Hedging Carbon Price Risk on EU ETS: A Comparison of Green Bonds from the EU, US, and China

Abstract

This article aims to examine the hedging effect of green bonds in the US market, the European market, and the Chinese market on carbon price risk in the European Union Emission Trading System (EU ETS) from 2021 to 2023. By using daily datasets extracted from Bloomberg and the Vector Error Correction Model (VECM), the research provides evidence of the hedging effect of green bonds in all three markets on carbon price risk in the EU ETS. The paper concludes that the hedging ratio is positive for green bonds in the EU and China, while the figure for the US market is negative. Moreover, there is a positive effect of oil prices on carbon returns in EU ETS. Meanwhile, the opposite is found for stock prices.

1. Introduction

The detrimental effects of global warming, primarily driven by greenhouse gas emissions like CO₂, have inflicted significant damage on human society, including increased healthcare costs and reductions in crop and forest yields. The primary driver behind the surge in global carbon emissions is the rapid economic growth and escalating energy demands of nations. Jamel and Maktouf (2017) and Onofrei et al. (2022) provide evidence of the bidirectional nexus between GDP and CO₂ emissions in Europe from 1985 to 2014 [1,2]. Similar results are also found by Tong et al. (2020) for the E7 countries from 1971 to 2014 [3], and by Galvan et al. (2022) for middle-income trap Latin American countries [4]. Conversely, the adverse effect of economic expansion on CO₂ emissions is evident in Singapore [5] and in China [6]. Furthermore, Destek et al. (2020) indicate various impacts of economic growth on carbon emissions in the G7 countries over the very long period from 1800 to 2010: M-shaped for Canada and the UK, N-shaped for France, inverted N-shaped for Germany, and inverted M-shaped (W-shaped) for Italy, Japan and the US [7]. Therefore, to mitigate the ongoing climate change and sustain robust economic growth, nations have implemented proactive measures to address its effects, such as the Kyoto Protocol in December 1997 in Japan and the Paris Agreement in 2016. In line with policies taken by national governments, the world’s first emission trading system called the EU ETS was launched in 2005. This pioneering carbon dioxide emissions trading system is the largest in the world and has been instrumental in guiding the formation of carbon emission trading markets worldwide, which facilitates the trading among regulated entities and different kinds of investors [8].

For many years, the carbon market has experienced significant price fluctuations. To be precise, the price of CO₂ emissions in the EU ETS has increased from €8 per ton at the beginning of 2018 to around €85 at the ending of 2023, a more than tenfold increase after around six years, which led to bubbles in carbon prices from August 2019 in the global ETS in the European Union [9]. The high volatility of prices in the carbon market has caused difficulties for market participants. For instance, enterprises cannot reduce long-term emissions [10,11] or efficiently allocate resources that are able to reduce emisions [12], and this weakens the effectiveness of measures applied to decrease emissions in the long term [10,11,12,13]. Additionally, carbon market risks impede the price discovery signals, leading to challenges for enterprises to determine optimal low-carbon technology investments and hindering the attainment of national emission reduction objectives [14]. Therefore, hedging carbon market risk has become a significant preoccupation for investors and policy makers. Beside hedging tools such as derivatives, scholars have been interested in many financial instruments that have a hedging effect on carbon market risk. Zhang and Umair (2023) provide evidence on the significant interdependence among green bonds, renewable energy stocks, and carbon markets from January 2010 to December 2020 [15]. Similar findings are also given by Liu et al. (2023) and Lyu and Scholtens (2024) for some key emission markets, such as European countries, New Zealand, California, and Hubei (China) [16,17]. There are various reasons why green bonds have been one of several financial instruments on which scholars have focused on in an attempt to find solutions to deal with carbon price risk.

In terms of theories, the signaling theory states that green assets with low carbon footprints, such as green bonds, are favored by investors due to their pro-environmental benefits to the market [18,19,20], potentially resulting in better yield rates during market depressions. Additionally, according to Keynes’ liquidity preference theory of Keynes in 1936, investors tend to favor highly liquid assets or cash, while green bonds, being relatively low risk in terms of liquidity [21,22,23], often exhibit higher liquidity compared to conventional bonds [21]. Moreover, the modern portfolio theory proposed by Markowitz (1952) and the postmodern portfolio theory proposed by Rom and Ferguson (1993) mention the benefits of diversification by showing that an investor can achieve greater returns without taking on higher risk by choosing less risky assets such as bonds or green bonds in their portfolio of multiple assets [24,25]. Furthermore, the theory of minimum variance hedging proposed by Johnson (1960), which is based on Markowitz’s modern portfolio theory, indicates that the minimum variance hedging ratio is obtained by minimizing the portfolio risk [26].

