Sector connectedness in the Chinese stock markets
Ying-Ying Shen, Zhi-Qiang Jiang, Jun-Chao Ma, Gang-Jin Wang, Wei-Xing Zhou
SSector connectedness in the Chinese stock markets
Ying-Ying Shen a , Zhi-Qiang Jiang a, ∗ , Jun-Chao Ma a , Gang-Jin Wang b, ∗ , Wei-Xing Zhou a a School of Business and Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China b Business School and Center for Finance and Investment Management, Hunan University, Changsha 410082, China
Abstract
Uncovering the risk transmitting path within economic sectors in China is crucial for understanding the stability of theChinese economic system, especially under the current situation of the China-US trade conflicts. In this paper, we tryto uncover the risk spreading channels by means of volatility spillovers within the Chinese sectors using stock marketdata. By applying the generalized variance decomposition framework based on the VAR model and the rolling windowapproach, a set of connectedness matrices is obtained to reveal the overall and dynamic spillovers within sectors. Itis found that 17 sectors (mechanical equipment, electrical equipment, utilities, and so on) are risk transmitters and11 sectors (national defence, bank, non-bank finance, and so on) are risk takers during the whole period. During theperiods with the extreme risk events (the global financial crisis, the Chinese interbank liquidity crisis, the Chinesestock market plunge, and the China-US trade war), we observe that the connectedness measures significantly increaseand the financial sectors play a buffer role in stabilizing the economic system. The robust tests suggest that our resultsare not sensitive to the changes of model parameters. Our results not only uncover the spillover effects within theChinese sectors, but also highlight the deep understanding of the risk contagion patterns in the Chinese stock markets.
Keywords:
Network connectedness, Volatility spillovers, Financial networks, Stock market sectors, Connectednessindexes
1. Introduction
The China-US trade war has severe impacts on the Chinese stock markets. During the period from 2008 to 2019,the Chinese stock markets exhibit extremely volatile, that the Shanghai Composite Index lost more than 1,000 pointsin 2018 (from the maximum 3587 to the minimum 2440) and followed by a very hard recovery of 500 points in2019. It is observed that the releasing of information about adding tariffs on specific Chinese products undermines theconfidence of investors and negatively shocks the markets. Naturally, such negative shocks may have direct impacts onthe sectors which export products on the US tariff lists and then transmit to the other sectors having direct and indirectconnections to the targeted sectors, mediated by global value chain interdependencies (Egger and Zhu, 2019). Becauseof the recent global financial crises, there are a plenty of empirical studies focusing on the risk contagions in differentfinancial markets (Jung and Maderitsch, 2014), in different financial institutions or assets (Fry-McKibbin et al., 2014;Elyasiani et al., 2015), and in different countries (Corradi et al., 2012; Cotter and Suurlaht, 2019; Kenourgios et al.,2011). However, very few efforts have been put on uncovering risk transmission between different economic sectorswithin China, which is especially crucial for understanding the stability of the Chinese economic system under thesituation of the China-US trade conflicts.Our goal here is to analyze the spillover dynamics within a set of Chinese sectors. Following Egger and Zhu(2019), our analysis is performed on the daily sector indexes from the Chinese stock markets, which allows us to detectimmediate responses to new events. A measure of connectedness or spillover proposed by Diebold and Yilmaz (2012,2014) is adopted to explore the direct and net spillovers across sectors. The connectedness measure is constructed ∗ Corresponding authors.
Email addresses: [email protected] (Zhi-Qiang Jiang ), [email protected] (Gang-Jin Wang ), [email protected] (Wei-Xing Zhou)
Preprint submitted to Elsevier February 24, 2020 a r X i v : . [ q -f i n . R M ] F e b ased on the concept of forecast error variance decomposition and is independence of the variable orders underthe framework of vector autoregression (VAR) (Diebold and Yilmaz, 2012, 2014). This method also allows us toexamine the time-varying dynamics of the connectedness index by means of a rolling-window approach. With thesame method, Da Fonseca and Ignatieva (2018) study volatility spillover effects among ten CDS sector indexes in theUS markets and Collet and Ielpo (2018) investigate spillovers within eight sectors in the US credit markets.The contributions of this paper are listed as follows. First, we extend the empirical literature by taking into accountthe spillover dynamics within economic sectors, especially paying attentions on the risk contagion behaviors aroundthe extreme risk events, which complements the existing studies on revealing the spillovers between oil markets andsectors (Arouri et al., 2011; Mensi et al., 2017; Ahmad et al., 2018; Wang and Wang, 2019) and between institutionswithin financial sectors (Wang et al., 2018; Cotter and Suurlaht, 2019; Li et al., 2019; Peltonen et al., 2019). Second,differing from the researches on the sector connectedness in the US CDS markets (Da Fonseca and Ignatieva, 2018)and in the US credit markets (Collet and Ielpo, 2018), our work focuses on the sector connectedness within theChinese stock markets. In our analysis, our data set is comprised of 28 different sectors, which is much larger than thesector number in Da Fonseca and Ignatieva (2018) and Collet and Ielpo (2018). Our data set spanning a period from 4January 2000 to 31 December 2019 not only covers the recent global financial crisises, but also includes the China-UStrade conflicts, which allows us to compare the risk contagion behaviors triggered by the two different events in theChinese economic sectors. Third, Egger and Zhu (2019) quantitatively estimate the impact of increasing 1% tariffby the US on the targeted sectors and indirect sectors in China. However, the spreading processes from the targetedsectors to the other sectors are not clear. We thus fill this gap by constructing a connectedness network based on theconnecteddness matrix given by Diebold and Yilmaz (2014) to detect the risk diffusing channels under the situationof the China-US trade conflicts.This paper is organized as follows. A brief literature review is presented in Section 2. Section 3 introduces thedata of sector indexes, the definition of volatility, and the estimation of connenctedness measure. Sections 4 presentsthe overview of the connectedness measure. Sections 5 and 6 give the evolution of the total connectedness and thepairwise directional connectedness. Section 7 discusses the net pairwise connectedness network in the subperiodshaving typical extreme risk events. The robust tests on different model parameters are presented in Section 8. Section9 concludes.
2. Literature review
Due to the high frequent occurrence of financial crises in recent decades, the research topics related to contagion(Karolyi and Stulz, 1996; Allen and Gale, 2000; Pericoli and Sbracia, 2003; Forbes and Rigobon, 2002) and interde-pendence (Broner et al., 2006) have been received considerable research interests. Contagion usually refers to that thenegative event (crisis) occurred in one market or region has the amplification of spillover effects on other markets orregions (Karolyi and Stulz, 1996; Allen and Gale, 2000; Forbes and Rigobon, 2002). Differing from contagions, inter-dependence corresponds to the cross-market linkage that there is no major change in market fundamentals (Forbes andRigobon, 2002). Pericoli and Sbracia (2003) also distinguish contagion and interdependence through clarifying thepropagating channels of negative shocks. Although there are differences between contagion and interdependence, theindex of financial interdependence, namely the spillover index, can also be used to quantitatively present the marketco-movements, in particularly, the evolution of risk contagion during crisis periods (Broner et al., 2006).
