1

Estimating the connectedness of commodity futures

using a network approach☆

Binqing Xiaoa, Libing Fanga, Sifan Dinga, Honghai Yua,

a School of Management and Engineering, Nanjing University, Nanjing, China

Abstract:

Using a network approach of variance decompositions, we measure the

connectedness of 18 key commodity futures and characterize both static (full-sample

estimation) and dynamic (rolling-window estimation) connectedness. Statically, we

show that, in general, metal futures are net transmitters of shocks to other futures and

energy futures, and agricultural futures are vulnerable to shocks from other futures.

Furthermore, almost two-thirds of volatility uncertainty for commodity futures is due

to the connectedness of shocks across the futures market. In terms of market dynamics,

we find connectedness always increases during times of turmoil, with clear peaks

shown during the 2007-2008 financial crisis, the 2011 European debt crisis and the

2013 to 2017 Brexit tumult. An analysis of connectedness networks, especially net

connectedness, suggests that investors could be forewarned that the connectedness of

various classes of futures could threaten their portfolios.

Keywords: Connectedness; Variance decompositions; Commodity futures

☆ The authors acknowledge financial support from the National Natural Science Foundation of China (71472085,

71401071 and 71672081). Corresponding Author: #22 Hankou Road, Gulou District, Nanjing, China, 210093. Tel: +86-25-83597501, Fax:

+86-25-83685630, Email Address: hhyu@nju.edu.cn (Honghai Yu).

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1. Introduction

The commodities futures market plays an important role in the global economy.

Due to low correlations with traditional financial assets and positive co-movements of

commodity prices with inflation, commodity futures, as a profitable hedging and

speculation asset, can help investors optimize asset allocation and diversify portfolio

risks (Chong and Miffre, 2010; Silvennoinen and Thorp, 2013; Kang et al., 2017). There

are three main types of commodity futures—metal futures, energy futures and

agriculture futures. The financialization of commodity markets is likely to increase the

degree of integration across different commodity markets, which is a significant

development for investors and policymakers (Tang and Xiong, 2012; Mensi et al., 2014;

Kang et al., 2017).

The global financial crisis of 2007-2009 has promoted increased interest in

systemic risk, which is now broadly applied to study shocks to other parts of the

financial system (Billio et al., 2012; Kang et al., 2017). Connectedness, a similar

concept, has also been investigated. The connectedness concept is crucial to modern

financial risk measurement and management (Diebold and Yılmaz, 2014; Diebold et

al., 2017; Demirer et al., 2018). However, while volatility spillovers between stock and

commodity markets have been studied extensively, there is little empirical research on

the interrelationships among different types of commodity futures, and this new area of

research may provide interesting insights.

In this paper, we use the network approach developed in Diebold and Yılmaz

(2009, 2012, 2014) to measure the connectedness of 18 key commodity futures markets.

This method captures the direction of shock transmissions based on forecast error

variance decompositions (FEVDs), which are estimated by vector autoregressions

(VARs). There are some important advantages to the network approach. First, this

approach builds a directed volatility spillover network and provides important

information for analyzing dynamic directional spillovers of futures markets into each

other (Shahzad et al., 2018). Second, it allows measurement of the returns or volatility

spillovers across a variety of assets and markets (Zhang and Wang, 2014; Batten et al.,

3

2015). Third, Diebold and Yılmaz (2014) stress that estimates of variance

decomposition are not impacted by the ordering of the variables due to invariant

forecast error variance decompositions (FEVD), which are independent of the Cholesky

factor identification of VAR. Due to these significant advantages, we make use of the

network approach to study the systemic risk within commodity futures markets and

seek to find the connectedness evolution for 18 important commodity futures.

Both static (full-sample) and dynamic (rolling-sample) connectedness have unique

characteristics. A static analysis shows that, in general, the net total connectedness of

metal futures is positive; the connectedness of lead futures is 34.6%, and zinc futures

have a connectedness of 30.2%, indicating that these futures are net transmitters of

shocks to other futures. However, energy futures and agricultural futures are relatively

vulnerable to shocks from other futures markets. Furthermore, the connectedness index

for the 18 commodity futures equals 69.6%; that is, almost two-thirds of the volatility

uncertainty for the commodity futures is traceable to the connectedness of shocks across

all futures. We find, according to dynamic analysis, that there is always a high degree

of connectedness during times of turmoil. For dynamic directional connectedness, the

“from” connectedness is much smoother than the “to” connectedness; therefore, the

trend of net total connectedness is similar to the pattern in the plots for connectedness

“to” others.

The contribution of our study is empirical rather than methodological. First, using

the variance decompositions from approximating models, we apply a unified

framework for the connectedness of global commodities futures at different levels, from

pairwise connectedness to system-wide connectedness. Second, based on a dataset that

includes the majority of the global commodities futures, our results show the overall

connectedness network during the 2008 financial crisis, the 2011 European debt crisis

and the 2013 to 2017 Brexit tumult. Our study complements existing research about the

interrelationships between commodity futures.

