Introduction

The carbon emission trading market can mitigate climate risks and promote the development of a low-carbon economy and has become an effective means to reduce greenhouse gas emissions. The financial attributes of the carbon market, which is one of the important components of financial markets (Zhang, 2016; Li et al., 2023; Meng et al., 2023), have made its relationship with other financial submarkets increasingly close such as the stock market. As the world’s largest developing country and greenhouse gas emitter (Hua & Dong, 2019) and an active administrator and regulator of green technologies development (Liu et al., 2023), the Chinese government is committed to reducing CO2 emissions and aims to peak CO2 emissions before 2030 and become carbon neutral by 2060. The Chinese carbon emission market is growing, comprising eight regional carbon markets and one national market. In addition, after more than 30 years of development, the Chinese stock market has become the second largest in the world (Carpenter et al., 2021). Therefore, an in-depth exploration of the information spillover relationship between Chinese carbon and stock markets is necessary, which is important for regulators to strengthen the risk management of the financial market and for investors to optimize their investment portfolios.

A lot of studies have focused on the relationship between carbon and stock markets. From a theoretical perspective, the rapid development of the economy can accelerate the consumption of fossil energy, leading to higher carbon emissions, which can give rise to higher prices of carbon emission allowances (Jiménez-Rodríguez, 2019). The stock market serves as a barometer and alarm for an economy, reflecting the development of the economy (Chen et al., 2023). Therefore, there is a connection between carbon and stock markets. Further, fluctuations in the carbon market can affect the stock market. On the one hand, as a major carbon emitter, the electricity industry is more affected by the prices of carbon emission allowances, which may influence the outputs and profits of other enterprises (Fabra & Reguant, 2014; Lin & Jia, 2019; Dagoumas & Polemis, 2020). On the other hand, the prices of carbon emission allowances can affect the profits and investment decisions of enterprises by encouraging them to invest more capital and technology in transitioning to a low-carbon economy (Dong et al., 2019; Lv & Bai, 2021).

Empirically, previous studies have focused on the return or volatility spillover relationship between the carbon and stock markets, as well as the causal relationship between the two markets, and have had inconsistent conclusions. Most of the studies have concluded that there is a significant return or volatility spillover from the stock market to the carbon market (Aslan & Posch, 2022; Zhang et al., 2022; Zhang & Han, 2022), especially from the oil, coal, and electricity industries (Nie et al., 2021; Xia et al., 2022). Chen et al. (2023) explored the dynamic connectedness between Chinese carbon and stock markets from the perspective of the lead-lag relationship and found that the stock market leads the carbon market on most trading days. Contrarily, Wen et al. (2020) found that the price effects can be transmitted from the carbon market to the overall stock market, but the reverse relationship is not significant. In addition, the price of carbon emission allowance is significantly related to energy-intensive sectors. Xu et al. (2022) found that the carbon-intensive stock market appears to be an information receiver in most cases. Regarding the causal relationship, Sun et al. (2022) investigated the positive, negative, and dark casualties between Chinese carbon market and the energy-intensive stock indices and found that there is weak bidirectional causality between these two markets. Zhao et al. (2022) found that both the stock and commodity markets can Granger cause the carbon market in China. However, Jiang et al. (2022) proved that a Granger causality from the carbon market to the stock market exists, and there is no significant impact from the stock market to the carbon market. In addition, these studies have mostly focused on the relationship between carbon and energy stock markets, lacking a comprehensive exploration of the relationship between carbon market and different stock sectors.

The complex relationship between time series caused by exogenous events (Ren et al., 2022) such as extreme weather events may be the main reason for the inconsistent conclusions in the above literature. With the severity of global warming and the frequent occurrence of extreme weather events, such as floods, extreme drought, and heat waves, climate risks have garnered attention from government and people (Zeng et al., 2023), and becoming one of the important risk sources driving financial markets (Venturini, 2022). The academic literature investigating the impact of climate risks on stock price behavior is extensive (Anttila-Hughes, 2016; Bourdeau-Brien & Kryzanowski, 2017; Lanfear et al., 2019; Choi et al., 2020; Diaz-Rainey et al., 2021), and some studies have begun to focus on the influence of climate risks on carbon prices (Batten et al., 2021; Shi et al., 2023). The influence of extreme risks on the information spillover relationship of carbon markets with other markets has also been noticed, especially in the energy market (Liu et al., 2013; Pizzutilo et al., 2020; Lu and Hamori, 2021; Ding et al., 2022; Li et al., 2023). However, relatively few studies have explored the dynamic information spillover relationships between the carbon and stock markets from both the perspectives of return and extreme risk, especially after the shocks of extreme climate.

To investigate the information spillover relationships between Chinese carbon market and the stock sectors with different polluting intensities, we employ a two-step procedure. We first classify all sectors into high-, medium-, and low-polluting sectors based on the industrial exhaust emissions of each industry. Second, we apply the LASSO (Least Absolute Shrinkage and Selection Operator)–VAR (Vector AutoRegressive)–DY (Diebold-Yilmaz) spillover approach, to calculate the degree and direction of return and extreme risk spillovers among markets. To explore the impact of extreme weather shocks on the information spillover relationship between carbon and stock markets, we construct an extremely high temperatures indicator and select four extreme weather events.

Briefly, we find that the extreme risk spillover among markets is much higher than the return spillover and that the carbon market is the main receiver of return spillover, but it can also turn into a risk transmitter under extreme risk conditions. The risk mainly spillover from high-polluting sectors to the carbon market. In addition, the shocks from extreme weather shocks reduce the extreme risk spillovers from the stock market to the carbon market and can even lead to risk spillovers from the carbon market to low-polluting sectors. Finally, after considering the extreme risk spillover relationship, the strategy based on the high-polluting stock market sector and the Guangdong carbon market performs better.