Regarding empirical results, Abakah et al. (2023) confirm that the extent of total connectedness between green bonds and other assets examined (including green investments, carbon markets, financial markets and commodity markets) is at a high degree [27]. Jin et al. (2020) illustrate that the S&P Green Bond Index returns exhibit the highest connectedness with carbon future returns, compared to the S&P 500 Dynamic VIX Futures Index, the S&P Dynamic Commodity Futures Index and the S&P Energy Index, suggesting the efficacy of green bonds for hedging carbon futures, even during crisis periods [8]. Similarly, some scholars such as Zhang and Umair (2023) and Liu et al. (2023) fully support the hedging role of green bonds for carbon price volatility [15,16]. However, the opposite finding can be seen in the research of Tian et al. (2022) in emerging economies [28]. Similarly, Zhong et al. (2023) underline that the US green bond market does not provide an effective tool against cryptocurrency risks [29]. Kong et al. (2023) also indicate that China’s green bonds are an effective hedge under high global supply chain stresses, but global supply chain pressure might accompany the development of a green bond market due to the need for ecological environment improvement [30].

Considering the potential risks within the carbon market and the varying perspectives on the efficacy of green bonds as a financial instrument for hedging price risk, this study endeavors to compare the hedging effect of green bonds on European, American, and Chinese markets for the carbon market risk within the EU ETS over the recent three-year period from 2021 to 2023. This research period is examined because the spot carbon price in the European market has been highly volatile (fluctuating by around 20%) from 2021 to 2023, while few papers have yet compared the price dynamics of green bond markets and the European carbon market during Phase IV of the EU ETS (2021–2023). Furthermore, green bonds from key markets, namely the S&P Green Bond Index (SPGRUSS) in the US market, the Solactive Green Bond Index (SOLGREEN) in the EU market, and the FTSE Chinese (Onshore CNY) Green Bond Index (CFIICGRB) in the Chinese market, have been chosen. This selection is based on data from the Climate Bonds Initiative in 2021 and Statista Research Department in 2023 that indicated that these markets witnessed the highest cumulative issuance of green bonds globally, thus making them particularly worthy of exploration [31]. To be precise, China was the biggest issuer of green bonds worlwide in 2022 with a value of 85 billion US dollars, followed by the United States with green bond inssuance of 64.4 billion US dollars. Moreover, the EU ETS ranks as the largest carbon market globally, with a value of 169 billion euros in 2019, trailed by the US green bond market. Concurrently, during this period, China’s green bond market started to gather momentum [32].

To accomplish the research objectives, this paper examines four time-series datasets sourced from Bloomberg and analyzed through the VECM model. The paper makes two primary contributions. Firstly, it adds to the existing literature on the hedging efficacy of green bonds by presenting evidence of their role in managing carbon price risk. This is achieved by demonstrating both short-term and long-term relationships between the spot carbon price in the EU ETS and three categories of green bonds including the S&P Green Bond, the Solactive Green Bond, and the FTSE Chinese (Onshore CNY) Green Bond in the US, EU, and Chinese markets respectively. Secondly, the paper proposes ideas for cross-country hedging for spot carbon price risk within the EU ETS. To be precise, market participants can utilize hedging ratios to mitigate this risk by using three green bonds issued in the EU, the US market, and the Chinese market.

The subsequent sections of this paper are structured as follows: Section 2 provides a literature review concerning green bonds and its hedging impact on carbon price risk, accompanied by the development of hypotheses. Section 3 outlines the variables, data collection, and the methodology for data analysis. Empirical results are presented in Section 4 and then discussed in Section 5. Lastly, concluding remarks are made in Section 6.

