/4
endf openf
cs
openl opens
PP
RPP
=+
where endf
P and openf
P are ending and opening balances of spread portfolio, openl
P and opens
P are
opening balances of long and short sides when spread is initialized. Their absolute sum is then divided by 4
to take account of the offsetting effect of a long-short strategy. The revised calculation solves the
“infinitesimal denominator” problem and makes different calendar spreads comparable across time and
markets.
19
6.1.2 Empirical results
Tables 12 to 17 provide summary statistics for momentum trading returns that
match six trading strategies—three outright long-only strategies and three calendar spread
strategies using contracts or spreads that expire in three months, six months and twelve
months respectively. The momentum (contrarian) strategy is deemed a success when the
“Momentum” column in tables is positive (negative) The purpose of using multiple
contracts or spreads to build momentum trading portfolios is two-fold: to check
robustness and to empirically test Miffre and Rallis’s (2007) assertion that the term
structure drives the momentum effect in commodity markets. 14
Please insert Tables 12 to17 about here
On the whole, the momentum strategy performs well in most cases for both
outright contracts and calendar spreads, particularly when the holding period is under six
months. Thus a short-term price continuation, analogous to that identified by Jegadeesh
and Titman (1993, 2001) for equity markets is also observed in these four commodity
markets. For these markets, momentum profits are maximized by longing the most
outperforming futures or calendar spread and shorting its most underperforming
counterpart in the previous month, holding the pair for one month and continuously
rolling it over to the next pair selected with the same criterion at each rebalancing point.
This strategy works equally well for outright contracts and calendar spreads with
different maturities. The annual return for this strategy ranges from 51.6% to 88.8%
with a corresponding Sharpe ratio from 232.74% to 284.83% for outright contract
14 Miffre and Rallis (2007) suggest that momentum profits are related to the market structure, trading in
long-term futures could generate more profits.
20
strategy, and an annual return from 18% to 76.8% with a Sharpe ratio from 118.09% to
217.36% for calendar spread strategy.
Extending the ranking and holding period reduces momentum profits. For the
outright futures strategy, the significant momentum effect disappears when both periods
exceed six months; significant contrarian profits are observed for holding periods of
twelve months. Momentum trading with the shortest three-month futures dominates all
strategies. For the calendar spread strategy, significant contrarian profits dominate all
scenarios when ranking and holding periods are longer than three months. Profits decline
as we move to shorter (i.e. six month followed by three month) spread positions. Miffre
and Rallis’s (2007) conjecture of a linkage between the momentum effect and the term
structure are thus empirically supported through these trading results.
6.2 Momentum strategy vs Backwardation and contango
The active trading results of the previous section support an empirical relationship
between the momentum effect and the term structure. A direct test for a momentum—
backwardation link, is provided by the following regression on active trading returns of
both winner and loser portfolios:
11
,0123
1
ft t i t
i
t
i
cy
RHD
βββ
α
ε
=
=+ + + +
(10)
where ,
f
t
R
is the return of longing (shorting) the winner (loser) portfolio, t
cy the
portfolio convenience yield, t
H the portfolio net hedging pressure; i
D are monthly
dummy variables, while εt is the error term. The regressors t
cy and t
H are constructed
from the convenience yield and net hedging pressure of the most outperforming and
underperforming commodities included in winner and loser portfolios at each period.
21
Returns are regressed on convenience yield derived from corresponding maturity, i.e., 3-
month convenience yield is regressed against returns of long-only the 1st-nearby futures
and the shortest calendar spread and so on and so forth.15
From (10) a linkage between momentum and backwardation (Miffre and Rallis’s
(2007)) would be supported if:
(1) The regression estimate of 1
β
is significantly positive (negative) for the long winner
(short loser) portfolio for a holding period of 12 months. A positive correlation
suggests that winner (loser) wins (loses) more when market becomes more
backwardated (contangoed). This is the simplest case since no rebalancing is
performed during the one year horizon, and as a consequence the roll yield can be
ignored.saves roll yield from being considered.
(2) Positive or negative estimates of 1
β
for portfolio returns under other ranking and
holding periods because of the dual forces offsetting each other. However, if the
winner (loser) portfolio does have more exposure to backwardated (contangoed)
contracts or both, 1
β
should, on average, be much larger in absolute value for the
winner portfolio than that for the loser portfolio because inventory influences price
more in a backwardated market than in a contangoed market.
(3) Since 1
β
is determined by the joint correlation between the convenience yield, the
spot return and the roll return, the sign of 1
β
demonstrates the dominant return
15 The effect of backwardation on futures return is complex since the futures excess return is roughly
made up of the spot returnand the roll return, which both correlate with the term structure, but in opposite
directions (see Till (2007)) Increasing backwardation (contango) should diminish (enhance) the spot
return and increase (decrease) the roll return. Thus, the overall effect of term structure on the portfolio
return should be a balance of both forces, either in backwardation or in contango. As per Till (2007) the
spot return is defined as distant futures price divided by nearby futures price, and roll return is the
difference between futures return and spot return.
22
explained. For a longed portfolio, in backwardation or contango, spot return always
declines with a rising convenience yield while roll return always rises with it, and
vice versa for a shorted portfolio. Therefore, a positive 1
β
points to an increased term
structure effect on roll return (spot return) in a longed (shorted) portfolio and so on
and so forth.
Empirical estimates of (10) are shown in Tables 18 to 23 for the six strategies.
Please insert Tables 18-23 about here.
It is clear that the convenience yield has significant explainatory power for
momentum trading returns under most of the ranking and holding periods. Consistent
with hypothesis one, 1
β
is significantly positive and significantly negative for longed
winner and shorted loser portfolios that are being held for and beyond six months.
Hypothesis two is also supported in most cases, since 1
β
is larger in size for winner
portfolios than for loser portfolios. Consistent with hypothesis three, both the 6-month
and 12-month convenience yields drive the futures roll return. However, the 3-month
convenience yield has a greater influence on the roll return of winner portfolios and on
the spot return of loser portfolios.
Net hedging pressure is another significant factor of momentum returns in most
cases. 2
β
is positive for winner portfolios and negative for shorted loser portfolios,
which means on average, a rising short hedging pressure boosts both winner and loser
returns and a declining short hedging pressure reduces both. The only exception occurs
in a scenario with a one-year ranking and one-year holding periods, which could be due
23
to a large number of short hedgers choosing one year as the hedging span and their
collective unwinding at the end of one year boosting portfolio returns.
In sum, both convenience yield and net hedging pressure contain information useful
for momentum strategies. These results provide motivation for two potentially
profitable trading strategies:
a) taking a long position in a portfolio with the highest convenience yield and short
portfolio with the lowest convenience yield.16 For spread trading, this strategy involves
going long the short spread with the highest convenience yield and short the short
spread with the lowest convenience yield.
b) long portfolio (short spread) with the highest hedging pressure and short portfolio
(short spread) with the lowest hedging pressure.
These two strategies are implemented to examine whether information contained in
convenience yield and net hedging pressure can be capitalized on and exploited into
abnormal profits.
6.2.1 Portfolio construction:
Relative convenience yield and net hedging pressure are used to assign commodities
into portfolios. Relative convenience yield (net hedging pressure) is defined as last
period’s convenience yield (net hedging pressure) divided by average convenience yield
(net hedging pressure) in the ranking period. In each period, these two ratios are
calculated and ranked to form two portfolios that have the highest and lowest ratios. A
relative ratio is used instead of the average convenience yield (net hedging pressure)
because the four commodities have very different historical levels of both factors, which
16 This coheres with Miffre and Rallis’s (2007) suggestion of consistently trading the most backwardated
and contangoed contracts.
24
invalidates a direct comparison between each other. Four strategies are simulated: two
outright futures and two spreads with the shortest and longest maturities.
6.3.1 Empirical results
6.3.2.1 Convenience yield trading strategy:
Please insert Tables 24-27 about here
Long-short outright futures fail to capitalize on term structure risk. Long-short the
first-nearby futures contract on average incurs an economically small but statistically
statistically significant loss. Long-short the 12-month futures on average yields no
significant trading gains or losses.
In contrast, spread trading provides significantly positive results in most scenarios.
Trading long-term spreads yields much higher profits in all circumstances, mainly driven
by low ratio portfolios. For both spreads, the highest returns come from strategies with a
six- to twelve-month ranking period and a one-month holding period, yielding 7.2%
annual return for short-term spread and roughly 14% for long-term spread. Trading
profits decrease with declining rebalancing frequency.
In conclusion, the spread strategy produces more consistent profits than the
outright futures strategy in capitalizing on convenience yield. The strategy of longing the
most backwardated short spread and shorting the most contangoed spread provides an
annualized expected return ranging from approximately 6% to 14% when using the long-
term spread. The shorter the holding period, the higher the trading profits.
6.3.2.2 Net hedging pressure trading strategy:
As is shown in Tables 29 to 31, the net hedging pressure strategy is less profitable than
the convenience yield strategy. . Long-short the long-term spread outperforms all other
25
strategies based on net hedging pressure, and is the only ith exploitable profits. This
result is consistent with Roon et al (2004), whereby hedging pressure effect can be
inferred ough spreads. Low ratio portfolio drives majority of trading profits. And trading
profits decrease rapidly with increasing holding period.
Please insert Tables 29 -31 about here
7. Conclusions
Convenience yield and net hedging pressure are two unique features of
commodity futures markets, which contain information for futures risk premium. This
paper provides some new evidence on the relationship between these factors and
commodity returns. It also looks at active trading strategies that make use of their time-
varying nature.
Estimates of VAR Granger-causality model demonstrate that the structure of all
the four commodities contain predictive power to corresponding term premiums, but only
that of oil and soybean lead their spot premiums. And no significant causality of net
hedging pressure is found on either risk premium.
Several active trading strategies are identified: momentum effects are observed in
all scenarios for both outright futures and spread trading strategies, especially for
continuously rolled-over short-term futures and long-term spread. For strategies based on
past hedging pressure, the long-short the long-term spreads strategy offers the highest
and most significant return, On average, spread trading outperforms outright futures
trading in capturing the term structure risk and hedging pressure risk.
26
REFERENCES
Bessembinder, H., (1992), “Systematic Risk, Hedging Pressure, and Risk Premiums in
Futures Markets”, The Review of Financial Studies 5, No. 4, 637-667.
Brennan, M.J., (1958), “The supply of storage,” American Economic Review 48, 50-72.
Carter C., Rausser G., and Schmitz A., (1983), “Efficient Asset Portfolios and the Theory
of Normal Backwardation,” Journal of Political Economy 91, 319-331.
Chang E., (1985), “Returns to Speculators and the Theory of Normal Backwardation”,
Journal of Finance 40, pp 193-208.
Cootner, P., (1960), “Returns to Speculators: Telser vs Keynes,” Journal of Political
Economy 68, August, 396-404.
De Roon, F., Nijman Theo E., and Veld Chris, (1998), “Pricing Term Structure Risk in
Futures Markets,”Journal of Financial and Quantitative Analysis 33, No.1, 139-157.
De Roon, F., R. van den Goorbergh, and T. Nijman, (2000), “Hedging pressure Effects in
Futures Markets,” Journal of Finance 55, 1437-56.
De Roon, F., R. van den Goorbergh, and T. Nijman, (2004), “An Anatomy of Futures
Returns: Risk Premiums and Trading Strategies”, WO Research Memoranda 757,
Netherlands Central Bank, Research Department.
Dincerler,C., Khokher, Z. and T. Simin, (2005), “An Empirical Analysis of Commodity
Convenience Yields,” Working Paper, Pennsylvania State University.
Erb, C. and C. Harvey, (2006), “The Strategic and Tactical Value of Commodity
Futures,” Financial Analysts Journal 62(2), 69-97.
Fama, E. F. and K. R, French, (1988), “Business Cycles and the Behavior of Metals
Prices,” Journal of Finance 43, 1075-1093.
Fama, E. F. and J. MacBeth (1973), “Risk, Return and Equilibrium: Empirical Tests,”
Journal of Political Economy 81, 607-637.
Fama, E.F. (1991), “Efficient Capital Markets: II,” Journal of Finance 46, 1575-1617.
Feldman, B. and H. Till, (2006), “Backwardation and Commodity Futures Performance;
Evidence Evolving Agricultural Markets,” Journal of Alternative Investments 9(3),
24-39.
Hicks, J. R., (1939), Value and Capital , Cambridge: Oxford University .Press.
27
Hirshleifer, D., (1988), “Residual Risk, Trading Costs, and Commodity Futures Risk
Premia,” Review of Financial Studies 1(2), 173-93.
Jegadeesh, N., and S. Titman, (1993), “Returns to Buying Winners and Selling Losers:
Implications for Stock Market Efficiency,”Journal of Finance 48, 65-91.
Jegadeesh, N., and S. Titman,(2001), “Profitability of Momentum Strategies: An
Evaluation of Alternative Explanations,” Journal of Finance 56, 699-720.
Kaldor, N., (1939) “Speculation and Economic Stability,” Review of Economic Studies
7(1), 1-27.
Keynes, J., (1930), “A Treatise on Money”, Volume 2, Macmillan, London.
Lutkepohl, Helmut (1993), Introduction to Multiple Time Series Analysis, Second
Edition (Springer-Verlag).
Miffre, J. and G. Rallis, (2007), “Momentum Strategies in Commodity Futures Markets,”
Journal of Banking & Finance 31, 1863-1886.
Moskowitz, T. J. and M. Grinblatt, (1999), “Do Industries Explain Momentum?” Journal
of Finance 54, pp 1249-1290.
Samuelson, P. (1965), “Proof that properly anticipated prices fluctuate randomly,”
Industrial Management Review 6, 41-49.
Till, Hilary, (2007), “A Long Term Perspective on Commodity Futures Returns: Review
of the Historical Literature,” in H. Till and E. Joseph, Intelligent Commodity
Investing: New Strategies and Practical Insights for Informed Decision Making
London: Risk Books.
Working, H., (1948), “Theory of the Inverse Carrying Charge in Futures Markets,”
Journal of Farm Economics 30(1), 1-28.
Working, H., (1953), “Futures Trading and Hedging,” American Economic Review 43,
341-43.
28
Appendix 1: Terminology
Term structure of commodity yield:
The term structure of commodity shows the relationship between the maturity of a
futures contract and the futures price at a specific point in time.
Backwardation and contango:
These terms are used to describe the shape of term structure. Backwardation
(contango) refers to a downward (upward) sloping term structure in which futures prices
decline (rise) with maturity. According to Keynes (1930) and Hicks (1939), futures
markets are used predominantly by short hedgers (producers in underlying commodities)
so that futures price should be biased down to remunerate speculators for being long.
Current futures price will rise to converge to the spot price as maturity approaches.
Carrying charge and inverse carrying charge:
Also called the “market-determined price of storage”, these terms refer to the
difference between two contract prices with different maturities. It is evident that a
backwardated market anticipates an inverse carrying charge and a contangoed market a
carrying charge from nearby to distant futures.