Compared with previous studies, our study makes several contributions to the literature. First, we integrate the different carbon markets and 38 stock sector indices with different polluting intensities together, to explore their dynamical interrelationship under extreme weather shocks meticulously, which present a complete picture of the relationship between carbon and stock markets in different market environments. Second, we comprehensively examine the dynamic connectedness between the carbon and stock markets, including the return and extreme risk spillovers, which complements the work on the information spillover relationship between the two markets. Our study can potentially help investors to optimize their investment portfolios and will be helpful to regulators to understand the mechanism of risk change in the carbon market and further strengthen risk management.

The rest of this paper is organized as follows. Section 2 describes the data and empirical methodology of this study; the empirical findings are presented in Section 3; and Section 4 concludes.

Data and Methodology

Data

The sampling period of this study spans from March 8, 2014 to December 30, 2022 for a total of 1,737 trading days. The current Chinese carbon emissions consist of a national market and eight regional carbon markets. The national carbon market opened for trading on July 16, 2021, resulting in a limited number of observed closing prices within the sample period, so we do not select it as a sample for the carbon market. Table 1 give the descriptive statistics of the eight regional carbon markets, one can see that the number of observations in the Shanghai, Fujian, Chongqing, Tianjin, and Beijing carbon markets is far lower than that in the Guangdong, Hubei, and Shenzhen carbon markets, due to inactive trading behaviors in the five market (Guo, Feng (2021)). Severe data missing may lead to the unreliable parameter estimation of the LASSO-VAR model, and even the biased and incorrect empirical results (Fan & Todorova, 2017; Wen et al., 2020). Therefore, we choose the Guangdong (GDEA), Hubei (HBEA), and Shenzhen (SZEA) pilot carbon emission trading markets as our samples, which have higher trading volumes and better market liquidity in China (Liu & Jin, 2020). There are a total of 1,737 trading days where all three markets were active.

Table 1 Descriptive statistics of the carbon emission trading markets.
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To explore the information spillover relationships between the carbon and stock markets with different polluting intensities, we select 88 China Securities Regulatory Commission (CSRC) secondary industry indices constructed by the Wind Economic Database (EDB), as a representative sample of the stock market. We classify them into high-, medium-, and low-polluting sectors based on the annual average of industrial exhaust emissions of each industry. Due to the lack of data of industrial exhaust emissions, we finally select 38 CSRC secondary industry indices as samples, and Table A.1 of the Appendix gives the annual average industrial exhaust emissions of 38 sectors. Based on the annual average industrial exhaust emissions of 38 sectors, we categorize the top 10 industries with the highest emissions as high-pollution sectors, the bottom 10 industries with the lowest emissions as low-pollution sectors, and the rest as medium-pollution sectors. The daily data of the carbon and stock markets are both retrieved from the Wind EDB, and the data on industrial exhaust emissions were retrieved from the CSMAR database. The descriptive statistics and unit root tests of the logarithmic return of all samples of this study are presented in Table A.2 of the Appendix, all variables are stationary series at the significance level of 1%.

Climate risk is one of the important factors driving the price dynamics of the carbon (Batten et al., 2021) and stock (Venturini, 2022) markets, which may also affect the risk connectedness between them. The typical manifestation of climate risk is the frequent occurrence of extreme weather events, which not only cause huge economic losses and casualties but also draw investors’ attention to the carbon and stock markets. In this study, we first use the Chinese daily temperature data and construct a dummy variable representing extremely high temperatures (Liu et al., 2013), and investigate the impact of extreme weather on the information spillover between carbon and stock markets. We further select four representative extreme weather events that caused significant economic losses and human casualties according to the China’s 2014–2022 Climate Bulletins, and explore the impact of them on the risk spillover. Greenhouse gas emissions contribute to the rise in global temperature and glacial melt, leading to frequent extreme heat and flooding in many countries and regions. Therefore, the four representative extreme weather events are related to extreme heat, heavy rainfall, and flooding as extreme weather shocks, the details of all the events are presented in Table 2Footnote 1.

Table 2 Details of extreme weather events.
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Research Method

To comprehensively investigate the impact of extreme climate shocks on risk connectedness, we calculate the risk spillovers between the carbon and stock markets from the perspectives of return and extreme risk. We use the logarithmic returns of closing prices of 3 carbon markets and 38 sector indices to calculate the return spillover, and all return series are stationary sequences. The logarithmic returns of market i can be written as follows:

$$R_{it} = ln\left( {P_{it}/P_{it - 1}} \right),$$
(1)

where Pit is the closing price of market i at time t. For extreme risk, we calculate the value-at-risk of each market using the conditional autoregressive value-at-risk model (CAViaR, Engle & Manganelli, 2004; Hong et al., 2009; Wang et al., 2021), which does not need to model the entire distribution and is time-adapted. A general CAViaR specification is defined as:

$$VaR_{it}\left( {\varphi _i} \right) = \varphi _{i0} + \mathop {\sum }\limits_{j = 1}^q \varphi _{ij}VaR_{it - j}\left( {\varphi _i} \right) + \mathop {\sum }\limits_{j = 1}^r \varphi _{i\left( {q + j} \right)}L\left( {R_{it - j}} \right),$$
(2)

where VaRit is the value-at-risk (VaR) of market i at time t, L is a function with respect to a finite number of lagged values of observations, and autoregressive components φijVaRit − j (φi) make VaR change smoothly across time. To estimate the VaR, we use the asymmetric slope model of CAViaR, i.e.,

