Yale School of Management
The Fundamentals of
Commodity Futures Returns
Gary Gorton
The Wharton School, University of Pennsylvania
Fumio Hayashi
Tokyo University
K. Geert Rouwenhorst
School of Management, Yale University
Yale School of Management
Commodity Futures, Stocks and Bonds
Inflation Adjusted Performance From 1959 to 2004
2,000
1,750
1,500
1,250
1,000
Commodity Futures
750
Stocks
500
250
Bonds
0
1959
1963
1967
1971
1975
1979
1983
1987
1991
1995
1999
1
2003
Yale School of Management
Risk and Return of Commodity Futures
Annualized Futures Risk Premiums and Stdev by Commodity 1990/12- 2006/12
25%
Propane
Avera
age Risk Pre
emium (% p
p.a.)
20%
Gasoline RBOB
15%
Crude Oil Nickel
Copper
10%
Platinum
Tin
Feeder Cattle
Live Cattle
5%
Soybean Meal
Gold
Aluminum
-5%
Coffee
Lumber
Soybean Oil
0%
10%
Natural Gas
Pork Bellies
Silver
Zinc
Lead
Soybeans Lean Oats
Hogs
EW Index
0%
Heating Oil
Sugar
20%
Cocoa
Orange Juice
30%
Wheat
Corn
40%
50%
60%
Cotton
Rough Rice
-10%
Sample Standard Deviation (% p. a.)
2
Yale School of Management
Explaining
p
g the Cross-section of Commodity
y
Futures Risk Premiums
z Commodity futures are “insurance contracts” to transfer
commodity price risk
z Insurance premiums are expected to be high when the
amount of risk to be insured is high
z Modern Theory of Storage by DL (1992) predicts that
p
spot
p pprice volatility
y is decreasing
g in inventories
expected
z Risk premium of commodity futures should be a negative
f ti off inventories
function
i
t i
3
Yale School of Management
D t
Data
z Futures Prices:
ß Commodityy Research Bureau ((CRB))
ß London Metals Exchange (LME)
z Inventory Data:
ß
ß
ß
ß
ß
US Department of Energy
US Department of Agriculture
NYBOT, LME warehouse stocks
American Forest & Paper Association
USDA Li
Livestock
t k andd Seed
S d Di
Division
ii
4
Yale School of Management
I
Issues
with
ith Inventory
I
t
Data
D t
z Measurement
ß Which inventories are relevant?
ß Data revisions
ß Publication lags
z Statistical Issues
ß Trends: we applied a HP filter to the data
ß Seasonality of inventories
5
Yale School of Management
Seasonality of Inventories: Corn (Table 2)
Seasonal Variation of Corn Inventories
Deviation of Inventories from Trend 1974/6-2006/12
50%
Percent Dev
viation
30%
10%
-10%
-30%
-50%
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
6
Yale School of Management
Seasonality of Inventories: Natural Gas
Seasonal Variation of Natural Gas Inventories
Deviation of Inventories from Trend 1975/9-2006/12
50%
Percent Dev
viation
30%
10%
-10%
-30%
-50%
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
7
C
Ti
n
ot
to
C n
oc
oa
Lu O J
m
b
C er
of
fe
W e
he
at
So Co
So yb rn
e
So ybe an
yb an s
ea O
n il
M
ea
l
Po
O
rk a
t
B s
Li ell
ve ie
s
Le Ca
t
a
Fe n tle
ed Ho
er g
C s
at
tle
M
ilk
H Bu
ea tt
tin er
C gO
ru
d il
G eO
as il
o
Pr lin
N op e
at
ur an
al e
G
as
C
oa
l
C
o
Pl ppe
at r
Pa inu
lla m
di
um
Zi
nc
Le
a
N d
