Comovement and contagion in commodity markets

Chalid, Dony Abdul; Handika, Rangga Article Comovement and contagion in commodity markets Cogent Economics & Finance Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Chalid, Dony Abdul; Handika, Rangga (2022) : Comovement and contagion in commodity markets, Cogent Economics & Finance, ISSN 2332-2039, Taylor & Francis, Abingdon, Vol. 10, Iss. 1, pp. 1-27, https://doi.org/10.1080/23322039.2022.2064079 This Version is available at: https://hdl.handle.net/10419/303632 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Cogent Economics & Finance ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/oaef20 Comovement and contagion in commodity markets Dony Abdul Chalid & Rangga Handika To cite this article: Dony Abdul Chalid & Rangga Handika (2022) Comovement and contagion in commodity markets, Cogent Economics & Finance, 10:1, 2064079, DOI: 10.1080/23322039.2022.2064079 To link to this article: https://doi.org/10.1080/23322039.2022.2064079 © 2022 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Published online: 25 Apr 2022. Submit your article to this journal Article views: 1663 View related articles View Crossmark data Citing articles: 5 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=oaef20 FINANCIAL ECONOMICS | RESEARCH ARTICLE Comovement and contagion in commodity markets Dony Abdul Chalid 1 * and Rangga Handika 2 Abstract: This article investigates comovement and contagions in the commodities markets. We examine the comovement by analyzing the unconditional correlation coefficients. We document that commodities tend to partially integrate. We perform contagion tests by identifying coexceedances and estimating multinomial logit to explain the joint occurrence of those coexceedances. We document that commodities price changes tend to affect the probability of both positive and negative coexceedances. Overall, we conclude that there are comovement and contagions among commodities. However, the degrees of comovement and contagion are different among commodities and between positive and negative extreme returns. The contagion among commodities is asymmetric. Subjects: Statistics for Business, Finance & Economics; Economics; Finance Keywords: Commodity markets; Correlation; Comovement; Contagion; Multinomial logit 1. Introduction There is a tremendous increase in investments in commodity markets. According to Basu and Miffre (2013), institutional investments in commodity markets have increased from $18 billion in 2003 to $250 billion in 2010. Basak and Pavlova (2016) also document that investments in commodity futures have increased from $15 billion in 2003 to over $200 billion in 2008. Overall, we can conclude that commodities markets have transformed into alternative investments (indeed, this perception is similar to Vivian & Wohar, 2012; Algieri & Leccadito, 2017). These ABOUT THE AUTHOR Our major research cluster is financial markets. Specifically, we are interested in analyzing and evaluating portfolios. One of the research subfields is examining the risk and return of commodities portfolios. We have worked and published a research manuscript investigating a risk component - GARCH volatility - in the commodities market. A thorough study of this volatility analysis inspires us to study hedging benefits (a further risk-return analysis) of commodities portfolios. We document that for stock portfolio managers, adding commodities will generate a more conservative strategy, whereas for bond and/or FX portfolio managers, adding commodities will generate a more aggressive strategy. Then, we examine another risk of commodities - whether there is another independencies risk - comovement and contagions. This manuscript will contribute to our bigger research theme in the commodities portfolio. PUBLIC INTEREST STATEMENT We are now living in an interconnected world. A consequence of interconnection is the contagion effect. Like a disease, a commodity could also transmit its properties into another commodity’s properties. Using statistical methods inspired by the biological definition of contagion, we investigate contagions in the commodities markets. We find that there are contagions among commodities. However, the degrees of contagion are different and asymmetric among commodities. An investment manager shall carefully weigh this contagion risk when investing funds in the commodity markets. Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 1 of 27 Received: 08 January 2022 Accepted: 02 April 2022 *Corresponding author: Dony Abdul Chalid Lecturer at the Faculty of Economics and Business, Universitas Indonesia, Depok, Indonesia E-mail: [email protected];abdul_- [email protected];; Reviewing editor: David McMillan, University of Stirling, Stirling, United Kingdom Additional information is available at the end of the article © 2022 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. phenomena are called the financialization of commodity markets (see also, Tang & Xiong, 2012; Cheng & Xiong, 2014). There are at least two thoughtful risk management questions given the financialization of commodity markets. First, as more investors consider commodities as investments, do commodities integrate? Second, is there any potential diversification benefit by investing among commodities? Those two questions are indeed related. A strong argument explaining the relationship comes from Elliott et al. (2014). They argue that there is no contagion without integration. This implies that integration tends to lead contagion. Therefore, a study assessing the degree of contagion will likely answer whether commodities integrate and possess (or have less) diversification benefits. If the commodities integrate, they tend to be more dependent. This dependence causes high comovement, even contagion, among commodities; thus, there would be less diversification benefits at all. In financial markets, a number of studies investigate financial networks and financial contagion (see, Aït-Sahalia et al., 2015; Allen & Gale, 2000; Bae et al., 2003; Brusco & Castiglionesi, 2007; Elliott et al., 2014; Kodres & Pritsker, 2002; Leitner, 2005; Pasquariello, 2007). Financial institutions tend to have strong dependencies. Thus, it is intuitive to think that a problem in a financial institution will spread quickly to other financial institutions. Suppose that a bank is suddenly shut down for any reason. Since a bank generally holds many positions with other banks, other banks will be affected and could also experience serious trouble. A recent example is the collapse of Lehman Brothers. As commodity markets become financialized, the question whether commodities integrate arises. Contagion and integration are closely related. Therefore, we can infer the integration of commodity markets by investigating the contagion in commodity markets. Understanding the degree of contagion in commodity markets is essential because we can explore whether the diversification benefits exist in commodity markets. This knowledge of diversification benefits is essential for investors wishing to develop a portfolio containing commodities. There are a number of studies on contagion in commodity markets (for instance, Algieri & Leccadito, 2017; Andriosopoulos et al., 2017; Ayadi et al., 2021; Chevallier & Ielpo, 2013; Ferrer et al., 2018; Han et al., 2015; Ignatieva & Ponomareva, 2017; Ji et al., 2017; Kang et al., 2017; Malik & Umar, 2019; Naeem et al., 2020; Nagayev et al., 2016; Nazlioglu et al., 2013; Reboredo et al., 2014; Yip et al., 2017; Zainudin & Mohamad, 2021). However, most of these studies investigate the contagion between commodities and economic variables. None of these studies investigate the contagion among commodities. While recent work from Han et al. (2015) and Zhou and Huang (2020) examine the price link between commodities, their scope is limited to the contagion between energy and/or agriculture commodities. Chevallier and Ielpo (2013) and Ji et al. (2017) also exclusively focus on risk spillover rather than price contagion among commodities. Likewise, recent papers by Adhikari and Putnam (2019), Cai et al. (2019), Nguyen and Prokopczuk (2019), Yahya et al. (2019), Zhu et al. (2019), and Nguyen et al. (2020) investigate only comovement or dependence (not contagion) among commodities. Umar et al. (2022) examine comovement (but not contagion) between commodities with the focus on energy as the leading series. Balcilar et al. (2021) examine the joint connectedness between oil and other agricultural commodities. This paper fills the research gap by investigating the contagion among commodities. We analyze both comovement and contagion (similar but different concepts) in commodity markets using methods that handle heteroskedasticity bias and resemble the biological definition of contagion. A simple approach to examine a contagion is calculating the correlation among variables. However, this method is not sufficiently robust (at least according to Bae et al., 2003). Bae et al. (2003) argue that it is not appropriate to use correlations to evaluate the different impacts of large returns. The propagation of large returns is hidden in correlation measures because correlation gives equal weight to small and large returns. Thus, a few days of large returns might be hidden by Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 2 of 27 numerous days of small returns. Furthermore, the definition of contagion is not straightforward (Forbes & Rigobon, 2002), and there were at least 124 empirical studies on financial market contagion in different journals from 1990 to 2016 (Seth & Panda, 2018). These findings demonstrate that investigation contagion is not simple. In this article, we perform the contagion in commodity markets by examining the comovement among commodities and then utilize the contagion test. Our methods in examining