The network connectedness of volatility spillovers across global futures markets

Physica A 526 (2019) 120756

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The network connectedness of volatility spillovers across global futures markets ∗

Sang Hoon Kang a,b , , Jang Woo Lee a a b

Department of Business Administration, Pusan National University, Busan, Republic of Korea School of Commerce, University of South Australia, Australia

highlights • • • •

We analyze the dynamic volatility spillovers between global futures markets. We find the highest level of spillover index during recent financial crises. FTSE 100 index futures is the largest transmitter of volatility spillover shocks. The direction and intensity of network connectedness are sensitive to financial and economic events.

article

info

Article history: Received 20 September 2018 Received in revised form 18 January 2019 Available online 9 April 2019 JEL classification: G14 G15 Keywords: Volatility spillover Network connectedness Global futures markets Financial crises

a b s t r a c t This paper analyzes the dynamic volatility spillovers and network connectedness between stock index and commodity futures markets using the multivariate DECOFIGARCH model and the spillover index method of Diebold and Yilmaz (2014). We estimate a positive equicorrelation between the index and commodity futures and find the highest level of spillover index during the 2008–2009 global financial crisis and 2010–2012 European sovereign debt crisis. Further, we adopt both static and dynamic spillover approaches to identify the net spillover transmitter or receiver across global futures markets. We also measure the directional spillover and assess the net pairwise spillover across global futures markets. Finally, our network connectedness provides specific information on the net pairwise connectedness and intensity of connectedness in different sub-periods. © 2019 Elsevier B.V. All rights reserved.

1. Introduction The recent financial crises have renewed interest in complex financial system, through market connectedness [1– 3]. In fact, connectedness is a crucial component of systemic risk [4,5].1 The systemic risk arise through a high degree of interconnectedness across the financial institutions, and a financial default of single institution may cause other institutions’ failure, with the chain reaction leading to collapse of an entire financial system [6,7]. Hence, the measures of systemic risk help us understand the contributions of financial institutions or markets to overall financial system risk. The network connectedness is an important tool to measure the systemic risk in recent complex financial systems [8–10]. The network topology also provides an ‘‘early warning system’’ for possible upcoming crises, and a financial system to track ∗ Correspondence to: Department of Business Administration, Pusan National University, Jangjeon2-Dong, Geumjeong-Gu, Busan 609-735, Republic of Korea. E-mail addresses: [email protected] (S.H. Kang), [email protected] (J.W. Lee). 1 Diebold and Yilmaz [4] stated that, to minimize portfolio risk, optimal portfolio allocation requires awareness and measurement of connectedness. https://doi.org/10.1016/j.physa.2019.03.121 0378-4371/© 2019 Elsevier B.V. All rights reserved.

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the progress of extant crises [11]. Network visualizes the propagation path of volatility shocks across financial institutions and markets [12–15]. Thus, the knowledge of market connectedness has increasingly become more important to measure entire systemic risk due to increasing regulatory and fundamental convergence across financial markets, confounding diversification potential for investors and magnifying financial market risk [16,17]. Recent finance and economics studies including econophysics literature are interested in proposed a variety of methodologies to measure the complex network that exists in financial markets (see [18–21]). In earlier studies, Eom et al. [22] used cross-correlations between stock prices and proposed the minimal spanning tree approach to measure network topology across international stock markets. [23] introduced the conditional value-at-risk (CoVaR) method, which measures the value-at-risk (VaR) of financial institutions conditional on other institutions experiencing financial distress. Billio et al. [24] applied principal components analysis and pairwise Granger-causality networks to measure systemic risk in the financial industry. Kocheturov et al. [25] proposed the cluster structures and the P-median problem approaches which allow us to compare the cluster structure between stock markets. Diebold and Yilmaz [4] used the spillover index approach to measure both system-wide and pairwise connectedness in US financial firms. Most recently, using the Granger-causality network approach, Baumöhl et al. [15] analyzed the volatility network across international stock markets. Also, Huang and Wand [26] also employed the same method to construct the dynamic return spillovers among Chinese financial institutions. Shahzad et al. [27,28] introduced a bivariate cross-quantilogram approach to examine the net transmitters and receivers of spillovers in complex financial networks. Qiu et al. [29] calculated the cross-correlation matrices and constructed the market state network among the 30 stocks of Dow Jones Industrial Average (DJIA). Li et al. [30] analyzed the network topology to measure systemic risk in Peer-to-Peer lending markets. In order to measure the network connectedness, many studies have used the VAR Granger-causality approach, the cross-correlation approach, the cross-quantilogram approach and multivariate correlation methods, and others [14,18]. Nevertheless, these models do not capture the direction of spillovers across assets and markets [31,32]. Diebold and Yilmaz [4,33] spillover index method allow measurement of the direction, intensity, and pairwise net direction of spillovers based on forecast-error-variance decompositions (FEVDs) from vector autoregressions (VARs) and easily construct the matrix of a weighted directed network in the system. In this context, this paper utilizes the spillover index approach of Diebold and Yilmaz [4] which assess the magnitude and direction of connectedness across financial variables over time, and hence it provides an alternative way to check the decoupling hypothesis (contagion effect) across global futures markets. In recent years, this spillover index approach has been widely used to examine the connectedness network across different assets [34,35], institutions [4,33], CDS sectors [27] and markets [36–38]. Nevertheless, a few studies have explored the network connectedness across global futures markets, while accounting for recent financial crises. In this context, this study analyzes the network connectedness to understanding the transmission of risk spillover across global futures markets. Our study contributes to the literature in several ways. First, this study uses a multivariate equicorrelation (DECO)Fractionally Integrated GARCH (FIGARCH) model to assess time-varying correlations between global index and commodity futures markets. The FIGARCH model allows us to capture the long memory property in volatility. The evidence of long memory indicates the predictability of futures prices against the validity of efficient market hypothesis. Second, The DECO model is, unlike the multivariate correlation matrix method, allow us correlations to be set equal across all market pairs providing identification of the co-movement of a group of markets with a single dynamic correlation coefficient (equicorrelation) [39,40]. This makes it possible to capture time-variations in the linkages of all included markets over the period of study. Third, this study investigates net and directional connectedness within the network topology of the spillover framework. The spillover index approach provides accurate information on the direction and intensity of risk spillover to investors, thus aiding precise asset allocation and investment decisions. Fourth, we analyze a rolling sample approach to detect the time-varying dynamics of the spillover index and observe how the recent financial crises may have affected the intensity and direction of volatility spillovers between index and commodity future markets. The rolling sample approach allows us to examine the risk spillovers over time without having to use a cutoff date to create subsamples. Similarly, possible economic and financial events must be considered when analyzing a financial time series because arbitrarily chosen sub-samples or non-overlapping intervals cannot capture this dynamic. Finally, we emphasize the connectedness in each market as a measure of how volatility shocks are transmitted across these markets. That is, we provide a visualization of the complex network to understand the net pairwise connectedness across global index and commodity futures markets. From a practical point of view, our network connectedness informs the price discovery and has profound importance to portfolio managers. Our result provides more useful and specific information for portfolio managers in constructing an international portfolio that can achieve the best possible diversification benefits. We found a significant dynamic equi-correlation among the considered markets which amplified during the 2008–2009 GFC and 2010–2012 ESDC, supporting the market contagion among the global futures markets. Subsequently, the lower dynamic equi-correlations are observed in 2013– 2014, indicating an opportunity of portfolio benefits between index and commodity futures. Second, we specifically measure the net transmitters (recipients) of volatility spillover shock among global equity and commodity futures markets. Our result shows that the UK and US futures index markets are the most important contributors of volatility spillover shock of the global futures markets. Our findings reinforce the importance of the UK and US equity market within our system and provide significant policy implication for the investors. Third, we conclude that adding commodity futures reduce the magnitude of the total volatility spillover effect and provides diversification benefits in the index futures portfolio. Finally,