Long spread and short spread:
In commodity trading, a long (short) spread is to long (short) a nearby contract
and short (long) a distant contract of the same commodity.
Outright futures strategy:
Outright futures position is a position in a futures contract that is not offset, in
contrast to spread trading strategy.
29
Figure 1: Term Structure of Average Commodity Futures Prices, daily data
Term structure of average oil price
26.4
26.6
26.8
27
27.2
27.4
27.6
27.8
28
01 23 4 5 67 8 9101112
Months to maturity
Average price of oil futures
Term structure of average gold price
364
366
368
370
372
374
376
378
0123456789101112
Months to maturity
Averge price of gold futures
30
Term structure of average copper price
107
108
109
110
111
112
113
114
0 1 2 3 4 5 6 7 8 9 10 11 12
Months to maturity
Average price of copper futures
Term structure of average soybean price
601.2
601.4
601.6
601.8
602
602.2
602.4
602.6
602.8
603
603.2
0123456789101112
Months to maturity
Average price of soybean futures
31
Table 1: Futures contract information
Contract Exchange Delivery months Last trading day
WTI crude oil New York Mercantile
Exchange
All months The third business day prior to
the 25th calendar day of the
month preceding the delivery
month.
Gold Commodity Exchange
Inc.
2 4 6 8 10 12 The third to last business day of
the maturing delivery month.
Copper Commodity Exchange
Inc.
All months The third to last business day of
the maturing delivery month.
Soybean Chicago Board of
Trade
1 3 5 7 9 1117 The business day prior to the
15th calendar day of the contract
month.
17 Soybean futures are also traded for delivery in August. We neglect the August contract when
constructing the time-series data in order to make data sets evenly spaced.
32
Table 2: Summary Statistics on Returns Based on the Spot price and the First-
nearby futures price
Panel A. Daily Returns Results
N Mean Median Std Dev Skewness Kurtosis Maximum Minimum Jarque-Bera
return of Oil SP 4262 0.0230% 0.0646% 0.0229 -1.3447 25.1474 0.1357 -0.3841 88390.31
return of Oil F1 4260 0.0237% 0.0559% 0.0203 -1.2388 21.9776 0.1235 -0.3282 65016.13
return of Gold SP 4258 0.0103% 0.0000% 0.0091 -0.2433 13.1188 0.0889 -0.0773 18207.74
return of Gold F1 4254 0.0100% 0.0000% 0.0090 -0.2676 12.5845 0.0883 -0.0775 16333.49
return of Copper SP 4260 0.0233% 0.0000% 0.0154 -0.2334 7.1863 0.1119 -0.1167 3149.40
return of Copper F1 4256 0.0241% 0.0000% 0.0152 -0.2664 7.2954 0.1156 -0.1152 3322.24
return of Soybean SP 4255 0.0036% 0.0000% 0.0147 -3.3217 74.7963 0.0673 -0.3409 921711.00
return of Soybean F1 4255 0.0036% 0.0000% 0.0139 -1.2417 21.3397 0.0677 -0.2122 60724.67
return of CRB 4250 0.0060% 0.0166% 0.0063 -0.0517 4.6147 0.0374 -0.0291 463.62
return of R3000 4250 0.0345% 0.0557%
0.0098 -0.1226 6.8065 0.0537 -0.0687 2576.4520
10-y T-bond 4172 -0.0006% 0.0000% 0.0006 0.3540 5.1400 0.0039 -0.0023 883.2510
Return of SP refers to return of spot markets; return of F1 refers to return of the most nearby
futures contracts. Return of CRB commodity index, return of Russell 3000 index and return of 10-year U.S.
Treasury bond are listed here as benchmarks.
Returns are calculated with daily data from January 1st 1990 to December 31st 2006. All returns
are calculated against the one-day price lag of the same time series and not across contracts with different
maturities.
33
Table 2.
Panel B. Annualized Mean and Standard Deviation of Spot and First Nearby Future
Returns
Return Oil SP Oil F1 Gold SP Gold F1 Copper
SP
Copper
F1
Soybean
SP
Soybean
F1 CRB R3000 10-y
T-bond
Annual
mean 5.75% 5.93% 2.58% 2.49% 5.83% 6.03% 0.90% 0.90% 1.50% 8.63% -0.16%
Annual
Std Dev 36.22% 32.09% 14.38% 14.29% 24.40% 24.05% 23.27% 21.97% 10.01% 15.51% 0.92%
34
Table 3: Summary statistics of spot premium and term premium,
Panel A. Daily Returns Results
Daily
Mean Spot premium
()
()
,
k
st t k t
f
s
π
+
=− Term premium
(
)
(
)
() ( ) ()
(,) knkn
kn
ttk
ttkt
f
ff
s
++
=−− −
Θ
k p=3 p=4 p=5 p=6 p=7 p=8 p=9 p=10 p=11 p=12
Oil 1.99% 0.34% 0.32% 0.30% 0.28% 0.27% 0.25% 0.23% 0.23% 0.23%
Gold 0.24% -0.59% -0.59% -0.58% -0.57%
Copper 1.91% 0.26% 0.24% 0.22% 0.21% 0.20% 0.19% 0.18% 0.18% 0.18% 0.12%
Soybean -0.07% -0.19% -0.16% -0.17% -0.19%
Daily
Std Dev Spot premium
()
()
,
k
st t k t
f
s
π
+
=− Term premium
(
)
(
)
() ( ) ()
(,) knkn
kn
ttk
ttkt
f
ff
s
++
=−− −
Θ
k p=3 p=4 p=5 p=6 p=7 p=8 p=9 p=10 p=11 p=12
Oil 15.84% 2.85% 3.77% 4.60% 5.35% 5.99% 6.56% 7.11% 7.58% 8.01%
Gold 6.83% 0.41% 0.50% 0.59% 0.70%
Copper 12.08% 1.53% 1.91% 2.19% 2.51% 2.80% 3.13% 3.46% 3.78% 4.10% 9.89%
Soybean 12.59% 4.99% 5.97% 5.97% 6.37%
Returns are calculated with daily data from January 1st 1990 to December 31st 2006.
Spot premium is obtained by longing the 1st-nearby futures mature in k days and term premium
obtained by longing the same futures maturing at t+k and shorting distant futures maturing at t+n (k<n)
and holding the spread for k days.
p refers to number of months until maturity for contract being shorted. n and k refer to number of
days until maturity for contract being shorted and for the 1st-nearby futures being longed in both strategies
respectively. In this paper, the 1st-nearby futures are mature in different months across four markets, i.e. 3
months, 4 months, 2 months and 3 months for oil, gold, copper and soybean respectively.
35
Table 3
Panel B. Annualized Mean and Standard Deviation of Spot and Term Premium.
Annual
Mean Spot premium
()
()
,
k
st t k t
f
s
π
+
=− Term premium
(
)
(
)
() ( ) ()
(,) knkn
kn
ttk
ttkt
f
ff
s
++
=−− −
Θ
k p=3 p=4 p=5 p=6 p=7 p=8 p=9 p=10 p=11 p=12
Oil 7.95% 4.08% 1.91% 1.20% 0.84% 0.64% 0.49% 0.40% 0.34% 0.30%
Gold 0.72% -3.54% -1.76% -1.16% -0.86%
Copper 11.45% 3.07% 1.42% 0.88% 0.62% 0.47% 0.38% 0.32% 0.27% 0.24% 0.14%
Soybean -0.28% -1.15% -0.49% -0.34% -0.28%
Annual
Std Dev Spot premium
()
()
,
k
st t k t
f
s
π
+
=− Term premium
(
)
(
)
() ( ) ()
(,) knkn
kn
ttk
ttkt
f
ff
s
++
=−− −
Θ
k p=3 p=4 p=5 p=6 p=7 p=8 p=9 p=10 p=11 p=12
Oil 31.69% 9.88% 9.22% 9.20% 9.26% 9.28% 9.28% 9.31% 9.28% 9.25%
Gold 11.84% 1.00% 0.86% 0.83% 0.85%
Copper 29.58% 5.30% 4.67% 4.39% 4.34% 4.34% 4.42% 4.52% 4.63% 4.73% 10.83%
Soybean 25.18% 12.22% 10.34% 8.44% 7.80%
T-test results for Significance of Premia:
(1) Oil: spot premium and term premiums up to p=8 are significantly different from zero at 1% level; term
premia p=9 and p=10 are significant at the 5% level; the rest are all significant at 10%.
(2) Gold: spot premium is significantly different from zero at the 5% level; the remaining premia are all
significant at 1%.
(3) Copper: term premium p=12 is not significantly different from zero; all other premia are all significant
at the 1% level.
(4) Soybean: spot premium is not significantly different from zero; term premium p=5 is significant at the
5% level; all other premia are significant at 10%
36
Table 4: Summary Statistics for the Estimated Convenience Yield Under Adequate
and Inadequate Inventory Levels, Daily Data
Unconditional Annualized Mean Annualized Std Dev
Annualized
Mean
Annualized
Std Dev % Positive Positive Negative Positive Negative
Oil 3-month 5.60% 4.16% 74.75% -3.48% 8.75% 1.81% 3.54%
6-month 8.04% 8.38% 73.14% -5.60% 13.17% 3.56% 6.62%
12-month 8.94% 10.24% 81.72% -5.18% 12.18% 4.14% 8.29%
Gold 4-month 2.39% 0.80% 99.95% -0.20% 2.39% 0.13% 0.80%
6-month 1.89% 0.79% 99.60% -0.04% 1.90% 0.02% 0.79%
12-month 1.40% 0.88% 99.88% -0.01% 1.40% 0.01% 0.88%
Copper 3-month 6.56% 4.16% 77.69% -1.52% 13.18% 0.34% 5.04%
6-month 7.64% 6.14% 76.45% -1.33% 10.47% 0.50% 5.73%
12-month 8.23% 10.39% 81.04% -1.22% 10.68% 0.65% 10.33%
Soybean 3-month 3.49% 6.19% 50.50% -2.03% 9.05% 0.67% 7.81%
7-month 3.44% 7.77% 51.29% -2.47% 9.20% 1.08% 8.88%
11-month 3.52% 7.68% 55.23% -2.02% 8.15% 1.28% 7.98%
The estimated convenience yield is the negative of the interest-adjusted basis, calculated as:
(, ) () (, ) ( )
f
tT st RtT T t−− −
. We provide estimates of the convenience yield under conditions of adequate
(“positive” column) and inadequate (“negative” column) inventory levels.
Three contracts—the 3-month futures, the 6-month futures and the 12-month futures are used to calculate
the short-term, intermediate-term and long-term convenience yield for the majority of commodities. Since
gold market only trades contracts maturing in even months and soybean market only in odd months,
different contracts other than the three maturities have to be chosen for both markets. The 4-month futures
is used to calculate the short-term convenience yield for gold, and the 7-month and 11-month contracts are
used to calculate the intermediate-term and long-term convenience yields for soybean.
Positive (negative) refers to a positive (negative) interest-adjusted basis, in other words a negative
(positive) convenience yield, which holds when inventory is adequate (inadequate).
% Positive (negative) refers to the percentage of observations for which the convenience yield is
positive (negative)
37
Table 5: Summary statistics of net hedging pressure variable, semi-monthly data
Mean Std Dev
Oil 0.57% 5.74%
Gold 12.28% 30.04%
Copper 13.15% 20.91%
Soybean 12.76% 20.99%
Oil Gold Copper Soybean
Year Obs Mean Std Dev Mean Std Dev Mean Std Dev Mean Std Dev
1990 24 -5.36% 3.39% 0.54% 15.64% 3.88% 17.03% 9.70% 10.63%
1991 24 0.82% 4.35% -7.23% 20.02% -3.94% 19.46% 19.76% 8.71%
1992 24 -2.12% 5.01% -6.18% 17.80% 7.83% 20.27% 24.29% 16.50%
1993 24 -3.74% 3.99% 25.79% 25.30% 5.37% 12.55% 42.62% 12.27%
1994 24 3.99% 3.62% 16.89% 19.99% 37.39% 7.15% 16.16% 28.23%
1995 24 5.49% 7.81% -0.82% 13.99% 14.91% 18.32% 19.68% 18.41%
1996 24 2.43% 3.14% 1.74% 20.18% 18.68% 12.57% 31.26% 12.40%
1997 24 -2.20% 7.03% -18.10% 11.73% 30.89% 19.66% 12.86% 22.46%
1998 24 -1.87% 4.72% -9.45% 15.89% 7.58% 13.90% -9.79% 10.62%
1999 24 7.37% 4.70% -23.94% 18.10% 19.72% 19.08% -3.25% 14.78%
2000 24 2.29% 2.58% -8.19% 16.47% 14.80% 14.22% 27.49% 7.38%
2001 24 -5.31% 4.31% 8.09% 34.04% -13.88% 10.35% 8.98% 13.53%
2002 24 3.19% 5.62% 40.36% 11.02% 13.30% 14.74% 20.48% 10.06%
2003 24 0.07% 5.37% 47.46% 11.29% 32.01% 15.36% 16.64% 14.55%
2004 24 3.82% 4.00% 45.28% 11.13% 27.12% 9.89% 0.43% 23.34%
2005 24 -0.67% 3.82% 48.73% 15.02% 16.61% 9.72% -7.55% 13.80%
2006 24 1.44% 2.52% 47.80% 8.04% -8.76% 12.57% -12.90% 10.25%
Net hedging pressure is calculated as the difference between short and long hedge positions of
commercial traders divided by their total hedge positions.