The remainder of this paper is organized as follows. Section 2 briefly reviews the

relevant literature. Section 3 describes our methodology, and Section 4 introduces the

data. In Section 5, we provide an empirical analysis. Finally, this paper summarizes its

4

conclusions in Section 6.

2. Literature Review

There is a growing library of research literature with regard to spillover effects and

systemic risk among commodity markets. Some research focuses on the relationships

between stock, bond and commodity markets. For example, Diebold and Yilmaz (2012)

found that cross-market volatility spillovers increased as the 2007-2008 financial crisis

became progressively serious. Other researchers studied the interrelationships among

different types of commodity futures. Wu et al. (2011) applied a volatility spillover

model and provided evidence of time-varying spillovers from the price of crude oil to

the spot prices of corn and futures prices. Nazlioglu et al. (2013) examined volatility

transmissions between oil and four agriculture futures including wheat, corn, soybeans

and sugar, showing that, with the exception of sugar, there was a risk transmission from

the oil market to the agricultural futures market in the post-crisis period. Kang et al.

(2017) employed a multivariate DECO-GARCH model and the spillover index to

analyze spillover effects between six commodity futures. The empirical results clarified

that the correlation with commodity futures is indeed positive and strengthened during

the crisis.

Our paper is also related to several strands of the research literature concerning

systemic risk contributions within the frameworks of financial network models. Billio

et al. (2012) examined the connectedness between banks, dealers, insurance companies

and hedge funds using a Granger-causality network and suggested that banks contribute

more to shock transmissions than do other financial institutions. Bluhm et al. (2014)

employed a network model of interconnected bank balance sheets to explore the

emergence of systemic risk and proposed a new macro-prudential risk management

approach. Based on the measure of the realized systemic risk beta, Hautsch et al. (2014)

ranked a firm’s share of the systemic risk in the U.S. financial system. Huang et al.

(2016) focused on the relationships between systemic risk contributions and

institutional local topology structure. From a systems perspective, in our research, we

5

apply the network approach proposed by Diebold and Yılmaz (2014) to measure the

connectedness in 18 key commodity futures and reveal a weighted and directed

volatility spillover network based on variance decompositions.

3. Methodology

In this section, we introduce the connectedness measurement framework. This

method was originally proposed in Diebold and Yilmaz (2009) to explicitly account for

interdependence in financial markets and then was expanded to study systems in the

finance and the economic fields. It is based on the vector autoregressive approximating

(VAR) models and the variance decomposition procedure, which we briefly describe

below.

3.1. Vector autoregressive model

We build our variance decomposition on a vector autoregressive approximating

model. Consider a K-dimensional VAR(p) process, assuming and a K × K positive

definite matrix:

1

, ~ 0,p

t i t i t t

i

where

y y (1)

where is a (K×1) vector which contains endogenous variables at t, and p is a lag

order. is the (K×K) dimensional coefficient matrix to be estimated. In our

setting, we use the restricted VAR.

The moving average process of the model, which is the key to understanding the

dynamics, is given by:

0

t i t i

i

y A (2)

Matrix satisfies the recursion process:

1 1 2 2 , 1,2,i i i p i p i A Φ A Φ A Φ A

where 0A is an K × K identity matrix and 0 0i for i A .

ty

1, p

iA

6

After estimating the VAR model, we depend on variance decomposition to split

the H-step-ahead forecast error variances of each variable into separate parts

attributable to the various system shocks.

3.2. Variance decomposition

Variance decomposition is often used to measure the contribution of different

structural shocks to the endogenous variable variation. However, since the shocks in a

reduced form are rarely orthogonal, we cannot simply calculate the variance

decompositions by the appropriately weighted sum of the variances.

The early literature proposed the Cholesky factor and the structural VAR to solve

this problem. The Cholesky factor orthogonalization generates orthogonalized

innovations and derives an order-dependent variance decomposition; thus, it is sensitive

to the ordering of the variables. Similarly, the structural VAR model maintains

assumptions from one or another theory, which makes it unattractive.

Hence, we apply the generalized variance decomposition (GVD) approach of

Koop et al. (1996) and Pesaran and Shin (1998), which allows for correlated (instead

of orthogonalized) shocks and constructs an order-independent variance decomposition;

that is, the generalized variance decomposition can analyze the directions of spillovers

and relies on a largely data-based identification system, but it keeps the same ordering.

The contribution of variable j to variable i’s H-step-ahead generalized forecast

error variance is given by:

11 2

0

1

0

( ' )

(H)

( ' ' )

H

ij i h jg h

ij H

i h h i

h

e e

e e

(3)

where is a selection vector with th element unity and zeros elsewhere, is the

coefficient matrix multiplying the h-lagged shock vector in the infinite moving-average

representation of the nonorthogonalized VAR, and is the standard deviation of .

Since, in the GVD scenario, shocks are not necessarily orthogonal, the variance shares

je j h

jj j

7

do not always add up to 1; thus, in general, .

Hence, we normalize each entry of the generalized variance decomposition matrix

by constructing

1

(H)(H)

(H)

g

ijg

ij Ng

ij

j

(4)

We then have and . Using , we can

immediately calculate the generalized connectedness measures.

