Extreme Spillover between Green Bonds and Clean Energy Markets

Abstract

This paper examines green bonds (GB), which have received much attention for providing funding for clean energy (CE) market reforms. We investigate the extreme spillover effects between GB and CE markets by using both MVMQ-CAViaR and Granger causality in risk methods over the period from 5 July 2011 to 24 February 2020. Since there are usually extreme asymmetric spillovers between financial markets, we examined whether this phenomenon exists between GB and CE markets. Our empirical analysis results find the significant extreme spillovers from GB to CE markets. In addition, we find that the upside and downside risk spillovers between GB and CE markets are asymmetric. The upside spillover is greater than downside spillover from GB to CE markets and the impact of GB on CE markets is greater. However, the extreme spillover from CE to GB markets is not significant by either the Granger causality in risk or the MVMQ-CAViaR model. Our findings have important implications for investors, policy makers and researchers.

1. Introduction

Climate finance has attracted attention from governments, scholars, institution investors, and so on, especially after the 21st Conference of the Parties (COP 21) in November 2015. A total of 165 countries/regions committed to reduce carbon emissions in line with their national circumstances at the Conference [1].

Many governments have attempted to use fiscal policy, including direct expenditure, taxes and carbon markets, to meet these commitments. However, relevant studies point out that these tools may not be sufficient and that more powerful actions are likely to be needed [2]. Sachs [3] suggests that the use of debt financing to address the current climate change problem may be an effective solution. The central banks can support the low-carbon transition by the development of a green bond (GB) market.

GB, which was launched in 2007 by the European Investment Bank (EIB), is growing rapidly as a popular innovative tool to address the environmental crisis. Similar to traditional bonds, GB is a fixed-income financial instrument used to raise a significant amount of capital in the bond markets. The key difference is that GB is designed to support the finance of “green” projects, which can benefit the environment, such as low-carbon, energy-efficient, and climate-friendly projects [4,5,6,7,8].

As an effective means of financing and refinancing for green projects, GB can facilitate the transition from traditional energy sources to CE [9]. CE, or green energy, does not emit pollutants and can be used directly in production and life, including nuclear energy and renewable energy. CE plays a key role in sustainable development by reducing carbon emissions and improving energy efficiency [10,11,12]. As a result, the investments and consumption of CE have attracted increasing attention from governments [13,14]. A series of policies have been established to promote the development of CE sources, such as solar and wind [15,16,17]. Environmentally friendly companies, such as CE companies, can obtain funding by issuing GBs, so GB markets can support the global transition to CE and low-carbon economic activities [18]. In addition, since GB and CE belong to the bond and stock markets, according to the theory proposed by Dean, et al. [19], the spillover phenomenon between bond and stock markets has its own intrinsic transmission mechanism and economic basis. Therefore, we predict that financial contagion will occur between the GB and CE markets.

The relationship between the GB and CE markets is worth further study, as GB provide significant funding benefits for CE projects [20]. However, just few literatures focused on it.

Some earlier literature argues that the relationship between GB and energy is weak, but they only consider the energy market as a whole, not the CE market. However, studies on the relationship between GB and CE markets are lacking. Recently, the relationship between the GB and CE markets has attracted attention from some researchers. However, the few papers have focused on the relationship between GB and CE markets from the mean and volatility spillovers perspective, ignoring the potential tail risk for participants [21,22]. The mean and volatility spillover between GB and CE markets represent only a portion of risk and may underestimate the actual impact of risk. Moreover, most studies used the GARCH models or spillover index models to explore the relationship between GB and CE markets. The main drawbacks by using the methods are as follows. First, the results may be biased because the model cannot be applied to specific market conditions, such as extreme risk. Second, the heterogeneity of the distribution is ignored and the dependence between GB and CE markets may differ across the return distribution. Only few articles have focused on extreme spillovers between GB and CE markets, not the potential tail risk, which consider a higher-order function of returns. While the mean and volatility represent only a small fraction of the risk and may underestimate the actual impact of risk.

In this context, this paper is to study the extreme spillover effects between GB and the CE markets with two models: the MVMQ-CAViaR model [23] and the Granger causality in risk model [24]. Our samples are the stock price of GB and CE during the period from 5 July 2011 to 24 February 2020.

From the two models, we can analyze the extreme spillover effects between GB and CE markets. In particular, the MVMQ-CAViaR presents the estimation and inference of multivariate, multivolume models. The frameworks can accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the relevant quantitative indicators simultaneously. Therefore, the models we used can avoid the drawbacks of GARCH models.

Our main results are as follows. First, we find significant extreme spillover effects from GB to CE markets by MVMQ-CAViaR model, not from the CE to GB markets. Furthermore, we find the upside and downside spillovers are asymmetric from GB to CE markets. Additionally, there is a significant upside risk spillover effect between the GB and CE markets, but without downside risk spillover effect. All of our results are also supported by Granger causality in risk. Finally, by quantifying impulse response functions (QIRFs), we show how the CE market reacts to extreme shocks from the GB market and that the impacts of GB shocks are stronger when larger fluctuations happen.

Our study makes several important contributions. First, this paper directly investigates the relationship between the GB and CE markets. Most of the existing papers have studied the relationship between GB and energy markets [5,22,25,26]. However, these studies have examined the energy market as a whole, and this paper complements the existing literature by spinning off the CE market from the energy market and examining the relationship between the GB and CE markets separately.

