COVID‐19 and tail risk contagion across commodity futures markets

Abstract

This paper examines the impact of COVID‐19 on tail risk contagion across commodity futures markets using a copula‐based network method. We document a significant increase in the lower and upper tail contagiousness of commodities following the COVID‐19 outbreak. Contagion shows an obvious clustering characteristic, that is, there is higher tail risk connectedness between commodities in the same category. Agricultural commodities are significantly less contagious than metals and energy commodities; soft commodities in particular can offer investors significant diversification benefits. There are several hub commodities in the contagion network, chief among them copper, which are good transmitters of shocks and should be treated with caution by investors and regulators. Although tail risk and contagiousness of individual commodities increase together during the pandemic, we find a negative cross‐sectional relationship between tail risk and contagiousness, that is, commodities with high tail risk are not necessarily highly contagious and may even be less so.

1. INTRODUCTION

As a once‐in‐a‐century public health crisis, COVID‐19 has brought unprecedented challenges to human society. The outbreak emerged in late December 2019 and quickly spread globally in early 2020, causing millions of infections and deaths. To contain the spread of COVID‐19, governments around the world have implemented a series of measures, including social distancing, travel bans, quarantines, and lockdowns. Affected by the outbreak and the containment measures against it, the global economy has fallen into a severe recession, with supply chain disruptions, soaring unemployment, and rising inflation occurring worldwide. Baker et al. (2020) argue that COVID‐19 has caused more economic damage than any other infectious disease outbreak in the past 100 years.

With the global economic downturn, commodity markets also experience severe turmoil. The COVID‐19 pandemic leads to a broad decline in commodity prices; however, the extent of the impact varies across commodity categories. As energy commodities are closely linked to economic activity, the pandemic‐induced global economic slowdown has severely slashed demand for these commodities, hitting their prices the hardest (Gharib et al., 2021; Khan et al., 2022). Crude oil, in particular, has suffered the most severe price drop, with its monthly price falling from nearly $62 per barrel in January 2020 all the way to $21 per barrel in April, an 18‐year low. Compared with energy commodities, the impact of COVID‐19 on the prices of metals is slightly less. Agricultural commodity prices are least affected by the outbreak, with only a slight negative change, a far cry from the crash of oil and metals prices. This is mainly because the demand for the most basic agricultural commodities is relatively sustained and most agricultural commodities are available in stock, which ensures the stability of supply and prices (Cariappa et al., 2022; Hobbs, 2020).

In view of the extreme price movements in most commodity markets during the COVID‐19 pandemic, a natural question is what linkages exist between the prices of different commodities and how those linkages have changed as the pandemic develops. Answering this question is crucial. On the one hand, as commodities are increasingly becoming an essential component of investment portfolios, investors urgently need to identify price linkages among commodities to optimize asset allocation and diversify portfolio risk (Tiwari et al., 2020; Xiao et al., 2020; Zhang & Broadstock, 2020). On the other hand, close price linkages make it easier for shocks to spread from one market to another, especially in times of crisis, so the investigation of them is important for understanding risk contagion mechanisms and preventing systemic financial risks (Gong et al., 2022; Liu et al., 2022; Zhu et al., 2021).

The investigation of linkages and spillovers between different commodity markets stems from commodity financialization (Ding et al., 2021; Gong et al., 2022).1 Due to the low correlation between the prices of commodities and traditional financial assets, many investors incorporate commodity futures, especially metals and agricultural commodities, into their portfolios as a tool for hedging and diversification. This directly accelerates the financialization of commodities, not only increasing the correlation between commodities and traditional financial assets, but also improving the connectedness within commodities, which have triggered heated discussions in academic circles (Silvennoinen & Thorp, 2013; Tang & Xiong, 2012). Since the global financial crisis in 2008, research on cross‐market price linkages and risk spillovers has grown rapidly due to the need for risk regulation (Billio et al., 2012; Kotkatvuori‐Örnberg et al., 2013).

To shed light on the aforementioned question and extend the research on cross‐market associations, this paper examines tail risk contagion across commodity markets during the COVID‐19 crisis. Although a number of studies have examined the impact of COVID‐19 on price linkages between commodity markets (e.g., Chen et al., 2022; Gong et al., 2022; Hung, 2021; Just & Echaust, 2022; Sun et al., 2021; Umar et al., 2022; Zhang & Ding, & Shi, 2022), most of them, however, have only focused on linkages between a few typical commodities (e.g., the linkages between crude oil and agricultural commodities) or various commodity indices, looking only at the connectedness of returns and volatility among commodities. To the best of our knowledge, little attention has been paid to the impact of COVID‐19 on the tail risk connectedness across commodities, and our study fills this gap. In this paper, the tail risk connectedness between two commodities is defined as the conditional probability that one of the commodities realizes a lower (upper) tail event given that the other commodity also realizes a lower (upper) tail event. We argue that the tail risk connectedness can provide more intuitive and useful information for portfolio risk diversification and systemic risk regulation.

Our empirical analysis uses a copula‐based network method and covers 29 major commodity futures traded on six exchanges (i.e., New York Mercantile Exchange, Chicago Board of Trade, Chicago Mercantile Exchange, Commodity Exchange, Intercontinental Exchange, and London Metal Exchange). We use the tail dependence coefficient estimated by the Symmetrized Joe–Clayton (SJC) copula of Patton (2006) as a measure of tail risk connectedness between commodities. To examine the impact of COVID‐19 on tail risk contagion across commodity markets, we first form a tail dependence network for the preoutbreak (postoutbreak) period, in which the nodes are the 29 commodities and the link between two nodes are their tail dependence coefficient. Using Dijkstra path search algorithm, we then determine the shortest contagion path from a node $i$ to another node $j$ in the tail dependence network, along which the tail risk contagion probability from $i$ to $j$ is the highest, and then define the shortest contagion distance from $i$ to $j$. Based on contagion distances, we further calculate a contagion centrality measure for individual commodities. The greater the contagion centrality of a commodity, the higher the average connectedness between it and the rest of the network, and hence the stronger the overall tail risk contagiousness of the commodity. We identify the impact of COVID‐19 on tail risk contagion by examining changes in contagion centrality measures following the outbreak.

The main findings of this paper are as follows. First, COVID‐19 has significantly increased the tail risk contagiousness of commodities and the impact is more prominent for the lower tail. Over time, the lower tail contagiousness declines to some extent but remains above the prepandemic level, whereas the upper tail contagiousness continues to rise. This result demonstrates the persistence of the impact of COVID‐19 on tail risk contagion across commodities, which should be noted by market participants. Second, contagion shows an obvious clustering feature, that is, the connectedness between the same kind of commodities is much higher than that between different kinds of commodities. This highlights the importance of holding different categories of commodity futures for diversifying portfolio risk. Third, the contagiousness of agricultural commodities is significantly lower than that of metals and energy commodities. Soft commodities, in particular, are not only loosely connected with other categories of commodities but also loosely connected with each other, exhibiting safe‐haven properties. Fourth, there are several hubs in the contagion network, such as copper and platinum before the outbreak and copper, heating oil, and soybeans after the outbreak. Hub commodities are good spreaders of shocks but are also more vulnerable to external shocks themselves and should therefore be treated with caution. Fifth, we document a negative cross‐sectional relationship between tail risk and contagiousness, that is, commodities with low tail risk tend to be highly contagious. A plausible explanation for this result is that the allocation of funds to low‐risk commodities by risk‐averse investors enhances the price comovement of these low‐risk commodities.

The contribution of this paper is twofold. First, our study contributes to the literature on the impact of COVID‐19 on commodity futures markets. Given the massive disruption caused by COVID‐19 to the global economy, a growing body of literature has investigated the impact of COVID‐19 on financial markets; however, most of it has focused on equity markets, whereas investigations into commodity futures markets remain relatively limited (Emm et al., 2022; Magalhães et al., 2022). In this regard, existing studies such as Zhang and Wang (2022), Salisu et al. (2020), Rubbaniy et al. (2021), Emm et al. (2022), Magalhães et al. (2022), and Sifat et al. (2021) have examined volatility, return predictability, safe‐haven properties, volumes and open interest, hedging efficiency, and speculative activity in commodity futures markets during the COVID‐19 crisis. We add to the literature by clarifying changes in tail risk contagion among commodity futures following the COVID‐19 outbreak, which has not been addressed by existing studies.

Second, our study contributes to the literature on cross‐commodity connectedness. Since the 2008 global financial crisis, connectedness between assets has been a hot topic in finance and economics. Prior studies have estimated the return (Xiao et al., 2020) and volatility (Diebold et al., 2017; Yang et al., 2021) connectedness between commodities. Our paper extends this line of research by comprehensively investigating the dependence of tail events in commodity markets for the first time. In a most recent study, Farid et al. (2022) also examines the extreme price linkages between commodities. However, our paper is different from their study. First, the links between nodes in their network is simply the connectedness of the $p$‐quantile of commodity return distributions ($p=5\%$ for lower tail connectedness and $p=95\%$ for upper tail connectedness), estimated using a method that combines the quantile VAR model and the connectedness measures of Diebold and Yilmaz (2012, 2014), whereas our network is constructed based on the lower (upper) tail dependence coefficient estimated by the SJC copula, which measures the conditional probability that a commodity's return does not exceed (fall below) its $p$‐quantile given that the return of another commodity is also at or below (above) its $p$‐quantile, as $p$ goes to 0 (1). Thus, our study examines the connectedness of tail events between commodity markets rather than their connectedness over specific return quantiles.2 Second, Farid et al. (2022) aims to show the structural changes of the entire quantile connectedness network of commodities after the COVID‐19 outbreak, whereas our paper focuses on the impact of COVID‐19 on the overall contagiousness of individual commodities. To this end, we further calculate the contagion distance and contagion centrality measures for commodities based on our tail dependence network. Third, our paper also investigates the relation between tail risk and contagion and the relation between COVID‐19 severity and contagion, which are not covered by Farid et al. (2022).

The rest of the paper is organized as follows. Section 2 introduces the methodology. Section 3 describes the data and variables. Section 4 presents our empirical results. Section 5 concludes.

2. METHODOLOGY

2.1. Tail dependence network

Let $R^i$ and $R^j$ denote the return variables of commodities $i$ and $j$. We characterize the likelihood of lower tail risk propagation from commodity $i$ to commodity $j$ by

$${\tau }_{i,j}^L=P(R^j\le Q_p\left[R_j\right]|R^i\le Q_p[R_i]),\text{for small}p\in (0,1),$$ (1)

And the likelihood of upper tail risk propagation from commodity $i$ to commodity $j$ by

$${\tau }_{i,j}^U=P(R^j>Q_p\left[R_j\right]|R^i>Q_p[R_i]),\text{for large}p\in (0,1),$$ (2)

where $P[\mathit{A|B}]$ denotes the conditional probability of an event $A$ given the event $B$, and $Q_p\left[Y\right]$ denotes the $p$‐quantile of random variable $Y$. Thus, ${\tau }_{i,j}^L$ (${\tau }_{i,j}^U$) refers to the conditional probability that $R^j$ realizes a lower (upper) tail event given that $R^i$ also does.