2. Literature Review and Developing Hypotheses

Green bonds are defined as debt securities issued explicitly to raise capital in financing climate-related or environmentally friendly projects [33]. According to Tang and Zhang (2020), they are issued by institutions to mobilize capital in support of environmental investments such as renewable energy, pollution prevention, and climate change adaptation [34]. Paranque and Revelli (2019) indicate that green bonds should not be viewed merely as financial instruments but rather as integral components of social projects embedded within collective governance structures, as their utilization extends beyond environmental concerns to encompass social issues [35]. Supporting this perspective, Zhang et al. (2023b) argue that green bonds contribute to an increase in environmental responsibility among individuals and organization, leading to business activities conducive to sustainable development [36]. Moreover, Alamgir and Cheng (2023) suggest that countries with higher issuance of green bonds are more likely to complete envỉonmental goals such as renewable energy generation and CO₂ emission reductions, while countries with lower levels of green bond issuance struggle to meet their sustainability targets [37]. Moreover, Zheng et al. (2023) find that green bond issuance leads to an average increase in ESG scores of approximately 20.5 among corporate entities [38].

There is a strong relationship between green bonds and financial assets such as the exchange rate, cryptocurrency, stocks, and bonds. Reboredo (2018) and Arif et al. (2022) assert that green bonds serve as a substantial hedge against rare disasters, particularly evident in exchange markets in both the US and China from August 2014 to August 2021 [39,40]. However, this hedging efficacy witnessed a decline over the COVID-19 pandemic. Moreover, Nguyen et al. (2021) and Martiradonna et al. (2023) argue that the green bond indices had positive dynamic conditional correlation values with other indices, and green portfolios consistently outperformed non-green portfolios in terms of risk reduction through portfolio diversification [41,42]. The same findings are also concluded by Rehman et al. (2023) for the UK, Australian, Canadian, Japanese, Norwegian, and New Zealand markets [43]. However, the hedging role of green bonds is different among sectors. For instance, green bonds acted as a hedge across all sectors except for the financial sector over the COVID-19 pandemic. Zhong et al. (2023) confirm the hedging role of green bonds for cryptocurrency markets in China and the US [29], while Kong et al. (2023) find evidence on the effective hedge of green bonds on the global supply chain pressure indicator in China from January 2010 to June 2023 [30]. However, risk transmission among financial markets is mostly found in the short term and not generally in the medium and long terms [44]. In addition, there are opposite findings about the hedging role of green bonds for financial assets. Abuzayed and Al-Fayoumi (2022) highlight that in the US market between November 2014 and November 2020, the majority of time-varying green bonds witnesed low correlations with stocks, commodities, and clean energy, and this correlation exhibited minimal change during the COVID-19 period, except for corporate bonds [45]. Meanwhile, Man et al. (2023) observe that the Chinese green bonds market demonstrates high positive connectivity with the bonds market and weaker connectivity with the stock and crude oil markets [46]. Furthermore, Wei et al. (2023) illustrate a noteworthy two-way interdependent impact between the green bond market and the US Treasury market [47].

Furthermore, green bonds are considered to have a strict connectedness with green financial markets such as carbon markets [8,15]. Heine et al. (2019) confirm that green transitions improve if green bonds are combined with carbon pricing [48], which is supported by the fact that the utilization of the green bond market by power firms as a supplement to the carbon futures market for short-term hedging or speculative endeavors over an extended period, transitioning to long-term hedging activities only since 2018 [49]. Leitao et al. (2020) imply that in the EU ETS carbon market, green bonds positively and significantly affect carbon price movements in the case of low and high volatility, whereas the opposite effect can be seen for conventional bonds only in high volatility regimes [50]. Jin et al. (2020) suggest that the S&P Green Bond Index serves as the most effective hedging tool for carbon futures and maintains strong performance even during crisis periods due to its high connectivity, outperforming other green financial instruments [8]. Similarly, Rannou et al. (2020) demonstrate that green bonds issued in Europe between 2014 and 2019 could serve as a hedging instrument against EU carbon price risk [49]. Examining the US and Chinese markets, Li et al. (2022) find that the green bond index has a positive effect on carbon prices in the short and medium term and a negative impact on the carbon efficiency index [51]. Recently, Wu et al. (2023) show that, regardless of the timescale and market conditions, the Chinese carbon market is always a Granger cause of the green bond market [31]. Furthermore, on a short-term basis, the dynamic relationship between green bonds and carbon prices is most pronounced, with a positive impact observed in China from 2018 to 2020 [52].