3.3. Connectedness table

As a matter of notation, we now convert from to a measure of directional

connectedness in pairs, which is natural and immediate and represents the

connectedness from to at horizon H. Sometimes ‘‘the net’’ is necessary, as

opposed to ‘‘the gross’’, for directional connectedness in a pair. We thus derive the net

pairwise directional connectedness: .

We can then advance to total directional connectedness measures. The total

directional connectedness from others to is defined as:

1 , 1 1

1/

N N NH H H

i ij ij ij

j i j jj i j i

INN

≠ ≠

(5)

Similarly, the total directional connectedness to others from j is:

1 , 1 1

1/

N N NH H H

j ij ij ij

i i j ii j j i

OTN

≠

(6)

As mentioned before, in a pairwise directional connectedness situation, “the net”

is sometimes important. We define the net total directional connectedness as

.

Finally, we obtain the system-wide connectedness measure. We measure the total

directional connectedness using the generalized variance decomposition matrix:

1(H) 1

N g

ijj

1(H) 1

N g

ijj

, 1

(H)N g

iji jN

(H)g

(H)g

ij

H

i jC

j i

H H H

ij j i i jC C C

i

i i iNT OT IN

8

(7)

This total connectedness is simply the sum of total directional connectedness

regardless of “to” or “from”. Thus, following Diebold and Yilmaz (2009, 2012, 2014),

we can construct a connectedness table with the notations above to comprehend the

different connectedness measures and their relationships, as shown in Table 1.

Table 1 Connectedness Table Schematic

1x 2x

Nx From others

1x 11

H 12

H 1

H

N 11, 1

N H

jjj

2x 21

H 22

H 2

H

N 21, 2

N H

jjj

Nx 1

H

N 2

H

N H

NN 1

,N H

Njjj N

To others 11

1

N H

ii

i

21

2

N H

ii

i

1

N H

iNi

i N

, 1

1 N H

iji jN

i j

We can learn from the connectedness table how one can aggregate the most

disaggregated connectedness measures in different ways to obtain overall

macroeconomic directional and total connectedness measures. Various agents may be

more or less interested in one measure than in others. For instance, firm may be

concerned with how different others connect to it ( , for different ) most, or how

all others connect to it, . From another perspective, regulators might be more

interested in finding systemically important firms by measuring total directional

connectedness from to others, , and they might also be more interested in

identifying total connectedness, .

, 1 , 1 , 1

1/ =

N N NH H H

ij ij ij

i j i j i ji j i j

TotalN

i

H

i jC j

iIN

j

j jOT

Total

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4. Data

We focus on 18 major commodity futures, downloaded from the Bloomberg

Database: eight metal futures (copper, aluminum, lead, zinc, nickel, tin, gold and silver),

three energy futures (gasoline, crude oil and natural gas), five agricultural futures

(soybeans, soybean oil, wheat, oats and corn) and two so-called “softs” (cotton and

sugar). The returns of different commodity futures are calculated as the log differences

of the daily price multiplied by 100. Due to data availability, the sample period spans

from October 3, 2005, to December 31, 2018.

Table 2 Descriptive statistics for daily returns of 18 commodity futures

Variable Obs Mean Max Min SD Skew Kurt ADF AC(1)

Copper 3345 0.01 11.36 -14.97 1.78 -0.29 7.95 -62.51*** -0.08***

Aluminum 3344 0.00 7.54 -9.90 1.40 -0.16 5.33 -60.58*** -0.05***

Lead 3345 0.02 11.43 -14.28 2.09 -0.27 6.41 -55.88*** 0.03**

Zinc 3345 0.02 9.78 -11.74 1.96 -0.23 5.40 -59.03*** -0.02

Nickel 3344 -0.01 15.63 -19.20 2.24 -0.20 6.96 -58.22*** -0.01

Tin 3342 0.03 12.63 -12.36 1.75 -0.42 9.55 -55.93*** 0.03*

Gold 3271 0.03 8.62 -9.47 1.18 -0.29 8.16 -56.33*** 0.02

Silver 3126 0.02 12.42 -14.91 2.14 -0.73 8.52 -57.03*** -0.02

Gasoline 3295 -0.01 22.11 -20.77 2.44 -0.12 10.31 -58.99*** -0.03

Crude oil 3335 -0.01 16.26 -17.05 2.57 -0.01 8.50 -69.05*** -0.18***

Natural

gas 3318 -0.05 26.77 -18.44 3.16 0.55 8.21 -60.61*** -0.05***

Soybeans 3330 0.01 20.32 -23.41 1.68 -1.12 26.08 -59.51*** -0.03*

Soybean

oil 3317 0.00 7.50 -7.77 1.45 0.08 5.71 -57.06*** 0.01

Wheat 3322 0.01 12.40 -13.43 2.11 0.07 5.41 -57.19*** 0.01

Oats 3229 0.02 14.44 -26.68 2.45 -0.93 14.09 -55.57*** 0.02

Corn 3334 0.02 10.88 -39.86 1.99 -2.58 54.01 -58.47*** -0.01

Cotton 3212 0.01 10.53 -17.29 1.87 -0.27 7.84 -53.10*** 0.07***

Sugar 3322 0.00 17.12 -12.43 2.20 0.02 6.49 -58.30*** -0.01

Note: The reported statistics include the number of observations (Obs), the mean (Mean), the minimum (Min) and

maximum (Max), standard deviation (SD), Skewness (Skew), Kurtosis (Kurt) Augmented Dickey–Fuller (ADF) and

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Autocorrelation (AC(1)). The sample period covers October 2005 to December 2018. ***, **, and * indicate

significance at the 1%, 5%, and 10% levels, respectively.