There are two main strands of literature on financial contagion. One is to capture the pairwise correlations betweeninstitutions or markets based on correlation measures (Baele, 2005; Chiang and Jeon, 2007; Teply and Kvapilikova,2017; Wang et al., 2017). The widely used methods include the GARCH models (Engle, 2002), the Granger causalitymodels (Sander and Kleimeier, 2003), the copula models (Patton, 2006; Ning, 2010), the CoVaR ( ? ), the quantileregression analysis (Nusair and Olson, 2019), and so on. The multivariate GARCH models are initially proposed tostudy the spillover between different assets. However, such model has difficulties in parameter estimation. Thus, aDCC-GARCH model is tailored for the high-dimensional system (Engle, 2002), in which spillover is characterizedby dynamic conditional correlations, and successfully applied to analyze up to 100 assets (Engle and Sheppard,2001). In empirical analysis, the number of assets is still limited by the computational and presentational difficulties2or the DCC-GARCH model. An updated model named dynamic equicorrelation (DECO) is proposed to tacklesuch drawback (Engle and Kelly, 2012). As the GARCH models are unable to capture the direction of contagion,the Granger test is applied to uncover the direct risk spreading patterns. Using the Granger causality tests, Sanderand Kleimeier (2003) provide a directional contagion pattern at the regional level during Asian crisis and Kalbaskaand Ga¸tkowski (2012) confirm the existence of contagion effects within France, Germany, the United Kingdom andother countries through direct causality networks. Both GARCH models and Granger tests have the drawback ofunderestimating tail risk and tail dependence, thus more sophisticate models are invented, for example the copulaand CoVaR. Wen et al. (2012) apply the copula and CoVaR to study the contagion effect between energy and stockmarkets during the recent financial crises and observe a significant characteristic of increasing tail dependence whichis a manifestation of contagion.The other is to uncover the path of financial contagions from the perspective of complex networks. Similar tothe rumour spreading on social networks, financial networks shape the risk contagion, thus play an important rolein stabilizing the financial system. Gai and Kapadia (2010) analytically reveal that the changes of network structurehave direct influences on the probability of risk contagion. Huang et al. (2016) investigate the potential effects oflocal structures of financial networks on the stability of financial system and argue that financial nodes with greaterstrength, centrality, tightness, and clustering coefficients have greater contribution to systemic risks. This meansthat high interwoven of local structure in financial networks has an amplifying effect on local risk. However, suchamplifying effect is not always true. When the negative impacts are small enough, financial networks with denseconnections can enhance the stability of financial system (Acemoglu et al., 2015). The fluctuations in one market or one region are found to have influences on the other markets and regions. Hamaoet al. (1990) find that for the markets with different trading time, the shocks happened in one market may have impactson the markets which open in the following. Melvin and Melvin (2003) provide evidence that volatilities of stock mar-kets are originated from those of exchange markets. Oil shocks are considered as an important source of risks andhave great impacts on financial markets, which inspires the researches on revealing the causality, interdependence,and spillovers between oil markets and stock markets. By applying the Granger causality tests on the prices of oil andrenewable energy company stocks, Henriques and Sadorsky (2008) find that the technology stocks and oil are Grangercauses to the renewable energy companies. By employing the multivariate GARCH (MGARCH) model to analyzethe volatility spillover effects within oil prices, stock prices of technology, and stock prices of clean energy compa-nies, Sadorsky (2012) found that the correlation between the clean energy company stock prices and the technologycompany stock prices is much stronger that between the oil prices and the prices of clean energy companies.Diebold and Yilmaz (2012, 2014) propose an econometric method (abbreviated as DY method hereafter) to capturethe dynamic spillovers within a set of representative financial variables (like returns or volatilities) associated withcountries, markets, institutions or companies, and so on. Intriguingly, this method is extremely useful to reveal theevolution of spillovers when it is combined with a rolling window approach, which leads to the wide applicationson risk spillover analysis (Fern´andez-Rodr´ıguez et al., 2016; Yang and Zhou, 2017; Barun´ık et al., 2017; Dahl andJonsson, 2018; Yoon et al., 2019). For example, DY method is applied to investigate the dynamic spillover effectsamong commodity futures (crude oil, precious metal, and agricultural products) (Kang et al., 2017) and to detect theasymmetric volatility connectedness in exchange markets during the periods of financial crises (Barun´ık et al., 2017).Furthermore, DY method is also employed to assess volatility spillovers in the seafood markets (Dahl and Jonsson,2018). The connectedness matrix generated by DY method is also used to construct risk spillover networks. Yang andZhou (2017) identify networks of volatility spillovers and investigate time-varying spillover among the U.S. Treasurybonds, global stock indexes, and commodities. Besides the markets mentioned in Yang and Zhou (2017), Yoon et al.(2019) also add the currency markets to investigate the risk spillover within the markets of bond, stock, commodity,and exchange. Both studies report that the US stock market is the greatest single risk contributor in the global financialmarkets (Yang and Zhou, 2017; Yoon et al., 2019). By building the connectedness network of EMU countries usingthe sovereign bond data, Fern´andez-Rodr´ıguez et al. (2016) identify the countries whether they locate in the networkcore or network periphery and find that the risk transmits from the core to the periphery. More importantly, suchconnectedness network can be further used of bank supervision and financial stability monitoring (Wang et al., 2018;Hale and Lopez, 2019). 3n contrast to the widely application of DY method in empirical studies, little attention has been paid to thespillover effects within sectors. A handful papers report the credit risk transmission within CDS sectors in the creditmarkets (Collet and Ielpo, 2018; Da Fonseca and Ignatieva, 2018; Shahzad et al., 2019). Particularly, Collet andIelpo (2018) investigate the cross-sector volatility spillovers in the US credit market and find that the sectors exhibitvery high spillover effects and the risk contributors are comprised of insurance, commodity, and energy sectors. Byperforming very similar analysis on the sectors in stock markets, Nguyen et al. (2018) move one step further toconstruct a complete tail risk connectedness network for the entire US industrial system and find that the tail riskdependence is mainly driven by the trade flow within sectors. Practically, examining the sectoral spillover effects instock markets is helpful to find potential sector-based hedging opportunities for investors. As no market is isolated inthe global financial markets, the sectors in one market could receive risk shocks from other markets. By investigatingthe dynamic risk spillovers across two major commodity markets (crude oil and gold), the aggregate Dow JonesIslamic (DJIM) index, and ten stock sectors, Mensi et al. (2017) find that the oil and gold markets and the sectors ofenergy, finance, technology, and telecommunication are net risk takers, receiving risks from the DJIM index and theother sectors. Yu et al. (2018) explore the risk contribution of crude oil markets to the sectors in the US stock marketsand find that the crude oil contributes the greatest risk to the energy sector and transmits the least risk to the consumerstaple sector.