In our study, we use a copula‐based method to estimate the probabilities in Equations (1) and (2). Let $F_{R^i}\left(r^i\right)$ and $F_{R^j}\left(r^j\right)$ denote the marginal cumulative distribution functions (CDF) of $R^i$ and $R^j$, and $H_{R^i,R^j}(r^i,r^j)$ denote the joint cumulative distribution function of $R^i$ and $R^j$. If $F_{R^i}\left(r^i\right)$ and $F_{R^j}\left(r^j\right)$ are continuous, then there is a uniquely determined copula function $C(u^i,u^j)$, such that

$$H_{R^i,R^j}(r^i,r^j)=C(F_{R^i}(r^i),F_{R^j}(r^j\left)\right).$$ (3)

Accordingly, for an extremely small probability level $p$, ${\tau }_{i,j}^L$ can be estimated as

$${\hat{\tau }}_{i,j}^L=\underset{p\to 0}{\lim }P(R^j\le Q_p\left[R^j\right]|R^i\le Q_p[R^i])=\underset{p\to 0}{\lim }\frac{C(p,p)}{p};$$ (4)

For an extremely large probability level $p$, ${\tau }_{i,j}^U$ can be estimated as

$${\hat{\tau }}_{i,j}^U=\underset{p\to 1}{\lim }P(R^j>Q_p\left[R^j\right]|R^i>Q_p[R^i])=\underset{p\to 1}{\lim }\frac{1-2p+C(p,p)}{1-p}.$$ (5)

${\hat{\tau }}_{i,j}^L$ and ${\hat{\tau }}_{i,j}^U$ are actually the lower and upper tail dependence coefficients between $R^i$ and $R^j$, which are functions of copula $C(u^i,u^j)$.3

We use the SJC copula developed by Patton (2006) to model the dependence structure of returns for each pair of commodities considered in our study. Compared to other common copulas, the SJC copula has the advantage of capturing both lower‐tail and upper‐tail dependencies between return variables and allowing them to be asymmetric. Copulas like t, Clayton, and Gumbel can also capture tail dependence. However, the t copula only allows symmetric lower tail and upper tail dependencies, while the Clayton (Gumble) copula is only able to model the lower (upper) tail of the distribution. Formally, the SJC copula is defined as

$$C_{\mathit{SJC}}(u^i,u^j)=0.5·(C_{\mathit{JC}}(u^i,u^j)+C_{\mathit{JC}}(1-u^i,{1-u}^j)+u^i+u^j-1),$$ (6)

where $C_{\mathit{JC}}(u^i,u^j)$ is the Joe‐Clayton copula, which is defined as

$$C_{\mathit{JC}}(u^i,u^j)=1-{\left(1-{\left\{{[1-{(1-u^i)}^{\kappa }]}^{-\gamma }+{[1-{(1-u^j)}^{\kappa }]}^{-\gamma }-1\right\}}^{-\frac{1}{\gamma }}\right)}^{\frac{1}{\kappa }},$$ (7)

where $\kappa =\frac{1}{{\log }_2\left(2-{\hat{\tau }}_{i,j}^U\right)}$, $\gamma =-\frac{1}{{\log }_2\left(2-{\hat{\tau }}_{i,j}^L\right)}$, and ${\hat{\tau }}_{i,j}^L\in (0,1)$ and ${\hat{\tau }}_{i,j}^U\in (0,1)$ are the tail dependence coefficients defined by Equations (4) and (5).

Equation (6) gives the expression for the static SJC copula, where the parameters ${\hat{\tau }}_{i,j}^U$ and ${\hat{\tau }}_{i,j}^L$ are assumed to be constant over time. We use the static SJC copula to estimate the average tail dependence coefficient over a period of time for each pair of commodities and form a tail dependence network corresponding to that period. The nodes in the network are commodities, and the link between each two nodes is their tail dependence coefficient, which describes the tail risk transmission probability between them. The network is fully connected, weighted, and undirected because each node in the network is linked to every other node and the tail dependence coefficient is a symmetric measure with a value between 0 and 1. In our study, we examine the structural changes in tail risk contagion across commodities before and after the COVID‐19 outbreak by taking a network snapshot in each of those two periods.

We also estimate the time‐varying tail dependence coefficients between commodities by fitting a dynamic SJC copula for each pair of commodity return series. On the basis of the static SJC copula, the dynamic SJC copula sets the following evolution processes for the parameters ${\hat{\tau }}_{i,j}^U$ and ${\hat{\tau }}_{i,j}^L$:

$${\hat{\tau }}_{i,j,t}^U=\mathrm{\Lambda }\left({\omega }_U+{\beta }_U{\hat{\tau }}_{i,j,t-1}^U+{\alpha }_U·\frac{1}{10}\sum _{k=1}^{10}\left|u_{t-k}^i-u_{t-k}^j\right|\right),$$ (8)

$${\hat{\tau }}_{i,j,t}^L=\mathrm{\Lambda }\left({\omega }_L+{\beta }_L{\hat{\tau }}_{i,j,t-1}^L+{\alpha }_L·\frac{1}{10}\sum _{k=1}^{10}\left|u_{t-k}^i-u_{t-k}^j\right|\right),$$ (9)

where $\mathrm{\Lambda }(x)={(1+e^{-x})}^{-1}$ is the logistic transformation used to keep ${\hat{\tau }}_{i,j,t}^U$ and ${\hat{\tau }}_{i,j,t}^L$ in the range $(0,1)$. Using the dynamic SJC copula, we construct a tail dependence network at each time point during the sample period to capture the variation in contagion centrality (defined shortly below) of individual commodities over time.

Our study estimates the SJC copula model using a two‐stage maximum likelihood method. First, we fit a GJR‐GARCH (1, 1) model for the marginal distribution of each commodity.4 The specification is as follows:

$$R_{i,t}={\mu }_i+{\sigma }_{i,t}{Z}_{i,t},$$ (10)

$${\sigma }_{i,t}^2={\omega }_i+\left({\alpha }_i+{\gamma }_i{D}_{i,t-1}^{-}\right)·{\left({\sigma }_{i,t-1}{Z}_{i,t-1}\right)}^2+{\beta }_i{\sigma }_{i,t-1}^2,$$ (11)

$$D_{i,t-1}^{-}=\left\{\begin{array}{l}1, {\sigma }_{i,t-1}{Z}_{i,t-1}<0,\\ 0, \mathrm{otherwise},\end{array}\right.$$ (12)

where ${\mu }_i=E(R_{i,t}|{{\rm I}}_{t-1})$, ${\sigma }_{i,t}^2=\mathit{Var}(R_{i,t}|{{\rm I}}_{t-1})$, and ${{\rm I}}_{t-1}$ is the information set available at time $t-1$. In the empirical analysis, we assume that the innovation term $Z_{i,t}$ follows the skewed $t$ distribution proposed by Hansen (1994) to account for the skewness of return series.5 The maximum likelihood method is used to estimate the marginal distributions of commodities. For each margin, we obtain a series of conditional CDFs $F_{i,t}(r):=P[R_{i,t}\le \mathit{r|}{{\rm I}}_{t-1}]$. Based on these CDFs, we compute the probability integral transforms of the commodity return observations ${\left\{r_{i,t}\right\}}_{t=\mathrm{1,2},\text{…},T}$ as ${\hat{u}}_{i,t}=F_{i,t}\left(r_{i,t}\right).$ We then use the maximum likelihood method again to estimate the SJC copula function with the sample pairs ${\left\{\right({\hat{u}}_{i,t},{\hat{u}}_{j,t}\left)\right\}}_{t=\mathrm{1,2},\text{…},T}$ as the data to fit.

2.2. Contagion distance and contagion centrality

Once a tail dependence network is established, we can find the shortest path of tail risk contagion between any two nodes in it. A path in a network is a route that travels from one node to another along the links in the network. Since a tail dependence network is fully connected, there are multiple paths connecting any given two nodes $i$ and $j$ in the network, and the shortest path of tail risk contagion from node $i$ to node $j$ refers to the path ${\gamma }_{i,j}^{*}$ along which the probability of tail risk contagion is highest from node $i$ to node $j$. Representing a path ${\gamma }_{i,j}$ from node $i$ to node $j$ as an ordered sequence of links ${\epsilon }_{{\gamma }_{i,j}}=\{(i=i_n,i_{n-1}),(i_{n-1},i_{n-2}),\text{…},(i_1,i_0=j)\}$, where $n\ge 1$ and $(i_n,i_{n-1})$ denotes the link between nodes $i_n$ and $i_{n-1}$, the path ${\gamma }_{i,j}^{*}$ can be expressed as the solution to the following optimization problem:

$$\underset{{\gamma }_{i,j}\in {\mathrm{\Gamma }}_{i,j}}{\max }\left(\prod _{(i_k,i_{k-1})\in {\epsilon }_{{\gamma }_{i,j}}}{\hat{\tau }}_{k,k-1}^{\mathit{tail}}\right),$$ (13)

where ${\mathrm{\Gamma }}_{i,j}$ is the set of all paths from node $i$ to node $j$; ${\hat{\tau }}_{k,k-1}^{\mathit{tail}}$ is the tail dependence coefficient between nodes $i_k$ and $i_{k-1}$ on the link $(i_k,i_{k-1})\in {\epsilon }_{{\gamma }_{i,j}}$; and the superscript $\mathit{tail}$ can take two values, $L$ and $U$, which denote “lower” and “upper” tails, respectively.

To facilitate the solution, we equivalently transform optimization problem (13) into the following form:

$$\underset{{\gamma }_{i,j}\in {\mathrm{\Gamma }}_{i,j}}{\min }\left[\sum _{(i_k,i_{k-1})\in {\epsilon }_{{\gamma }_{i,j}}}\left(-\log {\hat{\tau }}_{k,k-1}^{\mathit{tail}}\right)\right].$$ (14)

Since ${\hat{\tau }}_{k,k-1}^{\mathit{tail}}\in \left(\mathrm{0, 1}\right)$, we have $-\log {\hat{\tau }}_{k,k-1}^{\mathit{tail}}\in (0,+\infty )$ and that the larger ${\hat{\tau }}_{k,k-1}^{\mathit{tail}}$ is, the smaller $-\log {\hat{\tau }}_{k,k-1}^{\mathit{tail}}$ is. We define $-\log {\hat{\tau }}_{k,k-1}^{\mathit{tail}}$ as the length of edge $(i_k,i_{k-1})\in {\epsilon }_{{\gamma }_{i,j}}$, and accordingly $\sum _{(i_k,i_{k-1})\in {\epsilon }_{{\gamma }_{i,j}}}\left(-\log {\hat{\tau }}_{k,k-1}^{\mathit{tail}}\right)$ is the length of path ${\gamma }_{i,j}$. Hence, a higher tail dependence between nodes $i$ and $j$ are associated with a closer distance between them. We use Dijkstra algorithm to search for the shortest path of tail risk contagion from one node to another by minimizing the objective function in (14). We define the length of the shortest path ${\gamma }_{i,j}^{*}$ as the tail risk contagion distance $d_{\mathit{cont}}^{\mathit{tail}}(i,j)$ from node $i$ to node $j$, that is, $d_{\mathit{cont}}^{\mathit{tail}}(i,j)=\underset{{\gamma }_{i,j}\in {\mathrm{\Gamma }}_{i,j}}{\min }\left[\sum _{(i_k,i_{k-1})\in {\epsilon }_{{\gamma }_{i,j}}}\left(-\log {\hat{\tau }}_{k,k-1}^{\mathit{tail}}\right)\right]$. By solving optimization problem ((10), (14)) for all pairs of nodes in the tail dependence network, an $N\times N$ contagion distance matrix with diagonal elements being 0 is obtained for each $\mathit{tail}\in \{L,U\}$.6