the comovement closely follow Forbes and Rigobon (2002) by analyzing the unconditional correlation coefficients and Chan et al. (2007) by comparing the correlations between within-category and outside-category commodities. Our contagion tests closely follow Bae et al. (2003) by performing two steps: i) identifying coexceedances (extreme returns) and ii) performing multinomial logit to explain joint occurrence of those coexceedances. However, our work is different from theirs since we focus on the contagion among commodities, while they focus on the contagion across and within countries. This paper contributes to the literature by investigating the contagion among commodities. Assessing the contagion in commodity markets enables us to know not only whether commodities Table 1. Detailed information on the sixteen sampled financialized commodities NO Commodity Contract Category 1Crude Oil (COI) Crude Oil-WTI Spot Cushing U$/BBL Energy 2Heating Oil (HOI) Heating Oil DEU Exc. Tax E/kL Energy 3Natural Gas (NGA) Natural Gas, West Texas U$/MMBTU Energy 4Gold (GOL) Gold Bullion LBM U$/Troy Ounce Metal 5Silver (SIL) Silver, Handy&Harman (NY) U$/Troy OZ Metal 6Copper (COP) LME-Copper Grade A Cash U$/MT Metal 7Platinum (PLA) London Platinum Free Market $/Troy oz Metal 8Palladium (PAL) Palladium U$/Troy Ounce Metal 9Corn (COR) Corn No. 2 Yellow U $/Bushel Grain 10 Soybeans (SOY) US Soybeans KCty U$/BSH Grain 11 Kansas Wheat (WHE) HRW Wheat K.City Terminal U$/BSH Grain 12 Oats (OAT) Oats, No. 2 Milling Minneapolis $/Bu Grain 13 Coffee (COF) Coffee-Brazilian (NY) Cents/lb Soft 14 Cotton (COT) Cotton,1 1/16Str Low - Midl,Memph $/Lb Soft 15 Sugar (SUG) Raw Sugar-ISA Daily Price c/lb Soft 16 Cocoa (COC) Cocoa-ICCO Daily Price US $/MT Soft Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 3 of 27 integrate but also whether commodities have diversification benefits. If the contagion exists, the commodities integrate and have less diversification benefits. On the other hand, if the contagion does not exist, the commodities do not integrate and have diversification benefits by investing among commodities. The remainder of the paper is organized as follows. Section 2 explains the data. Section 3 describes the method. Section 4 discusses the empirical results. Section 5 concludes. 2. Data Our sample includes daily series of sixteen commodity prices. The sixteen commodities were listed in Tang and Xiong (2012). Table 1 describes further details about each commodity used in our sample. We obtained the data from Datastream. Our sample includes the commodities daily series from 1 January 1999 to 1 November 2017. The starting sample period is inspired by the fact that commodity futures have emerged as a popular asset class for many financial institutions (Han et al., 2015; Tang & Xiong, 2012). Tang and Xiong (2012) further noted that commodity markets tended to be fragmented from each other and from outside financial markets before 1999. They also observed that many institutions considered commodities as new asset classes after the 1999ʹs equity market shock. We end our sample in 2017 because we focus on the existence of the long-term impact of exogenous risks in the commodity markets. Those exogenous risks are clearly identified as geopolitical and trade policy uncertainties (see, C. Yang et al., 2022). 3. Method There are a number of contagion and cointegration tests, including Bai et al. (2018), Fry-McKibbin et al. (2019), and Bai et al. (2018) test deals with the nonlinear causality for multivariate variables, and Fry-McKibbin et al. (2019) test deals with coskewness, cokurtosis, and covolatility contagions. Our first focus here is filtering the heteroskedasticity biases in the comovement among commodities. It is not uncommon to find heteroskedasticity in commodity markets (Cavaliere et al., 2015; Liu & Tang, 2011). An appropriate test to filter such biases is Forbes and Rigobon (2002). Our second focus here is to examine financial contagion using the contagion test that is inspired by epidemiology research on contagious diseases. A financial contagion test that is close to the biological contagion analysis is Bae et al. (2003), who use multinomial logistic analysis. 