Second, this is the first time the MVQM-CAViaR model proposed by [23] has been used for the extreme spillover effects between GB and CE markets. Compared to the CoVaR and Copula models [5,25,26,27], we can find the extreme risk spillover between GB and CE markets by using the MVQM-CAViaR model without imposing any assumption on the returns distribution [28,29,30]. In addition, our model captures the impact of lagged effects of one market on the other market, while the CoVaR and Copula models do not.

Third, by distinguishing between upside and downside risks, we observe strong evidence of asymmetric risk spillovers in this context and find that the significant upside spillovers from GB to CE markets is irreversible. This suggests that the healthy GB market will promote the development of the CE market. Thus, our empirical results can provide useful policy implications for the development of GB markets to facilitate the energy structure transition.

The rest of the paper is organized as follows. Section 2 provides a literature review. Section 3 describes the econometric model and preliminary analysis of data. Section 4 discusses the empirical results of MVQM-CAViaR and Granger causality in risk. Section 5 concludes the paper.

2. Literature Review and Hypothesis

Many papers pay increasing attention to the development of the GB market. By using the S&P GB Index, the “unlabeled” GB market is less volatile than the “labeled” GB market [31].

Recently, many scholars have focused on the relationship between GB and traditional financial assets, especially the spillover relationship. Some papers show the strong correlation between the GB market and the corporate and Treasury bond markets. GB can receive a sizable spillover from the Treasury bond market [5,22]. In addition, the risk of spillover of GB to the Treasury and corporate bond markets is also significant [32]. The GB market also exerts a close price spillover effect on fixed income markets and currency markets [22]. However, the GB market has a weak volatility spillover relationship on equity markets [25], energy markets, and high-yield corporate bond markets [22]. Using quantitative autoregressive lagged approach (QARDL), ref. [33] find a strong long-run equilibrium relationship between the GB and energy, gold, and CE stock markets.

There is a growing literature that examines the relationship between CE and other markets. Several studies have examined the relationship between CE stocks and oil markets. Ref. [34] document a high correlation between CE markets and oil markets, which is confirmed by the subsequent work of [29,35,36,37]. The relationship between the two markets is affected by the condition of the state’s market [38]. Under extreme conditions, such as financial crises, the link between the two markets will increase significantly [39]. At the same time, [40] estimate the optimal hedging ratio between CE and crude oil, US bonds, gold, VIX, OVX, and European carbon markets and demonstrates that VIX, crude oil, and OVX are the optimal hedging assets for the CE market. Ref. [41] examine the causal relationships between CE and stocks exchange rates, bonds, and uncertainty. They conclude that the stock market and uncertainty have a strong impact on the CE market. Ref. [42] analyze the cross-quantitative dependence between CE stocks and oil prices, equities, exchange rates, and gold prices. The results show that there is a not symmetric across quantiles dependence between CE and other assets.

In addition, some papers focus on the relationship between CE and global financial markets. The returns of the world stock index and the world energy index are the main influencing factors of CE market volatility.

Following the prior study, the relationships between GB (CE) and other traditional assets, such as stocks, bonds, and energy commodities have been extensively explored. However, the existing papers rarely explore the relationship between the GB market and CE market. As the transition to a low-carbon economy requires significant financial resources, especially for CE market reforms. In addition, GB and CE markets have experienced rapid growth in scope and depth in recent years. Therefore, understanding how GB and CE markets interact will be of particular interest to researchers, investors, and policymakers with environmental preferences.

The GB and CE markets belong to the submarkets of the bond and equity markets, respectively. The spillover relationship between the two markets has its own internal mechanism and economic significance. Ref. [19] point out the mechanisms for risk spillovers in the stock market and bond market in the following hypotheses: (1) financial contagion; (2) asset substitution; and (3) hedging demand. Financial contagion refers to the fact that the price of a market, influenced by other markets, cannot react to its own fundamental information independently. Specifically, the price of the CE (GB) market is influenced not only by its own fundamentals, but also by the GB (CE) market. Asset substitution refers to the fact that investors need to sell bonds (stocks) if they buy stocks (bonds) with the limit of total invested money. Hedging demand refers to the fact that investors will move positions held into safe assets based on the hedge ratio of equities to bonds. This is similar to asset substitution, where good news in the stock market causes investors to increase the positions of stock and vice versa.

Since GB and CE are both part of the green industry, non-financial factors such as investors’ environmental preferences will influence the relationship between the two markets. Investors will treat the increase in the GB market as an important source of funding for CE companies. Therefore, if the overall GB market improves, the investors will expect the CE market to strengthen. Based on the above analysis, we predict there would be extreme spillover effects between GB and CE markets.

3. Econometric Methods and Data

We will introduce the methodological models used to investigate the risk spillover effects between GB and CE markets in this section. In addition, we will present the features of the used data for the GB and CE markets.

3.1. Econometric Methods

This paper uses two econometric approaches to investigate the risk spillover effects between GB and CE markets. The first is the MVMQ-CAViaR [23] model; the second is the Granger causality in risk proposed by [24]. These two approaches are described in detail as follows.