$$VaR_{it}\left( {\varphi _i} \right) = \varphi _{i0} + \varphi _{i1}VaR_{it - 1}\left( {\varphi _i} \right) + \varphi _{i2}\left( {R_{it - 1}} \right)^ + + \varphi _{i3}\left( {R_{it - 1}} \right)^ - ,$$
(3)

where \((R_{it - 1})^ + = max(R_{it - 1},0)\), and \((R_{it - 1})^ - = min(R_{it - 1},0)\). We further estimate extreme risk by a risk indicator as follows:

$$Z_{it} = {{{\boldsymbol{I}}}}\left( {R_{it} < - VaR_{it}} \right),$$
(4)

where I(·) is an indicator function, and Zit takes value 1 if the loss exceeds the estimated VaR, suggesting that an extreme risk event occurred, and otherwise, it takes value 0.

The DY spillover index was originally proposed by Diebold & Yilmaz (2009) to study the risk spillover relationship among global equity markets based on the VAR model. To address the problem that the variance decompositions depend on the ordering of the variables, Diebold & Yilmaz (2012) progressed by measuring the directional spillovers in a generalized VAR framework that eliminates the possible dependence of the results on ordering. Combined with complex network methods, Diebold & Yilmaz (2014) tracked daily time-varying connectedness of major US financial institutions’ stock return volatilities based on the rolling-window method. However, the dynamic DY spillover index would lead to the partial loss of data and the estimation results of spillover are influenced by the window width, due to the use of rolling-window estimation. To address these problems, Antonakakis et al. (2020) introduced a full-fledged time-varying parameter vector autoregression (TVP–VAR) on the basis of Diebold & Yilmaz (2012), which allows the variances to vary via a stochastic volatility Kalman Filter estimation with forgetting factors. In this paper, we have to estimate the information spillover among 41 markets. There are a large number of endogenous variables in the VAR model, the number of parameters grows exponentially with the number of variables, which in turn leads to the problem of dimensional catastrophe. Demirer et al. (2018) introduced the least absolute shrinkage and selection operator-vector autoregressive (LASSO–VAR) model to the estimation of the DY spillover index, which can address the problem of dimensional catastrophe well. Considering the strengths and weaknesses of various models, we ultimately adopt the LASSO–VAR–DY spillover index method and use a rolling-window approach to estimate the dynamic information spillover among markets.

First, we estimate the VAR model as follows:

$$X_t = \mu + \mathop {\sum }\limits_{i = 1}^p {{\Phi }}_iX_{t - i} + {\it{\epsilon }}_t,t = 1,2, \ldots ,N,$$
(5)

where μ is N × 1 dimensional intercept column vector; Xt and Xt−i are N × 1 and Np × 1 dimensional variable and lagged variable vectors, respectively; and Φi is an N × Np dimensional coefficient matrix. The basic principle of the LASSO method is to use a regularization method to impose constraints on the sum of absolute values and compress the smaller coefficient to zero with the penalized term to obtain a model with a smaller degree of freedom (Tibshirani, 1996). Following Nicholson et al. (2017), we consider the structured objectives of the form as follows:

$$min\mathop {\sum }\limits_{t = 1}^T \left\| {X_t - \mu - \mathop {\sum }\limits_{i = 1}^p {{\Phi }}_iX_{t - i}} \right\|_F^2 + \lambda \left\| {{\Phi }} \right\|_1,$$
(6)
$${{\Phi }} = \left[ {{{\Phi }}_1, \ldots ,{{\Phi }}_p} \right],$$
(7)

where \(||X_t - \mu - \mathop {\sum }\nolimits_{i = 1}^p {{\Phi }}_iX_{t - i}||_F\) is the Frobenius norm of the matrix \(X_t - \mu - \mathop {\sum }\nolimits_{i = 1}^p {{\Phi }}_iX_{t - i}\), and \(\lambda ||{{\Phi }}||_1\) is the penalized term. λ is the penalty parameter controlling the size of the compression degree, which is determined by the method of rolling cross-validation. \(||{{\Phi }}||_1\) denotes the one-norm of the parameter to be estimated, and the result is robust when λ is optimal. Thus, Eq.(5) can be rewritten as follows:

$$\begin{array}{l}X_t = {{\Psi }}_0{\it{\epsilon }}_t + {{\Psi }}_1{\it{\epsilon }}_{t - 1} + {{\Psi }}_2{\it{\epsilon }}_{t - 2} + \ldots = \mathop {\sum }\limits_{i = 0}^\infty {{\Psi }}_i{\it{\epsilon }}_{t - i},\\ {{\Psi }}_i = {{\Phi }}_1{{\Psi }}_{i - 1} + {{\Phi }}_2{{\Psi }}_{i - 2} + \ldots + {{\Phi }}_p{{\Psi }}_{i - p},t = 1,2,3 \ldots. \end{array}$$
(8)