3.1. Comovement The first step of our analysis is calculating the correlation among commodities. Calculating the correlation enables us to examine the linkages among commodities. However, simple correlation coefficients are conditional on market volatility (Forbes & Rigobon, 2002). Therefore, during a high volatility period, estimates of correlation coefficients tend to be biased upward. Forbes and Rigobon (2002) develop a procedure to adjust the bias. Furthermore, Chan et al. (2007) propose a more robust approach to compare the correlations between within-category and outsidecategory commodities. We follow Forbes and Rigobon (2002) in calculating the adjusted correlation coefficient as follows ρA¼ρ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þδ½1ρ2� pwhereas δ¼σh σl1 (1) where ρ A refers to the adjusted correlation coefficient, ρ refers to the unadjusted correlation coefficient, σ h denotes the average standard deviation (volatility) of two commodities during a high variance period, and σ l denotes the average standard deviation (volatility) of two commodities during a low-variance period. The low-variance period refers to the period of relative market stability, and the high-variance period refers to the period of market turmoil directly after a shock Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 4 of 27 or crisis. Following their definition, we defined the high-variance period as the period from 15 September 2008 to 16 October 2012. The high-variance period reflects the highest observed volatility in commodity markets (Han et al., 2015). Then, we use t-tests to evaluate whether there is a significant increase of both unadjusted and adjusted correlation coefficients during the highvariance period as follows: H 0 : ρ l ≤ ρ h H 0 : ρ Al ≤ ρ Ah AND (2) H 1 : ρ l > ρ h H 1 : ρ Al > ρ Ah If both the null hypotheses are not rejected, we conclude that there is no contagion, only interdependence. Then, we follow Chan et al. (2007) in comparing the correlations between within-category and outside-category commodities. First, we calculate the average pairwise correlations between commodity c’s return and the return on each of the other commodities of its category (CAT): ρci;CAT ¼∑cj 2CAT;cj�ciρci;cj N1(3) where ρ ci,cj is the time-series correlation between the return on commodity i (ci) and commodity j (cj), and N denotes the number of commodities in the category. Then, the average pairwise correlation between commodity i’s return and the return of all other commodities in different categories is calculated as follows: Φci;CAT ¼∑cj‚ci ρci;cj KN(4) where K denotes the number of all commodities in our sample. We then calculate the average within-category correlation over all commodities in the sample as follows: �ρCAT ¼∑K i¼1ρci;CAT K(5) The average correlation between a commodity and other commodities in different categories is calculated as follows � ΦCAT ¼∑K i¼1Φci;CAT K(6) Finally, similar to the hypotheses in equation (2), we compare the values of and assess the degree to which the commodity category distinguishes between similar and dissimilar commodities: H 0 : �ρCAT ≤ � ΦCAT (7) Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 5 of 27 H 1 : �ρCAT > � ΦCAT If the null hypothesis is not rejected, we conclude that there is no comovement difference between within-category and outside-category commodities. 3.2. Contagion The second step in our analysis is performing the contagion test. Our contagion test here follows Bae et al. (2003). First, we identify the extreme returns, i.e., exceedances, of the commodities in a category. We define the extreme return, or exceedance, as a return either below (above) the 5 th (95 th ) quantile of the commodity’s return distribution. Note that two exceedances mean one coexceedances, three exceedances mean 2 coexceedances, and so on. We should note that the exceedances in terms of extreme positive or negative returns in a particular commodity can be modeled as a dichotomous variable. However, our analysis investigating the coexceedances to capture contagion among commodities requires classification as a polychotomous variable. A popular approach to estimate the probabilities associated with events captured in a polychotomous variable is the multinomial logistic regression model (Bae et al., 2003). Equation (8) is our model investigating the contagion among commodities. P COECOt¼Xð Þ ¼ 1 1þ∑z y¼1exp βyRETt;CATy � � (8) where P(COECO t = X) refers to the X number of coexceedances (in our case, X equals 0, 1, 2 . . . m), RETt;CATy denotes the average return of commodities in different categories at time t. Then, equation (8) is estimated using the following maximum likelihood expression (Hill et al., 2011; Greene, 2017): LNL ¼∑ q p¼1 ∑ m X¼0 dpXLNðProbðCOECOt¼Xj∑ z y¼1 exp βyRETt;CATy � �ÞÞ (9) where L is the log-likelihood function for a sample of q observations, and d pX refers to an indicator variable where alternative X occurs at observation p. We follow Kleiber and Zeileis (2008) and Bilder and Loughin (2015) for the estimation procedure of the multinomial logit model and the postestimation analysis. Note that if the numbers of coexceedances are only 0 and 1, we use the logistic regression instead. 