Table 2 provides the summary statistics for daily returns of 18 commodity futures.

The mean of all returns is close to 0, and the unconditional standard deviation is more

than 1, which shows the high volatility in the commodity futures markets. According

to a unit root test such as the Augment Dickey-Fuller Test (ADF), the daily returns of

all futures are stationary.

5. Empirical Results

The return volatility of futures not only reflects the fear of investors but is also

particularly sensitive to crisis and uncertainty (Diebold and Yilmaz, 2014). Therefore,

we apply monthly realized volatility to conduct variance decompositions and measure

connectedness among commodity futures. We first discuss the static connectedness for

the full-sample data and then extend our discussions to include a dynamic analysis.

5.1 Full-sample network connectedness analysis

Under the framework of Diebold and Yilmaz (2014), we estimate the VAR model

for the full sample period and compute variance decompositions and corresponding

connectedness measures at horizon . The empirical results are reported in Table

3, which includes the connectedness index and the directional connectedness.

The main research finding is that the diagonal elements, which reflect the influence

they create themselves, are often the largest. The lower right element is the

connectedness index, and the value is 69.6%. In addition, there is strong clustering

within the same type of futures. For example, the pairwise directional connectedness

between gold and silver is high; the same is true between soybeans and soybean oil.

Moreover, the degree distribution of the ‘‘from’’ is noticeably less than that of the ‘‘to’’.

We conducted a detailed analysis of connectedness between 18 commodity futures and

made some interesting discoveries. We observe that the highest pairwise directional

connectedness is from the gold futures to the corn futures, at 21.9%. In contrast, the

=10H

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pairwise connectedness from the corn futures to the gold futures is 0.7%. The second

highest pairwise connectedness is 18.8%, which is from the wheat futures to the

soybean oil futures. Meanwhile, the connectedness from the soybean oil futures to the

wheat futures is 4.4%, so the directional connectedness is more pronounced from the

wheat futures to soybean oil futures in net terms.

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Table 3 Full-Sample Connectedness Table

Copper Aluminum Lead Zinc Nickel Tin Gold Silver Gasoline Crude oil Natural

gas Soybeans

Soybean

oil Wheat Oats Corn Cotton Sugar FROM

Copper 11.6***

(5.6)

4.1***

(4.1)

10.0***

(5.9)

8.7***

(7.7)

5.8***

(5.9)

6.6***

(6.0)

5.4***

(4.8)

6.9***

(6.4)

3.6***

(3.8)

4.3***

(4.5)

1.5**

(2.3)

10.0***

(3.8)

4.2***

(4.4)

8.3***

(3.8)

0.9***

(3.2)

1.5***

(2.7)

1.3**

(2.4)

5.2***

(3.9)

88.4***

(45.1)

Aluminum 8.3***

(5.9)

32.2***

(6.6)

10.8***

(6.0)

13.1***

(6.3)

6.6***

(4.0)

3.4***

(3.5)

1.3**

(2.5)

4.7***

(3.6)

1.6***

(3.0)

1.8***

(3.4)

0.8**

(2.0)

2.1**

(2.4)

2.8***

(3.2)

3.0**

(2.5)

0.8**

(2.5)

2.0**

(2.0)

1.0**

(2.3)

3.8***

(2.7)

67.8***

(15.2)

Lead 5.2***

(4.0)

4.5***

(3.1)

29.1***

(8.8)

11.9***

(4.9)

7.3***

(3.8)

2.9***

(3.1)

1.5***

(2.7)

2.5**

(2.4)

4.0**

(2.3)

1.4***

(2.6)

3.8**

(2.5)

5.7***

(3.1)

2.9***

(2.7)

9.4***

(3.3)

1.1**

(2.4)

1.3*

(1.9)

1.1**

(2.1)

4.5***

(2.6)

70.9***

(23.8)

Zinc 10.6***

(8.9)

8.1***

(4.2)

12.6***

(6.4)

23.5***

(15.5)

5.9***

(3.9)

5.6***

(4.9)

2.1***

(3.1)

5.0***

(3.9)

2.0***

(3.3)

4.9***

(4.2)

1.0*

(1.9)

5.8***

(3.4)

2.2***

(2.8)

4.0***

(3.0)

0.6**

(2.2)

2.0**

(2.1)

0.5**

(2.2)

3.4***

(2.8)

76.5***

(54.5)

Nickel 9.9***

(5.6)

3.4***

(4.7)

9.8***

(5.7)

7.0***

(5.9)

16.8***

(11.2)

6.4***

(5.2)

3.3***

(3.6)

6.1***

(5.3)

3.0***

(3.7)