3. Method and data V GKit = . H it − L it ) − .
019 [( C it − O it )( H it + L it − O it ) − H it − O it )( L it − O it )] − . C it − O it ) , (1)where H it , L it , O it , and C it are the natural logarithm of high, low, open, and close values of index i on day t . Foreach index, once we obtain its volatility, the corresponding mean, median, maximum, minimum, standard deviation,skewness, kurtosis, and ADF statistics are also estimated.Table 1 provides the summary statistics for each sector volatility during the entire period. We can find that foreach volatility the mean value is larger than its median value, suggesting that the tail is on the right, in accordancewith the positive skewness value. The kurtosis is much greater than 3 and the skewness is positive, implying that thesector volatility exhibits the characteristics of leptokurtosis and fat-tail. Furthermore, at the lag order of 2 and thesignificant level of 1%, the ADF statistics are significant, indicating the rejection of having a unit root in volatility. Diebold and Yilmaz (2014) propose a connectedness measure to investigate spillover effects among differentfinancial institutions in a framework of variance decomposition . The connectedness measure is constructed as follows.Let’s consider a vector autoregressive model (VAR) with N variables for a covariance stationary process (Diebold andYilmaz, 2009, 2012, 2014), Y t = p (cid:88) i = Φ t − i Y t − i + ε t , ε ∼ N (0 , Σ ) , (2)4 able 1: Descriptive statistics of the sector volatilities. This table reports sector name, abbr. of sector name, sector code, as well as the mean,median, max, min, std, skewness (skew.), kurtosis (kurt.), ADF test statistic (ADF) of the volatilities. The ADF tests are performed at the lag of 2and the results are all significant at the level of 1%. name abbr code mean median max min std skew. kurt. ADF( × − ) ( × − ) ( × − ) ( × − ) ( × − )Agriculture and forestry A&F 801010 3.07 1.66 79.28 159.16 4.57 5.25 50.47 -15.04 ∗∗∗ Mining Mining 801020 3.29 1.72 89.17 157.44 4.90 4.85 43.72 -15.40 ∗∗∗
Chemical Chem 801030 2.51 1.33 79.71 132.99 3.82 5.73 65.03 -16.01 ∗∗∗
Steel Steel 801040 2.90 1.55 93.02 293.48 4.40 5.66 64.10 -16.53 ∗∗∗
Non-ferrous metals NFMet 801050 3.35 1.90 65.05 454.31 4.59 4.35 34.08 -15.19 ∗∗∗
Electronic Elec 801080 3.06 1.75 84.91 217.92 4.28 5.14 52.67 -15.43 ∗∗∗
Household appliances HApp 801110 2.70 1.62 60.35 50.17 3.81 5.49 51.88 -15.44 ∗∗∗
Food and drink F&D 801120 2.33 1.35 83.81 382.48 3.53 7.38 107.60 -15.89 ∗∗∗
Textile and apparel T&A 801130 2.64 1.33 118.41 60.58 4.38 7.19 121.44 -16.97 ∗∗∗
Light manufacturing LMF 801140 2.55 1.32 76.40 0.48 3.98 5.66 58.61 -16.15 ∗∗∗
Biotechnology Biotech 801150 2.45 1.27 100.53 6.48 3.97 7.38 114.06 -16.50 ∗∗∗
Utilities Util 801160 2.33 1.07 72.14 54.13 3.99 5.97 62.47 -15.86 ∗∗∗
Transportation Trans 801170 2.36 1.16 61.44 12.07 3.90 5.86 58.10 -15.75 ∗∗∗
Real estate REst 801180 3.16 1.79 82.74 314.18 4.57 5.31 53.36 -15.53 ∗∗∗
Commercial trade ComT 801200 2.58 1.29 112.08 19.74 4.37 8.27 137.24 -16.48 ∗∗∗
Leisure and services L&S 801210 3.20 1.73 87.85 14.63 4.74 5.10 49.71 -15.20 ∗∗∗
Composite Cps 801230 2.93 1.56 94.19 14.56 4.22 5.38 65.50 -14.73 ∗∗∗
Building materials BM 801710 6.18 4.25 87.36 299.37 6.83 2.72 15.87 -9.81 ∗∗∗
Building and decoration B&D 801720 5.09 3.32 71.38 261.65 6.10 3.24 19.37 -11.07 ∗∗∗
Electrical equipment ElecE 801730 5.83 3.98 71.63 185.42 6.55 2.80 16.33 -10.29 ∗∗∗
National defense ND 801740 7.18 4.82 87.49 196.69 7.87 3.16 20.30 -11.76 ∗∗∗
Computer Cpt 801750 6.51 4.84 117.44 367.35 6.65 3.33 28.53 -11.64 ∗∗∗
Media Media 801760 6.76 4.83 81.26 36.79 6.96 2.60 15.46 -10.66 ∗∗∗
Communications Comm 801770 5.23 3.63 93.81 52.37 5.88 3.93 31.29 -13.18 ∗∗∗
Bank Bank 801780 3.58 1.89 72.84 4.86 5.21 4.48 35.09 -14.97 ∗∗∗
Non-bank financial NBF 801790 6.16 3.78 131.81 26.22 7.62 4.07 34.56 -13.16 ∗∗∗
Automobile Auto 801880 5.92 4.28 80.47 6.96 6.44 3.07 20.35 -10.85 ∗∗∗
Mechanical equipment MechE 801890 6.00 4.51 63.03 338.19 6.42 2.69 14.73 -10.09 ∗∗∗ where Y t = ( y t , y t , ..., y Nt ) (cid:48) is a N × t ( t = , , ..., T ), Φ i ( i = , , ..., p ) is aparameter matrix, ε is a vector of i.i.d. white noises, and p is the lag order of VAR. Y t can also be written in a movingaverage form, Y t = ∞ (cid:88) i = A i ε t − i , (3)where A i is a N × N coefficient matrix and obtained through a recursive way A i = Φ A i − + Φ A i − + · · · + Φ p A i − p with A being an identity matrix and A i = i <
0. In the framework of variance decomposition, we can decompose theforecast error variance of each variable into parts that are attributed to various shocks from other variables.We denote D gH = (cid:104) d gHi j (cid:105) as the H -step generalized variance decomposition matrix. H is the predictive horizon.The element d gHi j corresponds to the fraction of sector i ’s H -step-ahead generalized forecast error variance due to theshocks from sector j and is calculated as follows, d gHi j = σ − j j (cid:80) H − h = (cid:16) e (cid:48) i A h Σ e j (cid:17) (cid:80) H − h = (cid:16) e (cid:48) i A h Σ A (cid:48) h e i (cid:17) , (4)where σ j j is the j -th diagonal element of covariance matrix and e j is a selection vector with e j ( k ) = k = j and zerootherwise. Σ is the covariance matrix of the shock vectors in the non-orthogonal VAR. Due to the lack of orthogonality5n the generalized variance decomposition framework, the sum of the forecast error variance contributions is notensured to be 1, such that (cid:80) Nj = d gHi j (cid:44)