4. Empirical results Table 2 presents the descriptive statistics of daily price changes for the sixteen commodities. We find that the averages of daily price changes range from 0.0236 percent (cotton) to 0.1970 percent (natural gas). The volatilities of the daily price changes range from 0.0645 (natural gas) to 0.010 (gold). We can see that natural gas has the highest average return followed by crude oil, while that for cotton has the lowest. Note that the averages of daily price changes for the commodities tend to be zero. Regarding risk, as measured in the standard deviation of returns, the natural gas return also has the highest value followed by heating oil, while that for gold return has the lowest. This finding implies that gold was the superior investment asset of the six commodities due to possessing a higher risk reward ratio during the sample period. The skewness and kurtosis measures demonstrate that all the distributions of returns exhibit fat tails. All of the Jarque–Bera statistics for returns are positive and statistically significant, indicating non-normalities. Overall, the descriptive statistics of our sample commodities are similar to other papers on commodities (for example, Algieri & Leccadito, 2017; Han et al., 2015; Nagayev et al., 2016). Table 3 presents the estimated conditional (unadjusted) correlation coefficients, whereas Table 4 presents the estimated unconditional (adjusted—equation (1)) correlation coefficients for Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 6 of 27 Table 2. Descriptive statistics of daily price changes for the sixteen commodities Category Energy Metal Commodity COI HOI NGA GOL SIL COP PLA PAL Mean 0.0597% 0.0416% 0.1970% 0.0364% 0.0419% 0.0452% 0.0296% 0.0446% Std Dev 0.0241 0.0173 0.0645 0.0110 0.0185 0.0165 0.0144 0.0209 Max 0.2371 0.2419 1.6204 0.0766 0.1464 0.1244 0.0879 0.1716 Min −0.1582 −0.2133 −0.6228 −0.0966 −0.1219 −0.0984 −0.1587 −0.1636 Skewness 0.2144 0.7745 4.5598 −0.1588 −0.3404 0.0508 −0.5038 −0.0401 Kurtosis 8.20 45.18 103.94 8.99 8.57 7.56 10.96 8.98 JB-test 5,583 3,64,764 21,02,910 7,371 6,457 4,256 13,176 7,326 # of observation 4,913 4,913 4,913 4,913 4,913 4,913 4,913 4,913 Category Grain Soft Commodity COR SOY WHE OAT COF COT SUG COC Mean 0.0268% 0.0264% 0.0255% 0.0503% 0.0250% 0.0236% 0.0348% 0.0240% Std Dev 0.0187 0.0171 0.0182 0.0250 0.0220 0.0202 0.0213 0.0183 Max 0.1152 0.1339 0.1910 0.2879 0.2377 0.1000 0.1527 0.2138 Min −0.1142 −0.1371 −0.1646 −0.2260 −0.2391 −0.0988 −0.1759 −0.1754 Skewness 0.0028 −0.3154 0.2867 0.7145 0.3413 0.1451 −0.0698 0.2290 Kurtosis 6.08 11.18 10.65 25.58 13.97 4.82 6.66 17.05 JB-test 1,942 13,780 12,045 1,04,762 24,714 695 2,749 40,429 # of observation 4,913 4,913 4,913 4,913 4,913 4,913 4,913 4,913 Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 7 of 27 shown in Tables 8 and 9, respectively. Table 10 reports the t-values for one-tailed t-tests examining whether the cross-commodity unconditional correlation coefficient during the high-variance period is significantly greater than that during the low-variance period (hypotheses in equation (2)). We observe similar apparent patterns here. First, the significant increase in the conditional correlation coefficient during the high-variance period occurs only in 60 (or 50 percent) pairs of commodities. This finding implies that financial contagion occurred only to (slightly above) half of the commodities. This finding also indicates that commodities tend to be resilient assets during highly volatile markets. Our analysis reveals no significant difference between conditional and unconditional correlation coefficients. This finding implies that the heteroskedasticity bias is not significant, at least compared with the bias in the stock market. This finding is consistent with our argument stating that the lower biases in commodities are due to the heterogeneity characteristics. Second, palladium tends to be the most contagious commodity because the 13 (out of other 15) other commodities experience significant increases in the unconditional correlation coefficient during the high variance period when paired together. The next contagious commodity is platinum (12 out of other 15) followed by oat and cotton (10 out of other 15). Third, natural gas and gold (4 out of other 15) followed by coffee (5 out of other 15) tend to be the least contagious commodities. We can conclude that 1) commodities tend to partially integrate, 2) natural gas, gold and coffee are good portfolio diversifiers because they experience few significant increases in the conditional correlation coefficient, even during highly volatile markets, and 3) platinum and palladium are bad portfolio diversifiers because they experience many significant increases in the conditional correlation coefficient during highly volatile markets. There are two practical implications here. First, as a portfolio manager, I would use different commodities as diversifiers because commodities are partially integrated. Second, I might use a commodity to reduce the heteroskedasticity bias in our existing stock portfolio. We can see that the analysis using unconditional correlation coefficients is similar with that of using conditional correlation coefficients. Overall, we can conclude that 1) commodities tend to partially integrate, and 2) natural gas, gold and coffee are good portfolio