We then use contagion distances to compute contagion centrality, which is a measure of the overall tail risk contagiousness of a node. Formally, the contagion centrality ${\mathit{CC}}_i^{\mathit{tail}}$ of node $i$ is defined as

$${\mathit{CC}}_i^{\mathit{tail}}=\frac{1}{\sqrt{{\left({\mu }_i^{\mathit{tail}}\right)}^2+{\left({\sigma }_i^{\mathit{tail}}\right)}^2}},$$ (15)

where ${\mu }_i^{\mathit{tail}}=\frac{{\sum }_{j=1,j\ne i}^N{d}_{\mathit{cont}}^{\mathit{tail}}(i,j)}{N-1}$ and ${\sigma }_i^{\mathit{tail}}=\sqrt{\frac{{\sum }_{j=1,j\ne i}^N{\left(d_{\mathit{cont}}^{\mathit{tail}}(i,j)-{\mu }_i^{\mathit{tail}}\right)}^2}{N-2}}$ are the mean and standard deviation of the contagion distances from node $i$ to the rest of the network, respectively.7 As Abduraimova (2022) states, a highly contagious node is usually close to all other nodes in the network in terms of contagion distances, and accordingly, it has lower values of ${\mu }_i^{\mathit{tail}}$ and ${\sigma }_i^{\mathit{tail}}$ and thus higher contagion centrality. Lower tail risk contagion refers to the propagation of extreme downward price shocks (crisis) and upper tail risk contagion refers to the propagation of extreme upward price shocks (booms). A “contagion‐central” node with high contagion centrality is a good spreader of tail risk while at the same time being susceptible to external tail risk itself.

3. DATA AND VARIABLES

Our study focuses on 29 major commodity futures contracts: crude oil, heating oil, gasoline, natural gas, corn, oats, wheat, soybeans, soybean oil, soybean meal, live cattle, feeder cattle, lean hogs, coffee, cocoa, cotton, lumber, orange juice, sugar, gold, silver, palladium, platinum, copper, aluminum, nickel, tin, zinc, and lead. As shown in Table 1, these commodity futures contracts come from six futures exchanges (i.e., NYMEX, CBOT, CME, COMEX, ICE, and LME) and are divided into three broad categories (i.e., energy, agriculture, and metals) and six subgroups (i.e., energy, grains, livestock, softs, precious metals, and base metals). The price data on these commodity futures contracts are downloaded from Thomson Reuters Datastream. We use daily settlement price data for continuous nearby futures contracts with tickers being XXXC.01, where XXX represents the three‐character futures class code. The sample period spans from January 1, 2018, to February 23, 2022. Since the COVID‐19 pandemic in the United States began on January 20, 2020, our sample covers daily trading data for commodity futures contracts for approximately 2 years before and after the outbreak, respectively.8 Our sample period ends on February 23, 2022 to avoid the impact of the Russian–Ukrainian war that broke out on February 24, 2022 on commodity futures prices.

Table 1.

Commodity futures list

Category	Subgroup	Commodity	Exchange
Energy	Energy	Crude oil	NYMEX
		Heating oil	NYMEX
		Gasoline	NYMEX
		Natural gas	NYMEX
Agriculture	Grains	Corn	CBOT
		Oats	CBOT
		Wheat	CBOT
		Soybeans	CBOT
		Soybean oil	CBOT
		Soybean meal	CBOT
	Livestock	Live cattle	CME
		Feeder cattle	CME
		Lean hogs	CME
	Softs	Coffee	ICE
		Cocoa	ICE
		Cotton	ICE
		Lumber	CME
		Orange juice	ICE
		Sugar	ICE
Metals	Precious metals	Gold	COMEX
		Silver	COMEX
		Palladium	NYMEX
		Platinum	NYMEX
	Base metals	Copper	COMEX
		Aluminum	LME
		Nickel	LME
		Tin	LME
		Zinc	LME
		Lead	LME

Note: The reports of the 29 commodity futures covered by our study, and their categories and subgroups.

Abbreviations: CBOT, Chicago Board of Trade; CME, Chicago Mercantile Exchange; COMEX, Commodity Exchange; ICE, Intercontinental Exchange; LME, London Metal Exchange; NYMEX, New York Mercantile Exchange.

Our study estimates tail dependence coefficients based on daily simple returns, calculated as $r_{i,t}=P_{i,t}/P_{i,t-1}‐1$, where $P_{i,t}$ is the settlement price of commodity futures $i$ on day $\mathit{t}$. In the regression analysis, we use the daily growth rate ($\mathit{Growt}{h}_t$) of new confirmed COVID‐19 cases in the United States as a measure of pandemic severity. Formulaically, $\mathit{Growt}{h}_t={\mathit{Case}}_t/{\mathit{Case}}_{t-1}-1$, where ${\mathit{Case}}_t$ is the number of new confirmed COVID‐19 cases on day $t$. Our regressions also control for several variables that is known to affect commodity futures prices, namely, the return on the broad US dollar index ($\mathit{USD}$), the Aruoba et al. (2009) business conditions index ($\mathit{ADS}$), the default risk premium ($\mathit{DEF}$), the TED spread ($\mathit{TED}$), and the change in VIX index ($\mathit{VIX}$).9 We collect data on confirmed COVID‐19 cases from the WHO website and data on control variables from the websites of Federal Reserve Bank of St. Louis and Federal Reserve Bank of Philadelphia.10

4. EMPIRICAL RESULTS

4.1. Structural changes in tail risk contagion

Using January 20, 2020, the date when the first COVID‐19 case was confirmed in the United States as a breakpoint, we divide the sample period into two segments to examine the structural changes in tail risk contagion across commodity futures. The first period spans from January 1, 2018 to January 19, 2020, and the second period from January 20, 2020, to February 23, 2022. We construct a tail dependence network for each of the two periods and estimate the tail risk contagion centrality for 29 commodity‐nodes in both networks separately.

Table 2 reports the average contagion centrality and 95% confidence intervals for all commodities, as well as the energy, agriculture, and metals categories, for both periods.11 We find a significant increase in the average lower tail contagion centrality for all commodities after the outbreak of COVID‐19 (Panel A of Table 2); such an increase is also observed in the energy, agriculture, and metals categories and is statistically significant for the latter two. These findings suggest that COVID‐19 has significantly exacerbated the lower tail risk contagion across commodities. Moreover, the last column of Table 2 shows that the lower tail risk contagiousness of metals is most affected by the outbreak with an increase of 0.104, followed by agricultural commodities with an increase of 0.081, and finally energy commodities with an increase of 0.077.

Table 2.

Contagion centrality: overall results

	Full period	Prefirst case	Postfirst case	Difference
Panel A: Contagion in lower tail
All	0.263	0.219	0.308	0.089
	[0.244; 0.281]	[0.204; 0.231]	[0.285; 0.328]
Energy	0.290	0.239	0.316	0.077
	[0.187; 0.327]	[0.188; 0.257]	[0.186; 0.363]
Agriculture	0.243	0.203	0.284	0.081
	[0.217; 0.269]	[0.182; 0.223]	[0.256; 0.316]
Metals	0.284	0.236	0.340	0.104
	[0.272; 0.300]	[0.226; 0.247]	[0.322; 0.357]
Panel B: Contagion in upper tail
All	0.181	0.169	0.198	0.029
	[0.168; 0.191]	[0.158; 0.179]	[0.184; 0.209]
Energy	0.182	0.154	0.207	0.053
	[0.118; 0.205]	[0.117; 0.169]	[0.136; 0.232]
Agriculture	0.173	0.166	0.186	0.020
	[0.154; 0.189]	[0.149; 0.183]	[0.167; 0.201]
Metals	0.192	0.180	0.211	0.031
	[0.180; 0.207]	[0.168; 0.191]	[0.196; 0.226]

Note: The last column reports the difference between the values in the third and second columns. 95% confidence intervals produced by BCA bootstrapping (20,000 replications) are in square brackets.

COVID‐19 has also enhanced the upper tail risk contagiousness of commodities, albeit to a lesser extent (Panel B of Table 2). After the outbreak, the average upper tail contagion centrality of the entire network increases significantly by 0.029, but this figure is only about one‐third of the increase in the average lower tail contagion centrality. In fact, our results show that the upper tail risk contagion in the network is significantly weaker than the contemporaneous lower tail risk contagion, both for the entire sample period and for the two subperiods. This finding is in line with prior studies on risk spillovers (e.g., Hattori et al., 2021; Wen et al., 2019; Xu et al., 2018), which suggest that in times of crisis, asset prices are more correlated and more likely to crash together than rise together.

Another observation worth mentioning in Table 2 is that metals and energy commodities have higher contagion centrality values in the lower tail than agricultural commodities in all time periods and this difference is statistically significant between metals and agricultural commodities. This finding indicates that metals and energy commodities are on average more central to the network and negative price shocks originating from them would have a greater impact on the rest of the network. On the other hand, it also implies that the prices of agricultural commodities may be more independent and stable in a crisis, because the peripheral nodes are more resistant to risk shocks in the network.

Table B1 in the appendix reports the contagion centrality for individual commodities and the average contagion centrality for six subgroups. The results are similar to those in Table 2: the average lower and upper tail contagion centrality increase across all subgroups with the COVID‐19 outbreak and this increase is more pronounced for the lower tail. Moreover, we find that among the six subgroups, energy commodities have the highest lower tail risk contagiousness over the full sample period, while livestock commodities have the lowest. This implies that attention should be paid not only to the tail risks of energy commodities themselves, but also to their risk spillovers to other commodities. To facilitate observation, we use bar charts to visualize the contagion centrality of individual commodities before and after the outbreak. As shown in Figure 1, contagion centrality in the lower tail increases for all commodities except natural gas and orange juice, among which soybean oil, tin, and zinc show the largest increases. The three most contagion‐central commodities before the outbreak are copper, gasoline, and cotton, while after the outbreak they are soybean oil, copper and soybeans. In addition, we find that the difference between the maximum and minimum values of the contagion centrality of commodities is obviously enlarged after the outbreak, suggesting that the core‐periphery structure of the risk contagion network become more pronounced during the COVID‐19 pandemic.12 Figure 2 shows the upper tail contagion centrality of individual commodities. We observe a slight increase in upper tail risk contagiousness for 25 out of the 29 commodities following the outbreak.

Figure 1.

Lower tail contagion centrality for individual commodities. (a) The results before the COVID‐19 outbreak (January 1, 2018–January 19, 2020). (b) The results after the COVID‐19 outbreak (January 20, 2020–February 23, 2022). (c) The postoutbreak increase in lower tail contagion centrality for individual commodities.

Figure 2.