1. We thus define a normalized matrix ˜ D gH = (cid:104) ˜ d gHi j (cid:105) , which is calculated bynormalizing the matrix D gH for each row, ˜ d gHi j = d gHi j (cid:80) Nj = d gHi j . (5)One can have (cid:80) Nj = ˜ d gHi j = (cid:80) Ni , j = ˜ d gHi j = N . The normalized matrix ˜ D gH is nothing but the adjacent matrix ofvolatility connectedness network.To capture the direction of connectedness, we define the directional connectedness from sector j (respectively, i )to sector i ( j ) as C Hi ← j = ˜ d gHi j ( C Hj ← i = ˜ d gHji ). Usually, C Hj ← i does not equal to C Hi ← j . We further denote the directionalvolatility spillovers received by sector i from all other sectors as from-connectedness, C Hi ←· = (cid:80) Nj = , j (cid:44) i ˜ d gHi j (cid:80) Nj = ˜ d gHi j , (6)and the directional volatility spillovers transmitted by sector i to all other sectors as to-connectedness, C H ·← i = (cid:80) Nj = , j (cid:44) i ˜ d gHji (cid:80) Nj = ˜ d gHji . (7)The difference between to-connectedness and from-connectedness is defined as net-connectedness (from sector i toall other sectors), C Hi = C H ·← i − C Hi ←· . (8) C Hi measures the net spillover effect. The three connectedness measures are able to provide the information that eachsector receives (transmits) spillovers from (to) the other sectors. Furthermore, we introduce the total connectedness tomeasure the contribution of directional connectedness of all sectors, which is given by the mean of the off-diagonalelements in D H , C HT = N N (cid:88) i , j = , j (cid:44) i ˜ d gHi j . (9)Note that C HT locates in the range of [0% , Table 2: Definition of the connectedness measures. V i represents the volatility of the i -th sector. The ˜ d gHij is the fraction of industry i ’s H -step-aheadgeneralized forecast error variance due to the shocks from sector j . C Hi ←· and C H ·← i stand for from-connectedness and to-connectedness, respectively. V V · · · · · · V N C Hi ←· V ˜ d gH ˜ d gH · · · · · · ˜ d gH N (cid:80) Nj = ˜ d gH j , j (cid:44) V ˜ d gH ˜ d gH · · · · · · ˜ d gH N (cid:80) Nj = ˜ d gH j , j (cid:44) ... ... ... ... ... ... V N ˜ d gHN ˜ d gHN · · · · · · ˜ d gHNN (cid:80) Nj = ˜ d gHN j , j (cid:44) NC H ·← i (cid:80) Ni = ˜ d gHi , i (cid:44) (cid:80) Ni = ˜ d gHi , i (cid:44) · · · (cid:80) Ni = ˜ d gHiN , i (cid:44) N / N (cid:80) Ni , j = , j (cid:44) i ˜ d gHij
4. Overview of the connectedness
By setting the predictive horizon H =
10 and the lag order p =
2, we first estimate the volatility connected-ness measures within 28 sectors in the entire period. The corresponding pairwise directional connectedness, from-6onnectedness, to-connectedness, net-connectedness, and total connectedness are listed in table 3. The pairwise di-rectional connectedness measures between sectors form the volatility connectedness matrix. One can find that all theelements in connectedness matrix are in the range of [1% , C i ← i ). One can see that in each row or column the diagonal volatility connectednessis the largest, indicating that the largest volatility shocks of each sector originate from itself. We also notice thatthe bank sector and non-bank financial sector exhibit the strongest self volatility connectedness (namely, 12.94% and11.72%) and the chemical sector has the smallest self volatility connectedness (5.48%), meaning that the self shocksin financial sectors are greater than those in other sectors. One can also find that self volatility connectedness ( C i ← i )is much less than its from-connectedness ( C ·← i ) for all sectors, suggesting that the volatility connectedness of eachsector is dominated by the total external shocks from other sectors. The non-diagonal elements in the connectednessmatrix represent the volatility shocks of sector i coming from sector j . One can find that the volatility spillover frombank to commercial trade has the minimum value of 1.14% and the volatility connectedness from electrical equipmentto building materials achieves the highest value of 5.91%. Furthermore, we also observe that there are pairs of sectorshaving relatively high spillover effects, such as the pair of bank and non-bank finance and of mechanical equipmentand building materials. This can be explained by that bank and non-bank finance sectors form the financial industryand mechanical equipment and building materials have very strong connections to engineering constructions. (a) E l ec E M ec h E U til L M F C h e m T r a n s C p s E l ec A u t o B & D A & F C o m T B i o t ec h B M T & A R E s t L & S HA pp C p t N F M e t M i n i ng C o mm F & D S t ee l M e d i a ND N B F B a nk (b) C h e m T & A C o m T E l ec L M F B i o t ec h T r a n s R E s t U til C p s A & F L & S N F M e t HA pp F & D M ec h E C o mm A u t o S t ee l M i n i ng C p t B M B & D E l ec E ND M e d i a N B F B a nk E l ec E M ec h E U til L M F C h e m C p s T r a n s E l ec B & D A u t o A & F C o m T B M B i o t ec h T & A R E s t HA pp L & S C p t M i n i ng N F M e t C o mm F & D M e d i a S t ee l ND N B F B a nk (c)-50-2502550 Figure 1: Ranking plots of (a) to-connectedness C H ·← i , (b) from-connectedness C Hi ←· , and (c) net-connectedness C Hi . able 3: Volatility connectedness within 28 sectors in the Chinese stock markets during the sample period from 4 January 2000 to 31 December 2019. The results are obtained by setting thepredictive horizon H and the VAR lag order as 10 and 2 days. The sub-matrix from sector A&F to sector MechE reports the pairwise directional volatility connectedness between sector i and j (Eq. (5)), standing for the 10-day-ahead forecast error variance spilling from sector j to sector i . “From”, “To”, and “Net” correspond to the from-connectedness (Eq. (6)), to-connectedness(Eq. (7)), and net-connectedness (Eq. (8)) of sector i , respectively. The number in bold is the total connectedness (Eq. (9)). industry A&F Mining Chem Steel NFMet Elec HApp F&D T&A LMF Biotech Util Trans REst ComT L&S Cps BM B&D ElecE ND Cpt Media Comm Bank NBF Auto MechE From