short hedge positions - long hedge positions
total hedge positions
tH=
38
Table 6: Unit Root Tests for the Spot Premium, Term Premium, Convenience Yield,
and Net Hedging Pressure Variables
Intercept Trend &
Intercept None Intercept Trend &
Intercept None
Spot
premium t-Stat
ADF p-value
ADF t-Stat
ADF p-value
ADF t-Stat
ADF p-value
ADF t-Stat
PP p-value
PP t-Stat
PP p-value
PP t-Stat
PP p-value
PP
oilRF1 -5.70
0.00 -5.71 0.00 -5.65 0.00 -5.99 0.00 -6.00 0.00 -5.94 0.00
goldRF1 -6.25
0.00 -6.60 0.00 -6.24 0.00 -6.14 0.00 -6.47 0.00 -6.13 0.00
coppRF1 -5.36
0.00 -5.55 0.00 -5.33 0.00 -5.48 0.00 -5.68 0.00 -5.43 0.00
soybRF1 -5.04
0.00 -5.06 0.00 -5.04 0.00 -5.47 0.00 -5.49 0.00 -5.47 0.00
Term premium
oilSPR1 -5.76
0.00 -5.83 0.00 -5.72 0.00 -7.33 0.00 -7.39 0.00 -7.28 0.00
oilSPR2 -6.82
0.00 -6.87 0.00 -6.80 0.00 -7.13 0.00 -7.17 0.00 -7.12 0.00
oilSPR3 -6.35
0.00 -6.36 0.00 -6.34 0.00 -6.74 0.00 -6.76 0.00 -6.74 0.00
goldSPR1 -6.64 0.00 -6.62 0.00 -3.55 0.00 -9.95 0.00 -9.95 0.00 -5.49 0.00
goldSPR2 -4.99 0.00 -5.07 0.00 -3.85 0.00 -6.28 0.00 -6.35 0.00 -5.07 0.00
coppSPR1 -9.07 0.00 -9.06 0.00 -8.97 0.00 -8.90 0.00 -8.90 0.00 -8.81 0.00
coppSPR2 -8.62 0.00 -8.63 0.00 -8.62 0.00 -8.28 0.00 -8.30 0.00 -8.29 0.00
coppSPR3 -10.83 0.00 -10.86 0.00 -10.83 0.00 -75.61 0.00 -75.52 0.00 -75.63 0.00
soybSPR1 -6.36 0.00 -6.36 0.00 -6.35 0.00 -6.59 0.00 -6.60 0.00 -6.59 0.00
soybSPR2 -5.80 0.00 -5.81 0.00 -5.80 0.00 -5.93 0.00 -5.94 0.00 -5.93 0.00
soybSPR3 -5.72 0.00 -5.72 0.00 -5.71 0.00 -5.62 0.00 -5.62 0.00 -5.61 0.00
soybSPR4 -5.78 0.00 -5.78 0.00 -5.78 0.00 -5.94 0.00 -5.94 0.00 -5.94 0.00
Convenience yield
oilCY1 -5.14
0.00 -5.14 0.00 -4.59 0.00 -7.66 0.00 -7.98 0.00 -6.10 0.00
oilCY2 -5.37
0.00 -5.41 0.00 -4.73 0.00 -4.81 0.00 -4.85 0.00 -4.24 0.00
oilCY3 -4.16 0.00 -4.18 0.00 -3.42 0.00 -4.09 0.00 -4.10 0.01 -3.35 0.00
goldCY1 -8.21
0.00 -9.48 0.00 -4.27 0.00 -9.50 0.00 -11.29 0.00 -3.74 0.00
goldCY2 -6.76
0.00 -8.09 0.00 -3.67 0.00 -7.24 0.00 -9.17 0.00 -2.89 0.00
goldCY3 -4.51
0.00 -5.66 0.00 -2.72 0.01 -3.68 0.00 -5.18 0.00 -1.91 0.05
coppCY1 -4.76
0.00 -4.78 0.00 -4.12 0.00 -5.43 0.00 -5.60 0.00 -4.17 0.00
coppCY2 -3.41
0.01 -3.50 0.04 -2.83 0.00 -3.37 0.01 -3.46 0.04 -2.60 0.01
coppCY3 -28.77
0.00 -28.99 0.00 -21.77 0.00 -57.79 0.00 -58.58 0.00 -38.45 0.00
soybCY1 -6.82
0.00 -6.83 0.00 -6.55 0.00 -7.59 0.00 -7.60 0.00 -7.32 0.00
soybCY2 -4.02
0.00 -4.03 0.01 -3.82 0.00 -4.62 0.00 -4.63 0.00 -4.41 0.00
soybCY3 -3.86
0.00 -3.85 0.01 -3.55 0.00 -4.51 0.00 -4.53 0.00 -4.05 0.00
Net hedging pressure
oil -6.56
0.00 -6.62 0.00 -6.52 0.00 -6.84 0.00 -6.92 0.00 -6.81 0.00
gold -4.44 0.00 -5.25 0.00 -4.08 0.00 -4.51 0.00 -5.35 0.00 -4.16 0.00
copper -5.54
0.00 -5.51 0.00 -4.67 0.00 -5.74 0.00 -5.71 0.00 -4.76 0.00
soybean -3.45 0.01 -3.83 0.01 -2.94 0.00 -3.72 0.00 -4.01 0.01 -3.17 0.00
39
Table 7: VAR estimates—Spot Premia(RF1), convenience yield (CYp) and net
hedging pressure (QT), weekly data, from October 1992 to December 2006
OIL GOLD
RF1 CY1 CY2 CY3 QT RF1 CY1 CY2 CY3 QT
RF1(-1) 0.89 0.01 0.03 0.04 0.03 RF1(-1) 0.90 0.00 0.00 0.00 0.20
t-value 54.32*** 3.27*** 5.60*** 6.56*** 3.90*** t-value 55.01*** -2.17** -1.79* -1.14 4.24***
CY1(-1) -1.50 0.75 0.16 0.33 -0.04 CY1(-1) -0.89 0.11 -0.70 -0.74 -1.86
t-value -2.80*** 11.75*** 1.12 1.47 -0.19 t-value -0.59 0.78 -5.10*** -5.05*** -0.43
CY2(-1) 1.25 0.10 0.75 -0.35 0.09 CY2(-1) 1.04 0.68 1.46 0.57 1.86
t-value 3.00*** 1.96** 6.50*** -1.99** 0.53 t-value 0.57 4.16*** 8.88*** 3.22*** 0.36
CY3(-1) -0.43 -0.02 0.09 1.10 -0.05 CY3(-1) -0.47 -0.10 -0.06 0.89 -0.82
t-value -2.86*** -1.10 2.14** 17.42*** -0.76 t-value -0.95 -2.20** -1.38 18.34*** -0.57
QT(-1) 0.03 0.00 0.00 0.00 0.91 QT(-1) 0.00 0.00 0.00 0.00 0.95
t-value 0.76 -0.32 0.19 0.28 53.21*** t-value 0.19 -4.61*** -5.15*** -5.83*** 73.54***
C 0.01 0.00 0.00 0.00 0.00 C 0.00 0.00 0.00 0.00 0.02
t-value 2.73*** 2.02** -0.77 -0.67 0.88 t-value 1.48 8.15*** 8.25*** 8.24*** 1.76*
COPPER SOYBEAN
RF1 CY1 CY2 CY3 QT RF1 CY1 CY2 CY3 QT
RF1(-1) 0.93 0.00 0.01 0.02 0.08 RF1(-1) 0.90 -0.02 0.00 0.01 0.07
t-value 64.69*** 0.87 2.20** 3.74*** 4.02*** t-value 57.66*** -2.88*** 0.36 1.27 5.01***
CY1(-1) 0.05 0.41 -0.27 -0.25 -1.26 CY1(-1) 0.22 0.73 -0.26 -0.26 -0.20
t-value 0.10 5.78*** -2.77*** -1.74* -1.94* t-value 3.18*** 26.71*** -8.13*** -6.97*** -3.04***
CY2(-1) 0.09 0.32 1.01 0.02 1.75 CY2(-1) -0.22 0.10 1.00 0.10 0.02
t-value 0.20 4.56*** 10.41*** 0.16 2.75*** t-value -3.05*** 3.47*** 29.54*** 2.61*** 0.32
CY3(-1) -0.05 -0.04 0.04 1.02 -0.62 CY3(-1) 0.08 -0.02 0.02 0.92 0.00
t-value -0.35 -1.71* 1.44 22.80*** -3.11*** t-value 1.43 -1.00 0.88 31.01*** 0.03
QT(-1) 0.01 0.00 0.00 0.00 0.93 QT(-1) 0.00 0.00 0.00 0.01 0.98
t-value 0.79 -2.41** -1.52 -1.08 68.57*** t-value -0.51 0.28 1.18 1.97** 126.48***
C 0.00 0.00 0.00 0.00 0.01 C 0.00 0.00 0.00 0.00 0.00
t-value 0.00 2.42** 1.26 1.47 3.76*** t-value 0.64 1.41 1.34 1.82* 1.55
40
Table 8: VAR estimates—Oil Term premium (SPRp), Convenience Yield (CYp) and
Net Hedging Pressure (QT), weekly data, October 1992 to December 2006
OILSPR1 OILCY1 OILCY2 OILCY3 OILQT
OILSPR1(-1) 0.8629 -0.0001 -0.0173 -0.0429 -0.0304
[ 20.8510]*** [-0.01154] [-0.96186] [-0.87476] [-0.36736]
OILSPR1(-2) 0.0579 -0.0078 0.0243 0.0455 -0.1466
[ 1.06034] [-0.67435] [ 1.02364] [ 0.70274] [-1.34181]
OILSPR1(-3) -0.0208 0.0065 -0.0393 -0.0695 0.0217
[-0.38076] [ 0.56520] [-1.65283]* [-1.07368] [ 0.19822]
OILSPR1(-4) 0.0270 0.0046 0.0271 0.0564 0.0592
[ 0.49381] [ 0.39589] [ 1.14088] [ 0.87178] [ 0.54207]
OILSPR1(-5) -0.0383 -0.0031 0.0389 0.0898 0.1827
[-0.70521] [-0.26840] [ 1.64577]* [ 1.39445] [ 1.67923]*
OILSPR1(-6) 0.0080 -0.0300 -0.0094 -0.0428 -0.1480
[ 0.15077] [-2.66404]*** [-0.40536] [-0.67684] [-1.38518]
OILSPR1(-7) 0.0034 0.0444 -0.0208 -0.0214 0.0897
[ 0.06293] [ 3.94530]*** [-0.89615] [-0.33886] [ 0.84025]
OILSPR1(-8) -0.0715 -0.0236 0.0016 -0.0092 0.0801
[-1.32843] [-2.07816]** [ 0.07039] [-0.14443] [ 0.74364]
OILSPR1(-9) 0.1527 0.0077 0.0423 0.1064 -0.0578
[ 2.84413]*** [ 0.67625] [ 1.81338]* [ 1.67159]* [-0.53827]
OILSPR1(-10) -0.0178 -0.0080 -0.0158 -0.0274 -0.0858
[-0.32812] [-0.70057] [-0.67003] [-0.42647] [-0.79092]
OILSPR1(-11) -0.0815 0.0020 -0.0211 -0.0513 -0.0412
[-1.51284] [ 0.17419] [-0.90207] [-0.80374] [-0.38156]
OILSPR1(-12) -0.3935 0.6089 1.4206 1.9438 0.7521
[-7.32435]*** [ 53.6839]*** [ 60.8075]*** [ 30.5306]*** [ 6.99528]***
OILSPR1(-13) 0.4468 -0.5546 -1.2024 -1.7147 -0.9617
[ 3.27030]*** [-19.2274]*** [-20.2352]*** [-10.5890]*** [-3.51701]***
OILCY1(-1) -0.2564 0.6800 0.2283 0.4046 0.0452
[-1.48841] [ 18.6951]*** [ 3.04760]*** [ 1.98165]** [ 0.13124]
OILCY1(-2) -0.2184 0.0432 -0.0708 -0.0797 0.3040
[-1.17482] [ 1.10031] [-0.87501] [-0.36166] [ 0.81688]
OILCY1(-3) 0.2634 0.1065 -0.0158 -0.2005 -0.0395
[ 1.41264] [ 2.70573]*** [-0.19485] [-0.90707] [-0.10577]
OILCY1(-4) 0.0288 -0.0141 0.1742 0.4929 0.4169
[ 0.15420] [-0.35804] [ 2.14198]** [ 2.22356]** [ 1.11372]
OILCY1(-5) 0.0884 -0.0467 0.0021 0.0912 -0.3183
[ 0.47713] [-1.19322] [ 0.02582] [ 0.41512] [-0.85836]
OILCY1(-6) -0.2142 0.0381 -0.0752 -0.2311 0.3199
[-1.15749] [ 0.97637] [-0.93406] [-1.05340] [ 0.86372]
OILCY1(-7) -0.2628 -0.0010 0.0883 0.1885 0.2042
[-1.41473] [-0.02588] [ 1.09358] [ 0.85612] [ 0.54926]
OILCY1(-8) 0.4704 0.0000 -0.0267 -0.1218 -0.1592
41
[ 2.52498]** [-6.0e-05] [-0.32945] [-0.55175] [-0.42698]
OILSPR1 OILCY1 OILCY2 OILCY3 OILQT
OILCY1(-9) -0.2291 0.1134 -0.0312 -0.0510 -0.2135
[-1.22143] [ 2.86408]*** [-0.38256] [-0.22920] [-0.56874]
OILCY1(-10) 0.2449 -0.0194 -0.0945 -0.1756 0.0574
[ 1.29638] [-0.48617] [-1.15033] [-0.78430] [ 0.15180]
OILCY1(-11) -0.4583 -0.0350 0.2484 0.4984 -0.2863
[-2.42199]** [-0.87501] [ 3.01868]*** [ 2.22260]** [-0.75594]
OILCY1(-12) 0.2912 -0.2801 -0.7245 -1.0408 -0.6229
[ 1.53487] [-6.99395]*** [-8.78037]*** [-4.62867]*** [-1.64046]
OILCY1(-13) 0.0448 0.3223 0.4500 0.3926 0.5039
[ 0.27531] [ 9.37588]*** [ 6.35452]*** [ 2.03460]** [ 1.54648]
OILCY2(-1) 0.2349 0.1505 0.6965 -0.2873 0.0231
[ 1.24933] [ 3.79038]*** [ 8.51630]*** [-1.28914] [ 0.06145]
OILCY2(-2) 0.1618 -0.0061 -0.0844 -0.2844 -0.5040
[ 0.77419] [-0.13755] [-0.92844] [-1.14773] [-1.20472]
OILCY2(-3) -0.3031 -0.0785 0.0669 0.3723 0.7777
[-1.44761] [-1.77586]* [ 0.73493] [ 1.49999] [ 1.85576]*
OILCY2(-4) -0.2053 0.0220 -0.1133 -0.4278 -0.3391
[-0.97747] [ 0.49684] [-1.24024] [-1.71833]* [-0.80666]
OILCY2(-5) 0.2614 0.0654 -0.0707 -0.2142 -0.1284
[ 1.25100] [ 1.48312] [-0.77850] [-0.86514] [-0.30698]
OILCY2(-6) -0.0457 -0.0963 0.1258 0.3864 -0.4965
[-0.21963] [-2.19099]** [ 1.38974] [ 1.56655] [-1.19218]
OILCY2(-7) 0.1789 0.0146 -0.0454 -0.0928 0.4697
[ 0.85446] [ 0.33139] [-0.49808] [-0.37381] [ 1.12087]
OILCY2(-8) -0.2378 -0.0119 0.0259 -0.0282 -0.2481
[-1.13513] [-0.26951] [ 0.28380] [-0.11349] [-0.59165]
OILCY2(-9) 0.3123 -0.0545 0.0426 0.0873 0.3126
[ 1.49612] [-1.23541] [ 0.46873] [ 0.35273] [ 0.74827]
OILCY2(-10) -0.3246 0.0273 0.0576 0.2285 0.0830
[-1.54999] [ 0.61804] [ 0.63251] [ 0.92058] [ 0.19802]
OILCY2(-11) 0.4438 0.0387 -0.2191 -0.4641 0.2117
[ 2.10676]** [ 0.86978] [-2.39128]** [-1.85890]* [ 0.50215]
OILCY2(-12) -0.5816 0.3402 1.0509 1.5599 0.9653
