Are commodity futures a hedge against inflation?
A Markov-switching approach
Chunbo Liu
Xuan Zhang
Zhiping Zhou
a Southwestern University of Finance and Economics
b Nanjing Audit University
c Tongji University
Workshop
1 / 25
Motivation
The short-run effects of price increase may seem negligible, but the long-run
erosive effects of inflation on real asset returns can be substantial
2 / 25
Motivation
U.S. inflation is highest in 13 years as prices surge 5%
”We’ll get more inflation than we’re used to.” —— James Bullard
3 / 25
Motivation
The inflation protection ability of various asset classes (e.g.,
TIPS, commodities, real estate, bonds) has attracted much
attention from both researchers and the finance industry
Commodity futures represent a bet on commodity prices, where
the latter are the main drivers of inflation rates
Aggregate commodity futures vs. Specific commodity market
Gorton and Rouwenhorst (2004); Erb and Harvey (2006); Hoevenaars et al., (2008); Gorton et al.,(2013)
Baur and McDermott (2010); Wang et al., (2011); Van Hoang
et al., (2016); Lucey et al., (2017); and Bilgin et al., (2018).
4 / 25
Motivation
Conventional tools include:
Fisher coefficient (Fama and Schwert, 1977)
Pearson correlation (Bodie, 1982)
Johansen cointegration vector (Mahdavi and Zhou, 1997)
Vector error correction model (Levin et al., 2006)
Vector autoregressive model (Hoevenaars, et al., 2008; Spierdijk
and Umar, 2014)
Structural vector autoregressive model (Cologni and Manera,
2008; Lippi and Nobili, 2012; Blanchard and Riggi, 2013)
5 / 25
Motivation
Previous Studies: Constant Parameters do not change over time
Cannot reflect the different regimes in the economy
Chinn and Coibion (2014): The heterogeneity of sample period
in terms of inflationary regimes and commodity futures prices
Target: This paper applies Markov-switching cointegration and
error-correction models to investigate whether commodity futures index is able to hedge against inflation
6 / 25
Results Preview
Empirical approach
This study adopts a Markov-switching vector error correction
model and analyzes the question whether the commodity futures
index can hedge against inflation
Findings
Total commodity futures can not provide the ability to hedge
against inflation
Among several subindexes of commodity futures, industrial metals are the best inflation hedges
The hedging capacity exhibits substantial variation over time,
with most of the inflation hedging power emerging under relatively longer and more common regime
Results are robust to the inclusion of common stocks and bonds
into the model
7 / 25
Data and variables
The aggregate S&P GSCI Total Return Index includes 24 commodity futures contracts, categorized into five groups (Thomson Reuters Datastream):
Energy subindex: Crude Oil; Brent Crude Oil; Unleaded Gas;
Heating Oil; Gas Oil; Natural Gas
Industrial metals subindex: Aluminium; Copper; Lead; Nickel;
Zinc
Precious metals subindex: Gold; Silver
Agriculture subindex: Wheat; Red Wheat; Corn; Soybeans; Cotton; Sugar; Coffee; Cocoa
Livestock subindex: Live Cattle; Feeder Cattle; Lean Hogs
Our sample covers the period Jan. 1983 - Dec. 2017 because
of limited data availability of the subsector indices.
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Johansen’s Cointegration Test
We provide a brief method to analyze the inflation-hedging
characteristics of commodity futures in the long run.
If the cointegrating vector is (1, −θ), then its respective cointegration equation is
lnCPIt = θlnCOMMt + c
where COMM is the commodity futures index and c is the
intercept. We rewrite the equation above.
lnCOMMt = βlnCPIt + c
0
0
where β = 1θ , and c is also the intercept.
If β > 1, we can say that the commodity futures index can
hedge inflation efficiently in the long run.
If 0 < β < 1, then the commodity futures index can provide
some inflation-hedging ability.