We then calculate the variance share that variable j has on variable i based on the generalized forecast error variance decompositions, which can address any bias in the results caused by the ordering of variables (Diebold & Yilmaz, 2012) as follows:

$$\theta _{ij}^g\left( H \right) = \frac{{\sigma _{jj}^{ - 1}\mathop {\sum }\nolimits_{h = 1}^{H - 1} \left( {\left( {{{\Psi }}_h\Sigma } \right)_{i,j}} \right)^2}}{{\mathop {\sum }\nolimits_{h = 0}^{H - 1} \left( {{{\Psi }}_h\Sigma {{\Psi }}_h^\prime } \right)_{i,i}}},H = 1,2,3 \ldots ,$$
(9)

where H represents the H-step-ahead forecast horizon. As \(\mathop {\sum }\nolimits_{j = 1}^N \theta _{ij}^g\left( H \right) \ne 1\), each entry of the variance decomposition matrix is normalized by the row sum as follows:

$$\tilde{\theta }_{ij}^g\left( H \right) = \frac{{\theta _{ij}^g\left( H \right)}}{{\mathop {\sum }\nolimits_{j = 1}^N \theta _{ij}^g\left( H \right)}}.$$
(10)

Finally, we construct the total information spillover index using the below specification:

$$Ts\left( H \right) = \frac{{\mathop {\sum }\nolimits_{i,j = 1,i \ne j}^N \tilde{\theta }_{ij}^g\left( H \right)}}{{\mathop {\sum }\nolimits_{i,j = 1}^N \tilde{\theta }_{ij}^g\left( H \right)}} \ast 100 = \frac{{\mathop {\sum }\nolimits_{i,j = 1,i \ne j}^N \tilde{\theta }_{ij}^g\left( H \right)}}{N} \ast 100.$$
(11)

The directional information spillover to all other variables from variable i is given by:

$$Ds_{i.}\left( H \right) = \frac{{\mathop {\sum }\nolimits_{j = 1,i \ne j}^N \tilde{\theta }_{ji}^g\left( H \right)}}{{\mathop {\sum }\nolimits_{i,j = 1}^N \tilde{\theta }_{ji}^g\left( H \right)}} \ast 100 = \frac{{\mathop {\sum }\nolimits_{j = 1,i \ne j}^N \tilde{\theta }_{ij}^g\left( H \right)}}{N} \ast 100.$$
(12)

Similarly, the directional information spillover of variable i received from all other variables can be defined as follows:

$$Ds_{.i}\left( H \right) = \frac{{\mathop {\sum }\nolimits_{j = 1,i \ne j}^N \tilde{\theta }_{ij}^g\left( H \right)}}{{\mathop {\sum }\nolimits_{i,j = 1}^N \tilde{\theta }_{ij}^g\left( H \right)}} \ast 100 = \frac{{\mathop {\sum }\nolimits_{j = 1,i \ne j}^N \tilde{\theta }_{ij}^g\left( H \right)}}{N} \ast 100.$$
(13)

On the basis of Eqs.(12) and (13), we calculate the net total information spillover of variable i as follows:

$$Ns_i = Ds_{i.}^g\left( H \right) - Ds_{.i}^g\left( H \right),$$
(14)

where a positive value of Nsi means that variable i is driving the whole variables’ network. In contrast, variable i is driven by the network when Nsi is negative. The net pairwise information spillover between variables i and j can be defined as follows:

$$Ns_{i \to j} = \frac{{\tilde{\theta }_{ji}^g\left( H \right) - \tilde{\theta }_{ij}^g\left( H \right)}}{N} \ast 100.$$
(15)

In terms of computation, we calculate the daily logarithmic return and extreme risk series of each market according to Eqs.(1)-(4), and rely on R packages frequencyConnectedness and BigVAR to estimate the daily return as well as extreme risk spillover among markets based on Eqs.(5)-(15).

Empirical Results

Dynamic analysis of risk spillover

To obtain an intuitive understanding of the connectedness between carbon and stock markets with different polluting intensities, we first explore the dynamic evolution of the return and extreme risk spillovers between them. Following Diebold & Yilmaz (2012), our variance decompositions are based on 10-step-ahead forecasts, and a LASSO–VAR lag length of order 4 is selected using the BIC. We calculate the dynamic information spillover based on the rolling-sample estimation with window width of 90 trading days and step of 1 trading day.

Figure 1a displays the dynamic development of the total return (TsRet) and extreme risk (TsVaR) spillover. The figure depicts that the total return spillover ranges from 45% to 80%, and the total extreme risk spillover ranges from 75% to 95%. The extreme risk spillover among markets is much higher than the return spillover, and both have similar trends. The reason for this result may be that when the market is exposed to extreme event shocks and there is high fluctuation, the risk level of different components of financial markets increases, and the degree of risk spillovers among markets increases. Figure 1b depicts the sum (\(Ns_{EA}^{Ret}\)) of the net return spillovers of the Guangdong, Hubei, and Shenzhen carbon markets for each trading day, and the sum of the net extreme risk spillovers (\(Ns_{EA}^{VaR}\)) of the three markets for each trading day. We find that the net return spillover of the carbon market (\(Ns_{EA}^{Ret}\)) is less than 0 during the entire sampling period, which indicates that the carbon market is a risk receiver. However, the net extreme risk spillover of the carbon market (\(Ns_{EA}^{VaR}\)) exhibits distinctly different characteristics. We find that \(Ns_{EA}^{VaR}\) ranges from −3.5% to 6%, and the proportion of trading days with \(Ns_{EA}^{VaR}\) greater than 0 exceeds 20%. In addition, \(Ns_{EA}^{VaR}\) often fluctuates upward. The extreme risk spillover mainly captures the information spillover of the carbon market under extreme risk conditions, and investors of the carbon market may exhibit stronger herding behavior under extreme pressure (Wang et al., 2021), which may lead to increased volatility in the carbon market and ultimately increase risk spillovers to other markets.