3.1.1. MVMQ-CAViaR Model

Based on the time series generally having volatility clustering, ref. [43] proposed the CAViaR model to measure the tail risk of financial markets. The CAViaR model has been widely used in different financial markets. However, this model can only explore the dynamic risk characteristics of individual financial assets, not the spillover effect of different assets. In order to analyze the impact from different financial markets, ref. [23] extended the traditional CAViaR model into a multivariate quantile CAViaR (MVMQ-CAViaR) model. MVMQ-CAViaR extends the idea of single-equation quantile regression to a vector autoregressive structured equation and can analyze the tail risk spillover effect between GB and CE markets more intuitively and clearly. The specific expressions are as follows.

$$\begin{array}{c}\begin{array}{c}{q}_{1t}=c_1+a_{11}\left|r_{1\left(t-1\right)}\right|+a_{12}\left|r_{2\left(t-1\right)}\right|+b_{11}{q}_{1\left(t-1\right)}+b_{12}{q}_{2\left(t-1\right)}\\ q_{2t}=c_2+a_{21}\left|r_{1\left(t-1\right)}\right|+a_{22}\left|r_{2\left(t-1\right)}\right|+b_{21}{q}_{1\left(t-1\right)}+b_{22}{q}_{2\left(t-1\right)}\end{array} \end{array}$$

(1)

where $q_{it}$ represents the conditional quantile of the market return $r_{1\left(t-1\right)}$ (called tail risk in this paper), which can also be regarded as the value-at-risk (VaR) corresponding to the market return; i = 1, 2. 1 represents the GB; and 2 represents the CE markets. $\left|r_{i\left(t-1\right)}\right|$ represents the absolute value of the return of the market index i, which represents the market shock. It implies a lag of positive and negative shocks in one period, which have the same effect on the current VaR. $q_{it-1}$ represents the lagged conditional quantile, which can describe the autocorrelation of the financial market tail distribution.

Taking Equation (1) as an example, the $q_{2t-1}$ term represents the tail risk spillover from the CE market to the GB market; the $\left|r_{2\left(t-1\right)}\right|$ term represents the effect of shocks to the absolute value of CE market return on the tail risk of the GB market. The model can be rewritten as follows:

$$\begin{array}{c}\begin{array}{c}{q}_{1,t}=-Q_{\theta }\left(r_{1,t}\mid I_{t-1}\right)=-inf\left\{q\in R\mid \mathrm{Pr}\left(r_{1,t}\le q\mid I_{t-1}\right)\ge \theta \right\}\\ q_{2,t}=-Q_{\theta }\left(r_{2,t}\mid I_{t-1}\right)=-inf\left\{q\in R\mid \mathrm{Pr}\left(r_{2,t}\le q\mid I_{t-1}\right)\ge \theta \right\}\end{array}\end{array}$$

(2)

In the second step, we determine the magnitude and response of shocks across the market through a pseudo-quantitative impulse response function (QIRF) to research the transmission mechanism. In particular, we are able to study the reaction of the CE market to the extreme shocks from GB by measuring in terms of upside and downside quantiles. Following [23], we define the QIRFs (${\mathsf{\Delta }}_{is}$) for $r_{1t}$ as follows:

$$\begin{array}{c}{\mathsf{\Delta }}_{is}\left({\tilde{r}}_{1,t}\right)={\tilde{q}}_{i,t+s}-q_{i,t+s},s=1, 2, 3\dots ,T\end{array}$$

(3)

where ${\tilde{q}}_{i,t+s}$ is the θth conditional quartile of ${\tilde{r}}_{1,t}$ and $q_{i,t+s}$ is the θth conditional quartile of the unaffected series $r_{1,t+s}$. In addition, the QIRF can be expressed as follows:

$$\begin{array}{c}\begin{array}{c}{\mathsf{\Delta }}_{11}\left({\tilde{r}}_{1,t}\right)=a_{11}\left({\tilde{r}}_{1,t}-r_{i,t}\right)+a_{12}\left({\tilde{r}}_{2,t}-r_{2,t}\right)\mathrm{for}s=1\\ {\mathsf{\Delta }}_{1s}\left({\tilde{r}}_{1,t}\right)=b_{11}{\mathsf{\Delta }}_{1,s-1}\left({\tilde{r}}_{1,t}\right)+b_{12}{\mathsf{\Delta }}_{2,s-1}\left({\tilde{r}}_{1,t}\right)\mathrm{for}s>1\end{array}\end{array}$$

(4)

QIRFs have two main functions. First, they describe how the negative or positive shocks from GB spread to the CE market. Second, they describe how long it will take for the CE market to absorb the shocks from GB. The latter is fully absorbed when the pseudo-QIRFs converge to zero.

3.1.2. Granger Causality in Risk

For given time series $R_t$, the downside VaR ($Va{R}_t^{down}$) and upside VaR ($Va{R}_t^{up}$) at the confidence level of (1− θ) can be written respectively:

$$\begin{array}{l}P\left(R_t<-Va{R}_t^{\mathit{down}}\mid I_{t-1}\right)=\theta \\ P\left(R_t>V_t{R}_t^{up}\mid I_{t-1}\right)=\theta \end{array}$$

(5)

where $I_{t-1}=\left\{R_{t-1},R_{t-2},\dots \right\}$ is the available information set at time t − 1. In this paper, we study the significance level of θ at 1% and 5%.