A&F 6.18 3.22 4.52 2.78 3.64 4.36 3.65 3.43 4.27 4.37 4.46 4.27 4.17 3.81 4.37 4.04 4.15 3.19 3.27 3.75 2.39 3.06 2.36 2.92 1.27 1.40 3.06 3.65 93.82Mining 3.45 7.20 4.40 3.59 4.29 3.81 3.67 3.47 3.57 4.00 3.68 4.63 4.39 3.93 3.99 3.43 3.86 3.11 3.42 3.67 2.11 2.77 2.12 2.85 1.69 1.80 3.36 3.75 92.80Chem 4.22 3.59 5.48 3.25 3.75 4.28 3.57 3.52 4.48 4.56 4.47 4.69 4.46 3.90 4.56 3.98 4.08 3.05 3.16 3.58 2.16 2.85 2.16 2.81 1.32 1.47 3.15 3.46 94.52Steel 3.73 4.17 4.65 7.18 3.70 3.38 3.35 3.70 4.10 4.18 4.10 4.92 4.94 4.07 4.04 3.44 3.42 2.97 3.36 3.24 2.12 2.38 1.89 2.60 2.10 1.66 3.27 3.34 92.82NFMet 3.97 4.16 4.47 3.06 6.41 4.08 3.51 3.20 3.81 4.18 3.79 4.09 4.25 3.96 4.02 3.67 4.02 3.37 3.42 3.90 2.50 3.01 2.22 2.74 1.32 1.66 3.35 3.86 93.59Elec 4.20 3.34 4.40 2.48 3.59 5.69 3.84 3.08 3.90 4.48 4.12 4.21 4.05 3.53 4.14 3.75 4.69 3.21 3.27 3.96 2.45 3.84 2.73 3.31 1.15 1.48 3.30 3.81 94.31HApp 3.81 3.59 4.11 2.77 3.48 4.25 6.80 3.45 3.51 4.29 3.85 4.37 4.35 3.59 3.76 3.45 4.35 3.15 3.42 3.83 2.06 3.26 2.55 3.08 1.93 1.77 3.54 3.63 93.20F&D 4.11 3.86 4.57 3.32 3.52 3.90 3.84 6.95 4.20 4.17 4.77 4.55 4.37 3.89 4.65 3.97 3.52 2.73 3.07 3.28 1.95 2.55 2.05 2.64 1.59 1.92 2.87 3.20 93.05T&A 4.43 3.28 4.94 3.10 3.52 4.22 3.40 3.53 5.57 4.56 4.71 4.56 4.24 3.93 4.74 4.13 4.00 3.13 3.19 3.58 2.18 2.89 2.32 2.64 1.21 1.33 3.11 3.55 94.43LMF 4.07 3.31 4.56 2.94 3.54 4.36 3.67 3.21 4.14 5.72 4.04 4.31 4.23 3.68 4.18 3.85 4.82 3.25 3.27 3.97 2.14 3.31 2.44 2.97 1.43 1.36 3.41 3.83 94.28Biotech 4.57 3.38 4.92 3.10 3.52 4.41 3.72 4.01 4.68 4.46 5.76 4.66 4.36 3.89 4.81 4.19 3.93 2.80 2.95 3.42 2.04 2.83 2.24 2.69 1.15 1.28 2.93 3.28 94.24Util 3.95 3.94 4.70 3.45 3.39 4.04 3.83 3.61 4.08 4.23 4.28 6.00 4.82 3.68 4.41 3.77 4.16 2.92 3.37 3.55 2.17 2.86 2.24 2.84 1.56 1.50 3.18 3.47 94.00Trans 3.89 3.82 4.51 3.53 3.59 4.02 3.90 3.54 3.85 4.34 4.00 4.95 5.82 3.89 4.29 3.78 4.11 2.99 3.52 3.52 2.12 2.83 2.20 2.84 1.82 1.62 3.22 3.50 94.18REst 4.08 3.72 4.46 3.22 3.81 3.93 3.68 3.48 4.07 4.25 4.02 4.24 4.38 6.00 4.25 4.06 3.97 3.25 3.28 3.50 2.14 2.74 2.16 2.78 1.89 1.80 3.22 3.61 94.00ComT 4.39 3.76 4.93 3.02 3.68 4.38 3.67 3.90 4.57 4.45 4.76 4.79 4.57 3.99 5.66 4.15 4.12 2.70 2.92 3.34 2.05 2.84 2.07 2.66 1.14 1.41 2.77 3.28 94.34L&S 4.32 3.36 4.54 2.77 3.53 4.15 3.52 3.53 4.20 4.47 4.30 4.33 4.21 4.08 4.36 6.28 4.10 3.09 3.21 3.81 2.13 2.95 2.54 2.79 1.29 1.41 3.13 3.58 93.72Cps 3.93 3.28 4.12 2.47 3.44 4.57 3.80 2.82 3.62 4.90 3.61 4.26 4.05 3.49 3.84 3.66 6.17 3.53 3.51 4.23 2.30 3.69 2.71 3.16 1.50 1.62 3.64 4.06 93.83BM 3.40 2.94 3.32 2.28 3.09 3.47 3.08 2.38 2.98 3.77 2.77 3.34 3.27 3.15 2.83 3.03 3.88 7.45 5.42 5.91 3.04 3.96 3.26 3.40 1.99 1.98 4.97 5.67 92.55B&D 3.39 3.24 3.37 2.52 3.03 3.52 3.24 2.65 2.92 3.66 2.86 3.84 3.87 3.12 3.07 3.02 3.92 5.02 7.51 5.47 2.89 3.83 2.98 3.33 2.13 2.18 4.30 5.13 92.49ElecE 3.49 2.82 3.43 2.19 3.14 3.70 3.16 2.40 2.97 3.90 2.94 3.54 3.27 2.93 2.98 3.21 3.98 5.05 5.05 7.65 3.16 4.39 3.43 3.36 1.72 1.91 4.73 5.51 92.35ND 3.54 2.74 3.38 2.26 3.23 3.74 2.74 2.38 3.00 3.28 2.89 3.46 3.32 2.95 3.00 3.02 3.45 4.54 4.73 5.40 8.42 3.98 3.18 3.44 1.48 2.50 4.53 5.40 91.58Cpt 3.43 2.79 3.36 2.04 3.09 4.46 3.26 2.32 2.96 3.89 3.01 3.49 3.14 2.82 3.10 3.05 4.26 3.99 4.07 5.23 2.96 7.29 4.70 4.17 1.51 1.71 4.71 5.18 92.71Media 3.27 2.62 3.09 1.93 2.71 4.00 2.95 2.18 2.93 3.58 2.82 3.31 3.08 2.66 2.83 3.12 3.88 4.06 3.95 5.02 2.87 5.78 9.16 4.07 1.67 1.95 4.93 5.57 90.84Comm 3.59 3.15 3.57 2.39 3.07 4.13 3.39 2.64 3.01 3.86 3.08 3.73 3.56 3.12 3.18 3.20 4.01 3.81 3.92 4.50 2.85 4.67 3.63 7.02 1.91 1.80 4.37 4.82 92.98Bank 2.47 3.19 2.82 3.09 2.52 2.42 3.53 2.75 2.23 3.21 2.06 3.34 3.64 3.56 2.18 2.30 3.18 4.01 4.62 4.12 2.24 3.06 2.79 3.39 12.94 5.14 4.91 4.26 87.06NBF 2.53 3.26 2.94 2.38 2.96 2.91 3.18 2.83 2.32 2.79 2.19 3.21 3.21 3.21 2.53 2.55 3.18 3.93 4.63 4.56 3.36 3.21 3.13 3.01 5.19 11.72 4.43 4.66 88.28Auto 3.17 2.98 3.37 2.51 3.01 3.50 3.27 2.42 2.96 3.82 2.83 3.54 3.46 3.05 2.82 2.93 3.84 4.81 4.48 5.39 3.07 4.36 3.72 3.61 2.35 2.11 7.08 5.55 92.92MechE 3.36 3.04 3.31 2.26 3.13 3.65 3.01 2.47 2.96 3.76 2.79 3.51 3.37 3.05 3.00 2.99 3.86 5.02 4.87 5.57 3.26 4.42 3.86 3.64 1.81 2.03 5.05 6.96 93.04 To . able 3 reports the to-connectedness, from-connectedness, and net-connectedness for each sector. One canfind that the to-connectedness ranges from 47.14% to 113.28%, the maximum and minimum values of the from-connectedness are 94.52% and 87.06%, and the net-connectedness spans from -39.92% to 20.93%. For better visi-bility of the rank of the three connectedness measures, we plot the from-connectedness, to-connectedness, and net-connectedness in descending order in Fig. 1. For to-connectedness, the sectors like mechanical equipment, electricalequipment, and utilities have the strongest volatility spillover effects on the other sectors and their spillover weightsare as high as 110%, as evidenced in Fig. 1 (a). This can be explained by that these sectors are generally basic in-dustries, accounting for a great part of the economic structure in China and having strong relevance with the othersectors. However, the sectors like bank and non-bank finance have the lowest to-connectedness with values of 47.14%and 49.82%, indicating that the financial sectors have the minimum risk spillover effects on the other sectors. Asshown in Fig. 1 (b), the from-connectedness varies in a very narrow range from 87.06% to 94.52%, suggesting that foreach sector around 90% of its