3.1***

(3.3)

1.5**

(2.1)

11.2***

(3.6)

4.1***

(3.8)

6.1***

(3.6)

0.7**

(2.5)

1.2**

(2.1)

1.7***

(4.0)

4.4***

(3.5)

83.2***

(59.7)

Tin 8.5***

(4.1)

2.2***

(3.0)

7.8***

(4.1)

6.3***

(4.9)

4.1***

(3.8)

15.7***

(8.9)

3.5***

(4.2)

6.4***

(5.3)

5.4***

(4.3)

3.3***

(3.8)

2.2**

(2.1)

8.9***

(3.7)

5.2***

(4.2)

11.1***

(4.0)

1.0***

(3.1)

1.2**

(2.3)

2.0***

(2.7)

5.3***

(3.3)

84.3***

(51.5)

Gold 7.9***

(3.1)

2.3***

(3.3)

3.0*

(2.0)

3.5***

(2.9)

2.2**

(2.3)

4.6***

(4.1)

30.0***

(4.7)

12.6***

(3.9)

5.6***

(3.3)

4.0***

(4.1)

2.7

(1.6)

4.5**

(2.5)

2.4***

(2.9)

9.8***

(3.0)

1.1**

(2.4)

0.7**

(2.4)

1.9*

(1.8)

1.2

(1.6)

70.0***

(12.9)

Silver 8.8***

(4.6)

3.5***

(5.1)

3.6***

(3.2)

4.5***

(5.6)

5.8***

(4.3)

6.8***

(5.4)

7.8***

(3.9)

24.3***

(5.7)

4.6***

(3.9)

2.3***

(3.5)

1.4

(1.6)

5.5***

(2.9)

2.6***

(3.1)

8.0***

(3.6)

1.1***

(2.9)

1.3***

(2.8)

3.8***

(2.9)

4.2***

(3.3)

75.7***

(19.6)

Gasoline 2.7*

(1.7)

2.4*

(1.9)

1.0*

(1.9)

1.1*

(1.9)

1.2*

(1.8)

5.5***

(3.3)

1.6*

(1.8)

1.1**

(2.1)

42.1***

(10.1)

6.6***

(3.6)

4.3*

(1.9)

8.6***

(3.8)

6.9***

(4.0)

6.8***

(3.3)

2.7***

(2.9)

1.8**

(2.4)

2.0**

(2.4)

1.5**

(2.1)

57.9***

(16.2)

Crude oil 4.0***

(4.9)

3.4**

(2.6)

1.9**

(2.1)

11.3***

(5.7)

2.4***

(3.4)

6.8***

(4.1)

5.8***

(4.4)

8.1***

(3.9)

6.4***

(4.4)

28.1***

(6.9)

2.4***

(2.6)

6.6***

(3.5)

1.9***

(2.9)

2.5**

(2.3)

1.5**

(2.3)

2.3**

(2.0)

1.1**

(2.1)

3.6***

(4.4)

71.9***

(19.7)

Natural gas 4.9***

(4.6)

6.5***

(4.0)

8.1***

(3.6)

7.1***

(5.1)

3.0***

(4.1)

3.6***

(4.1)

1.3**

(2.2)

3.7***

(2.7)

1.7**

(2.3)

2.9***

(3.4)

46.9***

(7.6)

2.0**

(2.3)

1.1**

(2.1)

1.7**

(2.4)

0.6

(1.4)

2.7**

(2.3)

0.4*

(1.6)

2.0***

(3.7)

53.1***

(10.2)

13

Table 3 (Continued) Full-Sample Connectedness Table

Copper Aluminum Lead Zinc Nickel Tin Gold Silver Gasoline Crude oil Natural

gas Soybeans

Soybean

oil Wheat Oats Corn Cotton Sugar FROM

Soybeans 3.4**

(2.4)

2.4***

(2.9)

7.7***

(4.5)

5.1***

(3.5)

2.5***

(2.8)

2.2***

(2.8)

4.0**

(2.5)

1.4***

(2.7)

5.7***

(3.7)

1.6***

(3.0)

3.6**

(2.3)

30.9***

(6.8)

6.9***

(3.8)

11.5***

(4.4)

1.3**

(2.0)

1.2**

(2.5)

1.7***

(2.9)

7.0***

(4.8)

69.1***

(17.5)

Soybean oil 5.5**

(2.5)

1.4***

(2.6)

6.6**

(2.4)

3.7**

(2.5)

2.9***

(3.0)

3.3***

(3.3)

3.5***

(3.1)

1.3**

(2.3)

6.7***

(3.4)

1.3**

(2.3)

4.5*

(1.9)

15.4***

(4.8)

17.5***

(6.1)

18.8***

(4.6)

0.6

(1.6)

1.8*

(1.8)

1.6**

(2.5)

3.7***

(2.8)

82.5***

(31.8)

Wheat 2.7***

(3.1)

1.7*

(1.9)

9.8***

(4.4)

5.9***

(3.9)

3.0***

(3.4)

1.6**

(2.5)

1.8***

(2.6)

1.7**

(2.3)

4.0***

(3.0)

1.9*

(1.8)