Fig. 1: Dynamic evolution of the risk spillovers.
figure 1

a plots the total return (TsRet) and extreme risk (TsVaR) spillover indices; (b) plots the sum of the net return spillovers of Guangdong, Hubei, and Shenzhen carbon markets (\(Ns_{EA}^{Ret}\)), and the extreme risk spillovers of the three carbon markets (\(Ns_{EA}^{VaR}\)); (c) plots the sum of the net return spillovers of each industry in the high- (\(Ns_H^{Ret}\)), medium- (\(Ns_M^{Ret}\)), and low- (\(Ns_L^{Ret}\)) polluting sectors; and (d) plots the sum of the net extreme risk spillovers of each industry in the high- (\(Ns_H^{VaR}\)), medium- (\(Ns_M^{VaR}\)), and low- (\(Ns_L^{VaR}\)) polluting sectors.

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Figure 1c depicts the sum (\(Ns_H^{Ret}\)) of the net return spillovers of all industries in the high-polluting sector for each trading day, the sum (\(Ns_M^{Ret}\)) of the net return spillovers of all industries in the medium-polluting sector for each trading day, and the sum (\(Ns_L^{Ret}\)) of the net return spillovers of all industries in the low-polluting sector for each trading day. Figure 1d depicts the sum (\(Ns_H^{VaR}\)) of the net extreme risk spillovers of all industries in the high-polluting sector for each trading day, the sum (\(Ns_M^{VaR}\)) of the net extreme risk spillovers of all industries in the medium-polluting sector for each trading day, and the sum (\(Ns_L^{VaR}\)) of the net extreme risk spillovers of all industries in the low-polluting sector for each trading day.

Interestingly, the return spillover of the high-polluting sector (\(Ns_H^{Ret}\)) is almost greater than 0, and the return spillover of the low-polluting sector (\(Ns_L^{Ret}\)) is generally less than 0. The evolution of \(Ns_H^{Ret}\) and \(Ns_L^{Ret}\) has an obvious symmetric character, as depicted in Fig. 1c, which indicates that the return spillover is mainly from the high- to the low-polluting sector. To further verify this conjecture, we depict the mean (\(Ns_{H - L}^{Ret}\)) of the net return spillovers from the high-polluting sector to the low-polluting sector, and the mean (\(Ns_{M - L}^{Ret}\)) of the net return spillovers from the medium-polluting sector to the low-polluting sector, as shown in Fig. A1 of the Appendix. One can see that the net return spillovers from the high- (\(Ns_{H - L}^{Ret}\)) and medium- (\(Ns_{M - L}^{Ret}\)) polluting sectors to low-polluting sector are almost larger than 0 during the sampling period, and \(Ns_{H - L}^{Ret}\) is greater than \(Ns_{M - L}^{Ret}\) overall, which verifies the above conjecture. In Fig. 1d, we also find similar patterns, and these findings suggest that the high- and low-polluting sectors are the main risk transmitters and receivers, respectively. Table A.1 of the Appendix indicates that most of the industries in the high-polluting sector are the electric power and manufacturing industries; the listed companies in these industries are important enterprises that support national economic development; and their scale is generally larger and has better market liquidity. The prices of stocks with high market liquidity react quickly to information, which may lead to the risk of price fluctuation spillovers from high- to low-liquidity stocks. In Table 3, we present the average market capitalization (Mc), the average shareholding ratio of institutional investors (Rat), and the average trading volume (Volu) of the component stocks of each index in the high-, medium-, and low-polluting sectors. We also perform t-tests with the null hypothesis that the average measures of the high-polluting sector are smaller than those of the low-polluting sector. Compared with the low-polluting sector, the high-polluting sector has significantly higher market capitalization, shareholding ratio of institutional investors, and trading volume, and these results verify the above finding.

Table 3 Fundamental features of the component stocks of each index in various sectors with different polluting intensities.
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We investigate the net pairwise risk spillovers between Chinese carbon and stock markets among sectors with different polluting intensities. In Fig. 2a, we depict the sum (\(Ns_{H - EA}^{Ret}\)) of the net return spillovers from all industries in the high-polluting sector to the Guangdong, Hubei, and Shenzhen carbon markets, the sum (\(Ns_{M - EA}^{Ret}\)) of the net return spillovers from all industries in the medium-polluting sector to the three carbon markets, and the sum (\(Ns_{L - EA}^{Ret}\)) of the net return spillovers from all industries in the low-polluting sector to the three carbon markets. Figure 2b illustrates the time series of the sum (\(Ns_{H - EA}^{VaR}\)) of the net extreme risk spillovers from all industries in the high-polluting sector to the Guangdong, Hubei, and Shenzhen carbon markets, the sum (\(Ns_{M - EA}^{VaR}\)) of the net extreme risk spillovers from all industries in the medium-polluting sector to the three carbon markets, and the sum (\(Ns_{L - EA}^{VaR}\)) of the net extreme risk spillovers from all industries in the low-polluting sector to the three carbon markets. Figure 2c and d draw, respectively, the probability distributions for the return sums of \(Ns_{H - EA}^{Ret}\), \(Ns_{M - EA}^{Ret}\) and \(Ns_{L - EA}^{Ret}\), and the VAR sums of \(Ns_{H - EA}^{VaR}\), \(Ns_{M - EA}^{VaR}\) and \(Ns_{L - EA}^{VaR}\).