[-2.74606]*** [ 7.60698]*** [ 11.4091]*** [ 6.21415]*** [ 2.27736]**
OILCY2(-13) 0.2641 -0.3865 -0.7382 -0.9594 -0.9092
[ 1.48040] [-10.2598]*** [-9.51349]*** [-4.53679]*** [-2.54613]**
OILCY3(-1) -0.0762 -0.0510 0.0700 1.0294 0.2696
[-0.88738] [-2.81178]*** [ 1.87412]* [ 10.1190]*** [ 1.56924]
OILCY3(-2) -0.0714 0.0001 0.0631 0.1854 0.0994
[-0.65110] [ 0.00229] [ 1.32284] [ 1.42664] [ 0.45307]
OILCY3(-3) 0.0997 0.0246 -0.0377 -0.1722 -0.4583
[ 0.90971] [ 1.06448] [-0.79023] [-1.32586] [-2.08938]**
OILCY3(-4) 0.1338 0.0001 0.0037 0.0677 0.0605
42
[ 1.21752] [ 0.00290] [ 0.07787] [ 0.51957] [ 0.27503]
OILCY3(-5) -0.1805 -0.0367 0.0589 0.1550 0.1576
[-1.64587] [-1.58264] [ 1.23514] [ 1.19225] [ 0.71811]
OILSPR1 OILCY1 OILCY2 OILCY3 OILQT
OILCY3(-6) 0.0918 0.0494 -0.0719 -0.2091 0.2478
[ 0.83776] [ 2.13636]** [-1.50886] [-1.60987] [ 1.12990]
OILCY3(-7) -0.1025 -0.0027 0.0007 -0.0074 -0.3605
[-0.92944] [-0.11633] [ 0.01497] [-0.05688] [-1.63318]
OILCY3(-8) 0.0598 0.0042 0.0090 0.1136 0.2646
[ 0.54415] [ 0.17943] [ 0.18763] [ 0.87194] [ 1.20242]
OILCY3(-9) -0.1446 0.0088 -0.0137 -0.0423 -0.2510
[-1.32030] [ 0.38104] [-0.28734] [-0.32620] [-1.14527]
OILCY3(-10) 0.1932 -0.0191 -0.0118 -0.0972 -0.0643
[ 1.76624]* [-0.82509] [-0.24862] [-0.74978] [-0.29351]
OILCY3(-11) -0.2132 -0.0118 0.0588 0.1166 -0.0099
[-1.93264]* [-0.50691] [ 1.22479] [ 0.89164] [-0.04474]
OILCY3(-12) 0.2395 -0.0449 -0.2545 -0.4006 -0.3381
[ 2.16495]** [-1.92162]* [-5.29047]*** [-3.05541]*** [-1.52712]
OILCY3(-13) -0.0896 0.0722 0.1713 0.2533 0.2710
[-1.05626] [ 4.03371]*** [ 4.64540]*** [ 2.51973]** [ 1.59636]
OILQT(-1) 0.0088 -0.0022 -0.0153 -0.0117 0.8940
[ 0.37064] [-0.43877] [-1.47634] [-0.41580] [ 18.7364]***
OILQT(-2) 0.0062 -0.0030 0.0119 0.0054 -0.0398
[ 0.19426] [-0.44165] [ 0.86089] [ 0.14382] [-0.62573]
OILQT(-3) 0.0293 0.0097 -0.0157 -0.0395 -0.0594
[ 0.93716] [ 1.47756] [-1.15747] [-1.06566] [-0.94995]
OILQT(-4) -0.0160 -0.0066 0.0291 0.0853 0.1243
[-0.50762] [-0.98562] [ 2.11293]** [ 2.27642]** [ 1.96422]**
OILQT(-5) -0.0048 0.0035 -0.0082 -0.0443 -0.0540
[-0.15239] [ 0.52753] [-0.59291] [-1.17422] [-0.84860]
OILQT(-6) -0.0440 -0.0048 0.0097 0.0235 -0.0716
[-1.35996] [-0.69828] [ 0.69264] [ 0.61249] [-1.10685]
OILQT(-7) 0.0485 0.0013 -0.0184 -0.0266 0.0425
[ 1.48487] [ 0.19157] [-1.29689] [-0.68536] [ 0.64938]
OILQT(-8) -0.0011 0.0004 0.0107 0.0319 0.0462
[-0.03453] [ 0.06373] [ 0.76151] [ 0.83218] [ 0.71473]
OILQT(-9) 0.0283 0.0098 -0.0072 -0.0362 0.0466
[ 0.88597] [ 1.45462] [-0.51730] [-0.95654] [ 0.73035]
OILQT(-10) -0.0165 -0.0069 -0.0010 0.0071 -0.0518
[-0.51950] [-1.03808] [-0.06930] [ 0.18951] [-0.81790]
OILQT(-11) -0.0017 -0.0023 0.0264 0.0725 0.0343
[-0.05264] [-0.34906] [ 1.91758]* [ 1.93067]* [ 0.54077]
OILQT(-12) -0.0079 -0.0050 -0.0228 -0.0475 -0.0105
[-0.24797] [-0.74530] [-1.64607] [-1.25946] [-0.16419]
OILQT(-13) 0.0081 0.0095 0.0053 -0.0147 -0.0157
43
[ 0.36302] [ 2.01569]** [ 0.54196] [-0.55234] [-0.34938]
C 0.0016 0.0006 0.0011 0.0023 0.0013
[ 1.26795] [ 2.33118]** [ 1.98938]** [ 1.56027] [ 0.52071]
SPR1, SPR2 and SPR3 are calendar spreads that all long the 1st-nearby futures but short the 2nd-
nearby futures, the 6-month futures and the 12-month futures, respectively. Lag length tests show the
appropriate order of VAR model for each commodity is: 13 lags for both oil and soybean spreads and 1 lag
for both of the metal spreads. Limited by the paper length, only SPR1 is included in the table. However, it is
fair enough to do so since other two spreads show similar results that are already summarized in this paper.
Further details can be obtained by contacting the author.
Rows with numbers in square brackets are t statistics. According to Lutkepohl (1993, Chapter 3,
pp 69), for the stable time series with standard white noise process, when the sample size is not small, the t
statistics provided by common regression programs can be used to check the significance of individual
variables.
***, ** and * are indicates significance at the 1% level, 5% level and 10% level, respectively.
44
Table 9: VAR estimates—Gold Term Premium (SPRp), Convenience yield (CYp)
and Net Hedging Pressure (QT), weekly data, October 1992 to December 2006
GOLDSPR1
SPR1 CY1 CY2 CY3 QT
SPR1(-1) 0.7315 -0.0709 -0.0758 -0.0551 -1.9911
[
27.8301]***
[-
2.81943]***
[-
2.98484]***
[-
2.02656]**
[-
2.44328]**
CY1(-1) 0.4057 0.2793 -0.5317 -0.6212 -1.6550
[
2.75478]***
[
1.98300]**
[-
3.73733]***
[-
4.07945]*** [-0.36240]
CY2(-1) -0.6452 0.4235 1.2079 0.3826 0.7087
[-
3.56126]***
[
2.44411]**
[
6.90206]***
[
2.04243]** [ 0.12616]
CY3(-1) 0.1840 -0.0250 0.0100 0.9367 -1.0113
[
3.79440]*** [-0.54004] [ 0.21287] [
18.6872]*** [-0.67268]
QT(-1) -0.0003 -0.0021 -0.0023 -0.0027 0.9403
[-0.63704]
[-
5.11399]***
[-
5.68145]***
[-
6.13351]***
[
70.8960]***
C -0.0013 0.0018 0.0018 0.0021 0.0173
[-
4.48126]***
[
6.52379]***
[
6.67403]***
[
7.12950]***
[
1.96945]**
GOLDSPR2
SPR2 CY1 CY2 CY3 QT
SPR2(-1) 0.8685 -0.0212 -0.0252 -0.0121 -1.2244
[
44.2764]*** [-1.38635] [-1.63208] [-0.73294] [-
2.48287]**
CY1(-1) 0.4642 0.2235 -0.5835 -0.6782 -1.2664
[
2.53175]** [ 1.56538] [-
4.04539]***
[-
4.40100]*** [-0.27476]
CY2(-1) -0.6127 0.5261 1.3073 0.4801 1.0328
[-
2.77258]***
[
3.05684]***
[
7.51970]***
[
2.58474]*** [ 0.18591]
CY3(-1) 0.1501 -0.0579 -0.0232 0.9080 -1.4687
[
2.61564]*** [-1.29440] [-0.51477] [
18.8246]*** [-1.01792]
QT(-1) -0.0004 -0.0021 -0.0024 -0.0027 0.9331
[-0.71777]
[-
4.78731]***
[-
5.38235]***
[-
5.64422]***
[
66.0697]***
C -0.0008 0.0020 0.0021 0.0023 0.0229
[-
2.30536]**
[
7.72430]***
[
7.92011]***
[
8.14959]***
[
2.74273]***
GoldSPR1 and GoldSPR2 are calendar spreads that both long the 1st-nearby futures but short the
2nd-nearby futures also the 6-month futures, and the 12-month futures, respectively. For the overlapping
of the 2nd-nearby futures and the 6-month futures, only two gold spreads are used in this test.
45
Table 10: VAR estimates—copper term premium (SPRp), convenience yield (CYp) and net
hedging pressure (QT), weekly data, from October 1992 to December 2006
COPPERSPR1
SPR1 CY1 CY2 CY3 QT
SPR1(-1) 0.7593 0.0382 0.1135 0.2018 0.3218
[ 29.0232]*** [ 1.72354]* [ 3.71268]*** [ 4.48076]*** [ 1.58017]
CY1(-1) 0.0006 0.4372 -0.2032 -0.1146 -0.9030
[ 0.00764] [ 6.06686]*** [-2.04669]** [-0.78324] [-1.36471]
CY2(-1) -0.0694 0.3140 0.9912 -0.0191 1.5308
[-0.84661] [ 4.51872]*** [ 10.3517]*** [-0.13562] [ 2.39900]**
CY3(-1) 0.0489 -0.0427 0.0303 1.0037 -0.6035
[ 1.86253]* [-1.91832]* [ 0.98671] [ 22.2095]*** [-2.95365]***
QT(-1) 0.0007 -0.0034 -0.0025 -0.0018 0.9393
[ 0.38043] [-2.27191]** [-1.19964] [-0.60090] [ 68.3856]***
C -0.0010 0.0012 0.0011 0.0019 0.0155
[-2.05030]** [ 2.66694]*** [ 1.83699]* [ 2.15841]** [ 3.92362]***
COPPERSPR2
SPR2 CY1 CY2 CY3 QT
SPR2(-1) 0.8402 0.0313 0.0809 0.1437 0.1879
[ 39.4657]*** [ 2.57924]*** [ 4.85171]*** [ 5.86461]*** [ 1.67943]*
CY1(-1) -0.3079 0.4156 -0.2660 -0.2262 -1.0765
[-2.47231]** [ 5.84497]*** [-2.72683]*** [-1.57870] [-1.64469]
CY2(-1) 0.2370 0.3352 1.0456 0.0775 1.6559
[ 1.93770]* [ 4.80095]*** [ 10.9160]*** [ 0.55036] [ 2.57640]***
CY3(-1) -0.0496 -0.0464 0.0232 0.9913 -0.6096
[-1.27489] [-2.08823]** [ 0.76245] [ 22.1331]*** [-2.98036]***
QT(-1) 0.0017 -0.0037 -0.0032 -0.0031 0.9374
[ 0.66416] [-2.45755]** [-1.56672] [-1.04064] [ 68.2793]***
C 0.0001 0.0011 0.0009 0.0016 0.0149
[ 0.07883] [ 2.57125]** [ 1.54231] [ 1.80693]* [ 3.80901]***
COPPERSPR3
SPR3 CY1 CY2 CY3 QT
SPR3(-1) 0.8829 0.0156 0.0434 0.0830 0.1161
[ 48.6267]*** [ 2.28550]** [ 4.64102]*** [ 6.09175]*** [ 1.88915]*
CY1(-1) -0.5209 0.4014 -0.2784 -0.2510 -1.0843
[-2.69116]*** [ 5.53175]*** [-2.79550]*** [-1.72751]* [-1.65556]*
CY2(-1) 0.4495 0.3311 1.0131 0.0219 1.5050
[ 2.37656]** [ 4.66935]*** [ 10.4108]*** [ 0.15404] [ 2.35174]**
CY3(-1) -0.1186 -0.0396 0.0463 1.0327 -0.5283
[-1.98860]** [-1.76895]* [ 1.50905] [ 23.0581]*** [-2.61727]***
QT(-1) 0.0012 -0.0040 -0.0036 -0.0039 0.9409
[ 0.29743] [-2.59323]*** [-1.68397]* [-1.25302] [ 67.2087]***
C 0.0009 0.0010 0.0006 0.0010 0.0131
46
[ 0.79690] [ 2.33555]** [ 1.04233] [ 1.12918] [ 3.31049]***
Table 11: VAR estimates—soybean term premium (SPRp), convenience yield (CYp) and net
hedging pressure (QT), weekly data, from October 1992 to December 2006
SOYBSPR2 SOYBCY1 SOYBCY2 SOYBCY3 SOYBQT
SOYBSPR2(-1) 0.6219 0.0247 -0.0128 -0.0382 0.0234
[ 13.9118]*** [ 1.21700] [-1.37443] [-1.26347] [ 0.26942]
SOYBSPR2(-2) 0.1864 -0.0262 -0.0088 -0.0146 -0.0500
[ 3.58179]*** [-1.10859] [-0.81398] [-0.41459] [-0.49493]
SOYBSPR2(-3) -0.0502 -0.1419 -0.0309 -0.0668 0.0734
[-0.95476] [-5.94307]*** [-2.80895]*** [-1.87778]* [ 0.71912]
SOYBSPR2(-4) -0.0180 0.0712 0.0466 0.1340 -0.0280
[-0.33108] [ 2.89196]*** [ 4.10963]*** [ 3.65113]*** [-0.26600]
SOYBSPR2(-5) -0.0819 0.0109 0.0152 0.0001 -0.0021
[-1.47835] [ 0.43210] [ 1.31063] [ 0.00322] [-0.01991]
SOYBSPR2(-6) 0.1252 0.0017 0.0167 -0.0075 0.1594
[ 2.29432]** [ 0.06728] [ 1.46899] [-0.20213] [ 1.50596]
SOYBSPR2(-7) 0.1662 0.0550 0.0040 0.0697 0.0109
[ 3.04611]*** [ 2.22104]** [ 0.35509] [ 1.88837]* [ 0.10319]
SOYBSPR2(-8) 0.1256 -0.0030 -0.0270 -0.0289 -0.0122
[ 2.29821]** [-0.11988] [-2.36819]** [-0.78214] [-0.11530]