2.2**

(2.3)

6.6***

(3.8)

4.4**

(2.4)

39.9***

(7.5)

2.5**

(2.0)

1.8**

(2.0)

3.2***

(2.9)

5.4***

(4.0)

60.1***

(12.9)

Oats 1.4**

(2.5)

1.8***

(2.7)

1.5***

(2.8)

2.1**

(2.2)

0.9**

(2.4)

1.8***

(2.8)

10.6**

(2.4)

3.0**

(2.5)

3.2**

(2.4)

2.9***

(3.1)

4.2***

(3.1)

2.3***

(2.9)

1.2**

(2.5)

2.3***

(2.7)

52.5***

(5.1)

4.3**

(2.5)

2.4**

(2.4)

1.6**

(2.2)

47.5***

(5.9)

Corn 3.8***

(3.8)

2.4***

(3.2)

1.6***

(2.8)

2.8***

(3.1)

2.9***

(3.5)

2.3***

(2.8)

21.9**

(2.4)

5.5**

(2.5)

2.9***

(3.4)

0.7**

(2.0)

1.2*

(1.9)

3.0***

(3.1)

2.3***

(3.0)

1.1**

(2.5)

0.6*

(1.8)

41.1***

(3.8)

1.8***

(2.8)

2.0***

(2.6)

58.9***

(6.4)

Cotton 3.0***

(3.5)

3.0***

(3.7)

2.9***

(3.5)

2.3***

(4.1)

4.4***

(3.6)

4.5***

(4.8)

3.0***

(3.6)

6.3***

(2.7)

5.7***

(4.3)

3.9***

(4.0)

0.7**

(2.3)

7.5***

(4.1)

2.0***

(2.9)

13.3***

(5.0)

2.3**

(2.3)

1.1**

(2.0)

26.7***

(6.9)

7.5***

(4.9)

73.3***

(20.9)

Sugar 4.0***

(4.5)

5.8***

(2.7)

6.5***

(3.6)

10.3***

(3.9)

3.4***

(3.2)

1.4***

(3.0)

0.6**

(2.0)

0.7**

(2.4)

3.3***

(3.0)

1.9***

(3.4)

1.8***

(2.7)

9.2***

(4.0)

2.8**

(2.3)

4.2***

(2.7)

1.0

(1.6)

3.0**

(2.2)

2.7***

(3.1)

37.5***

(6.5)

62.5***

(12.1)

TO 94.5***

(6.1)

59.0***

(5.6)

105.6***

(5.7)

106.7***

(6.6)

64.2***

(6.6)

69.0***

(7.3)

79.1***

(4.3)

77.1***

(6.3)

69.7***

(5.1)

48.6***

(5.6)

39.6***

(2.6)

114.8***

(4.2)

55.7***

(4.7)

121.8***

(4.4)

20.3***

(3.3)

31.2***

(2.8)

30.2***

(4.6)

66.3***

(4.6)

69.6***

(57.8)

NET 6.2

(0.4)

-8.8

(-0.4)

34.6*

(1.7)

30.2*

(1.7)

-19.0

(-1.5)

-15.3

(-1.3)

9.1

(0.3)

1.4

(0.2)

11.8

(0.6)

-23.2

(-1.8)

-13.5

(-0.7)

45.7

(1.3)

-26.8

(-1.6)

61.7*

(1.8)

-27.2

(-2.0)

-27.7

(-1.3)

-43.1

(-4.6)

3.7

(0.3)

Note: The sample is Oct 3, 2005, through Dec 31, 2018, and the predictive horizon is 10 months. The ij-th entry of the upper-left 18 × 18 firm submatrix gives the ij-th pairwise directional

connectedness; i.e., the percent of 10-month-ahead forecast error variance of future i due to shocks from future j. The rightmost (FROM) column gives total directional connectedness (from); i.e.,

14

row sums (from all others to i). The bottom (TO) row gives total directional connectedness (to); i.e., column sums (to all others from j). The bottommost (NET) row gives the difference in total

directional connectedness (to–from). The bottom-right element (in boldface) is total connectedness (mean ‘‘from’’ connectedness, or equivalently, mean ‘‘to’’ connectedness).

15

We are particularly interested in the individual degrees for the commodity futures

that convey information on which sectors are sending the most uncertainty to others.

The “from” column, calculated as 100% minus one’s own share of the total forecast

error variance, reflects the directional connectedness received from the other 17

commodity futures. The copper futures, that has a from-degree of 88.4%, may be the

commodity futures that received the highest percentage of shocks from others. The next

two futures are the tin and nickel futures, which have from-degrees of 84.3% and 83.2%

respectively. The oats futures received the lowest impact (47.5%) of shocks from other

commodity futures, followed by natural gas futures (53.1%) and gasoline futures

(57.9%).

Similarly, the “to” column measures the total directional connectedness to other

commodity futures, and the effect on others’ forecast error variance is not limited to a

cumulative sum of 100%. The futures that contribute the top three impacts to others is

the wheat futures (121.8%), the soybean futures (114.8%) and the zinc futures (106.7%),

while the oats futures, the cotton futures and the corn futures contribute at similar rates

(20.3%, 30.2% and 31.2%, respectively). In summary, metal futures easily spread

shocks within their own ranks, and they are also easily affected by others. The energy

futures are robust, and their shocks to others and the influence from others are relatively

small. The agricultural futures are vulnerable and often receive shocks from others.