Upper tail contagion centrality for individual commodities. (a) The results before the COVID‐19 outbreak (January 1, 2018–January 19, 2020). (b) The results after the COVID‐19 outbreak (January 20, 2020–February 23, 2022). (c) The post‐outbreak increase in upper tail contagion centrality for individual commodities.

4.2. Contagion in prepandemic, pandemic, and postpandemic periods

For robustness, we also examine structural changes in contagion centrality using a three‐period division: prepandemic, pandemic, and postpandemic. This helps to validate the results of the two‐period analysis in Section 4.1 and shed light on the general trend of tail risk contagion across commodities as the COVID‐19 situation evolves. The three periods are defined as follows: prepandemic period from January 2018 to November 2019, pandemic period from December 2019 to July 2021, and postpandemic period from August 2021 to February 2022.13

Table 3 presents the average contagion centrality for all commodities and for different commodity groups over the three periods, where Panel A presents the results for the lower tail and Panel B presents the results for the upper tail. Consistent with our two‐period analysis, we find that risk contagion in the network intensifies significantly during the newly defined pandemic period, both in the lower and upper tails. In the postpandemic period, the average lower tail contagiousness for all commodities has declined compared to the pandemic period, but it remains significantly higher than the prepandemic level. Similar results are observed for each commodity group. This indicates that the impact of COVID‐19 on the downside risk connectedness across commodities is somewhat persistent and will not disappear in the short term, although the prices of various commodities have already recovered or even exceeded their prepandemic levels. In contrast to the lower tail, the average upper tail contagiousness for all commodities continues to increase postpandemic and the increase is even more pronounced than that in the pandemic period. This pattern is also true for each commodity group, indicating a common recovery and sustained rise in commodity prices.

Table 3.

Contagion centrality: prepandemic, pandemic, and postpandemic

	Prepandemic	Pandemic	Postpandemic
Panel A: Contagion in lower tail
All	0.224	0.320	0.300
	[0.209; 0.237]	[0.298; 0.341]	[0.280; 0.319]
Energy	0.248	0.337	0.314
	[0.199; 0.266]	[0.208; 0.385]	[0.174; 0.362]
Agriculture	0.207	0.295	0.278
	[0.186; 0.228]	[0.267; 0.327]	[0.257; 0.298]
Grains	0.238	0.340	0.306
	[0.205; 0.253]	[0.295; 0.377]	[0.274; 0.306]
Livestock	0.159	0.249	0.245
	[0.145; 0.170]	[0.221; 0.274]	[0.213; 0.265]
Softs	0.200	0.273	0.267
	[0.170; 0.229]	[0.240; 0.312]	[0.239; 0.299]
Metals	0.240	0.352	0.329
	[0.227; 0.253]	[0.332; 0.372]	[0.299; 0.353]
Precious metals	0.249	0.344	0.315
	[0.233; 0.261]	[0.319; 0.384]	[0.275; 0.345]
Base metals	0.234	0.357	0.338
	[0.218; 0.255]	[0.328; 0.379]	[0.291; 0.367]
Panel B: Contagion in Upper Tail
All	0.176	0.206	0.268
	[0.165; 0.187]	[0.195; 0.216]	[0.246; 0.283]
Energy	0.160	0.218	0.275
	[0.123; 0.175]	[0.182; 0.231]	[0.147; 0.319]
Agriculture	0.170	0.198	0.254
	[0.154; 0.186]	[0.182; 0.214]	[0.225; 0.279]
Grains	0.202	0.223	0.299
	[0.190; 0.213]	[0.213; 0.238]	[0.278; 0.318]
Livestock	0.127	0.161	0.228
	[0.119; 0.132]	[0.151; 0.168]	[0.215; 0.240]
Softs	0.160	0.191	0.222
	[0.145; 0.171]	[0.170; 0.216]	[0.176; 0.259]
Metals	0.193	0.214	0.285
	[0.178; 0.204]	[0.197; 0.229]	[0.273; 0.296]
Precious metals	0.201	0.216	0.286
	[0.190; 0.208]	[0.195; 0.233]	[0.275; 0.293]
Base metals	0.187	0.212	0.284
	[0.169; 0.207]	[0.187; 0.234]	[0.265; 0.301]

Note: 95% confidence intervals produced by BCA bootstrapping (20 thousand replications) are in square brackets.

Table B2 in the appendix presents the contagion centrality for individual commodities over the three periods. We find that during the pandemic and post‐pandemic periods, most of commodities shows a lower tail contagion centrality that increases first and then decreases, while only that of oats, lean hogs, cocoa, palladium, copper, and aluminum continues to rise. In terms of the upper tail, the contagion centrality of each commodity has remained on an upward trend since the outbreak, with the exception of natural gas, soybean oil, and lumber. An interesting observation is that the contagion behavior of natural gas seems quite different from the other three energy commodities, that is, crude oil, heating oil, and gasoline. Specifically, the contagion centrality of crude oil, heating oil, and gasoline ranks high in the network at all times, both for the lower and upper tails, whereas that of natural gas always remains at a low level.14

4.3. Contagion within and across commodity groups

In this section, we investigate differences in tail risk contagion within and across commodity groups. For each commodity group, we calculate the average contagion distance between commodities within the group and the average contagion distance from commodities within the group to those outside the group (the shorter the distance, the higher the probability of risk propagation between commodities). The results are presented in Table 4, where Panels A and B report the results for the lower and upper tails, respectively.

Table 4.

Average contagion distances within and across groups

	Prefirst case		Postfirst case
	Within group	Outside group	Within group	Outside group
Panel A: Lower tail
Energy	2.021	4.217	1.525	3.349
	[1.175; 2.871]	[3.928; 4.541]	[0.901; 2.162]	[3.057; 3.684]
Agriculture	4.922	4.872	3.480	3.502
	[4.619; 5.239]	[4.672; 5.078]	[3.285; 3.677]	[3.345; 3.672]
Grains	2.043	4.544	1.551	3.199
	[1.665; 2.511]	[4.335; 4.767]	[1.367; 1.742]	[3.025; 3.389]
Livestock	2.713	6.306	2.532	4.453
	[1.686; 3.465]	[5.965; 6.689]	[1.405; 3.183]	[4.243; 4.689]
Softs	5.523	5.032	4.366	3.513
	[4.829; 6.198]	[4.723; 5.379]	[3.877; 4.805]	[3.314; 3.732]
Metals	2.634	4.540	1.618	3.256
	[2.430; 2.837]	[4.318; 4.764]	[1.490; 1.751]	[3.120; 3.393]
Precious metals	1.202	4.117	0.915	3.026
	[0.891; 1.495]	[3.827; 4.429]	[0.733; 1.121]	[2.844; 3.219]
Base metals	2.442	4.349	1.199	3.005
	[2.188; 2.769]	[4.098; 4.612]	[1.088; 1.335]	[2.835; 3.180]
Panel B: Upper tail
Energy	4.559	6.350	2.538	5.055
	[2.507; 6.633]	[5.896; 6.843]	[1.445; 3.634]	[4.692; 5.470]
Agriculture	5.444	6.514	5.261	5.311
	[5.097; 5.797]	[6.243; 6.801]	[4.937; 5.596]	[5.086; 5.552]
Grains	1.764	5.266	1.595	4.937
	[1.519; 2.022]	[5.037; 5.496]	[1.383; 1.826]	[4.725; 5.179]
Livestock	5.140	8.116	3.962	6.529
	[1.783; 7.212]	[7.577; 8.620]	[1.605; 5.329]	[6.135; 6.946]
Softs	7.404	6.127	5.803	5.680
	[6.580; 8.103]	[5.809; 6.459]	[5.079; 6.530]	[5.346; 6.043]
Metals	3.136	6.100	2.616	5.287
	[2.881; 3.390]	[5.820; 6.404]	[2.399; 2.849]	[5.065; 5.522]
Precious metals	2.046	5.246	1.317	4.764
	[1.539; 2.519]	[4.903; 5.623]	[1.021; 1.543]	[4.434; 5.122]
Base metals	2.823	5.852	2.088	4.965
	[2.462; 3.245]	[5.473; 6.253]	[1.887; 2.331]	[4.697; 5.245]

Note: 95% confidence intervals produced by BCA bootstrapping (20,000 replications) are in square brackets.

We find that commodities within the same group are more closely connected with each other than with commodities outside the group, both before and after the COVID‐19 outbreak. This indicates that the tail risk contagion in commodity futures markets has an obvious clustering characteristic, also illustrating the importance of cross‐class commodity futures portfolio for risk diversification. This finding is similar to Yang et al. (2021), who reveal the clustering of volatility connectedness between commodity futures, that is, volatility shocks are more likely to be transmitted across commodities within the same group. The opposite is true for soft commodities only: the average contagion distance within the soft group is longer than that from softs to other groups of commodities in both periods. Moreover, we find that the average within‐group contagion distance of softs is significantly longer than that of any other commodity group and their average cross‐group contagion distance is the second longest in the network, second only to that of livestock. These suggest that soft commodities are typical peripheral nodes in the network; they contribute less to the risk spillover in the network, while at the same time being less susceptible to shocks from other nodes. Thus, soft commodities have safe‐haven properties. Investors seeking diversification opportunities can include soft commodities in their portfolios to reduce losses from crises such as the COVID‐19 pandemic. This finding is in line with Rubbaniy et al. (2021), Yang et al. (2021), and Farid et al. (2022), who also show that soft commodities are largely isolated from other commodity groups.

After the outbreak, both the within‐ and the cross‐group contagion distance decreases significantly for each commodity group; that is, COVID‐19 has intensified tail risk contagion not only between commodities of the same type but also across groups.

4.4. MST analysis

We have so far analyzed the structural changes in tail risk contagion from the perspective of the entire network and commodity groups. Next, we investigate the changes of central commodity‐nodes in the risk contagion network through the minimum spanning tree (MST) technique.15 This analysis helps to identify the major risk transmitters and vulnerable commodities in the network, which has implications for the portfolio decision‐making and risk management of commodity futures investors.

A spanning tree is a connected acyclic subset of a network (graph), in which (1) all nodes are included; (2) and there is one and only one path connecting any two nodes. A network may have multiple spanning trees, and its MST refers to the one with the smallest sum of lengths (contagion distances in our case) of the edges. In our study, we generate the MST of the risk contagion network using the Kruskal (1956) algorithm. We present the resulting MSTs before and after the COVID‐19 outbreak in Figure 3a,b. Compared with the complete risk contagion network in which any two nodes are connected to each other, the MST filters out the minor tail risk links between nodes and keeps only the most important and strongest links, thus providing a topological view of tail risk contagion across commodities.

Figure 3.