diversifiers, whereas platinum and palladium are bad portfolio diversifiers. Platinum is not only a bad portfolio diversifier but also demonstrated a speculative bubble (Emekter et al., 2012). Palladium is similar to platinum given their similar chemical characteristics (Kotzé et al., 2019; Rane, 2019). Gold is proven as a safe haven nature because gold protects investors by providing a fall back during harsh investment periods (Pereira et al., 2017). Natural gas and coffee are good portfolio diversifiers because they have small net spillover (Chevallier & Ielpo, 2013). Coffee is also a good portfolio diversifier because it exhibits stationarity after multiple structural breaks (C. H. Yang et al., 2012). We then compare the correlations between within-category and outside-category commodities using Equations (3), (4), (5), (6) and (7). Table 11 reports the conditional and unconditional correlations within a category (as expressed in Equation (3)), outside a category (as expressed in Equation (4)), the average within a category (as expressed in Equation (5)), the average outside a category (as expressed in Equation (6)), and the t-values for one-tailed t-tests examining whether the average within category correlation coefficient is significantly greater than the average outside category correlation coefficient. There are several patterns according to Table 11. First, almost all metals and grains (silver is the exception) have higher correlation coefficients within category than outside category correlation coefficients. Second, on the other hand, all energies have lower within category than outside category correlation coefficients. Third, regarding softs, coffee and cocoa have lower whereas cotton and sugar have higher within category than outside category correlation coefficients. Fourth, although the average within category correlation coefficient is greater than the average Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 14 of 27 Table 8. The estimated adjusted (unconditional) correlation during the high-variance period (from 15 September 2008 to 16 October 2012) Adjusted (unconditional) correlation during high variance period (from 15 September 2008 to 16 October 2012) Comm odity COI HOI NGA GOL SIL COP PLA PAL COR SOY WHE OAT COF COT SUG COC COI HOI −0.0504 NGA 0.0437 −0.1304 GOL 0.2284 −0.0160 0.0420 SIL 0.3078 −0.0491 0.0831 0.6081 COP 0.4618 −0.0800 0.0544 0.2493 0.3764 PLA 0.1902 −0.0782 0.1164 0.4558 0.4562 0.3024 PAL 0.2333 −0.0737 0.1568 0.3504 0.4057 0.3309 0.6998 COR 0.3029 −0.1045 0.1092 0.1160 0.2012 0.2808 0.1419 0.1613 SOY −0.0288 −0.0062 −0.0003 0.0375 0.0821 0.0020 0.1577 0.1361 0.0421 WHE −0.0330 −0.0304 0.0820 0.0691 0.0729 0.0083 0.1560 0.1556 0.0379 0.5203 OAT 0.1263 −0.0828 0.0743 0.0710 0.1163 0.1315 0.1550 0.1300 0.4060 0.1439 0.1213 COF 0.0718 −0.0231 0.0629 0.0918 0.1110 0.0577 0.1485 0.1608 0.0230 0.2322 0.2389 0.0998 COT 0.2770 −0.0810 0.0286 0.1296 0.1807 0.2820 0.1386 0.1403 0.2597 −0.0285 0.0007 0.1911 0.0414 SUG 0.2512 −0.0352 0.0764 0.0645 0.1562 0.2441 0.0911 0.1176 0.2445 0.0537 0.0144 0.1334 0.1018 0.1858 COC 0.0428 0.0204 0.0030 0.0914 0.0734 0.0350 0.1153 0.0974 0.0246 0.1680 0.1448 0.0814 0.1766 0.0498 −0.0148 Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 15 of 27 Table 9. The estimated adjusted (unconditional) correlation during the low-variance period (from 4 January 1999 to 12 September 2008 AND from 17 October 2012 to 1 November 2017) Adjusted (unconditional) correlation during low variance period (from 4 January 1999 to 12 September 2008 AND from 17 October 2012 to 1 November 2017) Comm odity COI HOI NGA GOL SIL COP PLA PAL COR SOY WHE OAT COF COT SUG COC COI HOI 0.0022 NGA 0.0335 0.0038 GOL 0.1053 0.0076 0.0507 SIL 0.1296 0.0003 0.0518 0.6198 COP 0.1435 −0.0003 0.0093 0.2340 0.3038 PLA 0.0673 −0.0230 0.0455 0.3747 0.3120 0.1597 PAL 0.0429 0.0076 0.0147 0.2610 0.2462 0.1496 0.4948 COR 0.0941 0.0035 0.0180 0.0637 0.0999 0.0719 0.0722 0.0486 SOY 0.0144 −0.0020 0.0504 0.0298 0.0419 0.0255 0.0647 0.0346 −0.0008 WHE 0.0122 0.0157 0.0216 0.0193 0.0285 0.0157 0.0306 0.0344 0.0115 0.2815 OAT 0.0346 0.0198 0.0235 0.0391 0.0474 0.0495 0.0254 −0.0010 0.2282 0.0096 0.0056 COF 0.0647 0.0227 0.0240 0.0454 0.0557 0.0020 0.0652 0.0641 0.0286 0.0480 0.0635 0.0401 COT 0.0793 0.0151 0.0358 0.0579 0.0741 0.0803 0.0466 0.0298 0.1142 0.0006 0.0157 0.0452 0.0416 SUG 0.0792 0.0061 0.0176 0.0700 0.0738 0.0773 0.0616 0.0563 0.0493 0.0321 0.0178 0.0499 0.0642 0.0669 COC 0.0229 0.0146 −0.0253 0.0231 0.0474 0.0001 0.0221 0.0337 0.0061 0.0303 0.0199 0.0248 0.0702 0.0174 0.0101 Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 16 of 27 Table 10. The t-values for one-tailed t-tests examining whether the cross-commodity unconditional correlation coefficient during the high-variance period is significantly greater than that during the low-variance period Test Statistics Comm odity COI HOI NGA GOL SIL COP PLA PAL COR SOY WHE OAT COF COT SUG COC