Considering the volatility clustering, high peak, fat tail, and asymmetric effects of financial time series [44,45], the time series $R_t$ in GB and CE markets in the AR(1)-GJR-GARCH(1, 1) model can be written as follows:

$$\begin{array}{c}{R}_t=c+{\mathsf{\Phi }}_1{R}_{t-1}+{\epsilon }_t\end{array}$$

(6)

$$\begin{array}{c}{\epsilon }_t={\sigma }_t{z}_t,z_t\sim \mathrm{i}.\mathrm{i}.\mathrm{d}.N\left(0,1\right)\end{array}$$

(7)

$$\begin{array}{c}{\sigma }_t^2={\alpha }_0+{\alpha }_1{\epsilon }_{t-1}^2+\gamma {\epsilon }_{t-1}^{2}I\left({\epsilon }_{t-1}<0\right)+{\beta }_1{\sigma }_{t-1}^2\end{array}$$

(8)

where $I\left({\epsilon }_{t-1}<0\right)$ = 1 if ${\epsilon }_{t-1}<0$, indicating the bad news; otherwise, $I\left({\epsilon }_{t-1}\ge 0\right)$ denotes the good news. Therefore, the parameter $\gamma$ is the asymmetric effects between good news and bad news. We denote ${\mu }_t=c+{\Phi }_1{R}_{t-1}$, ${\mu }_t$ and ${\sigma }_t^2$ as the conditional mean and variance of $R_t$, respectively.

The upside VaR and downside VaR of time series $R_t$ can be written in the following form:

$$\begin{array}{l}Va{R}_t^{\mathit{down}}=-{\mu }_t-{\sigma }_t{z}_{\theta },\\ Va{R}_t^{up}={\mu }_t+{\sigma }_t{z}_{1-\theta }\end{array}$$

(9)

where $z_{\theta }$ is the left-tailed critical value at significance level θ of the standardized innovation and $z_{1-\theta }$ is the upper α-quantile. Finally, the accuracy of the VaR model to evaluate extreme risk is tested by the statistic LR, which is proposed by [46] and follows ${\chi }^2\left(1\right)$ distribution asymptotically.

For the given time series $R_{1t}$ and $R_{2t}$, the extreme risk indicators of market l are defined as the following form:

$$\begin{array}{l}{Z}_{l,t}^{\mathit{down}}=\delta \left(R_{it}<-V_a{R}_t^{\mathit{down}}\right),l=1, 2\\ Z_{l,t}^{up}=\delta \left(R_{it}>Va{R}_t^{up}\right),l=1, 2\end{array}$$

(10)

where $\delta (·)$ is an indicator function. $\delta (·)$ takes 1 when the market l’s losses exceed the corresponding VaR, which indicates an extreme event occurring in market l, otherwise 0.

Hypothesis 0.

To study the extreme negative risk spillover between GB and CE markets, the Granger causality in risk from market 2(M2) to market 1(M1) can be written in the following form:

$$H_0:\begin{array}{c}E\left(Z_{M1,t}^{down}|I_{M1,t-1}^{down}\right)=E\left(Z_{M1,t}^{down}|I_{M1,t-1}^{down},I_{M2,t-1}^{down}\right)\\ E\left(Z_{M1,t}^{up}|I_{M1,t-1}^{up}\right)=E\left(Z_{M1,t}^{up}|I_{M1,t-1}^{up},I_{M2,t-1}^{up}\right)\end{array}$$

Hypothesis 1.

Against the alternative hypothesis:

$$H_1:\begin{array}{c}E\left(Z_{M1,t}^{down}|I_{M1,t-1}^{down}\right)\ne E\left(Z_{M1,t}^{down}|I_{M1,t-1}^{down},I_{M2,t-1}^{down}\right)\\ E\left(Z_{M1,t}^{up}|I_{M1,t-1}^{up}\right)\ne E\left(Z_{M1,t}^{up}|I_{M1,t-1}^{up},I_{M2,t-1}^{up}\right)\end{array}$$

If the alternative hypothesis $H_1$ holds, it means that there is the Granger causality in risk from market 2 to market 1, indicating that extreme spillovers exist from market 2 to market 1. In other words, an extreme drop (increase) in market 2 will cause an extreme drop (increase) in market 1. If market 1 and market 2 represent the GB and CE markets, respectively, it shows that an extreme drop (increase) in the GB market will cause an extreme drop (increase) in the CE market.

To estimate Granger causality in risk with kernel-based statistics, ref. [24] proposed the sample cross-covariance function (CCF) among risk indicators $Z_{1t}$ and $Z_{2t}$ as follows:

$$C\left(j\right)=\{\begin{array}{c}{T}^{-1}{\displaystyle {\displaystyle \sum }_{t=1+j}^T}\left(Z_{M1,t}-{\alpha }_1\right)\left(Z_{M2,t-j}-{\alpha }_2\right),0\le j\le T-1\\ T^{-1}{\displaystyle {\displaystyle \sum }_{t=1-j}^T}\left(Z_{M1,t+j}-{\alpha }_1\right)\left(Z_{M2,t}-{\alpha }_2\right),T-1\le j\le 0\end{array}$$

(11)

where j denotes the lag order and ${\alpha }_1=T^{-1}{{\displaystyle \sum }}_{t-1}^T{Z}_{M1,t}$. The sample cross-correlation function between two risk indicators $Z_{M1,t}$ and $Z_{M2,t}$ is shown in the following form:

$$\begin{array}{c}\rho \left(j\right)=\frac{C\left(j\right)}{S_1{S}_2},j=0,\pm 1,\dots ,\pm \left(T-1\right)\end{array}$$

(12)

where $S_l={\alpha }_l\left(1-{\alpha }_l\right)$ is sample variance of $Z_{M,t}$.