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we show a network of net pairwise connectedness, focusing on financial and economic events. Our result highlights that economic and financial crises intensify the spillovers across commodity and financial markets. We contribute and extend the related literature in the following two ways. First, we examine the direction and magnitude of volatility spillover indexes which helps to know the transmission of shocks across index-commodity futures markets. Thus, institutional and individual investors can have better understanding about market dynamics for portfolio diversification and efficient asset allocations. Any impending shock to the equity futures markets can lead to risk-off strategy where investors sell off their risky assets and move to safer assets like commodities. Second, our examination of network connectedness across futures markets through net directional approach using network connectedness disentangles the strength of a particular market and asset whether it is a recipient (transmitter) of shocks from (to) others. We emphasize the importance of net pairwise network connectedness in each market as a measure of how shocks are transmitted across these markets. That is, we provide a visualization of the complex network to understand the net pairwise directional connectedness among global futures markets. The remainder of this study is organized as follows. Section 2 discusses the methodology used in this study. Section 3 describes the data and presents the preliminary analysis. In Section 4 we report and discuss the results, while Section 5 provides concluding remarks. 2. Empirical method 2.1. The DECO-FIGARCH model In this section, we estimate the multivariate DECO model, allowing us to assess the average of the conditional correlations set equal to the average of all correlation pairs [41]. In the first stage, we estimate the univariate fractionally integrated GARCH (FIGARCH) model and we presume that the index return (rt ) is expressed by an autoregressive moving average (ARMA (1,1)) model as follows: rt = µ + ϕ1 rt −1 + εt + θ1 εt −1 , t ∈ N with εt = zt

√

ht ,

(1)

where ϕ1 is the AR(1) parameter, θ1 is the MA(1) parameter, zt are assumed under the Student-t distribution (zt ∼ ST (0, 1, v)), and ht is the conditional variance. The FIGARCH(1, d, 1) model of Baillie et al. [42] is defined as follows: ht = ω + β1 (L) ht + 1 − (1 − β1 L)−1 (1 − φ L) (1 − L)d εt2 ,

[

]

(2)

where, ω > 0, φ1 , β1 < 1, 0 ≤ d ≤ 1. d is the fractional integration parameter and L is the lag operator. For 0 ≤ d ≤ 1 , the FIGARCH process captures persistence of shocks to conditional volatility. The fractional differencing operator (1 − L)d is defined as:

(1 − L)d =

∞ ∑ k=0

Γ (k − d) Lk Γ (−d) Γ (k + 1)

(3)

In the second stage, the conditional correlation is estimated using the transformed return residual, which is estimated from the univariate FIGARCH (1, d, 1) model. The conditional variance–covariance matrix (Ht ) can be written as: Ht = Dt Rt Dt ,

(4)

where Rt denotes the (n × n) symmetric matrix of dynamic conditional correlation, and Dt = diag

1/2 h11,t

(

,...,

1/2 hNN ,t

)

, h11,t

represents the conditional variances of each return series. The dynamic conditional correlation matrix Rt decomposes to: Rt = (diagQt )−1/2 Qt (diagQt )−1/2 ,

(5)