9 / 25
Johansen’s Cointegration Test
Panel B: Johansen co-integration test
Model
COMM
EN
IM
PM
AGR
LC
Null: no co-integration
L-Max
p-value
Trace
p-value
156.315
0.000
160.448
0.000
138.084
0.000
142.389
0.000
88.043
0.000
92.477
0.000
68.356
0.000
74.693
0.000
94.496
0.000
99.970
0.000
95.131
0.000
103.560
0.000
Null: one co-integration
L-Max
p-value
Trace
p-value
4.133
0.393
4.133
0.393
4.305
0.369
4.305
0.369
4.434
0.351
4.434
0.351
6.337
0.166
6.337
0.166
5.474
0.235
5.474
0.235
8.429
0.069
8.429
0.069
(4)
(5)
(6)
Panel C: Co-integration vectors
(1)
(2)
(3)
Index
COMM
EN
IM
PM
AGR
LC
Commodity
t-statistics
Constant
t-statistics
-0.161
[-2.415]
-5.135
[-12.347]
-0.114
[-2.109]
-5.333
[-14.899]
-0.195
[-6.650]
-4.345
[-22.249]
-0.089
[-0.955]
-5.519
[-12.211]
-0.069
[-0.264]
-5.860
[-4.482]
-0.157
[-1.044]
-5.237
[-5.960]
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Econometric Model
The model specification is an M-regime, p-th order autoregressive with r co-integrating vectors, Markov-switching vector
error-correction model.
p
r
X
X
∆Xt = µ(st )+
Ai (st )∆Xt−i +
αj (st )Zt−1 +εt , εt |st ∼ NID(0, Σst )
i=1
j=1
Xt is the time t column vector of observations
st = 1, 2, · · · , M represents the regime in time t
µ(st ) denotes the regime-dependent intercepts
Ai (st ) is a row vector of i-th order autoregressive parameters
in regime st
αj (st ) measures the speed of error correction in regime st
Zt is the column vector containing the residuals from the errorcorrection equation, i.e. Zt = Ĉ Xt − Ĉ X̄t
Markov Chain: Pr (st = j|st−1 = i) = pij , where pij is the
generic [i, j] element of the M × M transition matrix P
11 / 25
Inflation and Commodity
Comparison of VECMs of CPI and prices of commodity index
VECM lag = 1
AIC
SIC
VECM lag = 2
AIC
SIC
Linear-VECM(1,1)
MSIA(2)-VECM(1,1)
MSIA(3)-VECM(1,1)
MSIAH(2)-VECM(1,1)*
MSIAH(3)-VECM(1,1)
-12.79
-13.01
-13.04
-13.09
-13.16
-12.68
-12.81
-12.72
-12.86
-12.78
Linear-VECM(2,1)
MSIA(2)-VECM(2,1)
MSIA(3)-VECM(2,1)
MSIAH(2)-VECM(2,1)
MSIAH(3)-VECM(2,1)
-12.81
-13.03
-13.13
-13.08
-13.16
-12.67
-12.75
-12.69
-12.78
-12.67
MSIA: the intercept terms, the autoregressive parameters are regime dependent
MSIAH: the intercept terms, the covariance matrix, and the autoregressive parameters are regime dependent
12 / 25
Inflation and Commodity
Estimates of a MSIAH(2)-VECM(1,1) for CPI and prices of commodity index
Parameter
Const.
∆ CPI(t-1)
∆ COMM(t-1)
EC
SE
Regime 1:
Transition matrix
Regime 2:
∆ CPI(t)
∆ COMM(t)
0.759
0.241
∆ CPI(t)
∆ COMM(t)
0.002
[5.616]
0.134
[1.791]
0.037
[7.624]
-0.002
[-1.005]
-0.001
[-0.093]
-2.073
[-0.920]
0.332
[2.628]
-0.105
[-1.915]
0.089
0.911
Ergodic prob.