Fig. 2: Dynamic evolution of the net pairwise risk spillovers.
figure 2

a depicts the net return spillovers from the high- (\(Ns_{H - EA}^{Ret}\)), medium- (\(Ns_{M - EA}^{Ret}\)), and low- (\(Ns_{L - EA}^{Ret}\)) polluting sectors to the Guangdong, Hubei, and Shenzhen carbon markets; (b) depicts the net extreme risk spillovers from the high- (\(Ns_{H - EA}^{VaR}\)), medium- (\(Ns_{M - EA}^{VaR}\)), and low- (\(Ns_{L - EA}^{VaR}\)) polluting sectors to the three carbon markets; (c) depicts the probability distributions of \(Ns_{H - EA}^{Ret}\), \(Ns_{M - EA}^{Ret}\), and \(Ns_{L - EA}^{Ret}\); (d) depicts the probability distributions of \(Ns_{H - EA}^{VaR}\), \(Ns_{M - EA}^{VaR}\), and \(Ns_{L - EA}^{VaR}\).

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As can be seen in Fig. 2a, the net return spillovers from the stock market to the carbon market are both larger than 0, and the net return spillover from the high-polluting sector to the carbon market (\(Ns_{H - EA}^{Ret}\)) is greater than \(Ns_{L - EA}^{Ret}\). These results suggest that the risk mainly spillovers from the stock market to the carbon market, especially from the high-polluting sectors; similar conclusions can also be drawn from Fig. 2c. These results are consistent with the findings of Wen et al. (2020) that compared with the low-polluting sector, the higher demand for carbon emissions from the high-polluting sector may lead to a closer relationship between the high-polluting sector and the carbon market and a high degree of information spillover from the high-polluting sector to the carbon market. Figure 2b and d depict that the dynamic evolution characteristics and probability distributions of \(Ns_{H - EA}^{VaR}\) and \(Ns_{L - EA}^{VaR}\) are similar to those in Fig. 2a and b, but the values of \(Ns_{H - EA}^{VaR}\) and \(Ns_{L - EA}^{VaR}\) are less than 0 on some trading days, especially in August 2016, February 2017, and April 2020. These results indicate that the information spillover relationship reverses at certain times, which may be attributed by the shocks from exogenous events, such as extreme weather events, and we will provide a detailed discussion on the effects of exogenous shocks in section 3.2.

We further calculate the static return and extreme risk spillovers between carbon and stock markets using the data of the entire sample period and present the information spillover networks in Fig. 3. Figure 3a displays the network diagrams of the net pairwise return spillovers among the markets. Figure 3b presents the network diagrams of the net pairwise extreme risk spillovers among the markets. Nodes represent different markets, red, blue and green nodes denote the industries in high-, medium-, and low-polluting sectors respectively, and yellow nodes denote the three carbon markets. Arrow represents the direction of net pairwise return spillover. We filter out the edge with the net pairwise spillovers less than 1. We find that compared with the return spillover network, the extreme risk spillover network has more edges, with network density of 0.1628 and 0.2841, respectively. These results suggest that there is a higher degree of information spillover between carbon and stock markets under extreme risk conditions. In Fig. 3b, the information spillover is mainly from the high- and medium-polluting sectors to the Guangdong and Hubei carbon market and then transmitted from the two carbon markets to most of the low-polluting sectors. The carbon market plays a certain intermediary role in risk transmission. Due to variations in market liquidity, different carbon markets may exhibit varying degree of connectedness with stock market. Higher liquidity implies that market responds quickly to information (Hou, Moskowitz (2005)), thus the Guangdong and Hubei carbon markets with higher trading volumes play an important role in risk transmission, especially in the process of transmitting extreme risks.

Fig. 3: Static information spillover network.
figure 3

a displays the network diagrams of the net pairwise return spillovers among the markets. b displays the network diagrams of the net pairwise extreme risk spillovers among the markets. Nodes represent different markets, red, blue and green nodes denote the industries in high-, medium- and low-polluting sectors respectively, and yellow nodes denote the three carbon markets. Arrow represents the direction of net pairwise return spillover. We filter out the edge with the net pairwise spillovers less than 1.

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Impact of extreme weather shocks on risk spillover

The frequent occurrence of extreme weather events is strong evidence of global warming (Coumou & Rahmstorf, 2012) and affects financial markets to a large extent (Anttila-Hughes, 2016), such as carbon and stock markets. In this section, we investigate the impact of extreme weather shocks on the information spillover between carbon and stock markets with different polluting intensities. Following Liu & Chen (2013), we use the Chinese daily temperature data and construct a dummy variable representing extremely high temperatures. The average daily temperature is calculated by weighting the daily temperature of 27 provincial capitals and 4 municipalities using the annual GDP of the province in which they are located. We then determine the trading days under extremely hot temperatures by the highest 5% from the average daily temperature series. In Table 4, we present the average values of net information spillover and net pairwise information spillover during the entire sampling period and the trading days under extremely hot temperatures. We also perform t-tests with the null hypothesis that the average values during the entire sampling period are larger or smaller than that during the trading days under extremely hot temperatures.

Table 4 Average values of net information spillover and net pairwise information spillover during the entire sampling period and the trading days under extremely hot temperatures.
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As presented in Table 4, during the entire sampling period and the trading days under extremely hot temperatures, there was no significant difference in the average net return spillovers of the carbon market (\(Ns_{EA}^{Ret}\)). However, the average \(Ns_{EA}^{VaR}\) increased significantly under extremely hot temperatures, which may be because the extreme risk spillovers from other markets to the carbon market decreased or the extreme risk spillovers from the carbon market to other markets increased under extremely hot temperatures. We also compare the net pairwise information spillover over different periods, finding that there were no significant changes in the net return spillovers from the high- (\(Ns_{H - EA}^{Ret}\)) and medium-polluting (\(Ns_{M - EA}^{Ret}\)) sectors to the carbon market under extremely hot temperatures. The net return spillover from the low-polluting (\(Ns_{L - EA}^{Ret}\)) sector to the carbon market decreased significantly under extremely hot temperatures but is still greater than 0. However, the values of \(Ns_{H - EA}^{VaR}\), \(Ns_{M - EA}^{VaR}\), and \(Ns_{L - EA}^{VaR}\) all decreased significantly under extremely hot temperatures, and the net extreme risk spillover from the low-polluting sector to the carbon market decreased to less than 0. These results indicate that extremely hot temperatures can significantly affect the extreme risk spillover between Chinese carbon and stock markets and even change the direction of risk spillover.