Qt = (1 − λ1 − λ2 ) Q + λ1 ut −1 u′t −1 + λ2 Qt −1 ,

(6)

where Qt defines the covariance matrix of the standardized residuals ut = ui,t , . . . , uk,t . Q = cov ut , ut = E ut , ut is the n × n unconditional covariance matrix of ut , while λ1 and λ2 are non-negative scalars, and λ1 +λ2 < 1. The framework of the DECO model is derived from the consistent DCC (cDCC) model of Aielli [43] by the correlation-driving process:

(

(

∗1/2

∗1/2

Qt = (1 − λ1 − λ2 ) Q + λ1 Qt −1 ut −1 u′t −1 Qt −1

)

+ λ2 Qt −1 ,

)

(

) ′

(

) ′

(7)

Using the cDCC framework, Engle and Kelly [41] document that ρt is calculated from the off-diagonal elements of conditional correlation matrix Qt . This model is named the dynamic equicorrelation (DECO). The equicorrelation is specified as [see 44]:

ρtDECO =

1 n (n − 1)

A′n RcDCC An − n = t

(

)

2

n−1 n ∑ ∑

n (n − 1)

i=1 j=i+1

√

qij,t

qii,t qjj,t

,

(8)

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where qij,t = ρtDECO + aDECO ui,t −1 uj,t −1 − ρtDECO + bDECO qij,t − ρtDECO , which is the (i, j) th element of matrix Qt from the cDCC model. The scalar equicorrelation is used to estimate the conditional correlation matrix:

(

)

(

)

Rt = (1 − ρt ) In + ρt An ,

(9)

where An is the n × n matrix of ones, and In is the n-dimensional identity matrix. This process allows us to generate a single time-varying correlation coefficient in large sets of assets. 2.2. Spillover index To analyze directional volatility spillover across global futures markets, we utilize the generalized VAR of the spillover index of Diebold and Yilmaz [4] as follows: Xt =

P ∑

Ψi Xt −1 + εt ,

(10)

i=1

where Xt is an N × 1 vector of endogenous variables, Ψi are N × N autoregressive coefficient matrices, and εt ∼ (0, Σ ) is a vector of error terms with an i.i.d. process. The above VAR process can be rewritten as a moving average process: Xt =

∞ ∑

Zi εt −1 ,

(11)

i=1

∑P

where the N × N coefficient matrix es Zi are recursively defined as Zi = k=1 Zi−k , with Z0 being the N × N identity matrix, and Zi = 0 for i < 0. We analyze the generalized version of H-step-ahead forecast-error variance decomposition as follows: g cij

)2 ( ∑ σjj−1 Hh=−01 e′i Zh Σ ej (H ) = ∑H −1 ( ) , ′ ′ h=0 ei Zh Σ Zh ej

(12)

where the term Σ is a non-orthogonalized covariance matrix of errors corresponding to the VAR system. The term σjj is a vector of standard deviations of the error term for the jth equation and ei is an N × 1 vector, which has 1 as the ith element and zero as the other elements. In the connectedness decomposition table, CiH←j indicates pairwise directional spillovers from the futures market j to another futures market i as follows: g

CiH←j = cij (H ) ,

(13)

The directional connectedness from all other futures markets to the futures market i are calculated as: CiH←· =

N ∑

g

cij (H),

(14)

i,j=1 j̸ =i

Conversely, the directional connectedness to others from j are calculated as: H C·← i =

N ∑

g

cji (H)

(15)

i,j=1 j̸ =i

We can also define net directional connectedness as: H H CiH = C·← i − Ci←· ,

(16)

Finally, total connectedness (system-wide connectedness) is the ratio of the sum of the ‘‘To’’ (‘‘From’’) elements of the variance decompositions matrix to the sum of all elements: CH =

N 1 ∑

N

g

cij (H).

(17)

i,j=1 j̸ =i

To build visual network connectedness, we interpret our connectedness table as the adjacency matrix of a weighted directed network [4,33]. The elements of the adjacency matrix are our pairwise directional connectedness, CiH←j ; the row sums of the adjacency matrix (node in-degrees) are our total directional connectedness ‘‘From’’, CiH←· ; and the column H sums of the adjacency matrix (node out-degrees) are our total directional connectedness ‘‘To’’, C·← i.

S.H. Kang and J.W. Lee / Physica A 526 (2019) 120756

Fig. 1. Dynamics of the global futures market prices. Note: The MS-DR model highlight the excess volatility in the shaded areas [Regime 1].

5

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Fig. 1. (continued).

3. Data and preliminary analysis 3.1. Data We use daily price data for twelve market index futures (Australia, Brazil, France, Germany, Hong Kong, India, Japan, Korea, Singapore, Spain, UK, and US). We also consider two commodity futures markets, WTI crude oil and gold futures contracts. The details of sample data are given in Appendix.2 The study period is January 1, 2002 to July 19, 2018, which covers several turbulent periods and crises, including the 2008–2009 Great Financial Crisis (GFC) and the 2010–2012 European Sovereign Debt Crisis (ESDC).3 The data for all series are extracted from DataStream. Unlike equity index, index futures provide a high speed of information transmission due to its greater leverage, lower transaction costs, and ability

2 According to 2017 FIA survey, these futures are the most active volume trading contracts in the world futures Exchanges. (https://marketvoice. fia.org/sites/default/files/uploaded/MARCH_2017_VOLUME_SURVEY.pdf) 3 We consider volatility jumps that are typically caused by economic and financial events such as the 2008–2009 GFC and the 2009–2012 ESDC. Such events might have taken place during the sample period and have influenced the direction or intensity the dependence across equity index and commodity futures markets.

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Table 1 Descriptive statistics of global equity and commodity futures markets.