Regime 1
0.269
0.002
[12.224]
0.228
[4.528]
0.015
[7.895]
-0.002
[-3.924]
0.010
[1.760]
-0.361
[-0.164]
-0.002
[-0.025]
0.008
[0.456]
0.003
0.079
Regime 2
0.001
0.041
Implied durations
Regime 1
4.150
Regime 2 11.280
0.731
In regime 2, the coefficient on the error-correction: positive but insignificant
In regime 2, total commodity futures cannot hedge against inflation
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Inflation and Commodity
1.00
Probabilities of Regime 1
0.75
0.50
0.25
1.00
1985
1990
Probabilities of Regime 2
1995
2000
2005
2010
2015
1985
1995
2000
2005
2010
2015
0.75
0.50
0.25
1990
During 1983-1989 and 1991-1998, the most dominant regime has been
regime 2. However, from 2007 to 2009, regime 1 has dominated regime 2
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Inflation and Industrial Metals
Estimates of a MSIAH(2)-VECM(1,1) model
Panel B: CPI and the industrial metals subindex
Parameter
Const.
∆ CPI(t-1)
∆ IM(t-1)
EC
SE
Regime 1:
Transition matrix
Regime 2:
∆ CPI(t)
∆ IM(t)
0.646
0.354
∆ CPI(t)
∆ IM(t)
0.001
[1.738]
0.381
[3.449]
0.012
[2.079]
-0.006
[-1.572]
0.019
[1.684]
0.340
[0.141]
0.533
[3.780]
-0.162
[-1.745]
0.089
0.911
Ergodic prob.
Regime 1
0.201
0.002
[10.071]
0.265
[4.357]
0.004
[2.705]
-0.003
[-3.976]
0.000
[-0.060]
1.116
[0.615]
-0.193
[-3.365]
0.057
[2.353]
0.004
0.082
Regime 2
0.001
0.049
Implied durations
Regime 1
2.830
Regime 2 11.230
0.799
In regime 2, there is a significant error-correction in inflation and a significant adjustment in industrial metals
The results of the MS model show that industrial metals provide a good
hedge against inflation
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Inflation and Industrial Metals
1.00
Probabilities of Regime 1
0.75
0.50
0.25
1.00
1985
1990
Probabilities of Regime 2
1995
2000
2005
2010
2015
1985
1995
2000
2005
2010
2015
0.75
0.50
0.25
1990
Regime 2 covers a relatively stable inflationary period, such as the Great
Moderation and the post-subprime crisis. Inflation tends to go hand in
hand with industrial metals futures subindex.
16 / 25
Robustness: including common stocks and bonds
Estimates of a MSIAH(2)-VECM(1,1) model
Table 6 Panel B: The industrial metals futures model
Parameter
Regime 1:
Regime 2:
∆ CPI(t)
∆ IM(t)
∆ Stock(t)
∆ Bond(t)
Regime 1
Regime 2
∆ CPI(t)
∆ IM(t)
∆ Stock(t)
∆ Bond(t)
Const.
0.001
[1.024]
0.017
[1.390]
-0.030
[-2.727]
0.014
[2.689]
0.606
0.093
0.394
0.907
0.002
[11.915]
0.007
[1.245]
0.020
[6.100]
0.004
[2.135]
∆ CPI(t-1)
0.436
[3.671]
-1.342
[-0.619]
0.171
[0.090]
-1.143
[-1.580]
Implied durations
0.224
[4.058]
1.511
[0.827]
-1.573
[-1.477]
0.128
[0.208]
∆ IM(t-1)
0.010
[1.677]
0.603
[4.884]
0.274
[2.549]
-0.007
[-0.136]
0.003
[1.919]
-0.114
[-1.852]
-0.063
[-1.872]
-0.007
[-0.321]
∆ Stock(t)
0.017
[1.969]
0.212
[1.167]
0.201
[1.314]
-0.145
[-2.379]
0.001
[0.651]
-0.280
[-3.277]
-0.062
[-1.260]
-0.037
[-1.255]
∆ Bond(t)
0.008
[0.389]
-0.651
[-1.485]
0.466
[1.292]
-0.045
[-0.310]
-0.006
[-1.310]
0.139
[0.878]
0.088
[0.941]
0.038
[0.695]
EC
-0.002
[-0.720]
-0.052
[-1.187]
0.073
[1.822]
-0.002
[-0.089]
-0.002
[-4.397]
0.028
[2.084]
0.001
[0.162]
-0.017
[-3.537]
SE
0.004
0.067
0.060
0.023
0.001
0.054
0.033
0.019
Regime 1
Regime 2
2.540
10.800
Ergodic prob.