To further explore the impact of extreme weather shocks on risk spillover, we investigate the influence of four extreme weather events presented in Table 2 on the return and extreme risk spillovers between carbon and stock markets with different polluting intensities. Figure 4 depicts the dynamic evolution of the net pairwise risk spillovers from the stock market to the carbon market after the shocks of extreme weather events for the event window [−15, 15]. Figure 4a, c, e, and g depict the results of net pairwise return spillovers after the shocks of events E1–E4, respectively. Figure 4b, d, f, and h depict the results of net pairwise extreme risk spillovers after the shocks of events E1–E4, respectively. Table 5 presents the average values of net pairwise information spillover after the shocks of extreme weather events during the event window [0, 15]. We also perform t-tests with the null hypothesis that the average net pairwise extreme risk spillover during the event window [0, 15] is greater than 0.

Fig. 4: Dynamic evolution of the net pairwise information spillover after the shocks of extreme weather events for the event window [−15, 15].
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a, c, e, g present the results of the net pairwise return spillovers after the shocks of events E1–E4, respectively. b, d, f, h present the results of the net pairwise extreme risk spillovers after the shocks of events E1–E4, respectively. \(Ns_{H - EA}^{Ret}\), \(Ns_{M - EA}^{Ret}\), and \(Ns_{L - EA}^{Ret}\) denote the sum of the net return spillovers from high-, medium-, and low-polluting sectors to the Guangdong, Hubei, and Shenzhen carbon markets, respectively. \(Ns_{H - EA}^{VaR}\), \(Ns_{M - EA}^{VaR}\), and \(Ns_{L - EA}^{VaR}\) denote the net extreme risk spillovers from high-, medium-, and low-polluting sectors to the three markets, respectively. E1 represents the 2016 heavy rainfall; E2 represents the 2018 extreme heat; E3 represents the 2021 Henan catastrophic flood; and E4 represents the 2022 extreme heat.

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Table 5 Average values of net pairwise information spillover after the shocks of extreme weather events during the event window [0, 15].
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Combining the results of Fig. 4a, c, e, and g, we find that the net return spillovers from the high-, medium-, and low-polluting sectors to the carbon market are generally greater than 0, and there is no significant change before and after events E1–E4, indicating that the effect of extreme weather events on the return spillover is not significant. From the results of Fig. 4b, d, f, and h, we find that the net extreme risk spillovers from the high-, medium-, and low-polluting sectors to the carbon market have an obvious downward trend after events E1–E4. The downward trend of extreme risk spillover from the low-polluting sector to the carbon market is the most obvious, where the average \(Ns_{L - EA}^{VaR}\) is significantly less than 0 at the 1% level, as presented in Table 5. These results are consistent with those presented in Fig. 3 and Table 4, suggesting that the extreme risk spillover between carbon and stock markets is more sensitive to the shocks from extreme weather events, and these shocks reduce risk spillovers from the stock market to the carbon market and can even lead to risk spillovers from the carbon market to the low-polluting sector.

In addition to the differences in market liquidity, investors’ attention to different markets can be one of the important reasons for the above conclusions. As one of the practical tools to reduce climate risks, the frequent occurrence of extreme weather events can draw investors’ attention to the carbon market (Choi et al., 2020; Li, et al., 2023; Zeng et al., 2023). This type of attention behavior may affect investors’ trading decisions (Goetzmann et al., 2015) and amplify the trading volume of the carbon market, which will lead to a greater spillover of carbon price fluctuations in the low-polluting sector with less liquid under extreme risk conditions.

Portfolio strategy based on the information spillover relationships

The empirical results of the above dynamic analysis of information spillover between Chinese carbon and stock markets show that the information spillover is mainly from the stock market to the carbon market, especially from high-polluting sectors to the carbon market. However, the empirical results of the impact of extreme weather shocks suggest the information spillover relationship from the stock market to the carbon market reverses under extreme risk conditions. In this section, we construct a portfolio strategy based on the reversal phenomenon. We first present the average returns of high-, medium-, and low-polluting sectors and the three carbon markets during the entire sampling period, the trading days under extremely hot temperatures, and the window [−15, 15] of events E1–E4, and the results are presented in Table 6. We find that during the entire sampling period, the average returns of all markets were greater than 0. The average returns of the high- (RH), medium- (RM), and low-polluting (RL) sectors during the trading days under the extremely hot temperatures were all smaller than 0, with values of −3.14 × 10−4, −6.34 × 10−4, and −1.49 × 10−3, respectively. The values of RH, RM, and RM reveal an almost similar pattern during the event window [−15, 15].

Table 6 Average return of the stock market sectors with different polluting intensities and carbon markets.
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However, compared with the entire sampling period, the average returns of the Guangdong carbon market (RGDEA) during the trading days under the extremely hot temperatures and the event window [−15, 15] were larger. The average returns of Hubei (RHBEA) and Shenzhen (RSZEA) carbon markets were also higher during the trading days under extremely hot temperatures. These results suggest that the returns of the stock market exhibit obvious opposite characteristics from those of the carbon markets under extreme risk conditions, especially from the Guangdong carbon market. Future climate change is a large but uncertain future cost to firms, making investors believe that this uncertainty information has signaled a decline in the discounted future corporate value and ultimately negative returns under extreme risk conditions (Anttila-Hughes, 2016). As an effective means to reduce greenhouse gas emissions, the carbon emission trading market can mitigate climate risks and promote the development of a low-carbon economy, which may lead to a better return for the carbon market under extreme risk conditions.