BOVESPA CAC40 DAX FTSE100 HANGSENG IBEX35 KOSPI200 NIFTY NIKKEI225 S&P500 SPI200 Strait times WTI Gold

Mean(%)

Max.

Min.

Std. dev.

Skewness

Excess Kurtosis

Jarque– Bera

Q(30)

Q2 (30)

ADF

KPSS

ARCHLM(10)

0.00276 0.00365 0.01714 0.00880 0.02969 0.01291 0.02801 0.04635 0.01804 0.02069 0.02020 0.01568 0.02769 0.03441

7.8723 6.7124 7.4452 5.4437 6.6695 6.3624 7.2308 9.5267 7.7977 6.3931 4.5405 4.7977 10.779 6.9042

−8.0414 −6.7216 −6.3284 −6.7481 −10.519 −7.5929 −7.2553 −11.67 −6.8094 −7.3791 −4.5688 −6.4426 −9.235 −6.8776

1.1978 0.9805 1.0063 0.7997 0.9952 1.018 0.9849 1.0294 0.9871 0.8028 0.6965 0.7637 1.5879 0.7950

−0.2612 −0.1993 −0.3172 −0.2903 −0.3874 −0.2593 −0.3882 −0.6881 −0.4075 −0.5541 −0.3616 −0.2467 −0.1626 −0.4246

2.7813 4.4685 4.3954 6.6569 6.8982 4.1127 4.5112 12.185 4.0694 8.7822 4.3007 5.8928 3.5509 5.2230

1434.6*** 3605.1*** 3532.7*** 7998.2*** 8631.3*** 3078.0*** 3753.4*** 26934.*** 3085.2*** 14035.*** 3406.8*** 6263.7*** 2277.5*** 5015.6***

556.9*** 432.0*** 438.9*** 398.0*** 432.4*** 431.3*** 449.8*** 297.0*** 502.7*** 300.9*** 491.2*** 443.8*** 517.0*** 455.4***

8272.*** 7116.*** 8131.*** 8988.*** 6052.*** 4820.*** 7162.*** 1949.*** 4311.*** 12281.*** 9059.*** 6828.*** 5695.*** 1829.***

−31.19*** −31.28*** −29.78*** −30.56*** −30.58*** −31.23*** −30.15*** −29.35*** −29.73*** −30.47*** −31.18*** −29.25*** −28.59*** −28.77***

0.0866 0.1082 0.1636 0.0634 0.0364 0.0486 0.1082 0.2599 0.1463 0.2184 0.0874 0.1122 0.2346 0.2944

182.37*** 135.02*** 157.62*** 181.93*** 155.54*** 133.18*** 204.70*** 88.634*** 120.22*** 256.57*** 194.23*** 208.44*** 107.66*** 84.792***

The asterisk*** denotes rejection of the null hypotheses of normality, no autocorrelation, unit root, stationarity, and conditional homoscedasticity.

to short-sell, among other factors [45]. Both oil and gold futures are undoubtedly the most valuable commodities and exert significant influence on global economy and cross-market investment. Fig. 1 below plots the dynamic prices of global futures for each of the above futures indices, together with crude oil and gold for the sample period. We apply the Markov-switching-dynamic regression (MS-DR) to detect two tranquil and volatile regimes in the price series that allows one to identify the beginning and the end of each phase of the financial crises, which is of great importance when one deals with the cross-futures market spillovers issue.4 The shaded regions [Regime 1] show the regimes of excess volatility according to the MS-DR and show the effects of the 2002 dotcom crisis, 2008–2009 GFC, and 2010–2012 ESDC. Comparing the two commodity markets shows that oil is more volatile than gold. These events took place during the sample period and may have influenced the direction or intensity of interconnectedness across these futures markets [2,15,27]. In this context, we further examine the time-varying volatility spillovers and network connectedness between the equity index and commodity futures markets. 3.2. Preliminary analysis We calculate continuously compounded daily returns by taking the difference in the logarithm percentage of two consecutive prices. To avoid biases from different trading time across borders (i.e. nonsynchronous trading and short-term correlations from noise), we apply the average two-day rolling returns to account for different market trading time [48]. Table 1 below provides descriptive statistics of daily futures returns and unit root tests, for the index and commodity futures markets. For the equity index futures markets, the highest average daily returns are observed for NIFTY (0.04634), while BOVESPA has the lowest average daily returns (0.00276). For the volatility, the BOVESPA shows the highest risk while the SPI records the lowest return volatility. As for the commodity futures markets, the WTI crude oil is more volatile than the gold futures. Looking at the skewness statistics, all of the equity index, WTI oil, and gold futures returns exhibit significant asymmetry since the skewness statistic is negatively signed for all considered series. Furthermore, the kurtosis is higher than three which is associated with the normal distribution, thereby documenting the presence of a leptokurtic distribution of all of the return series. The Jarque–Bera test confirms that all return series are not normally distributed. According to the ADF unit root statistics test, and the stationarity test of the KPSS test results, all return series are stationary. Further, the Ljung–Box Q(30) and Q2 (30) tests for serial correlation of residuals and square residuals, respectively, as well as the ARCH effect in the return series by applying the ARCH LM(10) tests. The results highlight the presence of both serial correlation and the ARCH effect in all cases. Therefore, we apply a FIGARCH model to capture some stylized facts, such as fat-tails, clustering volatility and persistence for index and commodity futures returns. Fig. 2 displays the heat map of Pearson’s correlation matrix among global futures markets. Note that the color indicates the strength of the correlation, from blue (positive) to red (negative). As shown in Fig. 2, the global futures returns have a significantly strong and positive correlation, indicating the connectedness among global futures markets. In particular, the Eurozone futures markets (IBEX35, FTSE 100, CAC 40, DAX) are significantly related to one another. For commodity futures markets, gold is negatively and weakly correlated with the most futures markets, implying that gold futures as a refuge asset provide a possible diversification benefit for investors.