The test statistic for Granger causality in risk from market 2 to 1 is:

$$Q_1\left(M\right)=\left[T{\displaystyle \sum }_{j=1}^{T-1}{k}^2\left(\frac{j}{M}\right){\rho }^2\left(j\right)-C_{1T}\left(M\right)\right]/D_{1T}{(M)}^{\frac{1}{2}}$$

(13)

where $k\left(x\right)=\sin \left(\pi x\right)/\left(\pi x\right)$. M denotes the lag order and means how many lags are utilized to examine extreme risk spillovers from financial market 2 to market 1.$C_{1T}(·)$ and $D_{1T}(·)$ are the centering and standardize constants defined as:

$$\begin{array}{l}{C}_{1T}\left(M\right)={\displaystyle {\displaystyle \sum }_{j=1}^{T-1}}\left(1-j/M\right)k^2\left(j/M\right)\\ D_{1T}\left(M\right)=2{\displaystyle {\displaystyle \sum }_{j=1}^{T-1}}\left(1-j/M\right)\left(1-\left(j+1/T\right)\right)k^4\left(j/M\right)\end{array}$$

(14)

Under the condition of the null hypothesis, $Q_1\left(M\right)$ obeys an asymptotic standard normal distribution. If the value of $Q_1\left(M\right)$ exceeds the right-tailed critical value at a specified significance level, it indicates that there exists an extreme risk spillover from market 2 to market 1.

3.2. Data

To examine the extreme spillovers between the GB and CE markets, this study uses daily data from the GB and CE stock price indices. Our sample period begins on 5 July 2011, runs through 24 February 2020, and includes a total of 2248 observations. All data were obtained from the Bloomberg database.

In our study, we use the Standard & Poor’s Dow Jones GB Index (S&P_GB) and the S&P Global Clean Energy Index to represent the global GB and CE markets, respectively [5]. S&P_GB includes only the bonds which are used to fund for environmentally friendly projects. These bonds must be labeled “green” by the Climate Bonds Market Intelligence. The S&P Global Clean Energy Index represents the performance of global clean-energy-related companies from developed and emerging markets. In addition, we calculate the daily returns of prices as:

$$r_{i,t}=\left[ln\left(p_{i,t}\right)-ln\left(p_{i,t-1}\right)\right]$$

(15)

where $p_{i,t}$ and r_i,t are daily price and return, respectively, of each market i at day t.

Table 1. Summary Statistics.

	N	Mean	Min	Max	Std.Dev	Skewness	Kurtosis	J-B
GB	2248	0.0019	−1.3850	1.4043	0.2965	−0.2024	4.8463	207.0587
CE	2248	0.0132	−6.5867	6.2996	1.4367	−0.2455	4.1356	88.7099

shows that the mean of returns for all series is close to zero. The standard deviation of S&P_GB (0.2965) is significantly smaller than the standard deviation of CE (1.4367), indicating that the GB market is less volatile than the CE market. For all indices, the skewness is negative and the absolute value of the skewness of CE is greater than that of GB, suggesting that CE returns are more likely to decline significantly than GB. In addition, all series have kurtosis values higher than 4, suggesting that each index has a leptokurtic distribution. The Jarque–Bera test rejects the null hypothesis of normality of the indices, indicating that the returns of GB and CE do not obey a normal distribution.

The table presents summary characteristics (mean) for all samples. GB is the stock price indices of green bond. CE is the stock price indices of clean energy. Our sample period begins on 5 July 2011, runs through 24 February 2020, and includes a total of 2248 observations.

4. Empirical Results

On the basis of the above data and methods, we will present the empirical results from the MVQM-CAViaR (1,1) model for the extreme spillover effects between GB and CE markets in Section 4.1 and the empirical results from Granger causality in risk in Section 4.2.

4.1. MVQM-CAViaR Estimation

In

Table 2. Estimation Result of MVQM-CAViaR.

Upside Quantiles θ = 0.99						Upside Quantiles θ = 0.95
	c1	a11	a12	b11	b12	c1	a11	a12	b11	b12
GB	0.0276	0.4103 ***	−0.0167	0.9486 ***	−0.0044	0.0786	0.4328 **	−0.0137	0.7384 ***	0.0062
	0.0436	0.1324	0.0451	0.0297	0.0143	0.0874	0.1893	0.0238	0.1905	0.0175
	c2	a21	a22	b21	b22	c2	a21	a22	b21	b22
CE	−0.1640 ***	−0.2829	0.2796 ***	0.1950 ***	0.9243 ***	0.0330	−0.1542 ***	0.4616 ***	0.4292 ***	0.7392 ***
	0.0564	0.5478	0.1065	0.0545	0.0148	0.1925	0.0538	0.0378	0.1108	0.0321
Downside Quantiles θ = 0.01						Downside Quantiles θ = 0.05
	c1	a11	a12	b11	b12	c1	a11	a12	b11	b12
GB	−0.0642	−0.5178 **	0.0004	0.7808 ***	−0.0036	0.0026	−0.1013 ***	0.0000	0.9868 ***	−0.0023
	0.8644	0.2710	0.0889	0.1089	0.2613	0.0094	0.0202	0.0103	0.0355	0.0157
	c2	a21	a22	b21	b22	c2	a21	a22	b21	b22
CE	−1.5833 *	−0.4151 **	−0.166 ***	−0.0366	0.5153 **	−0.1331	−0.3157	−0.1558 **	0.3925	0.7734 ***
	0.9314	0.1936	0.0624	0.2634	0.2227	0.1332	0.2194	0.0693	0.4816	0.1394

Note: *, **, and *** represent the 10%, 5%, and 1% significance levels, respectively.