COI HOI 1.21 NGA 0.24 3.11 GOL 2.93 0.55 0.20 SIL 4.33 1.14 0.73 0.43 COP 8.19 1.84 1.04 0.37 1.90 PLA 2.89 1.28 1.65 2.26 3.92 3.48 PAL 4.49 1.88 3.31 2.28 4.13 4.46 7.48 COR 5.04 2.50 2.11 1.22 2.39 4.99 1.63 2.63 SOY 1.00 0.10 1.17 0.18 0.93 0.54 2.17 2.36 0.99 WHE 1.04 1.06 1.40 1.15 1.03 0.17 2.92 2.83 0.61 6.63 OAT 2.13 2.37 1.18 0.74 1.60 1.91 3.02 3.04 4.58 3.12 2.68 COF 0.16 1.06 0.90 1.08 1.28 1.29 1.94 2.26 0.13 4.35 4.15 1.38 COT 4.73 2.22 0.17 1.67 2.50 4.83 2.14 2.57 3.48 0.67 0.35 3.42 0.01 SUG 4.09 0.95 1.36 0.13 1.93 3.96 0.68 1.43 4.62 0.50 0.08 1.94 0.87 2.79 COC 0.46 0.13 0.65 1.58 0.60 0.80 2.16 1.48 0.43 3.21 2.90 1.31 2.50 0.75 0.57 Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 17 of 27 outside category correlation coefficient, the one-tailed t-tests reveal that the differences are not statistically significant for both conditional and unconditional correlation coefficients. We can conclude that 1) metal and grain commodities tend to integrate, whereas energy commodities do not tend to integrate; 2) the integration of soft commodities is inconclusive; 3) there is no significant difference of comovement between within a category and outside a category in commodity markets; 4) (again) the heteroskedasticity bias is not significant for commodities. Our results in Table 11 can be explained as follows. First, recall that commodities are heterogeneous (Ausubel, 2006; Fleurbaey & Tadenuma, 2007; Pereira et al., 2017). Second, metal commodities offer much less diversification potential for equity investors (Pereira et al., 2017). Third, grain commodities have spillover risks (Ji et al., 2017) and the highest directional spillover effects (Chevallier & Ielpo, 2013). This property of commodities is due to seasonality factors (Pereira et al., 2017) or is highly dependent on climate (Adhikari & Putnam, 2019). Fourth, both metal and grain commodities have strong correlations (Cai et al., 2019). Fifth, energy commodities have different behaviors on spillover effects (Uddin et al., 2018). Sixth, we should note that i) soft commodities showed no jump comovement and ii) jumps for many soft commodities are even negatively correlated to Goldman Sachs Commodity Index jumps (Nguyen & Prokopczuk, 2019). Seventh, our insignificant difference of comovement between within category and outside category commodity markets is somewhat significant in light of the results of Adhikari and Putnam (2019) who also reported statistical insignificance. The next step is performing a multinomial logit analysis. First, the exceedance and coexceedances were identified as defined in section 3.2. We then estimated a multinomial logit model as expressed in Equation (8). Recall that if the numbers of coexceedances are only 0 and 1, we use logistic regression instead. Table 12 reports the multinomial logit (or logit) regression results for positive coexceedances in the four different commodity categories. According to Table 12, slightly more covariates (14 out of 27—excluding intercepts) tend to be statistically significant. This finding demonstrates that the probability of positive coexceedances is somewhat affected by the other categories price changes in the commodity markets. We can also see that softs tend to be contagious to metals and grains, metals tend to be contagious to energies, and energies and grains tend to be contagious to softs. However, energies do not tend to be contagious to grains. Table 13 reports the multinomial logit (or logit) regression results for negative coexceedances in the four different commodity categories. According to Table 13, most of the covariates (17 out of 27—excluding intercepts) tend to be statistically significant. This finding demonstrates that the probability of negative coexceedances is affected by the other categories price changes in the commodity markets. We can also see that softs tend to be contagious to grains, metals tend to be contagious to energies, and grains tend to be contagious to softs. However, energies do not tend to be contagious to grains. Overall, we document that commodity price changes tend to affect the probability of both positive and negative coexceedances. We also observe that a positive daily change tends to increase the probability of positive coexceedances, and a negative daily change tends to increase the probability of negative coexceedances. This finding indicates that contagion exists in both directions, i.e., positive and negative extreme events. Therefore, there is a contagion in the commodity markets. As a portfolio manager, I would need to carefully evaluate the commodities’ diversification benefits and contagion costs as financial instruments. On one side, commodities bring diversification benefits. On the other side, commodities have contagion effects. Further analysis based on AIC values and the multinomial (or merely) logit models demonstrate that the contagion is stronger for negative