4 See Hamilton [46] and Hamilton and Susmel [47] for details on the MS-DR model.

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Fig. 2. Heat map of the correlation matrix. Note: This figure shows a visual correlation matrix across global futures markets. The color boxes indicate the strength of the correlation. Blue indicates a positive correlation, while red indicates a negative correlation.

4. Empirical results 4.1. Estimation of DECO-FIGARCH model Table 2 reports the estimate results of the multivariate DECO-FIGARCH (1, d, 1) for global index and commodity futures markets. In Panel A, the moving average parameter is statistically significant at the 1% level for all futures returns. Both ARCH (φ1 ) and GARCH (β1 ) terms are significant. More importantly, the fractional integrated coefficient (d) is significant for all markets, thus revealing the presence of long memory behavior in global futures markets. The presence of long memory disconfirms the efficiency hypothesis in global futures markets and the investors can predict the future prices and beat the market [49–53]. In Panel B, the parameter (aDECO ) is positive and significant at the 1% level, indicating the importance of shocks across the global futures markets. The parameter (bDECO ) is significant and very close to one, confirming the higher persistence volatility across the global index and commodity futures markets. We also show that the dynamic equicorrelation (of DECO ) ρt is positive and weak (0.1976), providing the diversification benefits between index and commodity futures. The diagnostic results in the bottom row of Table 2 suggest no serial correlation estimated by Ljung–Box statistics for the squared standardized residuals thus validating our DECO-FIGARCH model. Fig. 3 plots the dynamic equicorrelation between the index and commodity futures markets. As shown in Fig. 3, we observe time-varying correlations over the sample period, suggesting that institutional investors do or should frequently change their portfolio structure. A significant increase in correlation is observed during the two recent crises (2008– 2009 GFC and 2010–2012 ESDC), supporting the market contagion among the global futures markets. Between 2013 and 2014, equicorrelation among futures markets decreased, before subsequently rising due to increased uncertainties relating to the 2015 commodity market collapse, Chinese market crash, 2016 Brexit, and the 2018 US Fed interest rate hike. Thus, portfolio investors reconstruct their portfolio structures based on the increase/decrease phases in time-varying correlations during the sample period. 4.2. Total volatility spillovers Tables 3–4 report the estimates of the static volatility spillover matrix. The (i, j)th entry in each panel is the estimated contribution to the forecast-error variance of variable i, coming from innovations to market j. The row sums, excluding the main diagonal elements (termed ‘‘From’’) and column sums (termed ‘‘To’’), report the total spillovers to (received by) and from (transmitted by) each volatility. The net pairwise spillovers (To-From) provide information on whether a variable is a receiver or transmitter of shocks in net terms. The column ‘Net’ indicates the total sum of the net-pairwise spillovers expressed as a negative value (net-recipient) and a positive value (net-transmitter), respectively.

Table 2 Estimation of multivariate ARMA(1,1)-FIGARCH(1,d,1)-DECO model. BOVESPA

CAC40

DAX

FTSE 100

HANGSENG

IBEX 35

KOSPI 200

NIFTY

NIKKEI225

S&P 500

SPI 200

Strait Times

WTI

Gold

0.073*** (0.016) −0.001 (0.015) 0.982*** (0.002) 0.642*** (0.275) 0.513*** (0.044) 0.080* (0.047) 0.550*** (0.065)

0.040*** (0.011) −0.033** (0.015) 0.991*** (0.001) 0.267*** (0.105) 0.494*** (0.041) 0.148*** (0.047) 0.552*** (0.061)

0.059*** (0.016) −0.010 (0.015) 0.986*** (0.002) 0.580*** (0.193) 0.456*** (0.060) 0.189*** (0.051) 0.624*** (0.086)

0.066*** (0.016) 0.003 (0.017) 0.979*** (0.002) 0.533*** (0.225) 0.467*** (0.043) 0.110*** (0.042) 0.514*** (0.054)

0.043*** (0.015) −0.025* (0.014) 0.989*** (0.001) 1.369*** (0.686) 0.585*** (0.059) 0.110*** (0.031) 0.696*** (0.056)

0.064*** (0.017) 0.025 (0.017) 0.983*** (0.002) 0.696** (0.292) 0.525*** (0.054) 0.228*** (0.054) 0.680*** (0.051)

0.061*** (0.017) −0.019 (0.015) 0.987*** (0.002) 0.988** (0.392) 0.536*** (0.052) 0.179*** (0.043) 0.643*** (0.058)

0.063*** (0.011) −0.060*** (0.015) 0.987*** (0.002) 0.860* (0.446) 0.534*** (0.053) 0.098 (0.076) 0.526*** (0.090)

0.047*** (0.011) −0.024 (0.016) 0.989*** (0.001) 0.191*** (0.056) 0.460*** (0.041) 0.290*** (0.047) 0.650*** (0.053)

0.039*** (0.011) 0.003 (0.015) 0.989*** (0.002) 1.047*** (0.584) 0.642*** (0.062) 0.178*** (0.039) 0.747*** (0.047)

0.064** (0.027) −0.040** (0.016) 0.983*** (0.002) 2.496** (1.051) 0.563*** (0.077) 0.313*** (0.046) 0.783*** (0.057)

0.028* (0.015) −0.014 (0.015) 0.986*** (0.001) 0.306*** (0.086) 0.409*** (0.063) 0.345*** (0.069) 0.708*** (0.068)

14.86 (0.990)

22.95 (0.817)

43.16 (0.056)

26.76 (0.635)

21.49 (0.871)

25.88 (0.681)

33.20 (0.313)

33.68 (0.293)

29.62 (0.484)

36.80 (0.182)

20.47 (0.903)

31.76 (0.307)

Panel A: Estimates of ARMA-FIGARCH(1,d,1) model Const.