, we report the estimates of the MVQM-CAViaR (1,1) model for upside risk (θ = 0.95/0.99) and downside risk (θ = 0.05/0.01). First, the top left part of Table 2 shows the extreme spillover results for the upside risk (θ = 0.99). According to Equation (1), it is shown that the quantile of GB (CE) can all be expressed as a linear combination of the lag absolute returns of GB and CE and their quantile. For the GB market, since the coefficient of a₁₁ is significant and positive (a₁₁ = 0.4103), this indicates that an increase in the lag absolute returns of GB positively increase the quantile of GB. For CE markets, GBs can provide important capital for CE companies, and environmentally preferential investors expect that CE companies will be strengthened when GB markets are generally good [20]. Because the coefficient of b₁₁ is significant and positive (b₁₁ = 0.9486), it indicates that there is a significant persistence among the quartiles of GB market. In addition, the coefficients of a₁₂ and b₁₂, although negative, are both insignificant, which indicates that there is no extreme spillover effect of CE on GB markets. For the CE market, the coefficient a₂₂ (0.2796), coefficient b₂₂ (0.9243), and coefficient b₂₁ (0.1950) are all significantly positive at the 1% significance level, indicating that the quantile of CE is positively correlated not only with the lagged absolute return and the quantile of CE, but also with the lagged term of the GB quantile. The lagged term of the GB quantile has a significant predictive effect on the quantile of CE, which means that there is a significant upside spillover from the GB market to the CE market. Second, the upper-right part of Table 2 (θ = 0.95) shows the results of the extreme spillover for upside risk. The results are similar to those for θ = 0.99, i.e., there is only a one-way extreme risk spillover from the GB market to the CE market. Our one-way spillover results are consistent with [47], possibly because the impact of the GB market depends mainly on the risk–return curve of GB and less on the CE market. GB are an important tool for CE to obtain financial support. When the market is boosted, investors can expect that the CE equity market will also strengthen.

The bottom left half of Table 2 reports the extreme spillover results for downside risk (θ = 0.01). For the GB market, since the coefficient on a₁₁ is significant and negative (a₁₁ = −0.5178), it indicates that an increase in the lagged absolute return of GB decreases the quantile of GB. In contrast, the coefficient of b₁₁ is significantly positive (b₁₁ = 0.7808), which means that there is significant persistence among the quartiles of GB market. In addition, the coefficients of both a₁₂ and b₁₂ are insignificant, which indicates that there is no extreme spillover effect of CE on GB. The results are similar to those of the upside risk spillover, i.e., there is no significant extreme downside spillover effect from CE to GB markets. For the CE market, the coefficient a₂₁ (−0.4151), coefficient a₂₂ (−0.1660), and coefficient b₂₂ (0.5153) are all significant at the 5% significance level, indicating that the quantile of CE is not only correlated with the absolute value of the lagged return and the quantile term of its own, but also negatively correlated with the lagged absolute value of the GB return. The significant negative coefficient a₂₁ also indicates that the absolute value of GB returns has predictive power for the quantile of CE, i.e., there is a one-way extreme spillover from GB to CE markets. Our results are consistent with [20], where downside return on GB significantly reduce downside risk in the CE market. Since there is limited capital to invest in the green market, when the GB market is down, green-preferring investors will choose CE as an alternative investment asset, thus reducing the downside risk of CE. Second, the bottom-right part of Table 2 (θ = 0.05) shows the results of the extreme spillover for downside risk. Not inconsistent with the result for θ = 0.01, there is no risk spillover from GB to CE markets, probably because investors who invest in the GB market will only choose CE as an alternative investment to the GB market when the market is in a more extreme downturn. In summary, there is a one-way extreme spillover from GB to CE markets, which is asymmetric, i.e., the upside spillover from GB to CE is larger than the downside extreme spillover.

From the above results, it is clear that extreme spillovers exist mainly from GB to CE markets. To investigate how the CE market reacts negatively or positively to GB shocks, this study constructs a QIRF based on the MVMQ-CAViaR model to discuss the dynamic process of shocks in the GB market on the CE market. Figure 1 shows the dynamic impulse response process of the CE market for the next 50 periods when the CE market is subjected to extreme shocks (extreme positive shocks θ = 0.01, 0.05; extreme negative shocks θ = 0.99, 0.95) in the GB market. The horizontal axis of Figure 1 represents time (days), and the vertical axis represents the magnitude of the impulse response (percent of CE returns). The QIRF has the advantage of being able to track the response of the CE market in the face of a positive or negative GB shock and to calculate how long it takes to fully absorb a GB shock. When the QIRF (red line) converges to zero, the shock is completely absorbed. The dashed line is the 95% confidence interval.