A ic
lu ke
m l
in
um
R-sq
quared
Yale School of Management
Seasonality (Table 2)
Seasonality of Physical Inventories
R-squared of Regressing Detrended Inventories on Monthly Dummies
1
0.75
0.5
0.25
0
8
Yale School of Management
Risk Premiums and Inventory-Sorted Portfolios
Cumulative Returns Inventory Sorted Portfolios
Performance of Equally-weighted Portfolios 12/1990-12/2006
800
Annualized Return
Volatility
Sharpe Ratio
EW Index
I d
8.98%
8.93%
0.55
Hi h Inventories
High
I
t i
4.62%
11.27%
0.05
L
Low
Inventories
I
t i
13.34%
10.80%
0.86
600
400
200
0
1990
1992
1994
EW Index
1996
1998
2000
High Inventories
2002
2004
2006
Low Inventories
9
Yale School of Management
Returns and Characteristics of Portfolios
Sorted on Relative Inventories (Table 5)
1969/12-2006/12
1986/1-2006/12
1990/12-2006/12
Panel A: Returns Relative to EW Index
Mean
Standard Deviation
t -statistic (mean)
% Excess Return>0
High
Low
H-L
High
Low
H-L
High
Low
H-L
-3.85
7.77
-3.03
42.57
4.21
7.80
3.32
56.53
-8.06
15.48
-3.19
43.47
-3.64
7.03
-2.34
41.04
3.61
7.04
2.33
57.37
-7.25
14.02
-2.34
42.23
-4.38
6.44
-2.83
41.67
4.37
6.47
2.80
57.29
-8.75
12.84
-2.82
43.23
Panell B: Average
A
Portfolio
f li Characteristics
Ch
i i
Prior 12m futures return
Prior 12m spot ret
return
rn
Basis
Inventories
Volatility (+1)
Commercials
Non-Commercials
Non Reportable
High
Low
t -stat
High
Low
t -stat
High
Low
t -stat
0.41
6 00
6.00
-7.78
36.37
23.40
15.31
9 78
9.78
4.61
-36.15
23.86
-6.45
-2.58
2 58
-14.51
1.24
5 00
5.00
-6.86
37.20
23.75
12.97
8 85
8.85
4.51
-35.19
23.90
-5.54
-2.39
2 39
-11.40
11.20
8 59
8.59
2.79
-31.07
23.46
-5.43
-1.95
1 95
-13.14
-0.27
0.05
5 33
5.33
-8.81
40.80
23.84
-11.71
-11
71
5.59
6.08
-7.97
-7
97
5.28
2.75
-5.03
-5
03
0.58
5.29
-12.33
-12
33
6.01
6.27
-8.00
-8
00
5.66
2.41
-4.81
-4
81
0.53
5.23
-1.15
0.66
10
Yale School of Management
Testing the Traditional Theory of Storage
Basis and Normalized Inventories of Copper
1
Basis (net of seasonal effe
ects)
0.75
Actual
Fitted
0.5
0.25
0
0
0.5
1
1.5
2
2.5
3
3.5
4
-0.25
-0.5
-0.75
Normalized Inventory
Copper is relatively easy to store…
11
Yale School of Management
Testing the Traditional Theory of Storage
Basis and Normalized Inventories for Crude Oil
1
basis (net off seasonal effe
ects)
0.75
Actual
Fitted
0.5
0.25
0
0
0.5
1
1.5
2
2.5
3
3.5
4
-0.25
-0.5
-0.75
Normalized Inventory
Crude is relatively expensive to store
12
Yale School of Management
Basis and Inventories
Cubic Spline Regression of Basis on Inventories (Table 3)
Commodity
slope at 1
t
slope at 0.75
t
difference
t
Metals group
Copper
Platinum
Palladium
Zinc
Lead
Nickel
Aluminum
Tin
-0.051
-0.032
-0.034
-0.045
-0.019
-0.146
-0.039
-0.057
-0.001
-2.46
-0.61
-1.10
-1.46
-0.39
-2.83
-1.06
-1.64
-0.02
-0.118
-0.153
-0.031
-0.032
-0.096
-0.270
-0.136
-0.094
-0.093
-6.01
-2.76
-0.93
-1.26
-2.22
-5.57
-4.13
-2.86
-3.03
0.067
0.121
-0.003
-0.013
0.076
0.124
0.096
0.037
0.092
4.70
5.64
