Returns in commodities futures markets
and financial speculation: a multivariate
GARCH approach
Joint with Matteo Manera and Ilaria Vignati
Università di Pavia
29/11/2011
1
Motivation
• From 2000 onwards we observe a number of severe
changes in financial markets. There has been a sharp
increase (at least until the crisis) in:
– Energy prices
– Food prices
– The numbers of financial participants (both hedgers
and speculators) in the futures markets.
• These stylized facts have lead to claims that:
– speculators drive energy and food prices
– speculators affect commodities’ volatility
– oil/energy prices induced an increase in food prices
2
Energy futures prices
50
100
150
CRUDE OIL
1995w1
2000w1
2005w1
2010w1
5
10
YEAR_W EEK
0
1990w1
1 MONTH FUTURE PRICE
1985w1
15
0
NATURAL GAS
1985w1
1990w1
1995w1
2000w1
YEAR_WEEK
2005w1
2010w1
3
Agriculture futures prices
2
4
6
8
CORN
0
WHEAT
2005w1
2010w1
8
6
YEAR_WEEK
10
12
2000w1
4
1995w1
2
1990w1
1 MONTH FUTURE PRICE
1985w1
1985w1
1990w1
1995w1
2000w1
YEAR_W EEK
2005w1
4
2010w1
Motivation
The aim of this paper is to answer the following
research questions:
• Is financial speculation significantly related to returns
in energy and non-energy commodities?
• Do macroeconomic factors explain returns in energy
and non-energy commodities?
• Are there spillovers between energy and non-energy
markets?
5
Literature review
oil prices and macroeconomic factors
The economic theory suggests few factors that should affect
commodities futures returns:
– Treasury bill yields
– Equity dividend yields
– Junk bond premium
(Sadorsky 2002, Chevallier 2009)
6
Literature review
oil prices and speculation
• Several papers suggest that the increasing presence
of speculators in oil future markets could explain the
spike in prices in 2007-2008 (Masters White 2008,
Medlock III and Myers Jaffe, 2009)
• However, empirical evidence generally shows that
there is not a relationship between the two
phenomena (Irwing Sanders 2010, Büyükşahin
Harris, 2011)
7
Literature review
oil prices and other commodities prices
• Oil prices have triggered the increase in food and
agricultural prices through costs of energy inputs
(Alexandratos, 2008, FAO, 2009)
• Increasing interaction between oil/energy and
food/non-energy prices is due to the growing demand
of bio-fuels (Du et al., 2009, Baffes and Haniotis,
2010)
• “Excess co-movement hypothesis” theory (Pindyck
and Rotemberg, 1990, Deb, Trivedi and Varangis,
1996)
• Spillover effects in futures markets have implications
in terms of cross hedging and cross speculation
(Malliaris and Urrutia, 1996)
8
Data description
• Dependent variable: returns of continuous series of
futures in:
– 4 energy commodities (oil, gasoline, heating oil, natural
gas)
– 5 non-energy commodities (corn, oats, soybean oil,
soybeans, wheat)
• Time period: 1986-2010
• Frequency: weekly
• Source: Datastream, CFTC (U. S. Commodity Futures
Trading Commission), FRED (Federal Reserve
Economic Data)
9
Data description
explanatory variables
• Macroeconomic factors:
– Return on the annual yield on the 90-day T-bill
– Returns of S&P 500 Index
– Junk bond yield= (return on the annual yield on
Moody’s long-term-BAA-rated corporate bonds) –
(return on the annual yield on Moody’s long-termAAA-rated corporate bonds)
10
Data description
explanatory variables
• Speculation:
Working’s T index (Working 1960) = proxies the excess
of speculation relative to hedging
1
SS
if HS  HL
HS  HL
SL
if HS  HL
1
HS  HL
SS = Speculation Short
SL = Speculation Long
HS = Hedging Short
HL = Hedging Long
11
Has speculation in energy futures market increased?
0
5
10
15
20
25
CRUDE OIL
1.4
NATURAL GAS
25
1.35
2006-2010
20
1986-2005
1.3
15
1.2
1.25
Working's T
10
1.15
5
1.1
0
1.05
kernel density
1
1
1.05
1.1
1.15
1.2
1.25
Working's T
1986-2005
1.3
2006-2010
1.35
1.4
12
Has speculation in agriculture futures market increased?
0
2
4
6
8
10
CORN
1.35
1.4
WHEAT
10
2006-2010
8
1986-2005
1.3
6
1.2
1.25
Working's T
4
1.15
2
1.1
0
1.05
kernel density
1
1
1.05
1.1
1.15
1.2
1.25
Working's T
1986-2005
1.3
2006-2010
1.35
1.4
13
Speculation (Working’s T index) across different commodities
Obs
Mean
Commodity
Std. Dev.
Min
Max
Gasoline
1039
260
1986- 2006- 198619862006-2010
2006-2010 1986-2005 2006-2010
2005 2010 2005
2005
1.033 1.044 0.019
0.018
1.000
1.013
1.126
1.121
Heating Oil
1018
260
1.043 1.065 0.032
0.022
1.001
1.020
1.178
1.134
Natural Gas
819
260
1.037 1.168 0.039
0.067
1.000
1.076
1.184
1.413
Crude Oil
1038
259
1.049 1.124 0.030
0.026
1.003
1.065
1.156
1.201
Soybean Oil
1039
260
1.068 1.088 0.047
0.044
1.005
1.024
1.222
1.209
Corn
1039
260
1.085 1.119 0.056
0.065
1.007
1.040
1.229
1.281
AGRICULTURE Oats
1039
260
1.061 1.050 0.053
0.043
1.000
1.000
1.407
1.192
Soybeans
1039
260
1.099 1.114 0.049
0.056
1.017
1.036
1.309
1.232
Wheat
1039
260
1.050 1.101 0.042
0.061
1.000
1.025
1.196
1.291
1986-2005 2006-2010
ENERGY
Notes: Summary statistics refer to the “filled” variables.