The impulse responses of the CE market under extreme negative shocks to GB (top left, θ = 0.01; top right θ = 0.05) and extreme positive shocks (bottom left, θ = 0.99; bottom right θ = 0.95) are given in the top and bottom halves of Figure 1, respectively. As can be seen in the top half of Figure 1, a negative extreme shock to GB will lead to a negative CE response. A more extreme negative shock (θ = 0.01; θ = 0.05) of GB will lead to a more negative response of CE (−0.61; −0.43) and the longer it will take for this negative response to be absorbed (8; 5 days). As can be seen in the lower part of Figure 1, the positive extreme shocks to GB will lead to a positive CE response. A more extreme positive heavy shock (θ = 0.99; θ = 0.95) of GB will lead to a more positive response of the CE (0.39; 0.37) and the longer it will take for this positive response to be absorbed (35; 48 days). The impulse responses of CE to extreme positive and negative shocks to GB indicate that more extreme shocks in the GB market will lead to a more dramatic response in the CE market and that it will take more time for this response to be absorbed. In addition, the response of CE to extreme negative shocks is larger than extreme positive shocks in the face of the same degree of shocks in the GB market. Our results are consistent with [20], where there is a very significant tail correlation between the GB and CE markets. These markets move together in an isotropic manner over the sample period, i.e., rising (falling) GB market prices attract (inhibit) capital inflows, expand (shrink) production, and raise (lower) CE prices.

The above results can be found that the spillover effect between GB and CE markets is asymmetric. That is, there is only an extreme spillover effect from GB to CE market. This is also consistent with the theory that the GB market can provide financing for CE companies and environmentally preferential investors expect the CE market to strengthen when the GB market is generally good. In addition, this one-way spillover effect may be due to the fact that GB returns are relatively fixed and their returns are mainly influenced by interest rates, which are relatively weakly influenced by the CE market. Therefore, the spillover effect of changes in the CE market on the GB market is not significant. However, the GB market is an important tool for financing CE companies, and when the GB market is boosted, investors expect the CE market to rise as well. Similarly, when the GB market is down, investors expect the CE market to be down as well.

Finally, in

Table 3. Asymmetric Response.

GB Shock	1%	99%	Asymmetric	5%	95%	Asymmetric
CE response	−0.61	0.39	0.18	−0.43	0.37	0.06

, we report the asymmetry of the extreme spillover. Following [12], we calculate asymmetry as the absolute difference between losses and gains, i.e., θ = 1% and 5%, and θ = 95% and 99%, respectively. The results show that the downside extremes have a greater impact than the upside extremes. This suggests that the extreme in the GB market leads to extreme CE market behavior, causing it to exhibit asymmetry in terms of market losses and gains. This finding is consistent with [19]; the financial contagion hypothesis predicts that bad news in one market may spillover to another market, regardless of economic fundamentals. Moreover, it can spillover in any direction, but may be asymmetric in the return shock.

4.2. Granger Causality in Risk

Before testing the extreme spillover effects across GB and CE markets by Granger causality in risk, the upside and downside VaRs of two markets should be evaluated. As some features of market returns are shown in Table 1, such as volatility clustering, the GARCH models are widely used to model volatility processes. It is more appropriate to use the GJR-GARCH models under skewed t distribution to filter the returns in GB and CE markets. The estimation results based on GJR-GARCH model with skewed-t distribution are reported in

Table 4. The GARCH Estimation of green bond and clean energy.

Mean Equation	GB	CE
c	0.0051	0.0062
$\mathsf{\varphi }$	0.0184	0.0169 ***
Volatility equation
${\mathsf{\alpha }}_0$	0.0003 *	0.0694
${\mathsf{\alpha }}_1$	0.0155 **	0.000
${\mathsf{\beta }}_1$	0.9754 ***	0.9177 ***
$\mathsf{\gamma }$	0.0107 *	0.0950 ***
$\mathsf{\lambda }$	−0.0113 **	−0.1754 *
$\mathsf{\eta }$	9.4209 ***	10.1459 ***
Diagnostics
ARCH-LM	8.5832	26.2043
	[0.1977]	[0.1592]
Q(12)	18.7945	25.2274
	[0.5352]	[0.1929]
${\mathrm{Q}}^2\left(12\right)$	8.2243	9.6699
	[0.9903]	[0.9738]

Note: *, ** and *** represent the 10%, 5%, and 1% significance levels, respectively.

. The conditional variance ${\beta }_1$ of all returns are statistically significant at 1% level, indicating the presence of volatility clustering. Moreover, the leverage effect can be captured by γ at the 1% level of significance for all markets. For all markets, λ are below 0 at 10% level, which suggests that all returns are left-skewed. The freedom degree η of all returns is above 4 at the 1% level, indicating a heavy tail of returns. In addition, the diagnostic tests confirm the evidence against any misspecification in GB and CE markets. Indeed, the results of the Ljung–Box test and ARCH-LM test suggest that the selected models successfully filter the heteroskedasticity and autocorrelation of each variable.

Based on the parameters of GJR-GRACH, the downside and upside VaRs of GB and CE markets are presented in

Table 5. The downside and upside VaRs for green bond and clean energy.