MA(1) Const. dFIGARCH ARCH

(φ1 ) (φ1 ) GARCH

(β1 ) (β1 )

0.055*** (0.014) −0.029** (0.016) 0.979*** (0.002) 0.538** (0.216) 0.496*** (0.042) 0.081 (0.058) 0.512*** (0.074)

Panel B: Estimates of the DCC model

ρtDECO aDECO bDECO df Q2 (30)

0.1976*** (0.0432) 0.0140*** (0.0032) 0.9857*** (0.0033) 7.3539*** (0.2288) 29.70 (0.480)

32.19 (0.358)

S.H. Kang and J.W. Lee / Physica A 526 (2019) 120756

AR(1)

0.025 (0.022) −0.028 (0.015) 0.984*** (0.003) 0.856*** (0.267) 0.358*** (0.075) 0.112 (0.130) 0.449** (0.181)

The p-values are reported in brackets [.]. The standard error values are reported in parentheses (.).** and*** indicate significance at the 5% and 1% levels, respectively.

9

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Fig. 3. Dynamic equicorrelation among the global futures markets. Table 3 Total volatility spillovers within equity index futures markets. BOVE SPA

CAC40

DAX

FTSE 100

HANG SENG

IBEX 35

KOSPI 200

NIFTY

NIKKEI 225

S&P 500

SPI 200

Strait Times

From

BOVESPA CAC40 DAX FTSE100 HANGSENG IBEX35 KOSPI200 NIFTY NIKKEI225 S&P500 SPI200 Strait Times

35.9 1.31 1.39 1.39 3.93 0.78 5.09 3.47 2.81 2.17 2.41 4.43

9.17 27.74 21.99 21.13 6.06 23.56 7.39 1.69 6.73 12.28 10.81 9.29

4.93 11.71 23 9.29 3.57 7.14 6.27 0.7 2.79 6.67 3.43 3.2

16.26 22.08 19.73 32.93 9.16 14.41 8.92 3.44 8.24 18.05 13.42 14.48

1.27 1.46 1.58 1.25 31.72 0.96 7.86 2.59 8 1.68 4 7.63

6.02 18.28 12.7 10.71 5.1 39.7 4.95 2.07 5.31 8.37 7.2 5.54

0.1 0.24 0.02 0.44 0.04 0.26 30.83 0.33 0.13 0.5 2.6 0.19

1.16 0.55 0.55 0.65 4.09 0.47 3.31 70.67 1.34 0.47 1.65 3.26

0.52 0.56 0.73 0.67 4.93 0.81 3.86 0.5 44.56 0.91 3.55 3.67

16.64 10.55 12.85 13.98 6.28 6.29 10.25 0.75 4.38 39.78 7.04 7.27

1.96 1.39 0.9 1.61 10.99 1.93 1.74 2.96 6.19 2.93 34.17 6.67

6.06 4.13 4.55 5.96 14.13 3.68 9.53 10.81 9.52 6.19 9.7 34.38

64.1 72.3 77 67.1 68.3 60.3 69.2 29.3 55.4 60.2 65.8 65.6

To All Net

29.2 65.1 −34.9

130.1 157.9 57.8

59.7 82.7 −17.3

148.2 181.1 81.1

38.3 70 −30

86.3 125.9 26

4.9 35.7 −64.3

17.5 88.2 −11.8

20.7 65.3 −34.7

96.3 136.1 36.1

39.3 73.4 −26.5

84.3 118.6 18.7

754.6 62.90%

Notes: The (i, j)th element of the table shows the estimated contribution to the variance of the 10-day-ahead forecast error of i from innovations to variable j. The diagonal elements (i = j) are the own variance shares estimates, which indicate the fraction of the forecast error variance of market i that is the result of its own shocks.

Table 3 presents the total spillovers across the global index futures markets only. In the lower right corner of Table 3, the total spillover reaches 62.90%, implying a high connectedness across the global index futures markets. Looking at the directional spillovers transmitted ‘To,’ the FTSE 100 is the largest transmitter to other futures markets, contributing 148.2%, followed by CAC 40 (130.1%) and the S&P 500 (96.3%). The results suggest that the UK futures market is the main source of volatility spillover shock to other index futures markets. Notably, the KOSPI 200 index futures market of the Korean Exchange (KRX) contributes only 4% of total volatility spillover to other index futures markets, and it receives a total of 69.2% of its return spillover from other index futures markets. This indicates that the KOSPI 200 index futures market is the largest receiver of volatility spillover from other futures markets. Table 4 presents total volatility spillovers across index futures markets by adding commodity futures markets (WTI futures and gold futures). The lower right corner in Table 4 reveals that the total spillover reaches 55.6%. Although the overall spillover shock is still high, there is a reduction of total volatility spillover from 62.90%, the total spillover of the index futures markets only in Table 3. The results also show the role of commodity futures markets as refugee index futures markets, consistent with results from previous studies including, among others, [54], [55], and [56]. Using a rolling window approach, Fig. 4 plots the time-varying total volatility spillover index of the index futures markets, adding commodity futures markets. Fig. 4 highlights significant variation in the volatility spillover index, which is shown to be very responsive to the various financial and economic events. It can be seen that the total volatility spillovers attain their maximum level during 2008–2009 and 2010–2012, corresponding to the GFC and two ESDC stages. Moreover, (d) the Chinese stock market collapse and commodity market crash in August 2015, and the changes of interest rates by