• 1986-2005: energy commodities have mean values lower than nonenergy one
• 2006-2010: means increase
• For oil and natural gas the increase is bigger than for other
commodities
14
The econometric model
• The model specification: returns of each commodity are a function of
– Treasury bill yields
– Equity dividend yields
– Junk bond premium
– Measures of speculation (Working’s T index)
• The econometric strategy:
1. Test for stationarity of series
2. Estimate the model using OLS and test for autocorrelation and
ARCH effects in the residuals
3. If present, move to a GARCH (1,1) and/or ARMA specification
rit   0   1 S & Pt   2 int_ ratet   3 junk _ bond _ yield t  4WTit   5 rit 1   it
 i2,t  si   j 1 j  i2,t  j   j 1  j i2,t  j
pi
qi
Then we extend the analysis to a multivariate GARCH model
15
Stationarity tests
• Macroeconomic variables and futures generally
present a unit root, and are transformed taking the
first difference of the logs to gain stationarity
• Working’s T index is stationary and considered in
levels
16
Results
Univariate GARCH(1,1)
Gasoline
Constant
Mean Equation
Tbill
Junk Bond Yield
S&P 500
Working’s T
AR(1)
Variance
Equation
Constant
ARCH(1)
GARCH(1)
LM test for ARCH
0.155
(0.066)
0.032
(0.015)
-0.052
(0.032)
0.056
(0.054)
-0.149
(0.064)
0.188
(0.029)
0.000
(0.000)
0.111
(0.025)
0.838
(0.036)
58.515
**
**
**
***
***
***
***
***
Heating Oil
0.041
(0.037)
0.022
(0.012)
-0.025
(0.027)
0.082
(0.049)
-0.038
(0.036)
0.186
(0.030)
0.000
(0.000)
0.161
(0.028)
0.756
(0.043)
149.335
*
*
***
***
***
***
***
Natural Gas
0.052
(0.029)
0.016
(0.017)
0.055
(0.049)
0.152
(0.082)
-0.048
(0.027)
0.204
(0.033)
0.000
(0.000)
0.154
(0.037)
0.766
(0.052)
8.522
*
*
*
***
***
***
***
***
Crude Oil
-0.054
(0.030)
0.017
(0.015)
-0.037
(0.027)
0.125
(0.051)
0.052
(0.028)
0.163
(0.029)
0.000
(0.000)
0.127
(0.026)
0.832
(0.032)
54.849
*
**
*
***
***
***
***
***
Soybean Oil
0.038
(0.018)
0.011
(0.010)
-0.014
(0.019)
0.098
(0.036)
-0.035
(0.017)
0.226
(0.027)
0.000
(0.000)
0.060
(0.016)
0.900
(0.029)
29.359
**
***
**
***
**
***
***
***
Corn
0.045
(0.015)
0.017
(0.011)
-0.014
(0.021)
0.068
(0.036)
-0.041
(0.014)
0.195
(0.028)
0.000
(0.000)
0.152
(0.030)
0.797
(0.037)
21.932
Oats
***
*
***
***
***
***
***
***
-0.039
(0.023)
-0.002
(0.012)
-0.021
(0.028)
0.069
(0.049)
0.036
(0.021)
0.172
(0.028)
0.000
(0.000)
0.117
(0.032)
0.769
(0.061)
84.914
Soybeans
*
*
***
***
***
***
***
0.027
(0.014)
0.008
(0.010)
-0.022
(0.018)
0.091
(0.033)
-0.024
(0.013)
0.207
(0.030)
0.000
(0.000)
0.172
(0.029)
0.799
(0.030)
30.870
*
***
*
***
***
***
***
***
Wheat
0.025
(0.017)
0.011
(0.012)
-0.003
(0.019)
0.038
(0.036)
-0.024
(0.016)
0.213
(0.028)
0.000
(0.000)
0.088
(0.018)
0.892
(0.022)
32.409
Ljung-Box Q test (lag 1)
2.293
0.219
0.633
0.510
0.382
0.003
0.616
0.031
0.408
Log Likelihood
2281
2388
1559
2397
2910
2818
2441
2992
2887
AIC
-4542
-4757
-3098
-4774
-5800
-5616
-4862
-5964
-5755
BIC
-4490
-4705
-3048
-4722
-5749
-5565
-4811
-5912
-5703
1298
1277
1078
1296
1298
1298
1298
1298
1298
N. of Obs.
Notes: error distribution is a Student’s T. Standard errors in parentheses. * significant at 10% level, ** significant at 5% level, *** significant at 1% level.
• Apart from crude oil and oats, Working’s T index is negative
17
or not significant
***
**
***
***
***
Multivariate GARCH
• The analysis developed so far is univariate.