		Mean	Std. Dev	Failure Times	Failure Rate	LR Statistics
GB	Downside VaR	0.3499	0.0828	133	0.0956	0.3012
	Upside VaR	0.3583	0.0824	141	0.1014	0.0287
CE	Downside VaR	1.8002	0.3965	143	0.1028	0.1205
	Upside VaR	1.679	0.3587	131	0.0942	0.5334

. The results show that the CE market has the largest mean value of both upside and downside VaR, indicating more volatility in CE market. Compared to CE markets, investments in GB markets are more rational and their volatility better reflects the true level of risk in the market. At the same time, both upside and downside VaRs of the GB market are the lowest. To verify the reliability of the GJR-GARCH, failure rates and LR statistics are calculated. The failure rate is the ratio between the number of failures and the number of all trading days. All failure rates are between 0.0942 and 0.1028, indicating that the selected model of this paper can be used accurately to estimate the VaR for the GB and CE markets. LR statistic is used to examine the accuracy of VaR in backing test techniques. All LR statistics are between 0.0287 and 0.5334, which is less than the critical value 2.706 at the 10% significance level. The results indicate that the selected GJR-GARCH with skewed t distribution for GB and CE markets are reasonable for calculating the VaR.

In this subsection, to investigate the risk spillover between these markets, we compute the Granger causality in risk proposed by [24]. In real-world economic and financial behavior, market participants and regulators typically do not react quickly to past information (e.g., market shocks), but rather take time to understand the information before acting, thus contributing to time lag effects in extreme risk spillovers. It is necessary to examine how the time lag effects in extreme risk spillovers change. Therefore, the test statistics Q1 with the effective lag orders M = 1, 2,…,30 = are used to measure the time lag effects.

The results of upside and downside spillover effects are shown in

Table 6. The extreme spillovers at lag order M = 5, 10, 20, and 30.

Spillover Direction	(a) Green Bond To Clean Energy				(b) Clean Energy To Green Bond
alpha = 0.01	M = 5	M = 10	M = 20	M = 30	M = 5	M = 10	M = 20	M = 30
Down to Down	−1.0663	−0.8541	−1.1264	−1.6697	0.0808	−0.0705	−0.3088	−0.3462
Up to Up	−0.1286	0.3147	−0.1007	−0.4451	3.5212	2.3978	2.0218	1.6692
alpha = 0.05
Down to Down	−1.0474	−1.1246	−1.2112	−1.385	−0.6286	−0.9296	−0.9898	−0.1329
Up to Up	−0.6562	−0.4926	0.0326	−0.0074	1.9283	0.9630	1.2256	1.2075

Notes: at 1%, 5%, and 10% significance levels, the right-tail critical values for the statistics are 2.3263, 1.6449, and 1.2816, respectively. The value in bold indicates that there is an extreme spillover effect at the 10% significance level under corresponding lag order condition.

. To save space, Table 6 only reports the statistics Q1 results at lag order M = 5, 10, 20, and 30. According to Equation (13), whenever Q1 exceeds the critical value of the corresponding significant level, it indicates that there are the extreme risk spillovers between GB and CE markets. In Table 6, if the statistical value is greater than the critical value at the 10% significance level, it is indicated in bold to make it easily detectable. The results show that there is a significant tail spillover effect from the GB market to the CE market in the upside quantile distribution. This implies that the upside quantile information from the GB market has significant predictive power for the returns of GB. In addition, the value of the statistic Q1 becomes smaller as the lag order increases, but at lag order M = 30, Q1 (alpha = 0.01) is 1.6692 is still greater than the critical value at the 10% significance level. This indicates that the tail spillover effect of GB on CE has a very significant time lag effect. However, Q1 (alpha = 0.05) is significant only in the case of lag order M = 5 and M = 20. On the other hand, we find that CE does not induce a Granger effect in the GB market. The results confirm the conclusion of the multivariate quantitative model that GB influences the CE market in the higher upside quantile. In the downside quantile, the Granger results are not consistent with the MVQM-CAViaR results, and the spillover effect of the MVQM-CAViaR results in the downside quantile is mainly caused by having GB absolute returns and not by the quantile of GB returns.

5. Conclusions

In this paper, we have examined the extreme spillover effects between the GB and CE markets with the MVMQ-CAViaR model over the period from 5 July 2011 to 24 February 2020. We find a significant risk spillover effect from the GB market to the CE market, but not from the CE market to the GB market. It can be seen that the spillover effect of CB on CE markets should not be underestimated.

Our research has the following implications for investors, policymakers and scholars. First, our study can help the investors design the optimal portfolio with GB and CE by considering the correlations between GB and CE the extreme spillover effects. Because the GB and CE move in the same direction under different market conditions. A correlation between the GB and CE would significantly reduce the overall risk of the portfolio.

Second, our study can help the policymakers support CE by considering the development of financial market. An extreme rise in the GB market leads to a rise in the CE market. The strong upside spillover relationship from the GB to CE markets suggests that the better developed the GB market is, the better the CE market will develop. Moreover, as the QIRF suggests, the slow adjustment to equilibrium allows policymakers to intervene quickly and facilitate upside lagged risk spillovers between the two markets. Therefore, in order to promote the transition from traditional to CE as soon as possible, we need to continue to improve GB standards, improve GB-related regulatory mechanisms, optimize policy support on the issuance side, strengthen product optimization and innovation, further increase support on the investment side, and optimize investor structure and risk compensation mechanisms. Finally, our study further complements the theoretical foundation related to risk management in the GB and CE markets. However, there are some weaknesses in our study. The methodology used in this paper has some limitations and requires further research. In this paper, we use MVMQ-CAViaR and Granger causality in risk models only to explore the static tail risk spillover effect between GB and CE markets, but we do not consider the time-varying characteristics of this tail spillover effect. In fact, the tail spillover effect between these two markets is not constant, so we should also consider the spillover effect between the two markets from a time-varying perspective in future studies.