Regime 1
Regime 2
0.190
0.810
In regime 2, the positive error correction coefficient on industrial metals
implies the inflation hedging ability. Taken together, these results suggest
that our main findings are robust to the inclusion of stocks and bonds
17 / 25
Robustness: including common stocks and bonds
1.00
Probabilities of Regime 1
0.75
0.50
0.25
1.00
1985
1990
Probabilities of Regime 2
1995
2000
2005
2010
2015
1985
1995
2000
2005
2010
2015
0.75
0.50
0.25
1990
This figure depicts the smoothed probabilities of being in regime 1, which
prevails the dotcom bubble and the subprime crisis, and regime 2, which
prevails during 1991-2001 and post-subprime crisis
18 / 25
Inflation and Energy
Estimates of a MSIA(2)-VECM(1,1) for CPI and prices of energy subindex
Panel A: CPI and the energy subindex
Parameter
Const.
∆ CPI(t-1)
∆ EN(t-1)
EC
SE
Regime 1:
Transition matrix
Regime 2:
∆ CPI(t)
∆ EN(t)
0.746
0.254
∆ CPI(t)
∆ EN(t)
0.003
[7.734]
0.028
[0.433]
0.051
[14.073]
0.003
[1.722]
-0.025
[-1.300]
-3.664
[-1.126]
0.436
[2.485]
-0.275
[-2.551]
0.024
0.977
Ergodic prob.
Regime 1
0.085
0.002
[16.888]
0.112
[2.808]
0.011
[11.385]
-0.002
[-5.455]
0.016
[2.321]
-3.350
[-1.444]
0.120
[2.296]
-0.015
[-0.662]
0.001
0.083
Regime 2
0.001
0.083
Implied durations
Regime 1
3.930
Regime 2 42.640
0.916
In regime 1, the error-correction coefficient in the energy index indicate the
energy prices diverge from the inflation index.
In regime 2, the sign of the error-correction coefficient is negative, implying
that the divergence continues
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Inflation and Energy
1.00
Probabilities of Regime 1
0.75
0.50
0.25
1.00
1985
1990
Probabilities of Regime 2
1995
2000
2005
2010
2015
1985
1995
2000
2005
2010
2015
0.75
0.50
0.25
1990
Both regimes are strongly persistent, with regime 2 lasting 42.64 months
on average and prevailing 91.6% of the time, while regime 1 lasts 3.93
months on average and prevails during the remaining 8.5% of months.
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Inflation and Precious Metals
Estimates of a MSIAH(2)-VECM(1,1)
Panel C: CPI and the precious metals subindex
Parameter
Const.
∆ CPI(t-1)
∆ PM(t-1)
EC
SE
Regime 1:
Transition matrix
Regime 2:
∆ CPI(t)
∆ PM(t)
0.836
0.164
∆ CPI(t)
∆ PM(t)
0.001
[2.845]
0.439
[4.722]
0.021
[2.791]
-0.003
[-1.617]
0.012
[1.915]
-3.640
[-3.054]
-0.092
[-0.853]
0.006
[0.171]
0.060
0.940
Ergodic prob.