16

Fig. 1. Full-sample Total Connectedness

Note: The thickness of the line of an arrow reflects the size of the connectedness. The sample is from Oct 3, 2005,

to Dec 31, 2018, and the predictive horizon is 10 months.

Figure 1 presents the full sample of total connectedness. We observe that each

variety of metal futures is vulnerable to systemic risk and can receive shocks in a

financial crisis. Compared to metal futures, energy futures are relatively less affected.

They are transmitters, rather than receivers, of their own shocks. Agricultural futures

are more susceptible to systemic risk, especially soybeans, soybean oil, corn and other

farm commodities with large market shares.

17

Fig. 2. Full-sample Total Directional Connectedness: Empirical Survivor Functions.

Note: The empirical survivor functions for total directional connectedness ‘‘to’’ others and ‘‘from’’ others. The

predictive horizon for the underlying variance decomposition is 10 months.

Next, the net total connectedness is obtained by calculating the difference between

the contribution to others and from others. For some of the 18 commodity futures, the

total net directional connectedness is positive, such as the wheat futures (61.7%) and

the soybean futures (45.7%), implying that these futures are net transmitters of shocks

to other futures. Among the futures where the difference of to-degree and from-degree

is negative, the smallest three differences are from the cotton futures (-43.1%), the corn

futures (-27.7%) and the oats futures (-27.2%). In Figure 1, we show the differences

between full-sample “to” and “from” degree distributions based on the respective

empirical survivor functions.

Finally, we discuss the connectedness index in the lower right corner. The value is

69.6%, indicating that almost two-thirds of the volatility uncertainty for the

commodities futures is due to the connectedness of shocks across futures, while the

remaining 30.4% can be explained by idiosyncratic fluctuations. Some futures are more

vulnerable to outside shocks, and they are also likely to transmit these shocks to others,

causing a high degree of connectedness.

18

5.2. Rolling-sample network connectedness analysis

The above analysis is for the full sample and displays the unconditional

connectedness of commodity futures over a fourteen-year period. In contrast to bonds

or stocks, the price of commodity futures is more likely to be affected by traditional

supply and demand considerations. The supply of different futures may be affected by

very different factors. For example, the trade policies of an exporting country’s

government can play a significant role in the metals and oil supply, while the supply for

agricultural futures is partly determined by weather conditions. However, commodity

demand may be more closely linked to global events, such as the financial crisis in 2008

or Brexit from 2013 to 2017. Therefore, to better understand the evolution of the total

connectedness index and directional connectedness, we will take our lead from Diebold

and Yilmaz (2014) and focus on the dynamic connectedness of the commodity futures

in this subsection.

We show the total dynamic connectedness index in Figure 3 using 36-month

rolling windows. The total connectedness index fluctuates in a range from 73.3% to

94.4%, where the minimum appears in the window ending in May 2015 and the

maximum in the window ending in July 2013.

Fig. 3. Rolling window plots of total connectedness

19

Note. The rolling estimation window width is 36 months, and the predictive horizon for the underlying variance

decomposition is 10 months.

From a birds-eye perspective, there are some revealing patterns in Figure 3. In the

beginning, the total connectedness reaches a peak (93.2%), and after a brief respite, it

goes up to 90.8% in September 2009. This trend is a reaction to the global financial

crisis caused by the U.S. recession in the first half of 2008. As a result, some developed

economies, such as the US, launched a new quantitative easing monetary policy. The

total connectedness changes gradually to 89.5% by May 2011 and broadly drops to 78.6%

by the end of August 2011. The total connectedness starts a short-lived upward journey

and reaches 86.7% in August 2012. In addition, it jumps from 79.0% to 94.4% in July

2013, rising by almost 20%. This spike may be associated with the debt crisis in Europe.

However, due to the positive action taken by the Eurozone and Great Britain exiting

from the European Union, the total connectedness experienced some severe bumps

from August 2013 to December 2015 and went as low as 73.3% in May 2015 during

this tumultuous period. Between January 2016 and December 2018, the total

connectedness fluctuated in a narrow band of 75.4%-81.1%, except for a peak of 87.9%

in April 2018.

20

Fig. 4. Rolling Window Total Connectedness During the 2008 Financial Crisis

Note: The thickness of the line of an arrow reflects the size of the connectedness. The first plot is for September

2008, the bottom left October 2008, and the bottom right November 2008.

Next, we focus on the evolution of total connectedness during three notable

periods. Lehman Brothers declared bankruptcy on September 15, 2008, which further

worsened the subprime mortgage crisis. Figure 4 displays the rolling window total

connectedness during the 2008 financial crisis. In that period, we intuitively know that

systemic risks were severe and commodity futures markets suffered dramatically. Over

the next two months, with the systemic risk decreasing, the situation gradually

improved but remained serious.