SOYBSPR2(-9) -0.0203 -0.0222 0.0030 -0.0123 0.0253
[-0.37363] [-0.90006] [ 0.26221] [-0.33562] [ 0.24032]
SOYBSPR2(-10) -0.2213 -0.0537 0.0033 -0.0063 0.0197
[-4.10077]*** [-2.19427]** [ 0.29692] [-0.17175] [ 0.18782]
SOYBSPR2(-11) -0.0823 -0.0501 -0.0026 -0.0121 0.1334
[-1.52136] [-2.04201]** [-0.23441] [-0.32979] [ 1.27108]
SOYBSPR2(-12) -0.4011 0.5737 0.9672 0.8490 0.0377
[-7.40024]*** [ 23.3338]*** [ 85.4357]*** [ 23.1638]*** [ 0.35872]
SOYBSPR2(-13) 0.8667 -0.2089 -0.2399 1.0506 0.3721
[ 3.98997]*** [-2.12077]** [-5.28836]*** [ 7.15253]*** [ 0.88261]
SOYBSPR2(-14) -0.1523 -0.1988 -0.4664 -1.0929 -0.4037
[-0.66483] [-1.91274]* [-9.74660]*** [-7.05479]*** [-0.90790]
SOYBCY1(-1) -0.0459 0.6881 0.0155 -0.0097 -0.2731
[-0.45992] [ 15.2019]*** [ 0.74129] [-0.14309] [-1.40996]
SOYBCY1(-2) -0.0169 0.0583 0.0645 0.0871 0.3958
[-0.13986] [ 1.06133] [ 2.54865]** [ 1.06314] [ 1.68355]*
SOYBCY1(-3) 0.2059 0.0561 -0.0300 -0.0304 0.0235
[ 1.76236]* [ 1.05822] [-1.23147] [-0.38455] [ 0.10346]
SOYBCY1(-4) 0.0356 0.0798 0.0203 -0.0260 -0.0482
[ 0.30645] [ 1.51351] [ 0.83448] [-0.33140] [-0.21357]
SOYBCY1(-5) 0.3485 0.0185 -0.0531 -0.0470 0.1207
[ 3.08921]*** [ 0.36199] [-2.25175]** [-0.61564] [ 0.55155]
SOYBCY1(-6) -0.1347 -0.1987 -0.0141 -0.0193 -0.2736
[-1.22710] [-3.99127]*** [-0.61674] [-0.25966] [-1.28420]
47
SOYBCY1(-7) -0.4282 -0.0718 -0.0163 -0.0743 -0.2781
[-3.90538]*** [-1.44299] [-0.71286] [-1.00193] [-1.30720]
SOYBSPR2 SOYBCY1 SOYBCY2 SOYBCY3 SOYBQT
SOYBCY1(-8) 0.0922 0.1201 0.0154 0.0620 0.4601
[ 0.83505] [ 2.39723]** [ 0.66700] [ 0.83044] [ 2.14690]**
SOYBCY1(-9) -0.4986 -0.3745 -0.0031 -0.1224 -0.1459
[-4.59710]*** [-7.61356]*** [-0.13611] [-1.66940]* [-0.69314]
SOYBCY1(-10) 0.4020 0.2728 0.0028 0.0064 -0.2023
[ 3.55775]*** [ 5.32376]*** [ 0.11726] [ 0.08431] [-0.92248]
SOYBCY1(-11) 0.2510 0.0645 -0.0078 0.0133 -0.0899
[ 2.18691]** [ 1.23878] [-0.32589] [ 0.17158] [-0.40364]
SOYBCY1(-12) 0.3836 -0.6234 -0.9336 -0.8834 0.0506
[ 3.33515]*** [-11.9520]*** [-38.8706]*** [-11.3605]*** [ 0.22663]
SOYBCY1(-13) -0.9059 0.2088 0.2327 -0.8745 -0.3031
[-3.92011]*** [ 1.99258]** [ 4.82247]*** [-5.59691]*** [-0.67582]
SOYBCY1(-14) 0.3401 0.2196 0.4432 1.0348 0.3508
[ 1.46108] [ 2.08047]** [ 9.11799]*** [ 6.57532]*** [ 0.77674]
SOYBCY2(-1) -0.7663 -0.2411 0.2099 -1.9065 -0.5772
[-2.92341]*** [-2.02845]** [ 3.83474]*** [-10.7574]*** [-1.13466]
SOYBCY2(-2) 0.5424 0.2856 0.5249 1.1910 0.1722
[ 1.86419]* [ 2.16379]** [ 8.63748]*** [ 6.05331]*** [ 0.30487]
SOYBCY2(-3) -0.2187 -0.1403 -0.0043 -0.0763 -0.1236
[-1.64726]* [-2.32905]** [-0.15430] [-0.84957] [-0.47954]
SOYBCY2(-4) -0.2151 -0.0099 -0.0586 0.0184 0.3907
[-1.62369] [-0.16396] [-2.11825]** [ 0.20485] [ 1.51940]
SOYBCY2(-5) -0.2672 -0.1096 0.0464 -0.0077 -0.1770
[-1.98362]** [-1.79361]* [ 1.65016]* [-0.08418] [-0.67718]
SOYBCY2(-6) -0.2461 0.1947 0.0319 0.0310 0.1701
[-1.81892]* [ 3.17287]*** [ 1.12774] [ 0.33925] [ 0.64769]
SOYBCY2(-7) 0.6625 0.0935 -0.0099 0.0801 0.3255
[ 4.94941]*** [ 1.53926] [-0.35584] [ 0.88468] [ 1.25294]
SOYBCY2(-8) 0.1548 -0.0704 -0.0391 -0.0887 -0.5837
[ 1.13699] [-1.13936] [-1.37387] [-0.96321] [-2.20922]**
SOYBCY2(-9) 0.4894 0.3658 0.0098 -0.0544 0.4441
[ 3.58624]*** [ 5.90943]*** [ 0.34259] [-0.58931] [ 1.67698]*
SOYBCY2(-10) -0.4775 -0.4060 -0.0037 0.0639 -0.1158
[-3.39478]*** [-6.36300]*** [-0.12610] [ 0.67224] [-0.42421]
SOYBCY2(-11) -0.2778 -0.0811 -0.0845 -0.0475 0.3487
[-1.91343]* [-1.23194] [-2.78762]*** [-0.48388] [ 1.23745]
SOYBCY2(-12) -0.4533 0.7759 1.1361 0.9236 -0.2527
[-3.10126]*** [ 11.7033]*** [ 37.2145]*** [ 9.34550]*** [-0.89079]
SOYBCY2(-13) 1.2631 -0.2379 -0.2499 1.2181 0.5236
[ 4.31409]*** [-1.79152]* [-4.08672]*** [ 6.15340]*** [ 0.92164]
SOYBCY2(-14) -0.6066 -0.1431 -0.5440 -1.2031 -0.3815
48
[-2.15659]** [-1.12133] [-9.26019]*** [-6.32564]*** [-0.69895]
SOYBCY3(-1) 0.1940 0.0214 0.0380 0.9414 0.3125
[ 2.27580]** [ 0.55442] [ 2.13658]** [ 16.3297]*** [ 1.88878]*
SOYBCY3(-2) -0.2762 -0.0683 -0.1133 -0.1721 -0.1984
[-2.76808]*** [-1.50874] [-5.43454]*** [-2.55034]** [-1.02452]
SOYBSPR2 SOYBCY1 SOYBCY2 SOYBCY3 SOYBQT
SOYBCY3(-3) 0.0936 0.0577 0.0288 0.0637 -0.0458
[ 1.12705] [ 1.53317] [ 1.66177]* [ 1.13527] [-0.28427]
SOYBCY3(-4) 0.1792 -0.0642 0.0290 0.0033 -0.1451
[ 2.15992]** [-1.70496]* [ 1.67129]* [ 0.05870] [-0.90135]
SOYBCY3(-5) 0.0488 0.0556 0.0111 0.1050 0.0178
[ 0.58185] [ 1.46281] [ 0.63450] [ 1.85236]* [ 0.10948]
SOYBCY3(-6) 0.2993 0.0058 -0.0181 0.0128 0.0931
[ 3.55991]*** [ 0.15337] [-1.02874] [ 0.22519] [ 0.57055]
SOYBCY3(-7) -0.2093 0.0044 0.0211 -0.0316 -0.1148
[-2.48238]** [ 0.11582] [ 1.19663] [-0.55464] [-0.70184]
SOYBCY3(-8) -0.1601 -0.0298 0.0231 -0.0122 0.1448
[-1.88385]* [-0.77387] [ 1.29982] [-0.21214] [ 0.87829]
SOYBCY3(-9) -0.0195 -0.0197 -0.0073 0.1362 -0.1823
[-0.22918] [-0.51095] [-0.40850] [ 2.36959]** [-1.10507]
SOYBCY3(-10) 0.0631 0.0968 0.0039 -0.0005 0.2267
[ 0.74013] [ 2.50445]** [ 0.22176] [-0.00802] [ 1.37052]
SOYBCY3(-11) 0.0163 0.0326 0.0925 0.0324 -0.3033
[ 0.19059] [ 0.84400] [ 5.19402]*** [ 0.56262] [-1.83296]*
SOYBCY3(-12) 0.0886 -0.1484 -0.2005 -0.0464 0.1817
[ 1.01241] [-3.73861]*** [-10.9698]*** [-0.78405] [ 1.06949]
SOYBCY3(-13) -0.2992 0.0387 0.0039 -0.3491 -0.2170
[-2.94756]*** [ 0.83976] [ 0.18520] [-5.08639]*** [-1.10179]
SOYBCY3(-14) 0.2153 -0.0751 0.1044 0.1950 0.0449
[ 2.56016]** [-1.96819]** [ 5.94178]*** [ 3.42932]*** [ 0.27486]
SOYBQT(-1) -0.0012 0.0061 -0.0031 0.0115 1.1422
[-0.05676] [ 0.63846] [-0.71311] [ 0.81049] [ 27.9909]***
SOYBQT(-2) 0.0032 -0.0044 0.0104 -0.0032 -0.2173
[ 0.09948] [-0.30754] [ 1.56435] [-0.14696] [-3.53204]***
SOYBQT(-3) 0.0034 0.0013 -0.0059 0.0058 0.0799
[ 0.10503] [ 0.09231] [-0.88185] [ 0.26666] [ 1.28708]
SOYBQT(-4) 0.0025 0.0029 0.0037 0.0200 -0.0009
[ 0.07801] [ 0.19876] [ 0.54942] [ 0.92250] [-0.01423]
SOYBQT(-5) -0.0387 -0.0221 -0.0048 -0.0411 -0.1049
[-1.21283] [-1.52672] [-0.72623] [-1.90477]* [-1.69477]*
SOYBQT(-6) 0.0143 0.0233 0.0050 0.0194 0.0731
[ 0.44583] [ 1.60063] [ 0.74588] [ 0.89281] [ 1.17118]
SOYBQT(-7) 0.0030 -0.0132 -0.0046 -0.0198 -0.0459
[ 0.09397] [-0.90977] [-0.68915] [-0.91041] [-0.73597]
SOYBQT(-8) 0.0149 0.0090 0.0020 0.0217 0.1109
49
[ 0.46469] [ 0.61915] [ 0.30382] [ 1.00556] [ 1.78790]*
SOYBQT(-9) -0.0111 -0.0127 -0.0024 -0.0145 -0.0353
[-0.34740] [-0.87659] [-0.35585] [-0.67259] [-0.56977]
SOYBQT(-10) 0.0146 0.0078 -0.0007 0.0008 -0.0276
[ 0.45994] [ 0.54233] [-0.10870] [ 0.03711] [-0.44629]
SoybSPR2 is the calendar spread that longs the 1st-nearby futures and shorts the 7-month futures.
For the same reason as the oil calendar spreads, it is the only soybean spread the results of which are
included in this paper. Further details can be obtained by contacting the author.
The rationale for displaying results of the second soybean spread is that the term structure effect
is ostensibly the most significant in term slope derived from the July contract, since this is the only contract
that expires just prior to the upcoming harvest season starting in September. The test results show that it is
the case. Among all the three spreads, in this spread I have found the largest number of lags of the overall
term structure that contains valuable information for predicting future term premiums.
50
Table 12: Summary statistics of momentum trading returns, long-only the 1st-
nearby futures, bi-weekly data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
Winner Loser MMT Winner Loser MMT Winner Loser MMT Winner Loser MMT
Panel A: ranking period of 1 month
Mean 45.60% -48.00% 88.80% 32.40% -24.00% 57.60% 15.60% -8.00% 23.00% 9.20% -3.00% 11.90%
Prob* <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.0086 <.0001
Std Dev 24.94% 24.25% 31.18% 24.40% 20.80% 28.20% 24.75% 21.78% 30.69% 23.80% 20.30% 27.80%
SharpeR 182.83% -197.95% 284.83% 132.79% -115.38% 204.26% 63.03% -36.73% 74.95% 38.66% -14.78% 42.81%
Panel B: ranking period of 3 months
Mean 39.60% -36.00% 73.20% 18.80% -12.00% 31.60% 9.80% -2.00% 11.40% 5.80% 0.90% 4.90%
Prob* <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.2992 <.0001 <.0001 0.3359 0.0006
Std Dev 25.29% 24.60% 33.26% 26.20% 22.40% 32.20% 25.46% 21.50% 31.96% 23.60% 19.80% 28.50%
SharpeR 156.60% -146.37% 220.11% 71.76% -53.57% 98.14% 38.50% -9.30% 35.67% 24.58% 4.55% 17.19%
Panel C: ranking period of 6 months
Mean 24.00% -12.00% 38.40% 10.80% -4.00% 14.00% 6.80% 3.60% 3.40% 2.70% 6.10% -3.00%
Prob* <.0001 0.0003 <.0001 <.0001 0.1151 <.0001 0.0003 0.0091 0.1128 0.0232 <.0001 0.0096
Std Dev 28.41% 21.82% 33.95% 27.40% 20.40% 32.00% 27.15% 19.23% 30.26% 23.80% 19.00% 26.60%
SharpeR 84.49% -54.99% 113.11% 39.42% -19.61% 43.75% 25.04% 18.72% 11.23% 11.34% 32.11% -11.28%
Panel D: ranking period of 12 months
Mean 20.40% -12.00% 30.00% 10.00% -4.00% 12.80% 4.80% 3.60% 1.20% 0.00% 7.30% -7.00%
Prob* <.0001 0.0057 <.0001 <.0001 0.2022 <.0001 0.0083 0.0079 0.583 0.8887 <.0001 <.0001
Std Dev 25.98% 21.82% 31.52% 25.20% 20.80% 30.00% 25.88% 19.66% 29.56% 23.60% 18.70% 27.30%
SharpeR 78.52% -54.99% 95.17% 39.68% -19.23% 42.67% 18.55% 18.31% 4.06% 0.00% 39.04% -25.64%
MMT refers to momentum. Mean and standard deviation are annualized by multiplying by 250 and
250 respectively.