volatility shocks are contributed by other sectors. One can see that the sectors of bankand non-bank finance relatively have the least from-connectedness with values of 87.06% and 88.28%, however, thegaps to the maximum from-connectedness are small, suggesting that the financial sectors receive comparable volatil-ity shocks comparing with the other sectors. We further estimate the net-connectedness by calculating the differencebetween to-connectedness and from-connectedness. The positive (respectively, negative) net-connectedness meansthat a sector is a risk “transmitter” (“receiver”), transmitting its shocks to (accepting shocks from) other sectors. Asshown in Fig. 1 (c), one can find that 17 sectors, including mechanical equipment, electrical equipment, utilities, andso on, are risk transmitters and 11 sectors, such as national defence, non-bank finance, bank, and to list a few, are riskreceivers.Finally, we estimate the total connectedness to uncover the average level of risk spillover within sectors. Onecan see that the total risk spillover score reaches 92.93%, indicating that sectors in the Chinese stock markets exhibitextremely high intensity of spillovers, comparing with the total connectedness of 33.46%, 45.79%, and 76.93% withinsectors in the Eurozone credit markets (Shahzad et al., 2019), in the US CDS markets (Da Fonseca and Ignatieva, 2018)and the US credit markets (Collet and Ielpo, 2018), respectively.
5. Evolution of the total connectedness
In this section, a rolling window analysis is performed to uncover the evolution of the risk spillovers within sectorsin the Chinese stock markets. The window with a fixed size of 240 days rolls from January 4, 2001 to December 31,2019 with a step of one day. In each window, the total connectedness is estimated with the same model parameters(the lag order p = H =
10) as the whole sample analysis. Fig. 2 illustrates the plot of the totalconnectedness. One can see that the total connectedness presents a volatile style with fluctuations between 84.43%and 96.43%. We also highlight the peaks associated with the events that have great impacts on the Chinese stockmarkets in shadow areas.As shown in Fig. 2, the first shadow locating in the period from mid 2001 to mid 2002 exceeds the score of94%, which can be ascribed to that the policy of reducing the state-owned shares in 2001 makes the Chinese stockmarkets shift into a bear state in the following two years. And at the beginning of 2004, the State Council introduceda policy to promote the reform and opening of the Chinese capital markets and further to encourage the developmentof the markets. However, such policy initiated a stock market decline lasting a period from April 2004 to June 2005(Shadow 2), which made the total connectedness increase sharply during that period. On April 29, 2005, the reform ofthe shareholder structure in listed companies was launched, which stopped the falling of the stock markets, triggeredthe price increment in the following, and finally drove the market into a bubble state, agreeing well with the “V”shape of the total connectedness between mid-2005 and mid-2007. The total connectedness reached 92% near theend of 2007, in consistent with the fact that the Chinese stock markets crashes in October of 2007 (Jiang et al., 2010).Because of the 2008 global fianncial crisis (Shadow 3), the total connectedness also stayed in a state of high value inthe following years.Due to the high frequency of financial crisis (the subprime crisis 20072009, the global 2008 financial crisis,and the European sovereign debt crisis 20112015 (Jiang et al., 2018)) around the world in recent years, the totalconnectedness fluctuated greatly in the Chinese stock markets. The total connectedness achieved the score of 96%in June 2013 (Shadow 4), which was caused by the most serious “money shortage” (interbank liquidity crisis) in thefinancial industry. The overnight interest rate of the Shanghai Interbank Offered Rate (“Shibor”) rose to 13.44%,9
Figure 2: Plots of the evolution of the total connectedness within sectors in the period from January 2, 2001 to December 31, 2019. The totalconnectedness is obtained from the rolling window analysis with a window size of 240 days, a moving step of one days, a lag order of 2, and apredictive horizon of 10 days. The six shadow areas highlight the peaks associated with the events that have great impacts on the Chinese stockmarkets. the highest record since 2006. On June 24, 2013, the Chinese market index plunged 5.3%, leading to a sharp peakin the total connectedness curve around that day. The money shortage was ended by the policy that the centralbank introduced 416 billion Yuan into the market through SLF (Standard for Loan Facility). In 2015 (Shadow 5),the total connectedness significantly increased again and reached the score of 95%. The Chinese stock marketsushered in a plunge in June, 2015, and more than thousands of stocks depreciated than 50%. Many listed companieshad suspended the share trading for different reasons to stop price dropping. In June 2018 (Shadow 6), the totalconnectedness exceeded the score of 95% once again. On June 19, thousands of stocks slumped by the maximum10% daily limits, suggesting very high overall risk in the markets. There are many reasons which cause this marketcrash. One possible explanation could be the China-US trade conflicts in June 2018. Trump announced that it wouldimpose a 10% punitive tariff on 200-billion dollars of Chinese goods, which had a heavy impact on the Chinese stockmarkets. Another reason could be that the confidence of investors was greatly hurt by the seasoned equity offering oflist companies.