coexceedances. This finding implies that commodities tend to be contagious in negative rather than positive extreme returns. This asymmetric contagion is somewhat similar to that reported by Amonlirdviman and Carvalho (2010). They find that Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 18 of 27 Table 11. The conditional and unconditional correlations within a category (as expressed in equation (3)), outside a category (as expressed in equation (4)), the average within a category (as expressed in equation (5)), the average outside a category (as expressed in equation (6)), and the t-values for one-tailed t-tests examining whether the average within category correlation coefficient is significantly greater than the average outside category correlation coefficient Conditional correlations Category Commodity Equation (3) Equation (4) Eq (5) Eq (6) Within Outside Average Within Average Outside Test Statistics Category Category Category Category Energy COI 0.0134 0.1185 0.1701 0.1045 0.17 HOI −0.0157 −0.0064 NGA 0.0079 0.0371 Metal GOL 0.4309 0.0635 SIL 0.4582 0.7535 COP 0.2915 0.0857 PLA 0.4173 0.0694 PAL 0.3721 0.0646 Grain COR 0.1088 0.1005 SOY 0.1441 0.0409 WHE 0.1470 0.0418 OAT 0.1219 0.0516 Soft COF 0.0638 0.0536 COT 0.0604 0.0848 SUG 0.0614 0.0768 COC 0.0386 0.0357 (Continued) Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 19 of 27 Table 11. (Continued) Conditional correlations Category Commodity Equation (3) Equation (4) Eq (5) Eq (6) Within Outside Average Within Average Outside Test Statistics Uncon ditional correlations Category Commodity Eq (3) Eq (4) Eq (5) Eq (6) Within Outside Average Within Average Outside Test Statistics Category Category Category Category Energy COI 0.0131 0.1052 0.1535 0.0933 0.16 HOI −0.0157 −0.0059 NGA 0.0071 0.0364 Metal GOL 0.3849 0.0578 SIL 0.4001 0.6555 COP 0.2464 0.0738 PLA 0.3780 0.0645 PAL 0.3368 0.0597 Grain COR 0.1015 0.0867 SOY 0.1330 0.0390 WHE 0.1346 0.0380 OAT 0.1156 0.0500 Soft COF 0.0664 0.0551 COT 0.0562 0.0745 (Continued) Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 20 of 27 Table 11. (Continued) Conditional correlations Category Commodity Equation (3) Equation (4) Eq (5) Eq (6) Within Outside Average Within Average Outside Test Statistics SUG 0.0585 0.0695 COC 0.0395 0.0332 Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 21 of 27 Table 12. Result of the multinomial logit (or logit) regression results for positive coexceedances in the four different commodity categories. The asterisk indicates a significant covariate at the *) 10 percent significance level, **) 5 percent significance level, ***) 1 percent significance level Multinomial logit regression equation (8) PðCOECOt¼XÞ ¼ 1 1þP z y¼1 expðβyRETt;CATy Þ Positive Coexceedances Coexceedances Energy (using Logit) Metal Grain Soft (using Logit) Coef t-Stat Coef t-Stat Coef t-Stat Coef t-Stat 1 Intercept −7.76 −11.57 ***) −4.30 −33.11 ***) −5.14 −26.30 ***) −6.55 −16.68 ***) Energy 6.79 2.01 *) 4.16 0.91 −8.10 −0.62 ***) Metal 68.64 2.84 ***) 27.29 2.01 *) 55.37 3.00 Grain 4.59 0.10 22.64 2.37 **) 44.14 2.07 **) Soft 34.51 0.74 29.29 2.85 ***) 26.64 1.71 *) 2 Intercept −5.97 −19.95 ***) −7.09 −13.69 ***) Energy 5.90 0.99 −19.06 −1.23 Metal −28.68 −0.88 Grain 27.59 1.52 Soft 65.62 4.00 ***) 67.78 2.46 **) 3 Intercept −6.55 −16.66 ***) −9.40 −6.19 ***) Energy 10.46 2.52 **) 2.75 0.10 Metal Grain 21.66 0.87 33.32 0.56 Soft 68.62 3.31 ***) 92.76 1.76 *) 4 Intercept −8.20 −9.63 ***) Energy 10.09 1.54 Metal Grain 28.18 0.60 Soft 88.90 2.74 ***) AIC 64.52 1,195.24 509.41 152.76 Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 22 of 27 Table 13. Result of the multinomial logit (or logit) regression results for negative coexceedances in the four different commodity categories. The asterisk indicates a significant covariate at the *) 10 percent significance level, **) 5 percent significance level, ***) 1 percent significance level Multinomial logit regression equation (8) PðCOECOt¼XÞ ¼ 1 1þP z y¼1 expðβyRETt;CATy Þ Negative Coexceedances Coexceedances Energy (using Logit) Metal Grain Soft (using Logit) Coef t-Stat Coef t-Stat Coef t-Stat Coef t-Stat 1 Intercept −7.58 −12.37 ***) −4.34 −32.33 ***) −4.86 −28.28 ***) −5.80 −21.60 ***) Energy −5.49 −1.07 −2.77 −0.44 2.80 0.33 Metal −78.45 −4.02 ***) −33.09 −3.15 ***) −36.77 −2.84 ***) Grain −21.56 −0.74 −30.31 −3.33 ***) −61.14 −4.53 ***) Soft −24.78 −0.69 −45.90 −4.64 ***) −41.11 −3.20 ***) 2 Intercept −5.51 −23.07 ***) −7.82 −11.81 ***) Energy −14.24 −2.09 **) −8.23 −0.69 Metal −61.28 −3.18 ***) Grain −41.50 −3.09 ***) Soft −53.40 −3.50 ***) −97.34 −3.68 ***) 3 Intercept −6.33 −17.83 ***) Energy −21.41 −2.49 **) Metal Grain −33.16 −1.44 Soft −27.74 −1.04 4 Intercept −8.34 −9.36 ***) Energy 6.10 0.33 Metal Grain −67.89 −1.98 *) Soft −81.40 −2.08 **) AIC 81.51 1,295.99 590.49 270.73 Chalid & Handika, Cogent Economics & Finance (2022), 10: 2064079 https://doi.org/10.1080/23322039.2022.2064079 Page 23 of 27