Therefore, the working paper proposes the first hypothesis as follows:

Hypothesis 1 (H1). 

There is a hedging effect of green bonds on carbon price risk.

Moreover, market mechanisms also play a role in influencing green bonds and the hedging effect they have on carbon prices. According to the equilibrium price theory, CO₂ emission rights function as commodities, with their price determined by the law of supply and demand. Typically, there is a positive relationship between the demand for CO₂ emission rights and carbon prices. An increase in the demand for these rights leads to an increase in carbon prices, while a decrease in demand results in a price drop [53]. This market mechanism significantly affects carbon price volatility. Tang et al. (2017) discovered that market frequency was high, with durations of less than two months and amplitudes smaller than one euro [54]. Additionally, they found that external factors influenced carbon prices at a lower frequency, with durations larger than five months and ranges of more than two euros. Therefore, the working paper proposes the second hypothesis as follows:

Hypothesis 2 (H2). 

There are differences in the hedging effect of green bonds in the US market, EU market, and Chinese market on carbon price risk in the EU ETS.

Moreover, carbon price volatility also stems from many control factors, including the energy market, the stock market, policy uncertainty, market mechanisms, and other factors.

Firstly, energy markets affect the volatility of carbon prices. In fact, the growth of businesses is closely tied to their energy use. As businesses progress through different stages of development, their energy needs change, leading to movements in carbon prices. In addition, energy prices significantly influence energy demand and the energy structure [55]. As fossil fuels are identified as the primary contributors to CO₂ emissions [56,57], fluctuations in fossil fuel prices impact both the supply and demand for carbon credits. Consequently, these dynamics influence the carbon price [58]. Increases in fossil fuel prices initially result in higher production costs and lower profits for businesses, leading them to consider reducing production. A decrease in carbon dioxide emissions implies a reduced need for carbon credits, thereby leading to a reduction in carbon prices [59]. On the other hand, when governments implement policies for energy conservation and emission reduction, businesses turn to clean energy technologies, replacing traditional energy with clean energy, enhancing energy efficiency, and decreasing CO₂ emissions per unit of output. This reduces overall carbon emissions and ultimately brings down carbon prices [60,61,62,63]. Li et al. (2021) and Zhu et al. (2022) strongly affirm the interconnectedness between oil, gas, electricity, stock prices, and carbon prices [64,65]. Similarly, Wei et al. (2022) contend that price bubbles within the European Union Emissions Trading System (EU ETS), as well as those in New Zealand, South Korea, and Shenzhen (China), are closely associated with new and renewable energy and energy prices [9]. Vellachami et al. (2023) suggest that uncertainties in the crude oil and coal prices significantly and negatively impact the carbon market in Europe, while carbon market volatility is notably influenced by fluctuations in crude oil and coal prices [66]. Yufei (2023) provides evidence of the influence of coal prices, oil prices, and natural gas prices on trading prices within the Guangdong carbon market [67]. Jiang et al. (2023) emphasize the predominant impact of non-renewable energy on fluctuations in carbon prices [68]. They suggest that non-renewable energy and carbon markets mainly function as net recipients and can serve as hedge assets. Specifically, crude oil, which serves as a primary energy source for businesses, profoundly influences several financial dimensions of a company, encompassing investments and stock yields. Variations in oil prices significantly contribute to determining carbon emissions [69,70], leading to significant impacts on carbon prices [55,64,65]. Therefore, the working paper proposes the third hypothesis as follows:

Hypothesis 3 (H3). 

Oil prices have a negative impact on carbon price risk.