6. Evolution of the sector connectedness
We further consider the evolution of to-connectedness, from-connectedness, net-connectedness for each sector.Fig. 3 illustrates the evolution of three connectedness measures, which are also obtained by the rolling window analysiswith a window size of 240 days, a moving step of one day, a lag order of 2, and a predictive horizon of 10 days. Onecan find that except the sectors of bank and non-bank finance, the from-connectedness of other sectors stays above thescore of 80% and varies in a very narrow range, as evidenced by the small gap between their maximum and minimumvalue. And the from-connectedness of bank and non-bank financial sectors exhibits volatile fluctuations and goesunder the score of 80% in some periods. This means that the financial industry is more sensitive and vulnerable tothe risk events including policy changes, international economic situations, financial crash events, and to list a few.It is observed that to-connectedness is greatly larger than from-connectedness for all sectors, which indicates that nosector is solo in the markets and each sector has risk spillover to other sectors. One can also see that all sectors havepeaks around the same time point, which corresponds to the events of market crashes. Such events are signals of riskrelease, thus increasing the to-connectedness of all sectors.The net-connectedness is allowed to have both positive and negative values according to its definition. The posi-tive and negative values represent the shocks transmitted to and received from other sectors, respectively. As shownin Fig. 3, the net-connectedness and to-connectedness curves have peaks at the same time for all sectors, howeverthe net-connectedness exhibits much greater fluctuations. For the sectors of agriculture & forestry, chemical, elec-tronic, textile and apparel, light manufacturing, biotechnology, utilities, transportation, commercial trade, composite,building materials, building & decoration, electrical equipment, and mechanical equipment, their net-connectedness10
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Figure 3: Evolution of from-connectedness, to-connectedness, and net-connectedness for 28 sectors from January 2, 2001 to December 31, 2019.The from-connectedness, to-connectedness, and net-connectedness are obtained from the rolling window analysis with a window size of 240 days,a moving step of one day, a lag order of 2, and a predictive horizon of 10 days. Each panel represents the results of one sector. L M F M ec h E C p t A u t o C h e m T r a n s E l ec C o m T C p s E l ec E T & A B i o t ec h B & D U til B M M e d i a A & F F & D N F M e t HA pp R E s t S t ee l L & S M i n i ng C o mm B a nk ND N B F (a)-50-2502550 T & A C h e m C p s M ec h E U til L M F E l ec E E l ec C o mm B & D B M L & S B i o t ec h C o m T A & F R E s t C p t A u t o T r a n s F & D M i n i ng S t ee l N F M e t ND M e d i a HA pp N B F B a nk (b)-54-28-22450 HA pp B M A u t o E l ec T r a n s M i n i ng E l ec E C o mm U til B & D M ec h E N F M e t A & F M e d i a R E s t C h e m C p s F & D ND L & S B i o t ec h L M F C p t S t ee l C o m T T & A N B F B a nk (c)-50-20104070 M ec h E C h e m T r a n s U til E l ec E C o m T T & A L M F C p s B M A u t o M i n i ng M e d i a B & D C p t N F M e t E l ec C o mm N B F ND B i o t ec h R E s t L & S S t ee l A & F F & D HA pp B a nk (d)-50-2502550 Figure 4: Bar plots of the net-connectedness in descending order for the four subperiods. (a) The global financial crisis from 2007 to 2008. (b)The Chinese interbank liquidity crisis (money shortage) in 2013. (c) The Chinese stock market plunge in 2015. (d) The China-US trade war since2018.
7. Connectedness networks around extreme risk events
In this section, we further perform the analysis of risk spillover within sectors in four subperiods correspondingto the shadow area 3, 4, 5, and 6 in Fig. 2. The four subperiods are chosen because they cover the four typicalextreme risk events in the Chinese stock markets, such as the global financial crisis from 2007 to 2008, the Chineseinterbank liquidity crisis (money shortage) in 2013, the Chinese stock market plunge in 2015, and the China-US tradewar since 2018. In each subperiod, we estimate the volatility connectedness matrix ˜ D gH within 28 sectors using theVAR model with the same model parameters as the full sample analysis and the rolling window analysis, which allowus to estimate the to-connectedness, from-connectedness, and net-connectedness for each subperiod. We thus plotthe net-connectedness in descending order in Fig. 4 for the four subperiods. In comparison of Fig. 1 (c), one cansee that in the four subperiods and entire period the sectors of bank and non-bank finance are always the top 3 riskreceivers, indicating that the financial sectors are crucial for stabilizing the whole economic system. Moreover, thesectors of national defence, steel, and food and drink also act as the same role as the financial sectors. However,the top risk transmitters are not always the same and are dependent on the specific risk events. Specifically, the top3 risk contributors are the sectors of light manufacturing, mechanical equipment, and computer (respectively, thesectors of textile and apparel, chemical, and composite, the sectors of household appliances, building and materials,and automobile, and the sectors of mechanical equipment, chemistry, and transportation) during the subperiods of the12lobal financial crisis (the Chinese interbank liquidity crisis, the Chinese stock market plunge, and the China-US tradewar).To illustrate the risk transmitting path, we take the latest risk event, the China-US trade war, as an example . OnMarch 22, 2018, the US government announced to add 25% tariff on the aluminium, iron and steel imported fromChina. In June 2018, the US government put more Chinese goods onto the tariff list, including semiconductors andchips, robotics and machinery, navigation and automation, and information and communication technology. Thus, therelated sectors which produce the products on the tariff list were severely impacted. For example, adding tariffs on themachinery will directly increase the risk of the mechanical equipment sector. As a role of basic industry, the chemicalsector offers raw materials to the sectors receiving the shocks from the trade war, and its risk gradually increased.Furthermore, the trade war certainly reduces the orders, thus adds the risk exposure of the transportation sector. Theaccumulating of the risks in other sectors are finally accepted by the sectors of bank, household appliances, food anddrink, and other sectors. (a) (b) (c) (d)(e) (f) (g) (h) Figure 5: Plots of the connectedness networks associated with four typical extreme risk events occurred in four subperiods. The node size isproportional to the value of net-connectedness. The nodes in red and blue represent risk contributors and risk receivers, respectively. The linkwidth is proportional to the value of the pairwise directional connectedness. The links in red and blue are sourced from risk contributors and riskreceivers, respectively. (a) The global financial crisis from 2007 to 2008. (b) The Chinese interbank liquidity crisis (money shortage) in 2013. (c)The Chinese stock market plunge in 2015. (d) The China-US trade war since 2018. (e), (f), (g), and (h) are subgraphs of (a), (b), (c), and (d),respectively. In each subgraph, only the outgoing link with maximum net pairwise connectedness is shown for each node.