• It is interesting to estimate a system where returns for
different commodities are jointly estimated, allowing for
conditional variances and covariances (spillover effects)
• Possible contribution of this econometric exercise:
– Indentify if and how returns on oil/energy futures
prices are related to food/non-energy commodities
futures prices
• Model implemented: CCC model and DCC model,
which allows for time-varying conditional correlations
18
Multivariate GARCH
• General multivariate GARCH:
rt  Cxt   t
rt = mx1 vector of dependent variables
 t  H t1/ 2t
C = mxk matrix of parameters
hij ,t   ij hii,t h jj ,t
H t  Dt1 / 2 RD t1 / 2
xt = kx1 vector of independent variables
H t1 / 2 = Cholesky factor of the time varying
conditional covariance matrix of the
disturbances
 t = mx1 vector of i.i.d. innovations
 ij = conditional correlations
R = matrix of unconditional correlations of the
standardized residuals Dt1 / 2  t
19
Multivariate GARCH
• CCC model:
H t  Dt1 / 2 RD t1 / 2
Dt
is a diagonal matrix of conditional variances in
which each  i2,t evolves according to a univariate
GARCH process defined as in the univariate
p
q
analysis as  i2,t  si   j 1 j  i2,t  j   j 1  j i2,t  j
i
i
R = matrix of time-invariant unconditional correlations
of the standardized residuals Dt1 / 2  t
• DCC model:
H t  Dt1 / 2 Rt Dt1 / 2
Rt = matrix of time-varying
conditional correlations
Rt  diag (Qt ) 1 / 2 Qt diag (Qt ) 1 / 2
~t = mx1 vector of
1 / 2
'
~
~
standardized
residuals
D
t
t
Qt  (1  1  2 ) R  1 t 1 t 1  2 Qt
1  2 = parameters for
dynamics of Rt
20
Multivariate GARCH
• We group the commodities in two subgroups:
1. “Fuels”: it includes the four energy commodities and
soybean oil (spillovers between energy markets and
a bio-fuel)
2. “Agriculture”: it includes the five agricultural
commodities (spillovers between food markets and a
bio-fuel)
• We consider one more group:
3. “Agriculture + factor of energy commodities”: it
includes the five agricultural commodities and a
factor of the energy ones (spillovers between energy
and agricultural markets)
21
Results
CCC model – “Fuels” group
Gasoline
Constant
Tbill
Junk Bond Yield
S&P 500
Gasoline(-1)
Mean Equation
Heating Oil(-1)
Natural Gas(-1)
Crude Oil(-1)
Soybean Oil(-1)
Working’s T Gasoline
Working’s T Heating Oil
Working’s T Natural Gas
Working’s T Crude Oil
Working’s T Soybean Oil
Variance
Equation
Constant
ARCH(1)
GARCH(1)
0.157
(0.073)
0.026
(0.016)
-0.052
(0.033)
0.177
(0.070)
0.091
(0.046)
-0.151
(0.058)
0.049
(0.020)
0.205
(0.058)
-0.014
(0.044)
-0.218
(0.064)
0.024
(0.042)
-0.002
(0.033)
0.088
(0.055)
-0.045
(0.026)
0.000
(0.000)
0.078
(0.019)
0.848
(0.041)
Heating Oil
**
**
***
**
***
***
*
***
***
***
0.011
(0.064)
0.007
(0.013)
-0.033
(0.029)
0.188
(0.061)
-0.041
(0.038)
-0.055
(0.055)
0.065
(0.018)
0.258
(0.052)
-0.048
(0.038)
-0.034
(0.056)
-0.024
(0.037)
-0.026
(0.028)
0.109
(0.046)
-0.035
(0.023)
0.000
(0.000)
0.087
(0.016)
0.864
(0.025)
Log Likelihood
***
***
***
**
***
***
***
Natural Gas
-0.071
(0.105)
-0.001
(0.019)
0.035
(0.047)
0.172
(0.087)
-0.080
(0.057)
-0.043
(0.073)
0.198
(0.034)
0.144
(0.069)
-0.049
(0.060)
0.051
(0.094)
0.015
(0.059)
-0.095
(0.043)
0.134
(0.076)
-0.036
(0.037)
0.000
(0.000)
0.134
(0.031)
0.773
(0.042)
***
**
**
*
***
***
***
0.093
(0.066)
0.004
(0.014)
-0.057
(0.030)
0.198
(0.063)
-0.007
(0.038)
-0.097
(0.055)
0.057
(0.018)
0.224
(0.056)
-0.053
(0.039)
-0.130
(0.057)
-0.009
(0.037)
-0.027
(0.029)
0.124
(0.047)
-0.047
(0.023)
0.000
(0.000)
0.103
(0.015)
0.848
(0.019)
*
***
*
***
***
**
***
**
***
***
***
Soybean Oil
-0.026
(0.046)
0.004
(0.011)
-0.006
(0.021)
0.157
(0.043)
0.030
(0.026)
-0.021
(0.032)
-0.034
(0.013)
-0.003
(0.033)
0.211
(0.031)
-0.034
(0.042)
0.028
(0.031)
-0.045
(0.024)
0.106
(0.037)
-0.029
(0.016)
0.000
(0.000)
0.101
(0.035)
0.839
(0.065)
***
***
***
*
***
*
***
***
***
11068
AIC
-21943
BIC
-21465
Degree of Freedom
9.617
(1.047)
N. of Obs.
**
Crude Oil
1076
1076
1076
***
22
1076
1076
Notes: error distribution is a multivariate Student’s T. Standard errors in parentheses. * significant at 10% level, ** significant at 5%
Results
CCC model – “Fuels” group
Conditional correlations:
Gasoline
Gasoline
Heating Oil
Natural Gas
Crude Oil
Soybean Oil
Heating Oil
Natural Gas
Crude Oil
Soybean Oil
1
0.723
(0.016)
0.234
(0.031)
0.748
(0.014)
0.121
(0.032)
***
1
***
0.324 ***
(0.029)
0.818 ***
(0.011)
0.167 ***
(0.032)
***
***
1
0.231 ***
(0.031)
0.124 ***
(0.032)
1
0.135 ***
(0.032)
1
Notes: * significant at 10% level, ** significant at 5% level, *** significant at 1% level.