-0.12
-1.03
3.32
4.34
5.95
2.16
5.06
SSofts
f group
Grains group
Meats group
Energies group
-0.193
0 193
-0.214
-0.598
-1.546
-5.65
5 65
-5.10
-7.03
-7.61
-0.257
0 257
-0.251
-0.602
-1.496
-8.37
8 37
-5.02
-6.27
-4.15
00.064
064
0.037
0.004
-0.050
44.93
93
1.39
0.12
-0.16
R-sq
0.41
0.41
0.19
0.32
0.54
0.55
0.25
0.40
Inventory sensitivity varies across commodity groups
13
T
C in
ot
to
C n
oc
oa
O
Lu J
m
b
C er
of
fe
W e
he
at
C
So o
yb rn
ea
n
So s
y
So O
yM il
ea
Po O l
rk ats
B
Li ellie
ve s
C
Le at
a
Fe n tle
ed Ho
er gs
C
at
tle
M
il
Bu k
t
H ter
ea
t
U Cru Oil
nl
ea deO
de il
dG
Pr as
op
a
N ne
at
G
as
C
oa
l
C
op
Pl pe
at r
Pa inu
lla m
di
um
Zi
nc
Le
a
N d
Al ick
um el
in
um
Basis relative to average
B
30%
10%
2
0%
0
-30%
High Inventory
Low Inventory
t-statistic
-2
-10%
-4
-20%
-6
14
-8
t-s
statistic Low minus High
Yale School of Management
State of Inventories and the Basis
Average Basis and Normalized Inventories
Monthly Data 1969/12-2006/12
8
6
20%
4
Yale School of Management
Returns and Characteristics of Portfolios
Sorted on Futures Basis (Table 6)
1969/12-2006/12
1986/1-2006/12
1990/12-2006/12
Panel A: Returns Relative to EW Index
Mean
Standard Deviation
t -statistic (mean)
% Excess Return>0
High
Low
H-L
High
Low
H-L
High
Low
H-L
5.42
7.76
3.98
58.56
-4.82
7.93
-3.44
42.79
10.23
15.58
3.73
57.88
5.04
6.87
3.55
61.35
-4.70
7.13
-3.14
39.04
9.74
13.93
3.36
61.35
5.71
6.08
4.04
63.02
-5.86
6.08
-4.10
37.50
11.57
12.10
4.08
63.02
High
Low
-5.93
0 00
0.00
-19.01
19.09
23.30
-13.76
0.99
-10.01
-10
01
3.92
5.73
0.13
0
13
4.81
-5.99
Panell B: Average
A
Portfolio
f li Characteristics
Ch
i i
Prior 12m futures return
Prior 12m spot ret
return
rn
Basis
Inventories
Volatility (+1)
Commercials
Non-Commercials
Non Reportable
High
Low
21.02
15 61
15.61
15.32
-14.87
24.07
-5.11
0 29
0.29
-18.40
15.31
23.23
t -stat
12.93
10 45
10.45
-17.08
2.13
High
Low
t -stat
19.68
14 39
14.39
15.44
-13.78
24.30
-5.40
-0.51
0 51
-17.73
15.95
23.31
-13.65
1.72
17.50
14 11
14.11
13.04
-9.34
23.98
-8.94
-8
94
6.89
2.38
-10.34
-10
34
3.95
6.12
1.46
1
46
4.24
-7.00
-9.87
-9
87
7.78
2.52
12.99
9 51
9.51
t -stat
10.56
7 16
7.16
15
T
C in
ot
to
C n
oc
oa
Lu OJ
m
b
C er
of
fe
W e
he
at
So Co
yb rn
ea
n
So s
y
So O
yM il
ea
Po O l
rk ats
B
Li ellie
ve s
C
Le at
Fe an tle
ed Ho
er gs
C
at
tle
M
il
Bu k
tte
H
ea r
tO
C
U
r
nl ud il
ea eO
de il
dG
Pr as
op
a
N ne
at
G
as
C
oa
l
C
op
Pl pe
at r
Pa inu
lla m
di
um
Zi
nc
Le
a
N d
Al ick
um e l
in
um
Prior return rela
ative to averag
ge
30%
10%
2
0%
0
-10%
-30%
High Inventory
Low Inventory
t-statistic
-2
-4
-20%
-6
-8
16
t-statistic Low
w minus High
Yale School of Management
State of Inventories and Prior Futures Returns
Prior 12-month Return and Normalized Inventories
Monthly Data 1969/12-2006/12
8
20%
6
4
Yale School of Management
Returns and Characteristics of Portfolios
Sorted on Prior 12-month Futures Return (Table 7)
1969/12 2006/12
1969/12-2006/12