51
Table 13: Summary statistics of momentum trading returns, long-only the 6-month
futures, bi-weekly data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
Winner Loser MMT Winner Loser MMT Winner Loser MMT Winner Loser MMT
Panel A: ranking period of 1 month
Mean 38.40% -36.00% 69.60% 26.00% -20.00% 45.60% 14.00% -4.00% 19.00% 8.90% 0.30% 8.60%
Prob* <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.7664 <.0001
Std Dev 21.82% 20.09% 25.98% 21.40% 17.00% 24.00% 23.05% 17.25% 25.60% 24.20% 17.50% 26.10%
Sharpe R 175.95% -179.18% 267.89% 121.50% -117.65% 190.00% 60.73% -23.18% 74.23% 36.78% 1.71% 32.95%
Panel B: ranking period of 3 months
Mean 31.20% -24.00% 52.80% 17.20% -8.00% 26.40% 10.00% 0.80% 9.20% 5.70% 3.20% 2.40%
Prob* <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.561 <.0001 <.0001 0.0002 0.0699
Std Dev 22.52% 18.71% 27.02% 22.40% 17.60% 26.00% 23.48% 18.10% 26.16% 23.80% 17.30% 27.10%
Sharpe R 138.56% -128.30% 195.41% 76.79% -45.45% 101.54% 42.60% 4.42% 35.16% 23.95% 18.50% 8.86%
Panel C: ranking period of 6 months
Mean 15.60% -12.00% 24.00% 11.20% 0.00% 12.00% 6.60% 4.40% 2.20% 3.30% 6.20% -3.00%
Prob* <.0001 0.0032 <.0001 <.0001 0.6286 <.0001 <.0001 0.0003 0.2154 0.0046 <.0001 0.0188
Std Dev 23.56% 16.63% 26.67% 23.40% 16.80% 26.00% 22.49% 17.11% 26.16% 23.20% 17.00% 25.20%
Sharpe R 66.23% -72.17% 89.98% 47.86% 0.00% 46.15% 29.35% 25.71% 8.41% 14.22% 36.47% -11.90%
Panel D: ranking period of 12 months
Mean 13.20% 0.00% 18.00% 9.20% 1.60% 7.60% 5.60% 5.00% 0.60% 2.60% 6.10% -3.00%
Prob* 0.0004 0.1287 <.0001 <.0001 0.3257 0.0028 0.0004 <.0001 0.7713 0.0161 <.0001 0.0065
Std Dev 21.82% 16.63% 25.63% 20.80% 17.60% 25.40% 22.20% 16.69% 26.16% 21.80% 17.30% 25.60%
Sharpe R 60.48% 0.00% 70.22% 44.23% 9.09% 29.92% 25.22% 29.96% 2.29% 11.93% 35.26% -11.72%
MMT refers to momentum. Mean and standard deviation are annualized by multiplying by 250 and
250 respectively.
52
Table 14: Summary statistics of momentum trading returns, long-only the 12-month
futures, bi-weekly data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
Winner Loser MMT Winner Loser MMT Winner Loser MMT Winner Loser MMT
Panel A: ranking period of 1 month
Mean 28.80% -24.00% 51.60% 22.00% -16.00% 36.40% 13.00% -4.00% 17.20% 7.70% 0.10% 7.60%
Prob* <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.8895 <.0001
Std Dev 18.71% 16.28% 22.17% 18.60% 13.80% 21.60% 20.93% 14.00% 22.34% 22.80% 14.90% 22.80%
Sharpe R 153.96% -147.41% 232.74% 118.28% -115.94% 168.52% 62.11% -28.57% 76.98% 33.77% 0.67% 33.33%
Panel B: ranking period of 3 months
Mean 24.00% -12.00% 39.60% 14.80% -8.00% 22.40% 9.80% 0.00% 10.40% 6.60% 2.00% 4.50%
Prob* <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.4913 <.0001 <.0001 0.0045 <.0001
Std Dev 19.40% 15.24% 23.21% 19.20% 13.80% 22.60% 21.64% 14.57% 22.77% 23.10% 14.50% 23.20%
Sharpe R 123.72% -78.73% 170.62% 77.08% -57.97% 99.12% 45.29% 0.00% 45.68% 28.57% 13.79% 19.40%
Panel C: ranking period of 6 months
Mean 12.00% -12.00% 19.20% 8.00% 0.00% 9.60% 6.20% 2.60% 3.80% 4.80% 4.00% 0.80%
Prob* 0.0007 0.0008 <.0001 <.0001 0.1685 <.0001 <.0001 0.014 0.0205 <.0001 <.0001 0.444
Std Dev 19.75% 13.86% 22.52% 19.80% 14.00% 22.00% 21.35% 14.85% 22.77% 22.90% 15.10% 21.80%
Sharpe R 60.77% -86.60% 85.27% 40.40% 0.00% 43.64% 29.03% 17.51% 16.69% 20.96% 26.49% 3.67%
Panel D: ranking period of 12 months
Mean 9.60% 0.00% 10.80% 7.20% 2.00% 5.20% 5.60% 3.20% 2.40% 3.30% 4.60% -1.00%
Prob* 0.0018 0.9421 0.0085 0.0002 0.1632 0.0262 0.0003 0.001 0.1817 0.0038 <.0001 0.2646
Std Dev 18.71% 14.90% 22.86% 19.60% 15.00% 23.20% 21.78% 13.72% 24.75% 22.70% 14.30% 24.30%
Sharpe R 51.32% 0.00% 47.24% 36.73% 13.33% 22.41% 25.71% 23.33% 9.70% 14.54% 32.17% -4.12%
MMT refers to momentum. Mean and standard deviation are annualized by multiplying by 250 and
250 respectively.
53
Table 15: Summary statistics of momentum trading returns, calendar spread that
longs the 1st-nearby futures and shorts the 2nd-nearby futures, bi-weekly data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
Winner Loser MMT Winner Loser MMT Winner Loser MMT Winner Loser MMT
Panel A: ranking period of 1 month
Mean 9.60% -12.00% 18.00% 4.00% -4.00% 8.00% 0.00% 0.00% 0.00% 0.10% 0.00% 0.40%
Prob* <.0001 <.0001 <.0001 0.0007 <.0001 <.0001 0.3904 0.5024 0.6051 0.7208 0.1471 0.2627
Std Dev 12.47% 8.31% 15.24% 12.20% 7.60% 14.40% 15.84% 6.93% 17.39% 6.20% 3.90% 7.00%
Sharpe R 76.98% -144.34% 118.09% 32.79% -52.63% 55.56% 0.00% 0.00% 0.00% 1.61% 0.00% 5.71%
Panel B: ranking period of 3 months
Mean 4.80% -48.00% 54.00% 0.00% -4.00% 2.00% -2.00% -6.00% 4.80% 0.00% -3.00% 2.90%
Prob* 0.041 <.0001 <.0001 0.4077 <.0001 0.1337 0.0129 <.0001 <.0001 0.4 <.0001 <.0001
Std Dev 14.20% 16.28% 16.97% 12.20% 2.60% 12.60% 9.33% 7.35% 7.92% 7.10% 5.60% 6.90%
Sharpe R 33.80% -294.82% 318.13% 0.00% -153.85% 15.87% -21.43% -81.59% 60.61% 0.00% -53.57% 42.03%
Panel C: ranking period of 6 months
Mean 0.02% 0.00% 0.02% -4.00% 0.80% -4.00% -2.00% 2.00% -4.00% -1.00% 0.70% -2.00%
Prob* 0.9923 0.9987 0.9929 0.0076 0.0064 0.0011 <.0001 <.0001 <.0001 0.0008 <.0001 <.0001
Std Dev 14.20% 3.46% 14.90% 11.00% 2.80% 11.20% 7.78% 5.94% 9.48% 5.70% 2.6% 6.00%
Sharpe R 0.17% 0.03% 0.15% -36.36% 28.57% -35.71% -25.71% 33.67% -42.22% -17.54% 26.92% -33.33%
Panel D: ranking period of 12 months
Mean 0.00% 0.12% 0.00% 0.00% 0.80% -4.00% -2.00% 1.00% -2.00% -1.00% 1.20% -2.00%
Prob* 0.9026 0.839 0.8643 0.1203 0.006 0.0245 0.0061 <.0001 <.0001 <.0001 <.0001 <.0001
Std Dev 13.51% 3.46% 13.86% 11.00% 3.20% 11.40% 8.06% 2.69% 8.34% 5.30% 3.20% 6.00%
Sharpe R 0.00% 3.46% 0.00% 0.00% 25.00% -35.09% -24.81% 37.22% -23.97% -18.87% 37.50% -33.33%
MMT refers to momentum. Mean and standard deviation are annualized by multiplying by 250 and
250 respectively.
54
Table 16: Summary statistics of momentum trading returns, calendar spread that
longs the 1st-nearby futures and shorts the 6-month futures, bi-weekly data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
Winner Loser MMT Winner Loser MMT Winner Loser MMT Winner Loser MMT
Panel A: ranking period of 1 month
Mean 24.00% -12.00% 42.00% 24.40% -8.00% 34.00% 2.20% -2.00% 3.80% 1.30% -1.00% 2.20%
Prob* <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.0464 0.0598 0.0043 0.0355 0.0409 0.0034
Std Dev 18.36% 14.90% 23.56% 24.80% 11.20% 22.80% 16.26% 12.02% 19.23% 12.60% 8.50% 14.90%
Sharpe R 130.72% -80.56% 178.30% 98.39% -71.43% 149.12% 13.53% -16.64% 19.76% 10.32% -11.76% 14.77%
Panel B: ranking period of 3 months
Mean 12.00% -12.00% 22.80% 2.80% -4.00% 6.80% 0.00% 1.80% -2.00% 0.00% 0.80% -1.00%
Prob* 0.002 <.0001 <.0001 0.2224 <.0001 0.003 0.6227 0.0228 0.1015 0.7761 0.0346 0.1936
Std Dev 22.86% 11.43% 25.98% 22.40% 5.20% 23.60% 18.24% 10.89% 20.65% 13.70% 7.50% 15.20%
Sharpe R 52.49% -104.97% 87.76% 12.50% -76.92% 28.81% 0.00% 16.53% -9.69% 0.00% 10.67% -6.58%
Panel C: ranking period of 6 months
Mean 3.60% 0.00% 6.00% 0.00% 0.00% 0.40% -4.00% 2.40% -6.00% -1.00% 1.50% -2.00%
Prob* 0.3512 0.1777 0.1932 0.6675 0.5545 0.8873 0.002 <.0001 <.0001 0.1543 <.0001 0.0005
Std Dev 23.56% 7.97% 25.29% 22.00% 23.80% 32.40% 15.56% 7.50% 17.25% 13.10% 6.60% 14.10%
Sharpe R 15.28% 0.00% 23.73% 0.00% 0.00% 1.23% -25.71% 32.02% -34.78% -7.63% 22.73% -14.18%
Panel D: ranking period of 12 months
Mean 1.20% 0.00% 2.40% 0.00% 0.80% 0.00% -2.00% 2.20% -4.00% -2.00% 3.10% -5.00%
Prob* 0.685 0.5578 0.5614 0.6625 0.1638 0.3901 0.0432 <.0001 0.0001 0.0007 <.0001 <.0001
Std Dev 22.17% 7.62% 23.21% 20.20% 6.80% 21.20% 14.85% 6.22% 15.98% 10.80% 8.30% 12.50%
Sharpe R 5.41% 0.00% 10.34% 0.00% 11.76% 0.00% -13.47% 35.36% -25.03% -18.52% 37.35% -40.00%
MMT refers to momentum. Mean and standard deviation are annualized by multiplying by 250 and
250 respectively.
55
Table 17: Summary statistics of momentum trading returns, calendar spread that
longs the 1st-nearby futures and shorts the 12-month futures, bi-weekly data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
Winner Loser MMT Winner Loser MMT Winner Loser MMT Winner Loser MMT
Panel A: ranking period of 1 month
Mean 42.00% -36.00% 76.80% 25.20% -20.00% 43.60% 11.40% -4.00% 16.00% 6.00% -2.00% 8.20%
Prob* <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.0022 <.0001 <.0001 0.0068 <.0001
Std Dev 27.71% 24.25% 35.33% 31.00% 19.00% 35.20% 24.75% 21.50% 30.97% 22.70% 16.30% 27.50%
Sharpe R 151.55% -148.46% 217.36% 81.29% -105.26% 123.86% 46.06% -18.61% 51.66% 26.43% -12.27% 29.82%
Panel B: ranking period of 3 months
Mean 27.60% -24.00% 46.80% 13.60% -4.00% 17.20% 4.80% 1.20% 3.60% 2.10% 0.40% 1.70%
Prob* <.0001 <.0001 <.0001 <.0001 0.0005 <.0001 0.0069 0.4157 0.1061 0.068 0.6227 0.2149
Std Dev 30.14% 22.52% 37.76% 31.80% 11.40% 34.60% 25.31% 20.93% 31.82% 23.30% 15.70% 28.00%
Sharpe R 91.58% -106.59% 123.94% 42.77% -35.09% 49.71% 18.96% 5.73% 11.31% 9.01% 2.55% 6.07%
Panel C: ranking period of 6 months
Mean 19.20% -12.00% 27.60% 6.40% -4.00% 9.20% 1.00% 1.40% 0.00% -1.00% 2.40% -4.00%
Prob* 0.0007 0.0031 <.0001 0.0293 0.0376 0.0031 0.6032 0.1948 0.8646 0.2535 0.002 0.0068
Std Dev 32.22% 17.32% 36.03% 29.40% 14.20% 31.60% 26.02% 14.42% 30.12% 22.30% 15.50% 27.10%
Sharpe R 59.60% -69.28% 76.61% 21.77% -28.17% 29.11% 3.84% 9.71% 0.00% -4.48% 15.48% -14.76%
Panel D: ranking period of 12 months
Mean 13.20% 0.00% 15.60% 4.80% 0.80% 3.60% 1.00% 3.80% -2.00% -2.00% 5.30% -7.00%
Prob* 0.0172 0.2755 0.0086 0.0867 0.5081 0.2215 0.5549 0.0001 0.1745 0.1119 <.0001 <.0001
Std Dev 31.18% 14.90% 34.29% 28.00% 14.40% 31.40% 25.46% 14.00% 28.85% 20.60% 17.90% 25.70%
Sharpe R 42.34% 0.00% 45.49% 17.14% 5.56% 11.46% 3.93% 27.14% -6.93% -9.71% 29.61% -27.24%
MMT refers to momentum. Mean and standard deviation are annualized by multiplying by 250 and
250 respectively.