Based on the connectedness matrix ˜ D gH , a net pairwise connectedness matrix is ˜ C gH defined as,˜ c gHi j = ˜ d gHi j − ˜ d gHji , ˜ d gHi j − ˜ d gHji > , , ˜ d gHi j − ˜ d gHji ≤ . (10)Figs. 5 (a - d) illustrate the net connectedness networks visualized from the pairwise directional connectedness matrixfor the four subperiods. The node size and link width are proportional to the net-connectedness and the net pairwisedirectional connectedness, respectively. The nodes in red and blue represent the risk contributors and the risk receivers.Figs. 5 (e - h) illustrate the subgraphs of the net connectedness networks in the four subperiods. The subgraphs areobtained through visualizing the outgoing links, representing the risk transmitted from the source to the target, withthe maximum connectedness for each node in each subperiod. One can see that for the global financial crisis in 2008(respectively, the Chinese interbank liquidity crisis in 2013, the Chinese stock market plunge in 2015, the China-UStrade war since 2018) the important risk absorbers are the sectors of non bank finance and national defence (the sectors13f banks and non bank finance, the sectors of bank and household appliances), which receive the maximum net riskspillover from the other sectors. To assess the importance of sectors, we further apply the algorithm of PageRank toestimate the centrality score of the sectors in each net connectedness network. Fig. 6 illustrates the PageRank score ofthe sectors in descending order for the four subperiod networks. Again, one can see that the sectors of bank and nonbank finance have the top PageRank score, indicating that the financial sectors act as buffer roles in turbulent periodsand keeping them stabilized and functional is critical in managing systematic risk. (a) N B F B a nk ND L & S C o mm M i n i ng S t ee l R E s t HA pp N F M e t M e d i a F & D A & F B M U til B & D B i o t ec h T & A E l ec E C o m T C p s T r a n s E l ec C h e m A u t o M ec h E C p t L M F B a nk N B F HA pp M e d i a ND S t ee l N F M e t M i n i ng F & D C p t T r a n s A u t o R E s t A & F C o m T L & S B i o t ec h B & D B M E l ec C o mm E l ec E L M F U til M ec h E C p s C h e m T & A S t ee l T & A B a nk N B F C o m T L M F F & D B i o t ec h L & S C p t ND R E s t C h e m A & F M e d i a C p s N F M e t M ec h E U til B & D C o mm M i n i ng T r a n s E l ec E E l ec A u t o B M HA pp B a nk HA pp F & D A & F S t ee l R E s t L & S B i o t ec h N B F ND C o mm E l ec C p t N F M e t B & D M i n i ng M e d i a B M A u t o C p s U til L M F T & A C o m T T r a n s E l ec E C h e m M ec h E Figure 6: Bar plots of the PageRank score in descending order for the net pairwise connectedness networks obtained from the four subperiods. (a)The global financial crisis from 2007 to 2008. (b) The Chinese interbank liquidity crisis (money shortage) in 2013. (c) The Chinese stock marketplunge in 2015. (d) The China-US trade war since 2018.
8. Robust tests
Our connectedness measure is constructed based on the generalized variance decomposition framework of VAR( p )model, which has three parameters including the lag order p , the predictive horizon H , and the size of rolling window W . In above analysis, the model parameters are set as p = H =
10, and W = p =
2, the rolling window size W is set as 220 days, 240 days, and 260 days, and the predictive horizon H is set as 5days, 10 days, and 15 days. The results are shown in Fig. 7. One can find that the tot-connectedness curves in the threepanels are almost overlapping on the same curve, indicating that our results are independent on the model parameters W and H . We then redo the analysis by setting the lag order p as 1, 2, 3, 4, 5 and fixing W =
240 and H =
9. Conclusion
Based on the generalized variance decomposition framework of VAR model, we analyze the volatility connect-edness within sectors in the Chinese stock markets. First, we construct a connectedness matrix based on the fulldata sample, which gives the from-connectedness, to-connectedness, net-connectedness among sectors, as well as tot-connectedness. It is found that the greatest risk contributor to each sector is itself as the largest element in each rowof the connectedness matrix all locates on the diagonal line. 17 Sectors (mechanical equipment, electrical equipment,utilities, and so on) are the risk transmitters and 11 sectors (national defence, bank, and non-bank finance and to list afew) are risk receivers. The sectors having interwoven economic connections are vulnerable to each other, for exam-ple, the pair of bank and non-bank finance and the pair of mechanical equipment and building materials. There maybe direct risk transmitting paths between sectors having service links, for instance, the finance sectors only receiverisks from the auto sector because the finance sectors may provide loan to auto companies and to car buyers.Then, a dynamic analysis is performed by means of a rolling window approach. It is observed that the connect-edness peaks are associated with the financial crisis in 2008, “money shortage” in June 2013, the events of thousands14 (a)
H = 5 H = 10 H = 15
05 10 15 208185899397 (b)
H = 5 H = 10 H = 15
05 10 15 208185899397 (c)
H = 5 H = 10 H = 15 (cid:11)(cid:71)(cid:12) (cid:19)(cid:21) (cid:19)(cid:23) (cid:19)(cid:25) (cid:19)(cid:27) (cid:20)(cid:19) (cid:20)(cid:21) (cid:20)(cid:23) (cid:20)(cid:25) (cid:20)(cid:27) (cid:21)(cid:19)(cid:27)(cid:22)(cid:27)(cid:25)(cid:27)(cid:28)(cid:28)(cid:21)(cid:28)(cid:24)(cid:28)(cid:27) (cid:48)(cid:72)(cid:71)(cid:76)(cid:68)(cid:81) (cid:11)(cid:48)(cid:68)(cid:91)(cid:15)(cid:48)(cid:76)(cid:81)(cid:12)
Figure 7: Results of rubost tests. (a) Plots of the tot-connectedness for p = W = H . (b) Plots of the tot-connectedness for p = W = H . (c) Plots of the tot-connectedness for p = W = H . (d) Plots of the tot-connectednessfor W = H =
10, and different p . The bounds of shadow area correspond to the maximum and minimum value of the tot-connectedness fordifferent lags. of stocks slumped by the maximum 10% daily limits in June 2015 and June 2018. More importantly, differing fromthe results of whole sample analysis, the sector of real estate acts as a role of risk receiver which is in contrast to ourintention. This can be explained by that the real estate is the pillar industry of the Chinese economy and receivesproducts and services from many sectors in its industry chain. It is also observed that the financial sectors play acritical important role in stabilizing the Chinese economic system during the turbulent periods. The recent trade warbetween the US and China also has significant impacts on the sectors of communication and computer, which turnfrom risk receivers to risk contributors. Furthermore, a risk transmitting path, mechanical equipment → chemicalsector → transportation → sectors of bank, household appliances, and food & drink, is observed.Finally, the robustness of the model is tested with different parameters (lag order p , predictive horizon H , androlling window width W ). We find that the generalized variance decomposition method based on the VAR model andthe rolling window method are not sensitive to the changes of model parameters, implying that our results are solidand sound. Our results not only uncover the spillover effects between the Chinese sectors, but also highlight the deepunderstanding of the patterns of risk contagion in the Chinese stock markets. Acknowledgements
We are grateful to Peng Wang, Mu-Yao Li, and Yin-Jie Ma for fruitful discussions. This work was partly supportedby the National Natural Science Foundation of China (U1811462, 71532009, 91746108, 71871088), the ShanghaiPhilosophy and Social Science Fund Project (2017BJB006), the Program of Shanghai Young Top-notch Talent (2018),the Shanghai Outstanding Academic Leaders Plan, and the Fundamental Research Funds for the Central Universities.
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