Secondly, there is a relationship between the stock market and carbon price volatility. In theory, the stock market would act as a macroeconomic or economic activity indicator. A rise in the stock index is typically linked with indications of a stable financial market, influencing market sentiment and facilitating an increase in the enterprises’ value, thereby expanding production. This surge in production subsequently leads to heightened demand for energy and results in increased carbon emissions, thus contributing to the rise of carbon prices [71,72]. There is evidence showing that stock prices are positively correlated with carbon prices [62] and that the stock market is one of the driving factors of carbon prices, with significant long-term impacts. Zhou and Li (2019) show that the Shanghai Industrial Index and Shanghai and Shenzhen 300 Index had positive and negative effects on carbon emission prices, respectively [73]. Yufei (2023) finds that the trading price of the Guangdong carbon market is highly influenced by the CSI 300 index [67]. Similarly, Duan et al. (2023) examine the dynamic cross-market risk interdependence between the carbon market and financial markets through a quantile-based research approach [74]. They utilize data on carbon futures from the Intercontinental Exchange and financial equities including various indices such as the Toronto Stock Exchange Index, the Financial Times Stock Exchange 100 Index, the STOXX Europe 600 Index, the Australian Securities Exchange Index, and the S&P 500 Index (SP500). Therefore, the working paper proposes the fourth hypothesis as follows:

Hypothesis 4 (H4). 

Stock indexes have positive impacts on carbon price risk.

Furthermore, carbon price volatility can result from the risks of policy uncertainty. The uncertainty surrounding economic policies theoretically prompts enterprises to constantly revise their production capacity expectations and engage in non-compliant trading, thereby contributing to the carbon price volatility. Additionally, economic policy uncertainty (EPU) creates speculative opportunities for financial intermediaries, intensifying information asymmetry between emitting firms and financial institutions. This, in turn, leads to fluctuations in prices within carbon markets [75]. Jiang et al. (2019) argue that EPU influences CO₂ emissions in two ways, including a direct policy adjustment effect and an indirect economic demand effect [76]. The direct policy adjustment effect suggests that when EPU is high, policy makers shift their focus from environmental conservation to stabilizing the economy, leading to an increase in CO₂ emissions. Conversely, the indirect economic demand effect indicates that EPU can modify economic conditions and decision-making processes, thereby impacting energy consumption. Consequently, any changes in energy consumption can ultimately affect CO₂ emissions. According to Dai et al. (2022), European and global economic policy uncertainty had a positive impact on the volatility of European carbon spot returns in the long term [75]. Furthermore, this fluctuation can be forecast more accurately by the predictor of global economic policy uncertainty. Similarly, Zhao and Wen (2022) provide evidence of the significant effects of structural breaks on risk-return relations in Chinese carbon markets from June 2013 to August 2020 [77]. The same conclusions are also provided by Tian et al. (2022) for emerging economies [28] and Ren et al. (2022) for the ECX EUA carbon futures [78]. Wang et al. (2022) investigated global events like the US exit from the Paris Agreement, the COVID-19 pandemic, and the Russian-Ukraine conflict, indicating that climate policy uncertainty consistently acts as a global recipient of risk [79]. They note its passive responsiveness to other markets such as energy, green bonds, and carbon markets. Li et al. (2023) present findings from China, suggesting that the effect of economic policy uncertainty on carbon prices varies over time, notably exhibiting a significant short-term effect [53].

Additionally, there exists a connection between renewable energy and the risk associated with carbon prices. Dai et al. (2018) highlight that increased development of renewable energy results in reduced costs for carbon mitigation and lower volumes of carbon trading, implying that higher usage of renewable energy in power generation significantly decreases both the quantity and prices of traded carbon [80]. Mu et al. (2018) also emphasize that an increase in renewable energy sources leads to job creation opportunities and a decrease in permit prices within the carbon market [81]. Furthermore, Tu and Mo (2017) demonstrate that the targets established by the Chinese government for 2020 may cause a decline in CO₂ prices due to subsidies for renewable energy power [82]. Ha (2023) reveals that the connections between various green energy sources (such as wind, solar, biogas, biofuels, and geothermal energy) and carbon risk fluctuate over time [83].

In addition, the risks in carbon emission trading markets also stem from other factors, such as macroeconomic factors [9] including market operation risks [14], geopolitical risk [84], or carbon market-related policies [14]. However, because of the challenges in data collection regarding these factors, this working paper only focuses on oil prices and stock indexes instead of investigating other factors such as EPU or the renewable energy market.