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11

Table 4 Total volatility spillovers within equity index and commodity futures markets. BOVE SPA

CAC40

DAX

FTSE 100

HANG SENG

IBEX 35

KOSPI 200

NIFTY

NIKKEI S&P 225 500

SPI 200

Strait times

WTI

Gold

From

BOVESPA CAC40 DAX FTSE100 HANGSENG IBEX35 KOSPI200 NIFTY NIKKEI225 S&P500 SPI200 Strait Times WTI Gold

35.74 1.33 1.4 1.38 3.96 0.82 5.35 3.69 2.74 2.16 2.41 4.36 0.13 0.58

9.01 27.63 21.87 20.89 5.92 23.42 7.39 1.46 6.62 12 10.56 9.08 1.61 0.83

4.92 11.84 23.2 9.37 3.57 7.15 6.23 0.7 2.8 6.68 3.46 3.23 0.07 0.12

15.97 21.77 19.5 32.66 8.91 14.2 9.01 3.08 8.01 17.66 13.03 14.09 4.35 3.13

1.27 1.45 1.57 1.24 32.2 0.94 7.76 2.58 8.12 1.67 4.06 7.89 0.38 0.41

6.04 18.44 12.74 10.75 5.1 39.76 4.88 1.98 5.34 8.34 7.26 5.64 0.53 0.78

0.06 0.19 0.02 0.34 0.02 0.24 29.95 0.38 0.15 0.44 2.4 0.12 0.23 0.2

1.13 0.46 0.49 0.55 4 0.42 3.21 70.93 1.28 0.41 1.48 3.17 0.04 0.8

0.45 0.54 0.7 0.63 4.9 0.81 4.02 0.52 45.08 0.87 3.53 3.54 0.1 0.38

16.46 10.41 12.77 13.82 6.21 6.2 10.3 0.66 4.27 39.76 6.9 7.13 0.82 0.51

1.76 1.21 0.79 1.38 10.74 1.85 1.85 2.76 5.93 2.71 34.29 6.22 0.37 2.63

5.77 4.01 4.45 5.75 14.01 3.65 9.94 10.98 9.24 6.03 9.53 34.59 0.15 0.54

1.11 0.59 0.44 1.07 0.36 0.44 0.05 0.05 0.39 0.98 0.75 0.76 88.53 1.88

0.31 0.13 0.03 0.19 0.1 0.1 0.07 0.23 0.03 0.3 0.34 0.16 2.69 87.22

64.3 72.4 76.8 67.3 67.8 60.2 70 29.1 54.9 60.2 65.7 65.4 11.5 12.8

To All Net

30.3 66.1 −34

130.7 158.3 58.3

60.1 83.3 −16.7

152.7 185.4 85.4

39.3 71.5 −28.5

87.8 127.6 27.6

4.8 34.7 −65.2

17.4 88.4 −11.7

21 66.1 −33.9

96.4 136.2 36.2

40.2 74.5 −25.5

84.1 118.7 18.7

8.9 97.4 −2.6

4.7 91.9 −8.1

778.4 55.60%

Notes: See Table 3.

Fig. 4. Dynamics of the volatility spillover index. Notes: The time evolution of spillovers indices is estimated using 200-day rolling windows.

(e) the U.S. Federal Reserve in March 2018, intensify the spillovers among global futures markets, which reduces the diversification opportunities for these markets. Therefore, the economic and financial crises intensify the total spillovers across global futures markets. We now discuss the pairwise directional volatility spillover across global futures markets. Fig. 5 shows the systemwide network connectedness of the pairwise direction volatility spillover index based on Table 4. Note that the pairwise spillovers between index futures and commodity futures markets are shown as nodes and edges, respectively, making it a typical complex network. We observe clear clustering between index futures markets, while the two commodity futures markets (gold and WTI) are isolated. In addition, we identify FTSE 100, CAC 40, S&P 500, IBEX 35, and Strait Times (red nodes) as transmitters of volatility shocks, whereas the remaining markets (green nodes) are receivers of shocks of different magnitudes. The graphical evidence is consistent with the results in Table 4. 4.3. Network connectedness To further explore the dynamic connectedness of risk spillovers, we depict net pairwise network connectedness, which reveal information about risk spillover among the stock–commodity futures markets. Fig. 6(a)–(e) give results for network connectedness of net pairwise directional spillovers, focusing on cases where the intensity was especially significant. The

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Fig. 5. System-wide network connectedness among the global futures markets. Note: This figure shows system-wide network connectedness among the global futures markets. A node’s red (green) color indicates the most significant transmitter (receiver). The edge size indicates the magnitude of the pairwise spillover, whereas the magnitude is also reflected in the color type (green (weak), light blue (medium), or blue and red (strong)).