23
Constant
Tbill
Junk Bond Yield
S&P 500
Constant
Mean Equation
Mean Equation
Gasoline(-1)
Tbill
Heating Oil(-1)
Junk Bond Yield
Natural Gas(-1)
S&P 500
Crude Oil(-1)
Gasoline(-1)
Soybean Oil(-1)
Heating Oil(-1)
Working’s T Gasoline
Natural Gas(-1)
Working’s T Heating Oil
Crude Oil(-1)
Working’s T Natural Gas
Soybean Oil(-1)
Working’s T Crude Oil
Working’s T Gasoline
Working’s T Soybean Oil
Working’s T Heating Oil
Variance
Equation
Constant
Working’s T Natural Gas
ARCH(1)
Working’s T Crude Oil
GARCH(1)
Working’s T Soybean Oil
Variance
Equation
Log
Likelihood
Constant
AIC
ARCH(1)
BIC
GARCH(1)
Degree
of Freedom
Gasoline
Heating Oil
Natural Gas
Crude Oil
Soybean Oil
0.154 **
(0.072)
0.030 *
(0.016)
-0.037
Gasoline
(0.033)
0.123 *
0.154 **
(0.070)
(0.072)
0.061
0.030 *
(0.046)
(0.016)
-0.125 **
-0.037
(0.055)
(0.033)
0.046 **
0.123 *
(0.020)
(0.070)
0.198 ***
0.061
(0.057)
(0.046)
0.004
-0.125 **
(0.045)
(0.055)
-0.200 ***
0.046 **
(0.063)
(0.020)
0.019
0.198 ***
(0.043)
(0.057)
0.013
0.004
(0.033)
(0.045)
0.050
-0.200 ***
(0.055)
(0.063)
-0.030
0.019
(0.026)
(0.043)
0.000 ***
0.013
(0.000)
(0.033)
0.089 ***
0.050
(0.020)
(0.055)
0.836 ***
-0.030
(0.039)
(0.026)
0.000 ***
(0.000)
0.089 ***
(0.020)
0.836 ***
(0.039)
-0.002
(0.064)
0.012
(0.014)
-0.024
Heating
(0.028)Oil
0.149 **
-0.002
(0.061)
(0.064)
-0.041
0.012
(0.037)
(0.014)
-0.034
-0.024
(0.052)
(0.028)
0.071 ***
0.149 **
(0.018)
(0.061)
0.229 ***
-0.041
(0.050)
(0.037)
-0.031
-0.034
(0.038)
(0.052)
-0.014
0.071 ***
(0.055)
(0.018)
-0.028
0.229 ***
(0.037)
(0.050)
-0.012
-0.031
(0.028)
(0.038)
0.073
-0.014
(0.046)
(0.055)
-0.016
-0.028
(0.023)
(0.037)
0.000 ***
-0.012
(0.000)
(0.028)
0.090 ***
0.073
(0.016)
(0.046)
0.855 ***
-0.016
(0.027)
(0.023)
0.000 ***
(0.000)
0.090 ***
(0.016)
0.855 ***
(0.027)
-0.034
(0.104)
0.000
(0.018)
0.044
Natural
(0.046)Gas
0.186 **
-0.034
(0.089)
(0.104)
-0.091
0.000
(0.056)
(0.018)
-0.014
0.044
(0.070)
(0.046)
0.201 ***
0.186 **
(0.034)
(0.089)
0.117 *
-0.091
(0.068)
(0.056)
-0.054
-0.014
(0.060)
(0.070)
0.034
0.201 ***
(0.093)
(0.034)
0.003
0.117 *
(0.058)
(0.068)
-0.072 *
-0.054
(0.044)
(0.060)
0.100
0.034
(0.076)
(0.093)
-0.030
0.003
(0.037)
(0.058)
0.000 ***
-0.072 *
(0.000)
(0.044)
0.148 ***
0.100
(0.033)
(0.076)
0.759 ***
-0.030
(0.044)
(0.037)
11116
0.000 ***
(0.000)
-22035
0.148 ***
(0.033)
-21547
0.759 ***
***
10.080
(0.044)
(1.125)
0.079
(0.065)
0.011
(0.015)
-0.053 *
Crude
(0.030)Oil
0.138 **
0.079
(0.065)
(0.065)
-0.020
0.011
(0.038)
(0.015)
-0.077
-0.053 *
(0.052)
(0.030)
0.067 ***
0.138 **
(0.018)
(0.065)
0.215 ***
-0.020
(0.054)
(0.038)
-0.038
-0.077
(0.039)
(0.052)
-0.108 *
0.067 ***
(0.056)
(0.018)
-0.014
0.215 ***
(0.037)
(0.054)
-0.010
-0.038
(0.029)
(0.039)
0.081 *
-0.108 *
(0.047)
(0.056)
-0.024
-0.014
(0.023)
(0.037)
0.000 ***
-0.010
(0.000)
(0.029)
0.105 ***
0.081 *
(0.015)
(0.047)
0.846 ***
-0.024
(0.019)
(0.023)
0.000 ***
(0.000)
0.105 ***
(0.015)
0.846 ***
(0.019)
-0.011
(0.046)
0.002
(0.011)
0.000
Soybean
(0.020) Oil
0.146 ***
-0.011
(0.043)
(0.046)
0.034
0.002
(0.026)
(0.011)
-0.016
0.000
(0.031)
(0.020)
-0.032 ***
0.146 ***
(0.013)
(0.043)
-0.015
0.034
(0.032)
(0.026)
0.202 ***
-0.016
(0.031)
(0.031)
-0.036
-0.032 ***
(0.041)
(0.013)
0.010
-0.015
(0.030)
(0.032)
-0.035
0.202 ***
(0.023)
(0.031)
0.106 ***
-0.036
(0.036)
(0.041)
-0.034 **
0.010
(0.015)
(0.030)
0.000 ***
-0.035
(0.000)
(0.023)
0.129 ***
0.106 ***
(0.045)
(0.036)
0.764 ***
-0.034 **
(0.098)
(0.015)
0.000 ***
(0.000)
0.129 ***
(0.045)
0.764 ***
(0.098)
Results
DCC model – “Fuels” group
Log Likelihood
Lambda
1
11116
0.051 ***
(0.010)
AIC
-22035
Lambda
2
0.821 ***
(0.043)
BIC
-21547
Test for Lambda 1 =
1408.85
Degree of
Freedom
10.080 ***
***
Lambda
2=
0 (Chi2(2))
(1.125)
N.