3. Methodology

3.1. Measuring Variables

3.1.1. Dependent Variable: Carbon Price Risk (CPR)

To assess carbon price risk, scholars such as Jin et al. (2020), Ye and Xue (2021), Wu et al. (2023), and Yang et al. (2024) selected the daily carbon spot price when they performed their empirical analyses. In this research, spot carbon dioxide (CO₂) emissions and the EUA Price/Europe (EUETSSY1 Index) were used [8,31,85,86]. Additionally, returns were calculated by taking natural logarithms of the daily carbon spot price as follows:

$${CPR}_t=ln\left( \frac{P_{c, t}}{P_{c, t-1}} \right)\times 100$$

where

○

${CPR}_t$: The return of carbon price on day t.

○

$P_{c, t}$: The carbon price on day t.

○

$P_{c, t-1}$: The carbon price on day t − 1.

3.1.2. Independent Variable: Green Bond Index (GBI)

In this working paper, there are three types of green bond indexes used, including the S&P Green Bond, the Solactive Green Bond, and the FTSE Chinese (Onshore CNY) Green Bond on the US, EU, and Chinese markets, respectively. The green bond index is measured through profitability, which can be depicted as follows:

$${GBR}_{ t}=ln \left( \frac{I_{gb, t}}{I_{gb, t-1}} \right)\times 100$$

where

○

${GBR}_{ t}$: The return of the green bond index on day t.

○

$I_{gb, t}$: The green bond index on day t.

○

$I_{gb, t-1}$: The green bond index on day t − 1.

3.1.3. Control Variables

This working paper used Brent prices as a representation of crude oil prices. Like the studies of Maghyereh and Abdoh (2020), this research used daily price oil to calculate oil price uncertainty [87]. The equation is as follows:

$${COR}_t=ln \left(\frac{{COP}_t}{{COP}_{t-1}}\right)$$

where

○

${COR}_t$: The crude oil returns on day t.

○

${COP}_t$: The crude oil price on day t.

○

${COP}_{t-1}$: The crude oil price on day t − 1.

Regarding the stock market index, this is understood as the stock index return of the FTSE Eurotop 100 Index. This variable is computed as follows:

$${SIR}_t=ln \left(\frac{{SI}_t}{{SI}_{t-1}}\right)$$

where

○

${SIR}_t$: The stock index returns on day t.

○

${SI}_t$: The stock index on day t.

○

${SI}_{t-1}$: The stock index on day t − 1.

Table 1. Description of variables.

Name	Code	Measure	References
Dependent variable (Carbon Price Risk)	CPR	${CPR}_t=ln\left( \frac{P_{c, t}}{P_{c, t-1}} \right)$	[8,31,85,86]
Independent variable (Green Bond Index)	GBR	${GBR}_{ t}=ln \left( \frac{I_{gb, t}}{I_{gb, t-1}} \right)$	[8,33,88]
Oil price	COR	${COR}_t=ln \left(\frac{{COP}_t}{{COP}_{t-1}}\right)$	[52,56,71,83,89]
Stock index	SIR	${SIR}_t=ln \left(\frac{{SI}_t}{{SI}_{t-1}}\right)$	[8,47,74,90]

Source: Authors.

describes in detail the variables used in this research.

3.2. Data Collection

In this paper, we used daily data spanning from 2021 to 2023 to examine the hedging effect of green bonds on carbon market price risk. The Spot Carbon Dioxide (CO₂) Emissions EUA Price/Europe (EUETSSY1) Index was used for the carbon price in EU ETS, while the S&P Green Bond, SOLGREEN Index, and CFIICGRB Index was used for the US, EU, and Chinese markets, respectively. These data were sourced from Bloomberg. In terms of control variables, daily data on crude oil prices were collected and the daily stock index (FTSE Eurotop 100 Index) was taken from Thomas Reuters Datastream. Regarding the research period, this study focuses on the three-year-period from 2021 to 2023. This is not only because this time period experienced the highest volatility of spot carbon price on the EU ETS but also because of the availability of Spot Carbon Dioxide (CO₂) data on Bloomberg.

3.3. Data Analysis

Firstly, this research paper uses the VECM model to examine the hedging effect of green bonds on carbon market price risk with five stages as follows:

▪

Step 1. Unit root test.