21

Fig. 5. Rolling Window Total Connectedness During the European Debt Crisis

Note: The thickness of the line of an arrow reflects the size of the connectedness. The first plot is for December

2009, the bottom left January 2010, and the bottom right February 2010.

The Greek debt crisis broke out in December 2009, which was the beginning of

the European debt crisis. We observe that metal futures and energy futures have thick

lines in Figure 5, showing that, during the debt crisis, metal futures and energy futures

are the main transmitters of severe systemic risk. For the next two months, the systemic

risk remained serious as the European debt crisis continued to fester.

Fig. 6. Rolling Window Total Connectedness During the Brexit

22

Note: The thickness of the line of an arrow reflects the size of the connectedness. The first plot is for June 2016, the

bottom left July 2016, and the bottom right August 2016.

A referendum on Brexit began on June 23, 2016, leading to Britain’s withdrawal

from the European Union and serious systemic risk in futures markets. Figure 6 shows

that systemic risk in the commodity futures markets was more severe in the next two

months than in June due to the result of the Brexit vote. The energy futures markets

were the most affected, followed by the metal futures markets, especially gold and

silver futures.

In the previous section, we analyzed the dynamics of total connectedness and

explained the factors affecting it. Following the analysis of the total connectedness, we

now focus, in this subsection, on the directional connectedness from the years 2005 to

2018. The reason why directional connectedness is important is that it can help us better

understand the role each commodity future plays in spreading shocks to others and

being influenced from others. Figure 7 presents a time series of three types of

directional connectedness (“connectedness to others”, “connectedness from others” and

“net connectedness”) based on a 36 month rolling window. The upper panel is the plot

of the to-degree, the middle panel displays the from-degree and the lower panel shows

the net total directional connectedness.

23

Fig. 7. Rolling window plots of total directional connectedness

24

Note. The rolling estimation window width is 36 months, and the predictive horizon for the underlying variance

decomposition is 10 months.

First, we briefly discuss the characteristics of the to-degree and from-degree panel.

Consistent with Diebold and Yılmaz (2014), the “from” connectedness plots are much

smoother than the “to” connectedness plots for the majority of the 18 commodity

futures. That is, when the commodities futures system faces volatility shocks, the effect,

in general, from one future to others is larger than that from other futures. This result

provides the evidence for spillover effects among commodity futures. The size of

shocks and the type of futures may contribute to the difference between the to-degree

and the from-degree. Though the shock of a commodity futures can be transmitted to

others, the shocks that other futures receive are likely to be very small or very large.

Moreover, the same event will have different impacts on different types of futures. For

example, the political upheavals in the Middle East, especially the civil war in Libya,

led to more fluctuations in energy futures rather than agriculture futures.

Next, we conduct a detailed analysis of the net-degree plot. Overall, since the

change of from-degree is relatively flat, the trend for net total connectedness is similar

to the pattern in the plots for connectedness “to” others.

Copper futures play an important role among the metal futures. We observe the net

connectedness of copper futures was negative during the global financial crisis in the

years 2008 through 2009 and has fluctuated around zero since the end of the year 2010

as a result of the dramatic 50% and more reduction in the copper price. For the lead and

zinc futures, their net connectedness includes both positive and negative episodes. The

only subperiod during which the net connectedness is negative is from the mid 2013 to

early 2015. The two precious metal futures, gold and silver, also display a similar trend,

and their total connectedness is high for the majority of the rolling sample windows.

For energy futures, we focus on the crude oil futures. During the earlier part of the

period, oil futures showed a negative net total connectedness. After 2014, the net

connectedness experienced two cycles and reached a peak of more than 100%. However,

the net connectedness of gasoline and natural gas futures shows completely different

25

plots.

Unlike crude oil futures, soybean futures had a high net connectedness during most

of the period, which can be attributed to its underlying asset, soybeans, which is not

only an important consumption item for households all over the world but also an input

for biofuel production.

6. Conclusion

Given the role of the commodities futures market in the global economy and the

fact that the properties of commodity futures are different from traditional assets,

commodity futures are an essential asset class for investors. The financialization of the

commodity markets and the potential for financial crises have caused researchers to

empirically scrutinize the connectedness between the volatility of different commodity

futures.

Using the framework of Diebold and Yılmaz (2014), we characterize the

connectedness of global commodity futures statically and dynamically. In respect of the

static net total connectedness, we find, in general, that metal futures are net shock

transmitters, while energy futures and agricultural futures are relatively vulnerable to

shocks from others. Furthermore, the connectedness of shocks across futures causes

almost two-thirds of the uncertain volatility. For the dynamic connectedness, there is

always a high degree of connectedness during times of turmoil, such as the 2008

financial crisis, the 2011 European debt crisis and the 2013 to 2017 Brexit tumult.

Our study is essential for portfolio and risk management. From the view of

investors whose portfolio concentration risk is directly related to connectedness, our

results construct a risk network and the potential to protect these positions from the

distress of other assets. Because connectedness tends to increase during commodity-

market crises, which may then spill over into the broader macroeconomy, the results in

our paper contribute to showing the importance of monitoring risk across commodity

futures and the need to manage overall risk more effectively.

26

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