of Obs.
1076
1076
1076 ***
1076
1076
Lambda
1
0.051
(0.010)
Notes: error distribution is a multivariate Student’s T. Standard errors in parentheses.
* significant at 10% level, ** significant at 5%
24
Results
DCC model – “Fuels” group
Dynamic conditional correlations – Mean tests:
Mean
Returns
T-stat
Before 2005
After 2005
Gasoline, Heating Oil
0.695
0.736
-9.762***
Gasoline, Natural Gas
0.207
0.255
-8.497***
Gasoline, Crude Oil
0.720
0.735
-3.759***
Gasoline, Soybean Oil
0.104
0.211
-20.005***
Heating Oil, Natural Gas
0.322
0.359
-7.225***
Heating Oil, Crude Oil
0.772
0.791
-4.830***
Heating Oil, Soybean Oil
0.136
0.271
-24.471***
Natural Gas, Crude Oil
0.214
0.242
-5.004***
Natural Gas, Soybean Oil
0.115
0.177
-12.310***
Crude Oil, Soybean Oil
0.097
0.224
-23.076***
25
Dynamic conditional correlations graphs
“Fuels” group
0
.2
.4
.6
.8
Corr(Gasoline, Heating Oil)
1990w1
1995w1
2000w1
2005w1
2010w1
Corr(Gasoline, Natural Gas)
0
-.2
0
.2
.2
.4
.4
.6
.6
Corr(Heating Oil, Natural Gas)
1990w1
1995w1
2000w1
2005w1
2010w1
1990w1
Corr(Gasoline, Crude Oil)
1995w1
2000w1
2005w1
2010w1
Corr(Natural Gas, Crude Oil)
1995w1
2000w1
2005w1
2010w1
1990w1
Corr(Gasoline, Soybean Oil)
-.2
1995w1
2000w1
2005w1
1990w1
2010w1
2000w1
2005w1
2010w1
Corr(Crude Oil, Soybean Oil)
Corr(Natural Gas, Soybean Oil)
.4
.4
.2
26
1990w1
1995w1
2000w1
2005w1
2010w1
-.2
-.1
-.2
-.2
0
0
0
0
.1
.2
.2
.4
.2
.3
.4
.6
.6
Corr(Heating Oil, Soybean Oil)
1995w1
.6
1990w1
0
0
.2
.2
0
.4
.4
.2
.6
.6
.8
.8
.4
Corr(Heating Oil, Crude Oil)
1990w1
1995w1
2000w1
2005w1
2010w1
1990w1
1995w1
2000w1
2005w1
2010w1
1990w1
1995w1
2000w1
2005w1
2010w1
Results
CCC model – “Agriculture” group
Corn
Constant
Tbill
Junk Bond Yield
S&P 500
Corn(-1)
Mean Equation
Oats(-1)
Soybeans(-1)
Wheat(-1)
Soybean Oil(-1)
Working’s T Corn
Working’s T Oats
Working’s T Soybeans
Working’s T Wheat
Working’s T Soybean Oil
Variance
Equation
Constant
ARCH(1)
GARCH(1)
0.016
(0.021)
0.014
(0.012)
-0.008
(0.018)
0.072
(0.035)
0.163
(0.037)
0.022
(0.021)
-0.042
(0.042)
-0.012
(0.029)
0.016
(0.035)
-0.030
(0.014)
0.026
(0.013)
0.002
(0.015)
-0.022
(0.017)
0.010
(0.017)
0.000
(0.000)
0.094
(0.018)
0.846
(0.029)
Oats
**
***
**
*
***
***
***
-0.041
(0.030)
-0.004
(0.013)
-0.022
(0.025)
0.085
(0.049)
-0.056
(0.047)
0.200
(0.032)
0.003
(0.055)
0.040
(0.040)
-0.017
(0.049)
-0.036
(0.020)
0.055
(0.018)
-0.001
(0.021)
0.005
(0.023)
0.016
(0.023)
0.000
(0.000)
0.095
(0.025)
0.769
(0.066)
Log Likelihood
Soybeans
*
***
*
***
***
***
***
0.029
(0.018)
0.016
(0.011)
-0.014
(0.015)
0.096
(0.031)
0.017
(0.030)
0.019
(0.017)
0.148
(0.039)
-0.025
(0.025)
0.030
(0.030)
-0.004
(0.012)
0.007
(0.011)
-0.014
(0.013)
0.000
(0.014)
-0.014
(0.014)
0.000
(0.000)
0.118
(0.017)
0.846
(0.020)
Wheat
***
***
***
***
***
*
***
**
***
***
***
0.022
(0.021)
0.017
(0.011)
-0.021
(0.019)
0.094
(0.037)
0.028
(0.032)
0.003
(0.020)
-0.027
(0.040)
0.003
(0.028)
0.209
(0.035)
-0.003
(0.014)
-0.010
(0.014)
-0.007
(0.015)
0.000
(0.016)
-0.009
(0.016)
0.000
(0.000)
0.042
(0.011)
0.922
(0.020)
**
***
***
***
***
15239
AIC
-30286
BIC
-29790
Degree of Freedom
7.475 ***
(0.630)