56
Table 18: Estimate of momentum trading returns with the 1st-nearby futures vs
convenience yield, net hedging pressure and monthly dummies, bi-weekly data
Holding period of 1
month
Holding period of 3
month
Holding period of 6
month
Holding period of 12
month
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Panel A: ranking period of 1 month
Variable
Intercept 0.0190 0.0543 0.0311 0.0807 0.0490 0.0595 0.0753 0.0533
(0.1253) (<.0001)*** (0.1391) (<.0001)*** (0.1135) (0.0249)** (0.0748)* (0.1296)
CY3MONTH 0.4123 0.4727 0.5175 0.3895 0.9506 -0.1883 1.3192 -0.4617
(0.0225)** (<.0001)*** (0.0906)* (0.0248)** (0.0348)** (0.4733) (0.032)** (0.1857)
HP 0.0440 -0.0964 0.1434 -0.1359 0.1469 -0.1329 0.1550 -0.1396
(0.014)** (<.0001)*** (<.0001)*** (<.0001)*** (<.0001)*** (0.0004)*** (0.011)** (0.0049)***
Panel B: ranking period of 3 months
Variable
Intercept 0.0016 0.0501 -0.0106 0.0402 -0.0044 0.0218 0.0077 0.0083
(0.9007) (<.0001)*** (0.6505) (0.0308)** (0.8903) (0.3963) (0.8573) (0.8093)
CY3MONTH 0.4717 0.4158 1.4735 0.3379 2.2020 0.3270 1.4925 -0.5818
(0.0153)** (0.0002) (<.0001)*** (0.0553)* (<.0001)*** (0.1799) (0.0202)** (0.073)*
HP 0.0339 -0.0724 0.0891 -0.1543 0.1101 -0.1665 -0.0456 -0.0991
(0.0625)* (<.0001)*** (0.0066)*** (<.0001)*** (0.015)** (<.0001)*** (0.4482) (0.047)**
Panel C: ranking period of 6 months
Variable
Intercept -0.0228 0.0219 -0.0385 0.0311 -0.0040 0.0167 -0.0671 -0.0771
(0.1168) (0.0378)** (0.1125) (0.0593)* (0.9065) (0.4569) (0.1081) (0.0175)**
CY3MONTH 0.4152 0.0426 0.9454 0.1601 2.0764 0.1193 2.7722 -0.6207
(0.048)** (0.7499) (0.0071)*** (0.443) (<.0001)*** (0.6754) (<.0001)*** (0.1309)
HP 0.0446 -0.0853 0.0929 -0.1680 0.1111 -0.1795 0.0066 -0.1803
(0.0286)** (<.0001)*** (0.0063)*** (<.0001)*** (0.0193)** (<.0001)*** (0.9105) (0.0003)***
Panel D: ranking period of 12 months
Variable
Intercept -0.0034 0.0177 0.0058 0.0369 -0.0026 -0.0102 -0.0689 -0.1035
(0.7949) (0.0973)* (0.7972) (0.0368)** (0.9361) (0.6611) (0.0905)* (0.0007)***
CY3MONTH 0.0043 0.0068 0.5904 -0.8578 1.8458 -0.3157 2.6517 -0.8330
(0.9817) (0.9754) (0.0654)* (0.0185)** (<.0001)*** (0.51) (<.0001)*** (0.1804)
HP 0.0581 -0.0749 0.0610 -0.1024 0.0097 -0.1993 -0.1332 -0.3999
(0.0015)*** (<.0001)*** (0.0505)* (0.0004)*** (0.8272) (<.0001)*** (0.018)** (<.0001)***
Numbers in parentheses are p-value. Coefficients with p-value highlighted by ***, ** and * are
significant at 1%, 5% and 10% levels, respectively.
57
Table 19: Estimate of momentum trading returns with 6-month futures vs
convenience yield, net hedging pressure and monthly dummies, bi-weekly data
Holding period of 1
month
Holding period of 3
month
Holding period of 6
month
Holding period of 12
month
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Panel A: ranking period of 1 month
Variable
Intercept 0.0082 0.0341 0.0126 0.0822 0.0258 0.0630 0.0230 0.0302
(0.4526) (0.0003)*** (0.4975) (<.0001)*** (0.3604) (0.0021)*** (0.5877) (0.309)
CY6MONTH 0.1073 0.1020 0.3371 0.0864 0.5630 -0.3869 1.0634 -0.5210
(0.0615)* (0.0733)* (0.0006)*** (0.301) (0.0002)*** (0.0018)*** (<.0001)*** (0.0039)***
HP 0.0370 -0.0831 0.0650 -0.1341 0.1368 -0.1307 0.0004 -0.1729
(0.0218)** (<.0001)*** (0.018)** (<.0001)*** (0.0011)*** (<.0001)*** (0.9944) (<.0001)***
Panel B: ranking period of 3 months
Variable
Intercept -0.0004 0.0214 -0.0179 0.0511 -0.0092 0.0395 -0.0124 -0.0085
(0.9718) (0.0205)** (0.3604) (0.0004)*** (0.7517) (0.066)* (0.7669) (0.7707)
CY6MONTH 0.0279 0.0056 0.4652 -0.1472 0.7903 -0.2260 1.2236 -0.6058
(0.6306) (0.934) (<.0001)*** (0.165) (<.0001)*** (0.1544) (<.0001)*** (0.0053)***
HP 0.0324 -0.0502 0.0427 -0.1413 0.1010 -0.1501 -0.0376 -0.1530
(0.0591)* (<.0001)*** (0.1413) (<.0001)*** (0.019)** (<.0001)*** (0.5459) (0.0002)***
Panel C: ranking period of 6 months
Variable
Intercept -0.0220 0.0084 -0.0418 0.0331 -0.0200 0.0043 -0.0280 -0.0667
(0.0648)* (0.2771) (0.042)** (0.0126)** (0.4769) (0.8248) (0.4958) (0.0191)**
CY6MONTH 0.1504 -0.3284 0.3496 -0.3668 0.5524 -0.2516 0.9385 -0.3660
(0.0112)** (0.0002)*** (0.0007)*** (0.0139)** (<.0001)*** (0.2538) (<.0001)*** (0.2516)
HP 0.0657 -0.0768 0.1009 -0.1586 0.0203 -0.2146 -0.0744 -0.2492
(0.0002)*** (<.0001)*** (0.001)*** (<.0001)*** (0.6297) (<.0001)*** (0.2255) (<.0001)***
Panel D: ranking period of 12 months
Variable
Intercept -0.0146 0.0046 -0.0109 0.0086 -0.0420 -0.0033 -0.0345 -0.1032
(0.1804) (0.5465) (0.5529) (0.5387) (0.1274) (0.8557) (0.3514) (<.0001)***
CY6MONTH 0.0718 -0.5205 0.2927 -0.8010 0.7103 -0.7245 1.1294 -1.0110
(0.1926) (<.0001)*** (0.0017)*** (<.0001)*** (<.0001)*** (0.0024)*** (<.0001)*** (0.0018)***
HP 0.0707 -0.0719 0.0795 -0.1307 0.0005 -0.2130 -0.2083 -0.4637
(<.0001)*** (<.0001)*** (0.0035)*** (<.0001)*** (0.9903) (<.0001)*** (0.0002)*** (<.0001)***
58
Table 20: Estimate of momentum trading returns with 12-month futures vs
convenience yield, net hedging pressure and monthly dummies, bi-weekly data
Holding period of 1
month
Holding period of 3
month
Holding period of 6
month
Holding period of 12
month
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Panel A: ranking period of 1 month
Variable
Intercept 0.0026 0.0177 -0.0056 0.0554 -0.0169 0.0638 0.0096 0.0562
(0.791) (0.0228)** (0.7329) (<.0001)*** (0.5169) (<.0001)*** (0.8114) (0.0225)**
CY12MONTH 0.0512 0.0128 0.2090 -0.0066 0.4555 -0.0776 0.7284 -0.3272
(0.0741)* (0.7385) (<.0001)*** (0.8996) (<.0001)*** (0.3184) (<.0001)*** (0.0073)***
HP 0.0348 -0.0603 0.0188 -0.1413 0.0358 -0.1604 -0.0873 -0.1977
(0.0145)** (<.0001)*** (0.4326) (<.0001)*** (0.3464) (<.0001)*** (0.1385) (<.0001)***
Panel B: ranking period of 3 months
Variable
Intercept -0.0030 0.0096 -0.0584 0.0284 -0.0329 0.0397 -0.0380 -0.0013
(0.7701) (0.1865) (0.0006)*** (0.0099)*** (0.2297) (0.0164)** (0.362) (0.9557)
CY12MONTH 0.0741 -0.0574 0.3468 -0.1542 0.5627 -0.1087 0.8006 -0.4202
(0.0129)** (0.1798) (<.0001)*** (0.017)** (<.0001)*** (0.2619) (<.0001)*** (0.003)***
HP 0.0310 -0.0556 0.0250 -0.1211 0.0124 -0.1799 -0.1300 -0.1719
(0.0379)** (<.0001)*** (0.3086) (<.0001)*** (0.7564) (<.0001)*** (0.033)** (<.0001)***
Panel C: ranking period of 6 months
Variable
Intercept -0.0252 0.0051 -0.0755 0.0153 -0.0702 0.0009 -0.0707 -0.0479
(0.0164)** (0.4304) (<.0001)*** (0.1732) (0.0103)** (0.9566) (0.0917)* (0.0523)*
CY12MONTH 0.1097 -0.2263 0.3128 -0.3330 0.6136 -0.3747 0.7427 -0.3108
(0.0003)*** (0.0002)*** (<.0001)*** (0.0015)*** (<.0001)*** (0.0194)** (<.0001)*** (0.1765)
HP 0.0414 -0.0651 0.0412 -0.1198 0.0093 -0.1574 -0.1788 -0.2492
(0.0044)*** (<.0001)*** (0.0993)* (<.0001)*** (0.8043) (<.0001)*** (0.0022)*** (<.0001)***
Panel D: ranking period of 12 months
Variable
Intercept -0.0204 0.0107 -0.0586 -0.0022 -0.0719 0.0209 -0.0815 -0.0442
(0.0361)** (0.125) (0.0006)*** (0.857) (0.0079)*** (0.1657) (0.0368)** (0.0352)**
CY12MONTH 0.1067 -0.2420 0.3631 -0.3530 0.6280 -0.1880 0.9508 -0.5483
(0.0003)*** (<.0001)*** (<.0001)*** (0.0004)*** (<.0001)*** (0.1343) (<.0001)*** (0.0018)***
HP 0.0597 -0.0604 0.0621 -0.1199 -0.0197 -0.1984 -0.2405 -0.3629
(<.0001)*** (<.0001)*** (0.0124)** (<.0001)*** (0.6161) (<.0001)*** (<.0001)*** (<.0001)***
59
Table 21: Estimate of momentum trading returns of calendar spread that longs the
1st-nearby futures and shorts the 2nd-nearby futures vs convenience yield, net
hedging pressure and monthly dummies, bi-weekly data
Holding period of 1
month
Holding period of 3
month
Holding period of 6
month
Holding period of 12
month
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Panel A: ranking period of 1 month
Variable
Intercept 0.0019 0.0067 0.0003 0.0044 0.0006 0.0211 -0.0068 0.0009
(0.7467) (0.091)* (0.9774) (0.4848) (0.9774) (0.0105)** (0.5405) (0.8909)
CY3MONTH 0.1350 0.1713 0.2284 0.0330 0.7779 -0.1915 0.6178 -0.3060
(0.1022) (<.0001)*** (0.1079) (0.6035) (0.0053)*** (0.0207)** (<.0001)*** (<.0001)***
HP 0.0084 -0.0072 0.0370 -0.0233 0.0147 -0.0188 0.0160 -0.0128
(0.3331) (0.2618) (0.014)** (0.023)** (0.6164) (0.1572) (0.3256) (0.2316)
Panel B: ranking period of 3 months
Variable
Intercept 0.0087 0.0326 -0.0039 0.0098 -0.0092 0.0358 -0.0232 0.0239
(0.199) (<.0001)*** (0.7078) (<.0001)*** (0.4267) (<.0001)*** (0.0737)* (0.0112)**
CY3MONTH -0.1937 0.2045 0.3286 -0.0717 0.3703 0.1144 0.5461 -0.3726
(0.0109)** (0.0628)* (0.0047)*** (0.0261)** (0.0044)*** (0.3564) (0.0002)*** (0.006)***
HP 0.0120 0.0371 -0.0060 -0.0151 0.0006 -0.0044 0.0243 -0.0223
(0.2753) (0.002)*** (0.7194) (<.0001)*** (0.9761) (0.744) (0.2472) (0.1299)
Panel C: ranking period of 6 months
Variable
Intercept 0.0121 0.0045 0.0050 -0.0015 -0.0231 0.0000 -0.0168 -0.0089
(0.0656)* (0.0094)*** (0.5881) (0.508) (0.0135)** (0.9957) (0.0988)* (0.0423)**
CY3MONTH -0.3646 -0.2931 -0.1338 -0.3707 0.2448 -0.6072 0.2491 -0.5983
(<.0001)*** (<.0001)*** (0.1346) (<.0001)*** (0.0072)*** (0.0066)*** (0.0119)** (<.0001)***
HP 0.0255 0.0023 0.0376 -0.0026 -0.0096 -0.0451 -0.0051 -0.0159
(0.0139)** (0.4029) (0.0091)*** (0.4608) (0.5088) (<.0001)*** (0.7501) (0.0212)**
Panel D: ranking period of 12 months
Variable
Intercept 0.0120 0.0017 0.0130 0.0006 -0.0159 -0.0017 -0.0113 -0.0193
(0.052)* (0.3048) (0.1408) (0.822) (0.0774)* (0.584) (0.2203) (0.0005)***
CY3MONTH -0.3886 -0.3376 -0.2096 -0.5377 0.2591 -0.5458 0.0139 -0.4056
(<.0001)*** (<.0001)*** (0.0154)** (<.0001)*** (0.0033)*** (<.0001)*** (0.8769) (0.0341)**
HP 0.0274 -0.0040 0.0589 -0.0028 0.0663 0.0000 -0.0071 -0.0143
(0.0081)*** (0.0838)* (<.0001)*** (0.4172) (<.0001)*** (0.9977) (0.6445) (0.065)*
60
Table 22: Estimate of momentum trading returns of calendar spread that longs the
1st-nearby futures and shorts the 6-month futures vs convenience yield, net hedging
pressure and monthly dummies, bi-weekly data
Holding period of 1
month
Holding period of 3
month
Holding period of 6
month
Holding period of 12
month
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Panel A: ranking period of 1 month
Variable
Intercept 0.0001 0.0108 0.0430 0.0127 0.0244 0.0241 0.0011 0.0472
(0.9866) (0.148) (0.0366)** (0.1828) (0.1912) (0.0948)* (0.9554) (0.0011)***
CY6MONTH 0.4079 0.0391 0.7072 0.0331 0.6923 -0.2776 0.9454 -0.3126