Minimum spanning trees before and after the outbreak. The minimum spanning trees (MSTs) of the lower tail risk contagion network. (a) The MST before the COVID‐19 outbreak (January 1, 2018–January 19, 2020). (b) The MST after the COVID‐19 outbreak (January 20, 2020–February 23, 2022). [Color figure can be viewed at wileyonlinelibrary.com]

Comparing the two trees in Figure 3, we have the following observations. First, in line with the findings in Section 4.3, commodities in energy, grains, livestock, precious metals, and base metals groups all exhibit significant clustering characteristics, whereas those classified as softs are widely dispersed throughout the network. The clustering of commodities of the same type weakens to some extent following the outbreak, suggesting an intensification of cross‐group risk transmission. Second, there are several “hubs” in the risk contagion network. Before the outbreak, copper and platinum are clearly the two most important hubs, both of which are metals; after the outbreak, hubs are more diversified, with the predominant ones including copper, soybeans, and heating oil. Third, the three agricultural commodity groups, that is, grains, livestock, and softs, tend to be more closely linked during the COVID‐19 epidemic, such that most agricultural commodities are clustered together into a subtree (bottom left of Figure 3b). The subtree shows a prominent core‐periphery structure, with soybeans being the only central node.

To quantitatively characterize the relative importance of various commodity‐nodes in risk transmission, we compute four centrality measures for each commodity‐node, namely degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality.16 These four measures are usually highly correlated empirically, but they differ in economic interpretation. The degree centrality of a node refers to the number of other nodes directly connected to it by an edge, which measures the immediate and direct influence of the node on the rest of the network. The betweenness centrality of a node is related to the number of geodesic paths passing through the node and it measures the extent to which the node acts as an intermediary for information transfer between other nodes.17 Closeness centrality measures the average closeness of a given node to all other nodes, reflecting the ability of the node to spread information throughout the network. Eigenvector centrality is an extension of degree centrality, which emphasizes that the importance of a node depends not only on the number of its neighboring nodes (the degree of the node), but also on the importance of its neighboring nodes. A node's eigenvector centrality can be large, either because it is connected to many other nodes, or because it is connected to some high‐influence nodes, or both. Overall, commodities with higher centrality are more influential in the network and have a greater ability to transmit shocks to other commodities in times of crisis. But at the same time, they are also more susceptible to shocks from other commodities.

Based on the MSTs in Figure 3, we compute the four centrality measures for each commodity before and after the outbreak.18 To facilitate comparisons across MSTs, we also normalize these measures so that they have values between 0 and 1. For each of the measures, Table 5 reports the five highest‐ranked commodities and their respective centrality values.19 We find that before the outbreak, copper and platinum are the two commodities with the highest overall centrality: in eigenvector centrality, platinum ranks first; in degree centrality, copper and platinum are tied for first place; in betweenness and closeness centrality, copper ranks first and third, respectively, while platinum ranks second in both. Other commodities showing high centrality include palladium and lead. After the outbreak, copper remains one of the two most influential commodities in the network; it ranks first in betweenness centrality and second and third, respectively, in degree and closeness centrality. The other commodity with high influence is heating oil, which ranks first in closeness centrality and second in degree and betweenness centrality. In addition, soybeans also show considerable influence during the epidemic; it ranks among the top in three (i.e., degree, betweenness, and eigenvector) out of the four centrality measures. These findings are consistent with our observations from Figure 3, suggesting that the high contagiousness of “hub” commodities, especially copper, should be taken into account when making investment decisions.

Table 5.

MST‐based centrality for the top five commodities

Degree centrality			Betweenness centrality			Closeness centrality			Eigenvector centrality
Rank	Commodity	Centrality	Rank	Commodity	Centrality	Rank	Commodity	Centrality	Rank	Commodity	Centrality
Panel A: Prefirst case
1	Copper	0.179	1	Copper	0.664	1	Palladium	0.197	1	Platinum	1.000
1	Platinum	0.179	2	Platinum	0.659	2	Platinum	0.195	2	Lumber	0.973
3	Lead	0.143	3	Palladium	0.519	3	Copper	0.195	3	Cocoa	0.620
4	Gasoline	0.107	4	Soybean oil	0.349	4	Silver	0.169	4	Coffee	0.506
4	Corn	0.107	5	Lead	0.323	5	Lead	0.164	5	Soybean oil	0.376
4	Soybeans	0.107
Panel B: Postfirst case
1	Soybeans	0.214	1	Copper	0.616	1	Heating oil	0.283	1	Soybeans	1.000
2	Heating oil	0.143	2	Heating oil	0.585	2	Gasoline	0.282	2	Orange juice	0.671
2	Copper	0.143	3	Soybeans	0.529	3	Copper	0.270	3	Live cattle	0.595
2	Zinc	0.143	4	Soybean oil	0.521	4	Soybean oil	0.268	4	Oats	0.334
3	Silver	0.107	5	Gasoline	0.516	5	Crude oil	0.256	5	Corn	0.242
3	Platinum	0.107
3	Corn	0.107
3	Soybean oil	0.107

4.5. Tail risk and contagiousness

In this section, we investigate the impact of COVID‐19 on commodity futures' tail risk and whether there is a correlation between commodity futures' tail risk and their contagiousness. We use two measures of tail risk. The first is value‐at‐risk (VaR), calculated as the $p$‐quantile of the empirical distribution of commodity daily returns over a given period, where $p\in (0,1)$ denotes the probability level. We use the VaR with $p=2.5\%(97.5\%)$ to characterize the lower (upper) tail risk of commodities. Since the VaR with $p=2.5\%$is usually negative, we multiply it by −1 so that higher values of VaR correspond to higher levels of lower tail risk.

The other measure of tail risk we use is the tail index, which is defined in the context of power law distributions. Prior studies (e.g., Gabaix, 2009; Gu & Ibragimov, 2018; Ibragimov et al., 2013) show that the tail distribution of asset returns $R$ exhibits power law characteristics; that is,

$$P(R<-z)~\frac{C_L}{z^{{\alpha }_L}},$$

$$P(R>z)~\frac{C_U}{z^{{\alpha }_U}},$$

as $z\to +\infty$, where $C_L>0$ and $C_U>0$ are constants, and ${\alpha }_L>0$ and ${\alpha }_U>0$ are the tail indices corresponding to the lower and upper tails, respectively. These indices indicate how heavy‐tailed the distribution of $R$ is. The smaller the tail index, the more heavy‐tailed the distribution, and thus the higher the probability of tail events. To estimate the lower and upper tail indices of commodity returns, we use the method proposed by Hill (1975), which is common in the literature.

Table 6 reports the average tail risk measured by VaR for all commodities and for various commodity groups over the prepandemic, pandemic, and postpandemic periods, where Panels A and B report the results for the lower and upper tails, respectively.20 Consistent with the trend of contagion centrality, the tail risk level across the network increases significantly during the pandemic, both for the lower and upper tails. This observation is also true for the six commodity groups. In the postpandemic period, both the lower and upper tail risks have declined across the network, but remain higher than their prepandemic levels. Furthermore, we find that among the six commodity groups, energy commodities have the highest tail risk; their average VaR is much higher than that of any other commodity group for all periods, especially during the pandemic.21 Similar results are obtained from the commodity tail indices, which are provided in Table B4 of the appendix.

Table 6.

Tail risk measured by VaR

	Prepandemic	Pandemic	Postpandemic
Panel A: Lower tail
All	3.05	4.23	3.47
	[2.73; 3.43]	[3.69; 4.92]	[3.03; 4.48]
Energy	4.51	7.16	5.57
	[3.72; 5.38]	[6.52; 8.10]	[3.44; 9.48]
Grains	2.62	3.21	2.82
	[2.09; 3.29]	[2.74; 3.71]	[2.54; 3.19]
Livestock	2.97	4.04	2.24
	[1.97; 3.88]	[3.03; 4.95]	[1.19; 3.06]
Softs	3.44	4.41	3.78
	[3.15; 3.77]	[3.65; 6.23]	[3.12; 5.28]
Precious metals	2.41	4.55	3.53
	[1.74; 2.80]	[2.98; 5.41]	[2.35; 4.22]
Base metals	2.58	2.99	3.00
	[2.21; 2.83]	[2.40; 3.25]	[2.53; 3.42]
Panel B: Upper tail
All	3.18	4.26	3.81
	[2.85; 3.59]	[3.72; 4.95]	[3.33; 4.77]
Energy	4.00	7.36	5.37
	[3.08; 5.28]	[6.87; 7.90]	[3.27; 9.36]
Grains	2.90	3.39	3.50
	[2.36; 3.44]	[2.81; 3.85]	[2.88; 4.14]
Livestock	3.43	4.51	2.59
	[2.17; 4.60]	[3.17; 5.81]	[1.78; 3.29]
Softs	3.82	4.25	4.18
	[3.39; 4.35]	[3.60; 5.19]	[3.39; 5.59]
Precious metals	2.34	4.26	3.84
	[1.70; 2.72]	[2.84; 5.10]	[2.30; 5.48]
Base metals	2.69	2.97	3.30
	[2.30; 3.03]	[2.61; 3.54]	[2.91; 3.72]

Note: 95% confidence intervals produced by BCA bootstrapping (20,000 replications) are in square brackets.

Given that the tail risk and contagiousness of commodities move in the same direction after the outbreak, we next examine whether there is some cross‐sectional correlation between the two variables as well. To answer this question, we run the following cross‐sectional regressions for the prepandemic, pandemic, and postpandemic periods, respectively:

$${\mathit{CC}}_i^L={\alpha }_1+{\beta }_1{\mathit{TR}}_i^L+{\epsilon }_i,$$ (16)

$${\mathit{CC}}_i^U={\alpha }_2+{\beta }_2{\mathit{TR}}_i^U+{ϵ}_i,$$ (17)

where ${\mathit{TR}}_i^L$ and ${\mathit{TR}}_i^U$ are the lower and upper tail risk of commodity $i$ in a given period, measured by VaR or Tail index; ${\mathit{CC}}_i^L$ and ${\mathit{CC}}_i^U$ are the lower and upper tail contagion centrality of commodity $i$ in the same period. We determine the cross‐sectional relationship between tail risk and contagiousness by the signs of the coefficients ${\beta }_1$ and ${\beta }_2$.

For each of the three periods, Table 7 presents the coefficient estimates for Equations (16) and (17) along with the $t$‐statistics in parentheses.22 When tail risk is measured by VaR, both ${\beta }_1$ and ${\beta }_2$ are estimated to be negative for all periods. Moreover, the estimate is statistically significant for ${\beta }_1$ in the post‐pandemic period and for ${\beta }_2$ before and after the pandemic period. These results suggest that there is a negative cross‐sectional relationship between tail risk and contagiousness, implying that a commodity with higher tail risk does not necessarily exhibit higher contagiousness and may even be the opposite. This relationship is true for both the lower and upper tails of the commodity futures return distributions. Similar results are obtained when tail risk is measured by Hill's tail index. The slope coefficient from the regression of contagion centrality on tail index is positive for all periods and for both the lower and upper tails. Since a high tail index indicates low tail risk, these results also confirm a negative correlation between commodities' tail risk and their contagiousness. Our findings are similar to Abduraimova (2022), who show that in a network consisting of major stock markets around the world, those with higher tail risk tend to have lower contagion centrality. Although somewhat counterintuitive at first glance, our findings make sense because if risky commodities are also generally highly contagious, price movements in commodity markets will be more volatile and uncertain, and commodity futures will therefore not be widely chosen as hedging and diversification instruments. A plausible explanation for our findings is that risk‐averse investors prefer to rebalance their portfolios with various less risky commodity futures, which makes prices in these commodity markets more closely linked (Magalhães et al., 2022). As a result, contagion is more likely to occur between commodities with lower tail risk, whereas those with higher tail risk are less prone to risk spillovers.