N. of Obs.
0.015
(0.021)
0.013
(0.011)
-0.007
(0.017)
0.050
(0.034)
-0.035
(0.034)
0.032
(0.019)
-0.013
(0.038)
0.174
(0.031)
0.028
(0.033)
-0.028
(0.014)
-0.004
(0.013)
0.012
(0.015)
-0.018
(0.016)
0.023
(0.017)
0.000
(0.000)
0.078
(0.019)
0.894
(0.027)
Soybean Oil
1297
1297
1297
27
1297
1297
Notes: error distribution is a multivariate Student’s T. Standard errors in parentheses. * significant at 10% level, ** significant at 5%
Results
CCC model – “Agriculture” group
Conditional correlations:
Corn
Corn
1
Oats
0.504
(0.022)
0.613
(0.019)
0.523
(0.022)
0.478
(0.023)
Soybeans
Wheat
Soybean Oil
Oats
***
1
***
0.384 ***
(0.025)
0.380 ***
(0.026)
0.333 ***
(0.026)
***
***
Soybeans
Wheat
Soybean Oil
1
0.344 ***
(0.026)
0.682 ***
(0.016)
1
0.280 ***
(0.027)
1
Notes: * significant at 10% level, ** significant at 5% level, *** significant at 1% level.
28
Corn
Constant
Tbill
Junk Bond Yield
S&P
500
Constant
Corn(-1)
Tbill
Mean Equation
Mean Equation
Oats(-1)
Junk Bond Yield
Soybeans(-1)
S&P 500
Wheat(-1)
Corn(-1)
Soybean
Oats(-1) Oil(-1)
Working’s
T Corn
Soybeans(-1)
Working’s
Wheat(-1) T Oats
Working’s
T Soybeans
Soybean Oil(-1)
Working’s
Working’s T
T Wheat
Corn
Working’s
Oil
Working’s T
T Soybean
Oats
Variance
Equation
Constant
Working’s T Soybeans
ARCH(1)
Working’s T Wheat
GARCH(1)
Working’s T Soybean Oil
Soybeans
Wheat
Soybean Oil
Results
DCC model – “Agriculture” group
*
***
*
***
**
*
**
*
***
***
***
-0.050
(0.029)
-0.005
(0.014)
-0.026
Oats
(0.025)
0.075
-0.050
(0.049)
(0.029)
-0.045
-0.005
(0.047)
(0.014)
0.189
-0.026
(0.032)
(0.025)
0.007
0.075
(0.054)
(0.049)
0.046
-0.045
(0.039)
(0.047)
-0.019
0.189
(0.049)
(0.032)
-0.035
0.007
(0.020)
(0.054)
0.056
0.046
(0.018)
(0.039)
0.003
-0.019
(0.021)
(0.049)
0.005
-0.035
(0.023)
(0.020)
0.019
0.056
(0.023)
(0.018)
0.000
0.003
(0.000)
(0.021)
0.099
0.005
(0.025)
(0.023)
0.777
0.019
(0.061)
(0.023)
*
*
***
***
*
***
*
***
***
***
***
0.026
(0.018)
0.016
(0.011)
-0.018
Soybeans
(0.015)
0.085
0.026 ***
(0.031)
(0.018)
0.021
0.016
(0.029)
(0.011)
0.016
-0.018
(0.017)
(0.015)
0.140
0.085 ***
***
(0.039)
(0.031)
-0.022
0.021
(0.024)
(0.029)
0.033
0.016
(0.030)
(0.017)
-0.007
0.140 ***
(0.012)
(0.039)
0.004
-0.022
(0.011)
(0.024)
-0.009
0.033
(0.013)
(0.030)
0.001
-0.007
(0.014)
(0.012)
-0.012
0.004
(0.014)
(0.011)
0.000 ***
-0.009
(0.000)
(0.013)
0.123
0.001 ***
(0.017)
(0.014)
0.848 ***
-0.012
(0.018)
(0.014)
0.013
(0.020)
0.012
(0.011)
-0.010
Wheat
(0.017)
0.040
0.013
(0.034)
(0.020)
-0.042
0.012
(0.033)
(0.011)
0.027
-0.010
(0.019)
(0.017)
-0.007
0.040
(0.038)
(0.034)
0.180
-0.042
(0.031)
(0.033)
0.031
0.027
(0.033)
(0.019)
-0.030
-0.007
(0.014)
(0.038)
-0.005
0.180
(0.013)
(0.031)
0.011
0.031
(0.015)
(0.033)
-0.012
-0.030
(0.016)
(0.014)
0.025
-0.005
(0.016)
(0.013)
0.000
0.011
(0.000)
(0.015)
0.089
-0.012
(0.022)
(0.016)
0.880
0.025
(0.030)
(0.016)
15269
0.000 ***
(0.000)
AIC
-30343
ARCH(1)
0.123 ***
(0.017)
BIC
-29836
GARCH(1)
0.848 ***
***
Degree
of Freedom
7.668
(0.018)
(0.659)
Log Likelihood
15269 ***
Lambda
1
0.023
(0.006)
AIC
-30343
Lambda
2
0.925 ***
(0.027)
BIC
-29836
Test for Lambda 1 =
4706
Degree of Freedom
7.668 ***
***
Lambda 2 = 0 (Chi2(2))
(0.659)
N.