1986/1 2006/12
1986/1-2006/12
1990/12 2006/12
1990/12-2006/12
Panel A: Returns Relative to EW Index
High
Mean
Standard Deviation
t -statistic (mean)
% Excess Return>0
6.54
8.52
4.82
58.78
Low
-6.82
8.62
-4.95
42.34
H-L
13.36
16.99
4.93
58.11
High
6.81
7.80
4.24
61.35
Low
-7.03
7.90
-4.35
39.44
H-L
13.84
15.53
4.34
60.96
High
7.69
6.84
4.56
64.58
Low
-7.67
6.83
-4.62
35.42
H-L
15.36
13.64
4.60
64.58
Panel B: Average Portfolio Characteristics
Prior 12m futures return
Prior 12m spot return
Basis
Inventories
Volatility (+1)
Commercials
Non-Commercials
Non Reportable
High
Low
32.62
26.22
6.73
-9.30
24.10
-16.65
-10.43
-9.96
9.88
23.28
t -stat
23.52
19.15
-8.26
1.71
High
Low
31.57
25.54
6.94
-7.29
24.43
-17.14
-11.70
-9.30
9.44
23.24
-11.57
9.02
2.74
-8.01
1.58
6.18
t -stat
High
Low
t -stat
24.16
17.97
-6.07
1.83
29.40
25.37
5.03
-3.51
24.37
-17.79
-11.23
-11.08
13.29
22.97
20.33
14.73
-5.74
1.83
-2.73
9.81
-4.31
-12.53
10.11
2.67
-7.46
1.24
5.89
-3.61
11.72
-3.67
17
Yale School of Management
Tradingg Strategies
g of Price-based Measures of Inventories
Cumulative Performance High Basis and Prior Return Portfolios
Performance of Equally-weighted Portfolios 12/1990-12/2006
1500
1250
EW Index
I d
8.98%
8.93%
0.55
Annualized Return
Volatility
Sharpe Ratio
High
Hi
h Basis
B i
14.67%
11.52%
0.92
High
Hi
h RS
16.67%
11.42%
1.11
Combination
C
bi ti
15.67%
11.00%
1.06
1000
750
500
250
0
1990
EW Index
1992
1994
1996
High Relative Strengh
1998
High Basis
2000
2002
2004
2006
Combination Basis and RS
18
Yale School of Management
Returns and Characteristics of Portfolios
Sorted on Prior 12-month Spot Return (Table 8)
1969/12-2006/12
1986/1-2006/12
1990/12-2006/12
Panel A: Returns Relative to EW Index
Mean
Standard Deviation
t -statistic (mean)
% Excess Return>0
High
Low
H-L
High
Low
H-L
High
Low
H-L
6.73
8.69
4.77
56.76
-7.12
8.58
-5.09
41.67
13.85
17.19
4.95
57.88
8.55
8.53
4.79
59.76
-8.82
8.34
-5.07
38.25
17.37
16.83
4.94
60.96
7.87
6.71
4.36
61.46
-8.16
6.78
-4.55
36.98
16.03
13.44
4.47
61.98
High
Low
-14.41
-14.01
14 01
-9.00
8.17
22.90
20.56
-5.83
-5
83
0.95
4.53
-7.80
-7
80
16.12
-0.93
Panell B: Average
A
Portfolio
f li Characteristics
Ch
i i
Prior 12m futures return
Prior 12m spot ret
return
rn
Basis
Inventories
Volatility (+1)
Commercials
Non-Commercials
Non Reportable
High
Low
t -stat
High
Low
28.61
29 78
29.78
3.94
-3.00
24.18
-12.79
-13.87
13 87
-7.08
3.27
23.25
18.13
27.98
28 60
28.60
4.71
-2.25
24.35
-13.58
-14.67
14 67
-7.05
4.09
23.33
22.84
12.40
-2.51
1.40
25.99
28 15
28.15
3.00
1.56
24.43
-13.02
-13
02
9.60
3.68
-6.45
-6
45
1.14
5.04
-6.29
-6
29
13.68
-1.87
-14.03
-14
03
10.59
3.78
11.57
-2.77
1.82
t -stat
t -stat
10.22
-2.57
1.91
19
Yale School of Management
Conditional Volatility and the Futures Basis
Conditional Distributions of Commodity Futures Returns
Normalized Monthly Basis-sorted Returns (1990/12 - 2006/12)
25%
Hi (20% Basis)
Low (20% Basis)
Avg.