Table 7.

Relation between tail risk and contagion centrality

	Lower tail			Upper tail
	Prepandemic	Pandemic	Postpandemic	Prepandemic	Pandemic	Postpandemic
Value‐at‐risk
Intercept	0.252***	0.330***	0.339***	0.219***	0.208***	0.318***
	(11.29)	(12.56)	(16.37)	(12.68)	(13.80)	(19.01)
TR	−0.009	−0.002	−0.011**	−0.013***	−0.004	−0.013***
	(−1.26)	(−0.35)	(−2.29)	(−3.04)	(−0.13)	(−3.08)
Hill's tail index
Intercept	0.146***	0.312***	0.243***	0.115***	0.184***	0.163**
	(4.42)	(8.72)	(5.45)	(3.53)	(8.13)	(4.41)
TR	0.028**	0.004	0.019	0.025*	0.009	0.032***
	(2.52)	(0.26)	(1.35)	(1.94)	(1.06)	(3.20)

Note: In parentheses are $t$‐statistics calculated from White's (1980) heteroscedastic‐consistent standard errors.

Abbreviations: TR, tail risk measure.

***$p<0.01$; **$p<0.05$; and *$p<0.1$.

4.6. Relation between COVID‐19 severity and contagion

In this section, we use time‐series regressions to quantify the impact of COVID‐19 severity on tail risk contagion across commodities. Through the time‐varying SJC copula, we calculate the daily tail dependence coefficients for each pair of commodities and form a tail dependence network on each day of the sample period. Based on these networks, we estimate the daily contagion centrality measures for each commodity. We use the cross‐sectional average of daily contagion centrality for all commodities (denoted by $\mathit{Contagion}$) as a proxy for the overall contagion level in the network. We use the daily growth rate of new confirmed COVID‐19 cases in the United States (denoted by $\mathit{Growth}$) to measure the severity of the pandemic. Our time‐series regression specification is as follows:

$${\mathit{Contagion}}_{t+1}=\alpha +\beta {\mathit{Growth}}_t+\mathit{\gamma }{\mathit{X}}_{\mathit{t}}\mathbf{+}{\epsilon }_{t+1}$$ (18)

where ${\mathit{X}}_{\mathit{t}}$ denotes a set of control variables, which are known to affect commodity markets. Specifically, we use the return of the US dollar index ($\mathit{USD}$) to capture exchange rate fluctuations, the Aruoba–Diebold–Scotti Business Conditions Index ($\mathit{ADS}$) to capture macroeconomic activity, the default risk premium ($\mathit{DEF}$) to capture financial cycles, the TED spread ($\mathit{TED}$) to capture liquidity in the market, and the change in the VIX index ($\mathit{VIX}$) to capture investors’ sentiment.

We provide the coefficient estimates for Equation (18) in Table 8, where Panels A and B report the results for the lower and upper tails, respectively. As shown in the first column of Panel A, the slope coefficient from the univariate regression of ${\mathit{Contagion}}_{t+1}$ on ${\mathit{Growth}}_t$ is 0.43% with a $t$‐statistic of 2.43, indicating a positive and statistically significant relation between COVID‐19 severity on day $t$ and tail risk contagion level on day $t+1$.23 Since the standard deviation of ${\mathit{Growth}}_t$ is about 47.51%, this result implies that an increase in ${\mathit{Growth}}_t$ by two standard deviations is accompanied by an average increase in ${\mathit{Contagion}}_{t+1}$ by four basis points. Columns 2–6 augment the univariate regression by adding control variables into the regressor set one at a time. In these specifications, the coefficients of ${\mathit{Growth}}_t$ remain significantly positive, with values ranging from 0.39% to 0.47% and $t$‐statistics between 2.14 and 2.35. These results suggest that COVID‐19 has a direct, robust impact on tail risk contagion across commodities, which cannot be subsumed by other effects. Moreover, Columns 5 and 6 show that the default risk premium and the TED spread also have a significantly positive coefficient; that is, the risk connectedness between commodities is also related to financial business cycles and market liquidity. An in‐depth discussion of these findings could be an interesting direction for future research. Similar results are observed for the upper tails (see Panel B of Table 8).

Table 8.

Determinants of the overall contagion level in the network

	(1)	(2)	(3)	(4)	(5)	(6)
Panel A: Lower tail
$\mathit{Growth}$	0.43**	0.47**	0.43**	0.39**	0.41**	0.41**
	(2.43)	(2.20)	(2.35)	(2.07)	(2.14)	(2.19)
$U\mathit{SD}$		0.47	0.38	0.35	0.37	0.31
		(1.17)	(1.38)	(1.26)	(1.15)	(0.93)
$A\mathit{DS}$			−0.06	−0.07	0.02	0.02
			(−1.04)	(−1.34)	(0.40)	(0.39)
$\mathit{DEF}$				0.57	1.56**	1.53**
				(0.80)	(2.40)	(2.40)
$\mathit{TED}$					3.64*	3.65*
					(1.90)	(1.85)
$\mathit{VIX}$						0.03
						(1.60)
$C\mathit{onst}.$	27.20***	27.15***	27.12***	27.64***	27.83***	27.81***
	(168.23)	(154.49)	(162.06)	(45.35)	(50.09)	(50.25)
Adj‐$R^2$(%)	1.82	3.41	9.75	11.00	15.30	15.40
Obs.	517	473	473	471	444	444
Panel B: Upper tail
$\mathit{Growth}$	0.29**	0.32**	0.31**	0.29**	0.32**	0.32***
	(2.53)	(2.51)	(2.49)	(2.56)	(2.50)	(2.86)
$U\mathit{SD}$		0.25	0.23	0.22	0.20	0.15
		(1.26)	(1.32)	(1.30)	(1.25)	(1.05)
$A\mathit{DS}$			−0.01	−0.02	0.04*	0.04
			(−1.32)	(−1.41)	(1.85)	(1.57)
$\mathit{DEF}$				0.30	0.90**	0.88**
				(1.06)	(2.30)	(2.43)
$\mathit{TED}$					2.20***	2.21***
					(2.67)	(2.67)
$\mathit{VIX}$						0.03**
						(2.53)
$C\mathit{onst}.$	20.21***	20.18***	20.17***	20.43***	20.56***	20.54***
	(226.70)	(231.97)	(229.87)	(68.15)	(67.11)	(71.25)
Adj‐$R^2$(%)	3.01	5.10	6.54	7.54	12.60	13.40
Obs.	517	473	473	471	444	444

Note: Newey and West (1987) $t$‐statistics are in parentheses.

Abbreviations: Adj‐R ², adjusted R‐square statistics; ADS, Aruoba–Diebold–Scotti (2009) business conditions index; Const., constant term; $\mathit{DEF}$, default risk premium; Obs., observations; $\mathit{TED}$, TED spread; USD, return on the US dollar index; $\mathit{VIX}$, change of the VIX index.

***$p<0.01$; **$p<0\text{.}05$; and *$p<0.1$.

4.7. Robustness check

In our main analysis, we use the bivariate SJC copula to model the joint distribution of commodities $i$ and $j$ to estimate the lower/upper tail dependence coefficient between them. A potential problem with such an estimator is that it may include the effect of other commodity prices on the tail dependence between $i$ and $j$. For example, a high lower tail dependence coefficient between $i$ and $j$ may simply be due to the fact that they would both experience a price collapse under a negative price shock from commodity $k$, without direct risk transmission between them per se. To address this issue, we further model the joint distribution of all 29 commodities in our study and estimate the conditional tail dependence coefficients for each pair of commodities controlling for the remaining 27 commodities.

We use the copula vine technique proposed by Joe (1996) to model the high‐dimensional distribution. This technique is widely used in the literature and its core idea is to decompose a multivariate distribution into the product of marginal distributions of variables and a cascade of bivariate copulas. For a high‐dimensional distribution, there are many possible decompositions. Here, we decompose the joint distribution of 29 commodities according to the D‐vine structure, following Sukcharoen and Leatham (2017).24

Denoting the joint density of the 29 commodity returns by $f(r_1,r_2,\text{…},r_{29})$, the decomposition of $f(r_1,r_2,\text{…},r_{29})$ corresponding to a D‐vine can be written as

$$f(r_1,r_2,\text{…},r_{29})=\prod _{k=1}^{29}f\left(r_k\right)\prod _{j=1}^{29-1}\prod _{i=1}^{29-j}{c}_{i,i+j|i+1,\text{…},i+j-1}\{F\left(r_i\right|r_{i+1},\text{…},r_{i+j-1}),F\left(r_{i+j}\right|r_{i+1},\text{…},r_{i+j-1})\}$$ (19)

where $f(·)$ and $F(·|·)$ denote the marginal density and conditional CDF of return variables, respectively; $c_{i,i+\mathit{j|i}+1,\text{…},i+j-1}\{·,·\}$ denotes the density of the bivariate copula that characterizes the conditional dependence structure between variables. In the D‐vine decomposition, we still use the GJR‐GARCH(1,1) model (see, Equations 10–12) to fit the marginal distribution of commodities and use the SJC copula to capture the dependence structure of commodity pairs (see, Equations 6 and 7). In this way, the parameters of factor $c_{\mathrm{1,29}|2,\text{…},28}\{F(r_1|r_2,\text{…},r_{28}),F(r_{29}|r_2,\text{…},r_{28})\}$ in the right‐had side of Equation (19) give the conditional tail dependence coefficients between commodities $r_1$ and $r_{29}$ controlling for the remaining commodities.

Based on the conditional tail dependence coefficients estimated by Equation (19), we calculate the contagion centrality measure for each commodity and replicate Table 2. The results are reported in Table B5 of the appendix. Similar to the findings in Table 2, from Table B5 we also observe a significant increase in the lower and upper tail contagion centrality of commodities after the COVID‐19 outbreak. In addition, the average contagion centrality of agricultural commodities remains the lowest of the three commodity categories. A major difference is that the contagion centrality values in Table B5 are smaller than those in Table 2, due to the general reduction in tail dependence coefficients between two commodities after controlling for the effects of other commodities. We also replicate Tables 3, 4, 5, and 7 using the conditional tail dependence coefficients and find that the corresponding empirical results still hold.25

5. CONCLUSION

This paper investigates the impact of COVID‐19 on tail risk contagion across commodity futures using a copula‐based network method. Our sample covers 29 major commodity futures traded on six exchanges (i.e., NYMEX, CBOT, CME, COMEX, ICE, and LME), divided into three broad categories (i.e., energy, agriculture, and metals) and six subgroups (i.e., energy, grains, livestock, softs, precious metals, and base metals). Using the static SJC copula, we first construct a tail dependence network for the period before and after the COVID‐19 outbreak, in which the nodes are commodities and the links between nodes are the tail dependence coefficients between them. Based on the tail dependence network and Dijkstra algorithm, we then determine the (shortest) contagion distance between any two commodities. Using contagion distances, we calculate the contagion centrality for individual commodities, which measures the overall risk contagiousness of a commodity.