(<.0001)*** (0.3028) (<.0001)*** (0.4932) (<.0001)*** (0.0002)*** (<.0001)*** (<.0001)***
HP 0.0020 -0.0108 0.0506 -0.0277 0.0339 -0.0253 0.0490 -0.0488
(0.877) (0.3381) (0.1173) (0.0531)* (0.2481) (0.2422) (0.1253) (0.0235)**
Panel B: ranking period of 3 months
Variable
Intercept -0.0132 0.0088 -0.0316 0.0156 -0.0204 0.0086 -0.0593 -0.0023
(0.2169) (0.1161) (0.0783)* (0.0003)*** (0.3275) (0.505) (0.0077)*** (0.8564)
CY6MONTH 0.3275 0.0420 0.7220 -0.0897 0.8748 -0.0345 1.0685 -0.2815
(<.0001)*** (0.2159) (<.0001)*** (0.0007)*** (<.0001)*** (0.6606) (<.0001)*** (0.0003)***
HP 0.0091 -0.0282 -0.0032 -0.0254 0.0290 -0.0413 -0.0015 -0.0404
(0.6023) (0.0009)*** (0.914) (0.0001)*** (0.3922) (0.0347)** (0.966) (0.0347)**
Panel C: ranking period of 6 months
Variable
Intercept -0.0042 0.0069 -0.0242 -0.0028 -0.0197 -0.0045 -0.0520 -0.0229
(0.7253) (0.0736)* (0.1945) (0.8899) (0.3014) (0.6024) (0.0223)** (0.0414)**
CY6MONTH 0.1077 -0.1284 0.4878 -0.2059 0.4290 -0.2404 0.7422 -0.4286
(0.0423)** (0.0027)*** (<.0001)*** (0.3639) (<.0001)*** (0.0123)** (<.0001)*** (0.0006)***
HP 0.0362 -0.0079 0.0549 0.0680 -0.0152 -0.0457 -0.0057 -0.0439
(0.0517)* (0.194) (0.0582)* (0.0369)** (0.6063) (0.0009)*** (0.8721) (0.0138)**
Panel D: ranking period of 12 months
Variable
Intercept -0.0017 0.0070 -0.0077 0.0053 -0.0259 -0.0115 -0.0354 -0.0459
(0.8787) (0.0468)** (0.6522) (0.3379) (0.1469) (0.1232) (0.0586)* (0.0012)***
CY6MONTH 0.0806 -0.2694 0.2842 -0.4381 0.3387 -0.5401 0.4372 -0.4041
(0.1249) (<.0001)*** (0.0005)*** (<.0001)*** (<.0001)*** (<.0001)*** (<.0001)*** (0.0304)**
HP 0.0465 -0.0080 0.0853 -0.0096 -0.0079 0.0000 -0.0839 -0.0837
(0.0109)** (0.114) (0.0025)*** (0.2273) (0.7873) (0.9997) (0.0069)*** (<.0001)***
61
Table 23: Estimate of momentum trading returns of calendar spread that longs the
1st-nearby futures and shorts the 12-month futures vs convenience yield, net hedging
pressure and monthly dummies, bi-weekly data
Holding period of 1
month
Holding period of 3
month
Holding period of 6
month
Holding period of 12
month
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Long
Winner
Short
Loser
Panel A: ranking period of 1 month
Variable
Intercept -0.0054 0.0464 0.0264 0.0451 0.0538 0.0384 0.0967 -0.0278
(0.68) (0.0002)*** (0.3105) (0.0085)*** (0.0619)* (0.1531) (0.0081)*** (0.0003)***
CY12MONTH 0.2963 -0.0041 0.3342 0.0112 0.5377 -0.1554 0.8795 -0.0857
(<.0001)*** (0.9167) (<.0001)*** (0.8321) (<.0001)*** (0.0611)* (<.0001)*** (<.0001)***
HP -0.0045 -0.0282 0.0670 -0.0458 0.1658 -0.0350 0.0740 -0.0398
(0.8194) (0.1166) (0.0862)* (0.0619)* (0.0001)*** (0.3626) (0.1747) (<.0001)***
Panel B: ranking period of 3 months
Variable
Intercept -0.0283 0.0218 -0.0295 0.0260 -0.0046 -0.0139 -0.0359 0.0335
(0.0534)* (0.0494)** (0.2549) (0.0072)*** (0.8798) (0.5777) (0.3506) (0.2052)
CY12MONTH 0.2707 0.0287 0.7154 -0.0997 0.6557 -0.2415 0.8850 -0.2696
(<.0001)*** (0.4737) (<.0001)*** (0.0044)*** (<.0001)*** (0.0078)*** (<.0001)*** (0.005)***
HP 0.0020 -0.0373 0.0185 -0.0377 0.0800 -0.0907 -0.0344 -0.1523
(0.9235) (0.0182)** (0.6193) (0.0061)*** (0.0645)* (0.0111)** (0.5327) (<.0001)***
Panel C: ranking period of 6 months
Variable
Intercept -0.0302 0.0213 -0.0438 0.0221 -0.0333 -0.0016 -0.1412 -0.0189
(0.0791)* (0.0126)** (0.0928)* (0.0631)* (0.2959) (0.9266) (0.0004)*** (0.4739)
CY12MONTH 0.1752 0.0040 0.4544 -0.0427 0.6743 -0.1091 0.8035 -0.2653
(0.0002)*** (0.9182) (<.0001)*** (0.4328) (<.0001)*** (0.1697) (<.0001)*** (0.0285)**
HP 0.0469 -0.0314 0.0990 -0.0761 0.1081 -0.0865 -0.0402 -0.1108
(0.0481)** (0.0105)** (0.0061)*** (<.0001)*** (0.0141)** (0.0006)*** (0.459) (0.0037)***
Panel D: ranking period of 12 months
Variable
Intercept -0.0147 0.0182 0.0220 0.0386 -0.0411 -0.0172 -0.1429 -0.0956
(0.3658) (0.0106)** (0.3707) (0.0009)*** (0.1867) (0.3004) (<.0001)*** (0.0015)***
CY12MONTH 0.1468 -0.1738 0.3579 -0.3807 0.5946 -0.4400 0.8284 -0.3626
(0.0022)*** (<.0001)*** (<.0001)*** (<.0001)*** (<.0001)*** (<.0001)*** (<.0001)*** (0.0458)**
HP 0.0418 -0.0226 0.0041 -0.0451 -0.0459 -0.0014 -0.2335 -0.2400
(0.0883)* (0.0434)** (0.9116) (0.014)** (0.3301) (0.9573) (<.0001)*** (<.0001)***
62
Table 24: Summary statistics of convenience yield trading returns using the 1st-
nearby futures, bi-weekly data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
High Low
High-
Low High Low High-
Low High Low High-
Low High Low High-
Low
Panel A: ranking period of 1 month
Mean 2.40% 3.60% 0.00% 1.60% 2.80% 0.00% 3.20% 3.20% 0.00% 2.60% 5.20% -3.00%
Prob* 0.5784 0.2766 0.7506 0.4913 0.2296 0.6602 0.0513 0.0465 0.9499 0.0142 <.0001 0.0506
Std Dev 25.29% 21.82% 30.83% 22.60% 23.80% 29.80% 22.77% 23.19% 29.70% 21.50% 21.40% 26.30%
Sharpe R 9.49% 16.50% 0.00% 7.08% 11.76% 0.00% 14.05% 13.80% 0.00% 12.09% 24.30% -
11.41%
Panel B: ranking period of 3 months
Mean 0.00% 3.60% -12.00% 2.40% 6.00% -4.00% 2.20% 5.80% -4.00% 2.40% 6.40% -4.00%
Prob* 0.6232 0.2696 0.2655 0.321 0.0091 0.21 0.1803 0.0002 0.0756 0.023 <.0001 0.002
Std Dev 27.02% 20.44% 32.22% 23.00% 23.40% 30.60% 23.19% 22.06% 29.56% 21.40% 21.20% 25.70%
Sharpe R 0.00% 17.61% -37.25% 10.43% 25.64% -13.07% 9.49% 26.29% -13.53% 11.21% 30.19% -
15.56%
Panel C: ranking period of 6 months
Mean 0.00% 7.20% -12.00% 0.40% 5.60% -4.00% 2.60% 4.60% -2.00% 3.00% 6.80% -4.00%
Prob* 0.7791 0.0547 0.1257 0.8671 0.0082 0.0775 0.1083 0.0034 0.3108 0.004 <.0001 0.0043
Std Dev 26.33% 21.13% 31.52% 24.60% 22.00% 30.60% 22.49% 22.06% 28.43% 21.20% 21.50% 26.30%
Sharpe R 0.00% 34.07% -38.07% 1.63% 25.45% -13.07% 11.56% 20.85% -7.04% 14.15% 31.63% -
15.21%
Panel D: ranking period of 12 months
Mean 4.80% 6.00% 0.00% 8.00% 2.00% 5.60% 8.00% 3.20% 4.80% 6.50% 5.90% 0.50%
Prob* 0.2421 0.1261 0.8529 <.0001 0.3126 0.0262 <.0001 0.0305 0.0072 <.0001 <.0001 0.6685
Std Dev 22.86% 20.78% 28.06% 19.60% 21.60% 26.00% 19.09% 21.64% 25.17% 20.80% 20.90% 25.00%
Sharpe R 20.99% 28.87% 0.00% 40.82% 9.26% 21.54% 41.90% 14.79% 19.07% 31.25% 28.23% 2.00%
Mean and standard deviation are annualized by multiplying by 250 and 250 respectively.
63
Table 25: Summary statistics of convenience yield trading returns using the 12-
month futures, bi-weekly data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
High Low High-Low High Low High-Low High Low High-Low High Low High-Low
Panel A: ranking period of 1 month
Mean 7.20% 0.00% 9.60% 4.00% 1.60% 2.80% 4.20% 2.80% 1.40% 3.30% 3.60% 0.00%
Prob* 0.0197 0.3893 0.0129 0.011 0.3259 0.1864 0.0007 0.0105 0.3435 <.0001 <.0001 0.7573
Std Dev 17.67% 14.55% 21.48% 16.40% 15.00% 20.60% 17.82% 15.70% 21.64% 16.90% 15.40% 18.50%
Sharpe R 40.75% 0.00% 44.70% 24.39% 10.67% 13.59% 23.57% 17.84% 6.47% 19.53% 23.38% 0.00%
Panel B: ranking period of 3 months
Mean 3.60% 0.14% 3.60% 2.80% 3.60% 0.00% 5.00% 3.60% 1.40% 4.00% 4.30% 0.00%
Prob* 0.2029 0.9557 0.3189 0.0673 0.0261 0.7963 <.0001 0.0011 0.3359 <.0001 <.0001 0.7589
Std Dev 17.67% 15.24% 21.82% 16.40% 16.00% 20.80% 17.54% 15.56% 20.79% 18.10% 15.80% 19.20%
Sharpe R 20.38% 0.94% 16.50% 17.07% 22.50% 0.00% 28.51% 23.14% 6.73% 22.10% 27.22% 0.00%
Panel C: ranking period of 6 months
Mean 4.80% 0.52% 3.60% 2.80% 2.40% 0.15% 4.40% 2.20% 2.20% 3.20% 3.70% -1.00%
Prob* 0.1534 0.8429 0.3191 0.1019 0.0799 0.9397 0.0001 0.0427 0.1125 0.0001 <.0001 0.5609
Std Dev 17.32% 15.24% 21.82% 16.40% 14.40% 20.40% 15.84% 15.27% 19.37% 16.50% 15.00% 17.90%
Sharpe R 27.71% 3.39% 16.50% 17.07% 16.67% 0.75% 27.78% 14.40% 11.35% 19.39% 24.67% -5.59%
Panel D: ranking period of 12 months
Mean 3.60% 0.09% 3.60% 5.60% 2.00% 3.60% 6.20% 2.60% 3.40% 4.90% 4.20% 0.60%
Prob* 0.164 0.9741 0.2915 0.0005 0.1763 0.0858 <.0001 0.0127 0.0095 <.0001 <.0001 0.4896
Std Dev 16.28% 15.24% 21.13% 15.80% 15.20% 20.20% 15.13% 15.13% 19.09% 16.40% 15.00% 18.20%
Sharpe R 22.11% 0.56% 17.04% 35.44% 13.16% 17.82% 40.97% 17.18% 17.81% 29.88% 28.00% 3.30%
Mean and standard deviation are annualized by multiplying by 250 and 250 respectively.
64
Table 26: Summary statistics of convenience yield trading returns using calendar
spread that shorts the 1st-nearby futures and longs the 2nd-nearby futures, bi-weekly
data
Holding period of 1 month Holding period of 3 month Holding period of 6 month Holding period of 12 month
High Low High-Low High Low High-Low High Low High-Low High Low High-
Low
Panel A: ranking period of 1 month
Mean 0.00% 0.00% 1.20% 1.20% 0.00% 2.40% 0.80% 0.00% 1.80% 0.30% -1.00% 1.00%
Prob* 0.8314 0.3731 0.5219 0.1149 0.1568 0.0364 0.061 0.0646 0.0092 0.1789 0.0021 0.0015
Std Dev 7.27% 11.78% 13.86% 7.20% 9.80% 12.00% 6.22% 7.35% 9.62% 4.40% 4.70% 6.40%
Sharpe R 0.00% 0.00% 8.66% 16.67% 0.00% 20.00% 12.86% 0.00% 18.72% 6.82% -21.28% 15.63%
Panel B: ranking period of 3 months
Mean 3.60% 26.40% -24.00% 1.60% 1.60% 0.00% 1.60% 3.00% -2.00% 0.60% 1.30% -1.00%
Prob* 0.0523 <.0001 <.0001 0.1342 <.0001 0.9997 0.0001 <.0001 0.0039 0.0013 <.0001 0.0035
Std Dev 9.35% 16.63% 17.32% 10.00% 3.80% 10.60% 5.94% 7.78% 6.51% 4.00% 5.30% 4.60%
Sharpe R 38.49% 158.77% -138.56% 16.00% 42.11% 0.00% 26.94% 38.57% -30.74% 15.00% 24.53% -21.74%
Panel C: ranking period of 6 months
Mean 3.60% 0.00% 7.20% 3.20% -4.00% 6.40% 1.60% -2.00% 3.20% 0.40% -1.00% 1.40%
Prob* 0.003 0.0365 0.0005 <.0001 0.0003 <.0001 <.0001 <.0001 <.0001 0.047 <.0001 <.0001
Std Dev 7.97% 9.01% 12.12% 7.20% 8.80% 11.60% 5.80% 5.66% 7.78% 4.20% 4.10% 5.80%
Sharpe R 45.18% 0.00% 59.38% 44.44% -45.45% 55.17% 27.59% -35.36% 41.14% 9.52% -24.39% 24.14%
Panel D: ranking period of 12 months
Mean 3.60% 0.00% 7.20% 0.80% 0.00% 2.80% 0.18% 0.00% 1.20% 0.00% -1.00% 0.70%
Prob* 0.0022 0.0489 0.0011 0.1587 0.0207 0.0101 0.5451 0.0129 0.0165 0.6421 0.0002 0.0071
Std Dev 6.58% 10.39% 12.12% 7.00% 8.20% 11.20% 4.24% 5.66% 6.93% 3.10% 3.90% 5.00%
Sharpe R 54.70% 0.00% 59.38% 11.43% 0.00% 25.00% 4.15% 0.00% 17.32% 0.00% -25.64% 14.00%
Mean and standard deviation are annualized by multiplying by 250 and 250 respectively.
65
Table 27: Summary statistics of convenience yield trading returns using calendar
spread that shorts the 1st-nearby futures and longs the 12-month futures, bi-weekly
data
Holding period of 1 month Holding period of 3 month