Hi Basis
0.0948
Low Basis -0.0489
Rela
ative Frequenc
cy
20%
Stdev.
1.2264
0.9350
Skew.
Kurt.
0.3319 4.8894
0.3550 4.2030
15%
10%
5%
0%
-6.75%
-4.50%
-2.25%
0.00%
R t
Returns
2.25%
4.50%
6.75%
20
Yale School of Management
Volatility of Characteristics Sorted Portfolios
t-test for Equality
li of Average Futures Return Volatility
l ili
of Commodities in High versus Low Portfolios
Characteristic
1969/12-2006/12
1986/1-2006/12
1990/12-2006/12
Panel A: De-meaned data
Inventories
Basis
Prior 12-month futures return
Prior 12-month
12 month spot return
-1.75
3.33
2.77
2.82
-1.59
5.61
3.42
2.75
-0.78
4.68
3.49
3.07
Panel B: Raw data
Inventories
Basis
Prior 12-month futures return
Prior 12-month spot return
-1.15
2 13
2.13
1.71
1.82
-0.27
1 72
1.72
1.83
1.40
0.66
0 99
0.99
1.83
1.91
21
-40
op
p
at er
Pa inu
lla m
di
u
C m
ot
to
C n
oc
oa
O
ra S u
ng ga
e
r
Ju
i
Lu c e
m
be
C r
of
fe
W e
he
at
So Co
rn
So ybe
a
So ybe ns
yb a n
ea O
n il
M
ea
l
R
O
ou a
g ts
Po h R
rk ic
B e
Li elli
ve es
Le Ca
t
Fe an tle
ed Ho
er gs
C
at
tle
H
M
ea
tin ilk
g
U Cru Oil
nl
ea de
de Oi
d l
G
Pr as
o
N
at pa
ur ne
al
G
as
Pl
C
Net Pos
sition as % o
of Open Inte
erest
Yale School of Management
Alternative Hypothesis:
yp
Hedging
g g Pressure (Table 11)
Average Positions of Traders as % of Open Interest
CFTC Classifications 1986 - 2006
40
Commercials
Non-Commercials
Non-Reportable
20
0
-20
22
C
op
p
C er
ot
to
C n
oc
o
W a
he
at
So Co
r
So ybe n
So yb ans
yb ean
ea O
nM il
ea
O l
a
Po S t s
rk uga
B r
el
lie
s
S
Li ilv
ve e
r
Le Ca
t
O an tle
ra H
ng og
eJ s
Pl uic
at e
in
Fe Lu um
ed m
e r be
C r
at
C tle
of
fe
e
Pa G o
ll ld
H adi
ea u
t in m
C gO
ru il
d
G eO
a
R s o il
ou li
gh ne
Pr Ric
N op e
at a
ur ne
al
G
as
M
ilk
Yale School of Management
Hedging Pressure and Risk Premiums (Table 12)
R-squared of Futures Returns on Commercial Positions
CFTC data1986/12 - 2006/12
0 25
0.25
0.20
0.15
0.10
0.05
0.00
Contemporaneous
Predictive
23
Yale School of Management
Summary and Conclusions
z We test several predictions of the Theory of Storage for a large crosssection of commodity futures using inventory data. We find that:
ß Basis is negatively
g
y related to inventories
ß Relationship is non-linear for many commodities
ß Basis and prior returns are indicators for the state of inventories
ß Inventories, the basis, and prior returns are correlated with
expected price volatility and predict future risk premiums
ß We reject Hedging Pressure as an alternative explanation for
commodity futures risk premiums
z Future research:
ß Reconcile the empirical evidence with Modern Asset Pricing
Theory
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