Our results show that the risk contagiousness of commodities both in the lower and upper tails increases significantly following the COVID‐19 outbreak and the increase is more prominent for the lower tail. Although contagiousness in the lower tail has declined over time, it is still significantly higher than the prepandemic level. In contrast, contagiousness in the upper tail has always shown an upward trend. These suggest that COVID‐19 has a significant, persistent impact on the risk connectedness between commodities; even if commodity prices have generally recovered and even surpassed their prepandemic levels, the impact has not gone away, which should be of concern to investors and regulators. Risk contagion exhibits an obvious clustering characteristic; that is, commodities in the same group are more closely connected with each other than with those outside the group. Hence, it is necessary to hold a portfolio of commodities across different groups for risk diversification.

In general, metals and energy commodities are more contagious than agricultural commodities—extreme price shocks from these two categories would have a greater impact on the rest of the network. Moreover, we find that soft commodities exhibit safe‐haven properties—they are isolated not only from other commodity groups but also from each other. Our MST analysis identifies several hub commodities in the risk contagion network, such as copper and platinum before the outbreak and copper, heating oil, and soybeans after the outbreak. Compared with other commodities, hubs have a stronger ability to transmit information while at the same time being more vulnerable to external shocks. Therefore, they should be treated with caution when making investment decisions.

Consistent with the change in contagiousness, the tail risk of commodities also increases significantly after the outbreak. However, we find a negative cross‐sectional relationship between tail risk and contagiousness. Thus, commodities with high tail risk are not necessarily highly contagious and may even be less so. Finally, using time‐series regressions, we show that the severity of COVID‐19 on day $t$ has a direct and robust positive effect on the overall contagion level in the network on day $t+1$, which cannot be explained by other factors affecting commodity markets.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

APPENDIX A. DEFINITION OF DEGREE CENTRALITY, CLOSENESS CENTRALITY, BETWEENNESS CENTRALITY, AND EIGENVECTOR CENTRALITY

• (i)
  Degree centrality for a node $i$ is defined as

  $$C_D(i)=\frac{{\sum }_{j=1,j\ne i}^N{A}_{i,j}}{N-1},$$ (A.1)

  where $A_{i,j}$ takes value 1 if there is an edge connecting nodes $i$ and $j$, and 0 otherwise; $N$ is the number of nodes in the network; the term $N-1$ in the denominator severs as a normalization factor.
• (ii)
  Closeness centrality for a node $i$ is defined as

  $$C_C(i)=\frac{N-1}{{\sum }_{j=1,j\ne i}^N\mathit{sd}(i,j)}$$ (A.2)

  where $\mathit{sd}(i,j)$ denotes the shortest distance between nodes $i$ and $j$, which equals the minimum number of edges to reach node $j$ from node $i$; $N-1$ is the scaling factor.
• (iii)
  Betweenness centrality for a node $i$ is defined as

  $$C_B\left(i\right)=\frac{2·{\sum }_{a\ne b\ne i}\frac{\lambda (a,b|i)}{\lambda (a,b)}}{(N-1)·(N-2)},$$ (A.3)

  where $\lambda (a,\mathit{b|i})$ denotes the number of shortest paths between nodes $a$ and $b$ that pass through node $i$; $\lambda (a,b)$ denotes the total number of shortest paths between $a$ and $b$; $(N-1)·(N-2)$ is the normalization factor.
• (iv)Suppose $\mathit{x}={[x_1,x_2,\text{…},x_N]}^T$ is an $N$‐dimensional column vector whose $i$th element $x_i$ is the eigenvector centrality of node $i$ in the network, then it satisfies

$$\mathit{Ax}={\lambda }_{\max }\mathit{x}$$ (A.4)

where $\mathit{A}={\left(a_{i,j}\right)}_{N\times N}$ is the adjacency matrix of the network, that is, $a_{i,j}=1$ if node $i$ is linked to node $j$, and $a_{i,j}=0$ otherwise, and ${\lambda }_{\max }$ is the greatest eigenvalue of $\mathit{A}$. That is, $\mathit{x}$ is the eigenvector corresponding to the greatest eigenvalue of the adjacency matrix. In our study, we normalize the eigenvector centrality of node $i$ by ${\tilde{x}}_i=x_i/x_{\max }$, where $x_{\max }$ is the maximum value of the elements in $\mathit{x}$.

APPENDIX B. TABLES

See Tables B1, B2, B3, B4, B5.

Table B1.

Contagion centrality: subgroups and individual commodities

	Contagion in lower tail				Contagion in upper tail
	Full period	Prefirst case	Postfirst case	Difference	Full period	Prefirst case	Postfirst case	Difference
Energy	0.290	0.239	0.316	0.077	0.182	0.154	0.207	0.053
	[0.187; 0.327]	[0.188; 0.257]	[0.186; 0.363]		[0.118; 0.205]	[0.117; 0.169]	[0.136; 0.232]
Crude oil	0.312	0.253	0.347	0.094	0.209	0.175	0.236	0.061
Heating oil	0.324	0.253	0.372	0.119	0.205	0.165	0.234	0.069
Gasoline	0.336	0.262	0.361	0.099	0.196	0.160	0.221	0.061
Natural gas	0.187	0.188	0.186	‐0.002	0.118	0.117	0.136	0.019
Grains	0.285	0.232	0.328	0.096	0.203	0.201	0.213	0.012
	[0.245; 0.314]	[0.201; 0.247]	[0.292; 0.368]		[0.195; 0.212]	[0.191; 0.210]	[0.205; 0.219]
Corn	0.285	0.236	0.331	0.095	0.205	0.202	0.218	0.016
Oats	0.213	0.180	0.263	0.083	0.202	0.187	0.212	0.025
Wheat	0.262	0.226	0.300	0.074	0.188	0.185	0.208	0.023
Soybeans	0.330	0.260	0.378	0.118	0.211	0.219	0.216	‐0.003
Soybean oil	0.337	0.252	0.400	0.148	0.220	0.211	0.227	0.016
Soybean meal	0.279	0.240	0.297	0.057	0.192	0.200	0.197	‐0.003
Livestock	0.187	0.159	0.228	0.069	0.133	0.123	0.152	0.029
	[0.173; 0.198]	[0.150; 0.167]	[0.209; 0.246]		[0.126; 0.137]	[0.108; 0.135]	[0.134; 0.163]
Live cattle	0.206	0.174	0.262	0.088	0.138	0.116	0.166	0.050
Feeder cattle	0.173	0.153	0.212	0.059	0.126	0.108	0.157	0.049
Lean hogs	0.181	0.150	0.209	0.059	0.136	0.145	0.134	‐0.011
Softs	0.228	0.195	0.269	0.074	0.163	0.152	0.177	0.025
	[0.200; 0.269]	[0.162; 0.226]	[0.232; 0.305]		[0.132; 0.183]	[0.139; 0.166]	[0.144; 0.202]
Coffee	0.230	0.205	0.265	0.060	0.193	0.178	0.193	0.015
Cocoa	0.181	0.130	0.236	0.106	0.105	0.130	0.135	0.005
Cotton	0.305	0.261	0.332	0.071	0.185	0.168	0.210	0.042
Lumber	0.206	0.174	0.255	0.081	0.142	0.135	0.125	‐0.010
Orange juice	0.191	0.202	0.200	−0.002	0.160	0.152	0.177	0.025
Sugar	0.259	0.199	0.323	0.124	0.190	0.152	0.220	0.068
Precious metals	0.284	0.240	0.333	0.093	0.189	0.189	0.209	0.020
	[0.266; 0.305]	[0.226; 0.251]	[0.309; 0.359]		[0.177; 0.200]	[0.179; 0.201]	[0.189; 0.227]
Gold	0.259	0.223	0.301	0.078	0.172	0.175	0.187	0.012
Silver	0.277	0.234	0.333	0.099	0.182	0.186	0.197	0.011
Palladium	0.286	0.251	0.329	0.078	0.206	0.206	0.236	0.030
Platinum	0.314	0.251	0.369	0.118	0.194	0.190	0.218	0.028
Base metals	0.284	0.233	0.345	0.112	0.194	0.174	0.212	0.038
	[0.262; 0.307]	[0.220; 0.253]	[0.317; 0.365]		[0.175; 0.214]	[0.158; 0.192]	[0.188; 0.232]
Copper	0.321	0.268	0.382	0.114	0.237	0.209	0.248	0.039
Aluminum	0.252	0.211	0.316	0.105	0.200	0.170	0.230	0.060
Nickel	0.318	0.251	0.368	0.117	0.204	0.177	0.229	0.052
Tin	0.282	0.216	0.351	0.135	0.167	0.145	0.184	0.039
Zinc	0.282	0.226	0.358	0.132	0.196	0.187	0.207	0.020
Lead	0.249	0.228	0.295	0.067	0.161	0.156	0.173	0.017

Note: Column “Difference” reports the difference between the values in Columns “Postfirst case” and “Prefirst case.” 95% confidence intervals produced by BCA bootstrapping (20,000 replications) are in square brackets.

Table B2.

Contagion centrality for individual commodities: prepandemic, pandemic, and postpandemic

	Contagion in lower tail			Contagion in upper tail
	Prepandemic	Pandemic	Postpandemic	Prepandemic	Pandemic	Postpandemic
Energy	0.248	0.337	0.314	0.160	0.218	0.275
	[0.199; 0.266]	[0.208; 0.385]	[0.174; 0.362]	[0.123; 0.175]	[0.182; 0.231]	[0.147; 0.319]
Crude oil	0.261	0.363	0.361	0.182	0.230	0.325
Heating oil	0.261	0.402	0.358	0.170	0.237	0.318
Gasoline	0.272	0.374	0.364	0.165	0.222	0.309
Natural gas	0.199	0.208	0.174	0.123	0.182	0.147
Grains	0.238	0.340	0.306	0.202	0.223	0.299
	[0.205; 0.253]	[0.295; 0.377]	[0.274; 0.306]	[0.190; 0.213]	[0.213; 0.238]	[0.278; 0.318]
Corn	0.244	0.351	0.323	0.201	0.251	0.282
Oats	0.184	0.253	0.278	0.187	0.206	0.315
Wheat	0.231	0.336	0.312	0.182	0.220	0.311
Soybeans	0.267	0.377	0.332	0.222	0.233	0.293
Soybean oil	0.253	0.414	0.338	0.216	0.213	0.336
Soybean meal	0.250	0.308	0.250	0.204	0.214	0.259
Livestock	0.159	0.249	0.245	0.127	0.161	0.228
	[0.145; 0.170]	[0.221; 0.274]	[0.213; 0.265]	[0.119; 0.132]	[0.151; 0.168]	[0.215; 0.240]
Live cattle	0.178	0.293	0.274	0.124	0.158	0.253
Feeder cattle	0.155	0.234	0.213	0.119	0.151	0.215
Lean hogs	0.145	0.221	0.247	0.137	0.173	0.216
Softs	0.200	0.273	0.267	0.160	0.191	0.222
	[0.170; 0.229]	[0.240; 0.312]	[0.239; 0.299]	[0.145; 0.171]	[0.170; 0.216]	[0.176; 0.259]
Coffee	0.216	0.268	0.249	0.182	0.205	0.258
Cocoa	0.142	0.220	0.278	0.131	0.153	0.197
Cotton	0.261	0.341	0.329	0.172	0.239	0.267
Lumber	0.170	0.259	0.227	0.152	0.166	0.139
Orange juice	0.211	0.226	0.222	0.158	0.179	0.186
Sugar	0.199	0.322	0.295	0.165	0.206	0.285
Precious metals	0.249	0.344	0.315	0.201	0.216	0.286
	[0.233; 0.261]	[0.319; 0.384]	[0.275; 0.345]	[0.190; 0.208]	[0.195; 0.233]	[0.275; 0.293]
Gold	0.229	0.314	0.266	0.186	0.191	0.272
Silver	0.242	0.339	0.303	0.202	0.205	0.297
Palladium	0.265	0.324	0.347	0.211	0.239	0.293
Platinum	0.259	0.399	0.344	0.206	0.227	0.284
Base metals	0.234	0.357	0.338	0.187	0.212	0.284
	[0.218; 0.255]	[0.328; 0.379]	[0.291; 0.367]	[0.169; 0.207]	[0.187; 0.234]	[0.265; 0.301]
Copper	0.271	0.388	0.398	0.226	0.254	0.308
Aluminum	0.211	0.324	0.336	0.179	0.234	0.281
Nickel	0.254	0.381	0.376	0.195	0.224	0.311
Tin	0.208	0.384	0.328	0.153	0.184	0.256
Zinc	0.228	0.359	0.339	0.200	0.212	0.294
Lead	0.232	0.310	0.250	0.166	0.166	0.256

Note: 95% confidence intervals produced by BCA bootstrapping (20,000 replications) are in square brackets.