Following Ren et al. (2022), we construct a portfolio strategy based on the above information spillover relationship between carbon and stock markets, as well as the return characteristics of different markets under extreme risk conditions. We buy 1 unit of carbon emission allowance on the carbon market at time t and sell short unit β of asset i when the net extreme risk spillover of the carbon market is greater than its 90% quartile due to the carbon market trading from a risk receiver to a risk transmitter under extremely hot temperatures. We close the position at which the net extreme risk spillover of the carbon market reverts, and the hedging ratio β is determined using the capital asset pricing model. For simplicity, we set the transaction cost and risk-free rate to zero, and there is no restriction on buying long and selling short in each market. Table 7 presents the descriptive statistics of the returns of the strategy. We find that the average return and Sharpe ratio of the portfolio strategy based on the high-polluting stock market sector and the Guangdong carbon market are both the largest, with values of 0.2557 and 1.1095, respectively. Moreover, compared with the Hubei and Shenzhen carbon markets, the portfolio strategy based on the stock market and the Guangdong carbon market can yield higher average returns. In addition, compared with the average return of a single carbon market or stock market sector in Table 1 and Table 6, our portfolio strategy based on the Guangdong and Hubei carbon markets after considering the extreme risk spillover relationship has a better performance.

Table 7 Descriptive statistics of the returns of the portfolio strategy.
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Discussion

Our study uses the LASSO–VAR–DY spillover index to analyze the information spillover relationships between Chinese carbon and stock markets under extreme weather shocks. The results of dynamic analysis of information spillover among markets show that the risk mainly spillovers from the stock market to the carbon market based on the return spillover relationship, especially from the high-polluting sectors. In contrast to Wen et al. (2020) who found that there are no significantly cointegration effects passing from stock market to carbon market in China based on the weekly data, we employ higher-frequency daily data and focus more on the information spillover effects between stock and carbon markets. Compared to the carbon market, the Chinese stock market has developed earlier and reached a higher level of maturity, resulting in a faster response to new information, which may be the main reason that risks are transmitted from stock market to carbon market in most cases. In addition, the extreme risk spillover among markets is much higher than the return spillover. The results of extreme weather shocks show that the carbon market turn from the main risk receiver into a risk transmitter under extreme risk conditions. In line with Chen et al. (2023) who also find that the relationship between financial time series reverses under exogenous shocks.

Due to the lack of quality data on industrial exhaust emissions, this study selects 38 representative samples from 88 CSRC secondary industry indices. Future research can consider incorporating additional stock sectors and explore their relationship with the carbon market. Future research can also consider the impact of more exogenous shocks on the relationship between carbon and stock markets, e.g., other extreme weather events and government policies. In addition, this paper focuses on the relationship between the carbon market and the stock market, with limited discussion on the prediction of information spillover and the mechanisms behind this relationship. Future research can select suitable models to accurately predict information spillover between carbon and stock markets, and further consider examining the mechanisms behind the information spillover relationships between the two markets, for instance, from the perspective of investor attention (Choi et al., 2020). In terms of applications, we can further optimize our portfolio strategies by considering the causality and lead-lag relationships between carbon market and other financial markets.

Conclusion and Policy Implications

We investigate the dynamic information spillover between Chinese carbon and stock markets for the period 2014–2022 using the LASSO–VAR–DY spillover index. Our study is motivated by a need to deep understand the relationships between Chinese carbon and stock markets with different polluting intensities, and whether the relationships are changed under extreme risk conditions.

Our findings reveal that compared with the return spillover, the level of extreme risk spillover among markets is higher. The carbon market is a receiver of return spillover, and the risk comes mainly from the high-polluting sector. However, the information spillover is mainly from the high-polluting sector to the carbon market and then transmitted from the carbon market to most of the low-polluting sectors under extreme risk conditions. We also find that the extremely hot temperatures can significantly affect the extreme risk spillover between Chinese carbon and stock markets and even change the direction of risk spillover. However, the impact of extremely hot temperatures on the return spillover among markets is not significant. Similar conclusions are drawn from the results of the shocks of extreme weather events. Finally, compared with the return of a single carbon or stock market, a portfolio strategy based on the high-polluting stock market sector and the Guangdong carbon market can achieve better performance.

The present study has practical value for regulators and market participants. Specifically speaking, for regulators, our findings show that the information spillover relationship between stock and carbon market is susceptible to the impact of exogenous shocks, especially extreme weather shocks. Further strengthening of the carbon market is critical to the stability of China’s financial market, which can help to enhance the ability of the financial market to withstand exogenous shocks. To give one example, municipalities should optimize their fiscal expenditure structure, increase spending on technology and sustainable protection, which can contribute to the reduction of CO2 emissions and the stabilization of the carbon price (Xia et al., 2022). Additionally, vigorously developing carbon financial derivatives products can also help hedge against carbon price risks. Turning to the perspective of investors, our results show that the strategy based on the Guangdong and Hubei carbon markets after considering the extreme risk spillover relationship has a better performance. Investors can use more high-frequent data to explore the relationship between carbon and stock markets, make timely adjustments to their investment portfolios based on our strategies.