directional spillover network diagram shows the pathway of shocks from one asset class to another, depicted through idiosyncratic shocks. The width of the arrows indicates the intensity of volatility spillovers and node diameter indicates the size of net spillover. For example, for the first event (November 19, 2008 Global financial crisis in Fig. 6(a)), the US futures market is the strongest sender of volatility shocks to gold, and Strait Times of Singapore futures market gives pairwise shocks to Hong Seng of Hong Kong, Nikkei 225 of Japan and SPI 200 of Australia. However, KOSPI 200 (Korea) and Hang Seng (Hong Kong) futures markets are net pairwise receivers of volatility shocks during the global financial crisis. This picture is reasonable because both the Korean and Hong Kong futures markets have the highest foreign (especially US and Europe) ownership ratio among the sample markets. Network connectedness depicted in Fig. 6(b) shows that during the Greek crisis (ESDC I) net pairwise connectedness is more complex. It can be noted that European countries (FTSE 100, IBEX35, CAC40, DAX) become strong or moderate net pairwise transmitters of volatility shocks during the ESDC I. Fig. 6(c) illustrates, for the ESDC II, that SPI 200 futures of Australia is the strongest net pairwise transmitter market of volatility shocks, while KOSPI 200 futures of Korea is the weakest. Moreover, the US and UK index futures markets dominate network connectedness during the 2015 Chinese and commodity market crashes (in Fig. 6(d)). More interestingly, the commodity futures (WTI and gold) markets are net receivers of volatility shocks in the commodity–stock pairwise connectedness. Practically, to minimize the risk of indexcommodity futures portfolio, we buy US and UK index futures and sell commodity futures, implying that the commodity futures serve as safe haven assets against the exposed risk of US and UK index futures. Finally, the US index futures market is the hub market of volatility shocks on 21st March 2018 due to the increase in the US Fed’s interest rate, as per Fig. 6(e). Overall, it is evident that the direction and magnitude of net volatility spillovers can be difficult to identify and are sensitive to financial and economic events. These findings are consistent with those of Forbes and Rigobon [48] which argued that contagion is characterized by a significant increase in degree of co-movement during turmoil periods after a shock to one market. Following this argument, we examine whether there is any significant increase in such co-movements across assets during crisis periods. 5. Conclusions Over the last decade, the network connectedness across complex financial systems is an important research area for investors, portfolio managers and policy makers. The knowledge of market connectedness through comovement, dependence, and spillovers is crucial issue to measure systemic risk across various markets or asset classes. In this context,

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Fig. 6. Net pairwise directional network during financial and economic events. Note: This figure shows the net pairwise directional connections among the global futures markets. The size of a node indicates the magnitude of a net pairwise connection. The edge size indicates the magnitude of the net pairwise connectedness, and the magnitude is also reflected through the color type (green (weak), light blue (medium), and blue and red (strong)).

we aim to understand dynamic connectedness between global index and commodity futures markets, using both the multivariate DECO-FIGARCH model and the spillover index model of Diebold and Yilmaz [4]. In particular, we analyze the dynamics of directional and net spillovers that reveal the intensity and direction of network connectedness in global complex futures markets. We also emphasize the importance of net pairwise network connectedness in each market as a measure of how shocks are transmitted across these markets.

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S.H. Kang and J.W. Lee / Physica A 526 (2019) 120756 Table A.1 Market index and commodity futures tickers. Futures

Exchange

S&P/ASX index futures iBovespa index futures (BOVESPA) CAC 40 index futures DAX index futures Hang Seng index futures (HANGSENG) NIFTY index futures (NIFTY) Nikkei 225 index futures (NIKKEI 225) KOSPI 200 index futures (KOSPI 200) Straits Times index futures (Strait Times). IBEX 35 futures index (IBEX 35) FTSE 100 futures index (FTSE 100) S&P 500 index futures (S&P 500) WTI (West Texas Intermediate) Crude Oil futures Gold futures

Australia Brazil France Germany Hong Kong India Japan Korea Singapore Spain UK US NYMEX COMEX

Our empirical results are summarized as follows. First, we observe a significant increase in the dynamic correlations between global futures indices and commodity futures during the recent global financial crisis and European sovereign debt crisis. The increase in correlation in 2008 is found to be related to the historical that time, indicating a contagion effect. Between 2013 and 2014 the correlation between commodity and index futures markets decreased. This result supports the evidence on the decoupling hypothesis and diversification opportunities. The increase/decrease phases in the time-varying correlations during the sample period indicate that investors frequently change their portfolio position. Second, we document that total volatility spillovers reach peaks during the 2008–2009 GFC and 2010–2012 ESDC, highlighting that economic and financial crises intensify the spillovers across global futures markets, which reduces the diversification opportunities for these markets. Third, we identify the FTSE 100 as the most significant spillover contributor within our system, while the KOSPI 200 is the largest net receiver of shocks. Fourth, we depict the main results for a network of net pairwise connectedness, focusing on financial and economic events. We find that the net pairwise direction and intensity of network connectedness are sensitive to financial and economic events. Our results have two important insights for portfolio investors. First, commodity futures reduce the magnitude of total volatility spillovers, indicating that the role of commodity futures serves as safe heaven assets against the risk of index futures markets during the market stress. The results emphasize the importance of constructing portfolios that are more preferred with commodity futures rather than index futures. Second, net pairwise volatility spillovers help in identifying the net transmitter and net recipient of information, as well as information connectedness network across global futures markets. This result provides information network connectedness across these markets to assist them in protecting against contagion risk and fostering market stability. To conclude, from our study of network connectedness we are able to reveal information about direction and intensity of volatility spillovers across global futures markets. Moreover, this study explores the implications of connectedness’ information on risk diversification, in the context of index and commodity portfolios involving different trading strategies or even across global futures markets. Following Mensi et al. [44], further research venues may investigate the network connectedness of stock–commodity futures portfolios to construct the optimal hedging ratio, risk effectiveness, and downside risk reduction. This analysis is expected to provide further insights on the stock–commodity futures while it may assist portfolio investors to construct an optimal portfolio with commodity futures. Acknowledgment The work reported in this paper was supported by the Korea Exchange in 2018. Appendix See Table A.1.

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