Table B3.

VaR values for individual commodities

	Lower tail			Upper tail
	Prepandemic	Pandemic	Postpandemic	Prepandemic	Pandemic	Postpandemic
Energy	4.51	7.16	5.57	4.00	7.36	5.37
	[3.72; 5.38]	[6.52; 8.10]	[3.44; 9.48]	[3.08; 5.28]	[6.87; 7.90]	[3.27; 9.36]
Crude oil	4.47	8.39	3.65	3.53	8.18	3.73
Heating oil	3.46	6.41	3.21	2.78	6.68	3.06
Gasoline	4.38	7.22	4.16	3.99	7.06	3.47
Natural gas	5.71	6.63	11.26	5.70	7.51	11.24
Grains	2.62	3.21	2.82	2.90	3.39	3.50
	[2.09; 3.29]	[2.74; 3.71]	[2.54; 3.19]	[2.36; 3.44]	[2.81; 3.85]	[2.88; 4.14]
Corn	2.66	3.52	2.41	3.19	3.83	2.56
Oats	3.84	3.70	3.53	3.52	3.24	4.79
Wheat	3.32	2.88	2.93	3.88	4.28	3.73
Soybeans	2.10	2.41	2.49	2.38	2.30	2.46
Soybean oil	1.79	4.12	3.08	1.90	3.66	3.54
Soybean meal	2.00	2.64	2.47	2.56	3.01	3.92
Livestock	2.97	4.04	2.24	3.43	4.51	2.59
	[1.97; 3.88]	[3.03; 4.95]	[1.19; 3.06]	[2.17; 4.60]	[3.17; 5.81]	[1.78; 3.29]
Live cattle	2.26	3.34	1.19	2.17	3.29	1.78
Feeder cattle	1.97	3.03	1.89	2.44	3.17	2.08
Lean hogs	4.69	5.75	3.65	5.68	7.07	3.90
Softs	3.44	4.41	3.78	3.82	4.25	4.18
	[3.15; 3.77]	[3.65; 6.23]	[3.12; 5.28]	[3.39; 4.35]	[3.60; 5.19]	[3.39; 5.59]
Coffee	3.30	4.14	3.41	4.11	5.01	4.23
Cocoa	3.31	4.33	3.18	3.94	3.32	3.05
Cotton	2.82	3.13	3.31	2.97	3.16	3.69
Lumber	4.13	7.48	6.28	4.88	6.01	6.75
Orange juice	3.64	3.69	3.94	3.42	3.95	4.51
Sugar	3.46	3.69	2.56	3.63	4.03	2.83
Precious metals	2.41	4.55	3.53	2.34	4.26	3.84
	[1.74; 2.80]	[2.98; 5.41]	[2.35; 4.22]	[1.70; 2.72]	[2.84; 5.10]	[2.30; 5.48]
Gold	1.48	2.40	2.03	1.46	2.34	1.68
Silver	2.54	5.85	4.22	2.51	5.70	2.93
Palladium	3.05	5.22	4.55	2.97	4.66	6.33
Platinum	2.56	4.72	3.33	2.41	4.33	4.44
Base metals	2.58	2.99	3.00	2.69	2.97	3.30
	[2.21; 2.83]	[2.40; 3.25]	[2.53; 3.42]	[2.30; 3.03]	[2.61; 3.54]	[2.91; 3.72]
Copper	2.38	3.11	2.40	2.39	2.83	3.06
Aluminum	2.48	2.02	3.66	2.52	2.37	3.22
Nickel	3.06	3.31	3.31	3.40	3.35	4.13
Tin	1.88	3.48	3.60	1.97	4.00	3.31
Zinc	2.84	3.15	2.82	2.98	2.47	3.62
Lead	2.83	2.86	2.22	2.90	2.80	2.49

Note: 95% confidence intervals produced by BCA bootstrapping (20.000 replications) are in square brackets.

Table B4.

Commodity tail indices

	Lower tail			Upper tail
	Prepandemic	Pandemic	Postpandemic	Prepandemic	Pandemic	Postpandemic
Energy	2.41	1.80	2.59	2.40	1.89	3.21
	[1.99; 2.57]	[1.33; 2.21]	[2.32; 2.98]	[2.04; 2.68]	[1.51; 2.17]	[1.96; 3.71]
Crude oil	2.63	1.29	2.45	2.80	1.41	3.32
Heating oil	2.47	2.12	3.12	2.56	2.03	3.93
Gasoline	2.55	1.48	2.58	2.30	1.79	3.64
Natural gas	1.99	2.30	2.23	1.95	2.30	1.96
Grains	3.04	2.36	3.29	2.46	2.97	3.53
	[2.59; 3.34]	[2.03; 3.01]	[2.77; 3.52]	[2.19; 2.83]	[2.58; 3.51]	[3.14; 4.21]
Corn	2.55	1.84	3.44	2.04	2.50	3.07
Oats	2.32	1.91	3.22	2.43	3.41	3.84
Wheat	3.17	3.48	3.46	2.84	2.53	3.43
Soybeans	3.45	2.06	3.77	2.25	2.89	4.78
Soybean oil	3.50	2.58	3.42	3.10	3.94	3.27
Soybean meal	3.25	2.29	2.41	2.09	2.51	2.81
Livestock	2.12	1.89	2.88	1.83	1.65	2.14
	[1.77; 2.35]	[1.62; 2.02]	[1.73; 3.51]	[1.36; 2.15]	[1.47; 1.74]	[1.99; 2.24]
Live cattle	1.77	1.62	3.60	2.32	1.47	1.99
Feeder cattle	2.48	2.01	3.33	1.82	1.73	2.12
Lean hogs	2.11	2.03	1.73	1.36	1.74	2.31
Softs	2.95	2.18	3.35	2.68	2.94	3.32
	[2.71; 3.05]	[1.96; 2.40]	[2.96; 3.90]	[2.46; 3.01]	[2.72; 3.10]	[2.95; 3.76]
Coffee	3.08	2.53	2.92	2.66	3.02	3.45
Cocoa	3.07	2.14	3.57	3.28	3.00	3.06
Cotton	2.94	2.04	2.79	2.93	3.29	4.17
Lumber	2.98	1.77	3.60	2.47	2.98	2.71
Orange juice	3.09	2.03	2.79	2.39	2.51	3.67
Sugar	2.56	2.56	4.44	2.35	2.84	2.83
Precious metals	2.57	1.98	3.11	2.71	2.30	3.39
	[2.43; 2.68]	[1.78; 2.30]	[2.19; 3.91]	[2.34; 3.37]	[2.00; 2.52]	[2.79; 3.94]
Gold	2.52	1.94	2.08	2.45	2.22	3.62
Silver	2.40	1.73	2.53	2.24	2.52	4.25
Palladium	2.64	1.84	3.85	3.66	1.92	2.73
Platinum	2.73	2.42	3.98	2.51	2.53	2.98
Base metals	3.12	2.42	3.08	2.57	2.99	3.45
	[2.84; 3.51]	[2.08; 2.76]	[2.47; 3.67]	[2.42; 2.73]	[2.35; 3.31]	[2.91; 4.05]
Copper	2.72	2.14	4.05	2.82	3.04	4.54
Aluminum	2.81	2.98	2.20	2.40	3.14	4.12
Nickel	3.68	2.51	3.60	2.36	3.02	2.92
Tin	2.85	1.76	2.13	2.38	1.84	3.54
Zinc	3.64	2.15	2.67	2.81	3.71	2.45
Lead	3.01	2.96	3.81	2.66	3.17	3.12
All	2.79	2.16	3.10	2.49	2.59	3.26
	[2.63; 2.96]	[2.00; 2.35]	[2.84; 3.34]	[2.34; 2.66]	[2.35; 2.82]	[3.00; 3.53]

Note: 95% confidence intervals produced by BCA bootstrapping (20 thousand replications) are in square brackets.

Table B5.

Contagion centrality based on the conditional tail dependence coefficients

	Full period	Prefirst case	Postfirst case	Difference
Panel A: Contagion in lower tail
All	0.193	0.178	0.220	0.042
	[0.179; 0.207]	[0.168; 0.188]	[0.204; 0.235]
Energy	0.217	0.188	0.237	0.049
	[0.146; 0.241]	[0.152; 0.199]	[0.153; 0.267]
Agriculture	0.172	0.167	0.193	0.026
	[0.156; 0.193]	[0.152; 0.178]	[0.183; 0.213]
Metals	0.216	0.192	0.254	0.062
	[0.207; 0.230]	[0.179; 0.202]	[0.243; 0.267]
Panel B: Contagion in upper tail
All	0.164	0.158	0.186	0.028
	[0.154; 0.172]	[0.149; 0.165]	[0.176; 0.196]
Energy	0.177	0.156	0.203	0.047
	[0.119; 0.198]	[0.119; 0.169]	[0.139; 0.225]
Agriculture	0.154	0.149	0.174	0.025
	[0.142; 0.165]	[0.138; 0.161]	[0.162; 0.187]
Metals	0.173	0.171	0.197	0.026
	[0.166; 0.180]	[0.162; 0.179]	[0.185; 0.207]

Note: The last column reports the difference between the values in the third and second columns. 95% confidence intervals produced by BCA bootstrapping (20,000 replications) are in square brackets.

Qiao, T. , & Han, L. (2023). COVID‐19 and tail risk contagion across commodity futures markets. The Journal of Futures Markets, 43, 242–272. 10.1002/fut.22388

DATA AVAILABILITY STATEMENT

The data used in this study can be obtained from Thomson Reuters Datastream and the websites of World Health Organization (WHO), Federal Reserve Bank of St. Louis, and Federal Reserve Bank of Philadelphia.