of Obs.
1297
1297
1297
Lambda
1
0.023 ***
(0.006)
Notes: error distribution is a multivariate Student’s T. Standard errors in parentheses. * significant at
Variance
Equation
Log
Likelihood
Constant
0.014
(0.021)
0.012
(0.012)
-0.011
Corn
(0.018)
0.064
0.014
(0.035)
(0.021)
0.158
0.012
(0.037)
(0.012)
0.022
-0.011
(0.021)
(0.018)
-0.041
0.064
(0.041)
(0.035)
-0.012
0.158
(0.029)
(0.037)
0.030
0.022
(0.034)
(0.021)
-0.032
-0.041
(0.014)
(0.041)
0.023
-0.012
(0.013)
(0.029)
0.003
0.030
(0.015)
(0.034)
-0.018
-0.032
(0.017)
(0.014)
0.012
0.023
(0.017)
(0.013)
0.000
0.003
(0.000)
(0.015)
0.107
-0.018
(0.019)
(0.017)
0.837
0.012
(0.028)
(0.017)
Oats
0.000 ***
(0.000)
0.107 ***
(0.019)
0.837 ***
(0.028)
0.000 ***
(0.000)
0.099 ***
(0.025)
0.777 ***
(0.061)
***
**
***
**
***
***
***
0.000 ***
(0.000)
0.089 ***
(0.022)
0.880 ***
(0.030)
0.020
(0.020)
0.014
(0.011)
-0.027
Soybean
(0.019) Oil
0.088
0.020 **
(0.037)
(0.020)
0.033
0.014
(0.032)
(0.011)
-0.004
-0.027
(0.020)
(0.019)
-0.028
0.088 **
(0.039)
(0.037)
0.010
0.033
(0.027)
(0.032)
0.210
-0.004 ***
(0.035)
(0.020)
-0.006
-0.028
(0.014)
(0.039)
-0.002
0.010
(0.013)
(0.027)
-0.002
0.210 ***
(0.015)
(0.035)
0.002
-0.006
(0.016)
(0.014)
-0.010
-0.002
(0.016)
(0.013)
0.000
-0.002 ***
(0.000)
(0.015)
0.052
0.002 ***
(0.011)
(0.016)
0.916
-0.010 ***
(0.020)
(0.016)
0.000 ***
(0.000)
0.052 ***
(0.011)
0.916 ***
(0.020)
29
1297
1297
10% level, ** significant at 5%
Results
DCC model – “Agriculture” group
Dynamic conditional correlations – Mean tests:
Mean
Returns
T-stat
Before 2005
After 2005
Corn, Oats
0.477
0.492
-2.978***
Corn, Soybeans
0.608
0.616
-1.704***
Corn, Wheat
0.505
0.532
-5.583***
Corn, Soybean Oil
0.483
0.503
-4.687***
Oats, Soybeans
0.379
0.381
-0.359***
Oats, Wheat
0.355
0.373
-3.839***
Oats, Soybean Oil
0.334
0.370
-8.366***
Soybeans, Wheat
0.341
0.354
-2.744***
Soybeans, Soybean Oil
0.684
0.714
-7.122***
Wheat, Soybean Oil
0.278
0.318
-9.340***
30
Dynamic conditional correlations graphs
“Agriculture” group
0
.2
.4
.6
Corr(Corn, Oats)
1985w1
1990w1
1995w1
2000w1
2005w1
2010w1
Corr(Corn, Soybeans)
1985w1
0
0
.2
.2
.4
.4
.6
.6
.8
Corr(Oats, Soybeans)
1990w1
1995w1
2000w1
2005w1
2010w1
1985w1
1990w1
Corr(Corn, Wheat)
1995w1
2000w1
2005w1
2010w1
Corr(Soybeans, Wheat)
1990w1
1995w1
2000w1
2005w1
2010w1
1985w1
0
1990w1
Corr(Corn, Soybean Oil)
1995w1
2000w1
2005w1
1985w1
2010w1
1990w1
1995w1
2000w1
2005w1
2010w1
Corr(Wheat, Soybean Oil)
Corr(Soybeans, Soybean Oil)
1985w1
1990w1
1995w1
2000w1
2005w1
2010w1
1985w1
1990w1
1995w1
2000w1
2005w1
2010w1
1985w1
31
0
0
0
0
.1
.2
.2
.2
.2
.4
.3
.4
.4
.6
.4
.6
.8
.6
Corr(Oats, Soybean Oil)
.5
1985w1
0
0
.1
.2
.2
.2
.4
.3
.4
.6
.4
.5
.6
.8
Corr(Oats, Wheat)
1990w1
1995w1
2000w1
2005w1
2010w1
1985w1
1990w1
1995w1
2000w1
2005w1
2010w1
Do energy markets influence non-energy commodities?