Regime 1 0.269
0.002
[8.804]
0.247
[3.552]
0.001
[0.632]
-0.002
[-4.570]
-0.005
[-0.844]
3.273
[1.395]
-0.136
[-2.125]
0.023
[1.592]
0.004
0.046
Regime 2
0.023
0.045
Implied durations
Regime 1
6.10
Regime 2 16.57
0.731
In regime 2, the error correction coefficient on previous metals reveals that
the precious metals index provides some ability to hedge against inflation
but with low statistical significance
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Inflation and Precious Metals
1.00
Probabilities of Regime 1
0.75
0.50
0.25
1.00
1985
1990
Probabilities of Regime 2
1995
2000
2005
2010
2015
1985
1995
2000
2005
2010
2015
0.75
0.50
0.25
1990
Regime 2 prevails during the period 1983-2004 (with a short period of
regime 1 in 1986, 1990 and 2000-2001) and the post-subprime crisis.
22 / 25
Inflation and Agriculture
Estimates of a MSIAH(2)-VECM(1,1)
Panel D: CPI and the agriculture subindex
Parameter
Const.
∆ CPI(t-1)
∆ AGR(t-1)
EC
SE
Regime 1:
Transition matrix
Regime 2:
∆ CPI(t)
∆ AGR(t)
0.857
0.143
∆ CPI(t)
∆ AGR(t)
0.001
[3.993]
0.462
[6.067]
0.015
[3.755]
-0.002
[-1.718]
0.006
[0.695]
-3.416
[-2.039]
-0.060
[-0.692]
-0.024
[-0.850]
0.077
0.923
Ergodic prob.
Regime 1 0.351
0.002
[9.287]
0.212
[2.911]
0.001
[0.296]
-0.001
[-3.990]
-0.010
[-1.941]
4.498
[2.271]
0.062
[0.891]
-0.003
[-0.251]
0.003
0.070
Regime 2
0.001
0.037
Implied durations
Regime 1
7.01
Regime 2 12.96
0.649
In regime 2, the speed coefficient on CPI indicates a significant error correction in inflation. However, the error correction coefficients on the agriculture index in both regimes are not statistically significant
23 / 25
Inflation and Livestock
Estimates of a MSIAH(2)-VECM(1,1)
Parameter
Const.
∆ CPI(t-1)
∆ LS(t-1)
EC
SE
Regime 1:
Transition matrix
Regime 2:
∆ CPI(t)
∆ LS(t)
0.813
0.187
∆ CPI(t)
∆ LS(t)
0.001
[2.875]
0.419
[4.312]
0.011
[0.911]
-0.003
[-1.493]
-0.009
[-1.616]
1.718
[1.919]
0.003
[0.029]
-0.031
[-1.438]
0.060
0.940
Ergodic prob.
Regime 1 0.243
0.002
[8.566]
0.298
[4.433]
0.000
[-0.060]
-0.001
[-3.787]
0.000
[-0.040]
2.334
[1.419]
0.017
[0.290]
-0.008
[-0.746]
0.004
0.033
Regime 2
0.001
0.043
Implied durations
Regime 1
5.34
Regime 2 16.67
0.757
In regime 2, the speed coefficient on the CPI provides an indication that
there is a significant error correction in inflation
Moreover, in both regimes, the error correction coefficients of the livestock
index suggest that we cannot use the livestock index to hedge inflation risk
24 / 25
Conclusions
The results reveal that commodity futures index does not show
significant ability to hedge against inflation
The industrial metals are the best inflation hedges. The hedging capacity exhibits under relatively longer and more common
regimes: the Great Moderation and the post-subprime crisis
The precious metals index provides some ability to hedge against
inflation but with low statistical significance
We do not find evidence that energy, agriculture and livestock
subindexes have significant inflation hedging ability
Our main findings are robust to the inclusion of common stocks
and government bonds into the model
It also would be interesting to calculate hedge ratios as well as
the degree of hedging effectiveness. We leave this exercise for
a future research project
25 / 25