• It is not feasible to estimate jointly fuels and
agriculture markets due to the large number of
parameters to be estimated (no convergence
achieved)
• We summarize energy markets into one variable
(“energy”) using principal factor analysis
• This allows to investigate if “energy” influence
agriculture prices, as often claimed
32
Results
CCC model – “Agriculture + factor energy” group
33
Results
CCC model – “Agriculture + factor energy” group
Conditional correlations:
Corn
Corn
1
Oats
0.524
(0.024)
0.611
(0.020)
0.527
(0.024)
0.471
(0.025)
0.061
(0.032)
Soybeans
Wheat
Soybean Oil
Energy factor
Oats
***
1
***
0.368
(0.028)
0.378
(0.028)
0.327
(0.029)
0.103
(0.032)
***
***
*
Soybeans
***
1
***
0.331
(0.029)
0.690
(0.017)
0.112
(0.032)
***
***
Wheat
***
1
***
0.283
(0.030)
0.101
(0.032)
***
Soybean Oil
***
1
***
0.144
(0.032)
***
Energy factor
1
Notes: * significant at 10% level, ** significant at 5% level, *** significant at 1% level.
34
Results
DCC model – “Agriculture + factor energy” group
35
Results
DCC model – “Agriculture + factor energy” group
Dynamic conditional correlations – Mean tests:
Mean
Returns
T-stat
Before 2005
After 2005
Corn, Oats
0.483
0.496
-2.504***
Corn, Soybeans
0.587
0.603
-2.852***
Corn, Wheat
0.501
0.532
-5.437***
Corn, Soybean Oil
0.453
0.489
-7.694***
Corn, Energy factor
0.042
0.117
-18.584***
Oats, Soybeans
0.343
0.354
-2.601***
Oats, Wheat
0.349
0.378
-6.117***
Oats, Soybean Oil
0.304
0.352
-12.509***
Oats, Energy factor
0.060
0.117
-13.039***
Soybeans, Wheat
0.324
0.343
-3.789***
Soybeans, Soybean Oil
0.668
0.715
-8.253***
Soybeans, Energy factor
0.090
0.203
-30.488***
Wheat, Soybean Oil
0.270
0.321
-11.431***
Wheat, Energy factor
0.091
0.132
-10.512***
Soybean Oil, Energy factor
0.099
0.264
-40.627***
36
Dynamic conditional correlations graphs
“Agriculture + energy factor” group
0
.2
.4
.6
Corr(Corn, Oats)
1990w1
1995w1
2000w1
2005w1
2010w1
Corr(Oats, Soybeans)
0
0
.2
.2
.4
.4
.6
.8
.6
Corr(Corn, Soybeans)
1995w1
2000w1
2005w1
1990w1
2010w1
1995w1
Corr(Corn, Wheat)
2000w1
2005w1
2010w1
Corr(Soybeans, Wheat)
.4
0
0
0
.1
.1
.2
.2
.2
.4
.3
.3
.4
.6
.5
.8
Corr(Oats, Wheat)
.5
1990w1
2000w1
2005w1
2010w1
1990w1
Corr(Corn, Soybean Oil)
1995w1
2000w1
2005w1
1995w1
2000w1
2005w1
2010w1
Corr(Soybeans, Soybean Oil)
Corr(Oats, Soybean Oil)
Corr(Wheat, Soybean Oil)
2000w1
2005w1
2010w1
1990w1
Corr(Corn, Energy factor)
1995w1
2000w1
2005w1
1990w1
2010w1
Corr(Oats, Energy factor)
0
2000w1
2005w1
2010w1
1990w1
Corr(Soybeans, Energy factor)
1995w1
2000w1
2005w1
2010w1
Corr(Soybean Oil, Energy factor)
Corr(Wheat, Energy factor)
.4
.3
.1
0
0
-.1
-.1
-.1
0
0
0
.1
.2
.1
.1
.1
.2
.3
.2
.3
.2
.2
.4
.3
1995w1
.5
1995w1
.3
1990w1
0
0
0
.1
.1
.2
.2
.2
.2
.4
.3
.3
.4
.4
.6
.4
.5
.6
1990w1
2010w1
.5
1995w1
.8
1990w1
1990w1
1995w1
2000w1
2005w1
2010w1
1990w1
1995w1
2000w1
2005w1
2010w1
1990w1
1995w1
2000w1
2005w1
2010w1
1990w1
1995w1
2000w1
2005w1
2010w1
1990w1
1995w1
2000w1
2005w1
2010w1
37
What’s next?
Recursive estimates allow to investigate the effect of Working’s T
index over time
.02
.04
.06
.08
.1
.12
Soybean oil returns equation
2000w1
2002w1
2004w1
2006w1
year_week
Working's T crude oil (coeff.)
sign. 10%
2008w1
sign. 5%
2010w1
sign. 1%
38
Conclusions
• Speculation
− Working’s T index is poorly significant in both univariate
and multivariate models suggesting that speculation is not
relevant in explaining commodities’ returns
• Macroeconomic factors
− equity returns are generally positive and significant
• Spillovers
− There are spillovers within the two groups of commodities
− Between groups (“energy” factor): high conditional
correlations between energy factor and agricultural
commodities after 2005
39
Thanks!
40