To test the stationarity of the time series, we can use various methods, which include the Dickey Fuller test (DF test), the Phillips–Perron test (PP test), and the extended Dickey–Fuller test (ADF test). The DF test proposed by Dickey and Fuller (1979) is commonly and widely used for unit root tests [91], while the ADF test is the autocorrelation of non-systematic components in DF models [92]. Therefore, the ADF test can be used for more extensive and sophisticated time-series models [93]. Thus, this research makes use of these methods. The formula estimated for the ADF test is as follows:

$$\Delta Y_t={\beta }_1+{\beta }_{2}t+\alpha Y_{t-1}+\delta \mathsf{\Sigma }\Delta T_{t-1}+{\epsilon }_t$$

where

○

${\epsilon }_t$: error term.

○

${\beta }_1$: drift term.

○

${\beta }_2$: time trend.

○

$\Delta$: differencing operator.

▪

Step 2. Estimate VAR–lag length selection.

For the optimal lag length, the Akaike information criterion (AIC), the Schwarz information criterion (SC), the final prediction error criterion (FPE), and the Hannan–Quinn information criterion (HQ), have been applied in many studies. This research determined the optimal lag length based on the one with the lowest statistical value.

▪

Step 3. Co-integration test.

Trace test statistics and Max Eigenvalue statistics are the two test statistics of cointegration that the research uses to determine the cointegrating vector number. This is based on the following equations:

$$\begin{gathered} \Delta ln{Y}_t={\alpha }_0+\mathsf{\Sigma } {\beta }_i\Delta ln{Y}_t+\mathsf{\Sigma } {\chi }_j\Delta ln{X}_t+{\epsilon }_t \\ \Delta ln{X}_t={\gamma }_0+\mathsf{\Sigma } {\sigma }_i\Delta ln{Y}_t+\Sigma {\tau }_j\Delta ln{X}_t+{\epsilon }_t \end{gathered}$$

where

○

$Y_t$ and $X_t$ are carbon and green bond price indexes, respectively.

○

$\Delta$ is a difference operator.

○

${\epsilon }_t$ is a random error term with a mean of zero.

○

${\alpha }_0$ and ${\gamma }_0$ are drift terms.

○

${\beta }_i$,${ \sigma }_i$, ${\chi }_j$ and ${\tau }_j$ are the coefficient estimates for independent variables.

There are two hypotheses:

○

$H_0$: No co-integrating equation between carbon prices and green bond prices.

○

$H_1$: Co-integrating equation between carbon prices and green bond prices.

The research will reject hypothesis $H_0$ if the value of the Trace and Max statistics exceeds the 5% critical value.

▪

Step 4. Modeling co-integrated time series data (VECM).

The following equation proposed by Masih and Masih (1996) can explain the ECM [94]:

$$\begin{gathered} {CPR}_{\mathrm{t}}={\alpha }_0+\sum _{i=1}^{k-1}{\beta }_i{CPR}_{\mathrm{t}-\mathrm{i}}+\sum _{j=1}^{k-1}{\beta }_j{GBI}_{EU, t-j}+\sum _{m=1}^{k-1}{\beta }_m{COR}_{t-m}+\sum _{f=1}^{k-1}{\beta }_f{SIR}_{t-f}+{+\gamma }_{it}{ECT}_{t-h}+{\epsilon }_t \\ {CPR}_{\mathrm{t}}={\alpha }_0+\sum _{i=1}^{k-1}{\beta }_i{CPR}_{\mathrm{t}-\mathrm{i}}+\sum _{j=1}^{k-1}{\beta }_j{GBI}_{US, t-j}+\sum _{m=1}^{k-1}{\beta }_m{COR}_{t-m}+\sum _{f=1}^{k-1}{\beta }_f{SIR}_{t-f}+{+\gamma }_{it}{ECT}_{t-h} \\ {CPR}_{\mathrm{t}}={\alpha }_0+\sum _{i=1}^{k-1}{\beta }_i{CPR}_{\mathrm{t}-\mathrm{i}}+\sum _{j=1}^{k-1}{\beta }_j{GBI}_{CN, t-j}+\sum _{m=1}^{k-1}{\beta }_m{COR}_{t-m}+\sum _{f=1}^{k-1}{\beta }_f{SIR}_{t-f}+{+\gamma }_{it}{ECT}_{t-h} \end{gathered}$$

where

○

t − h is the difference between the lag length t and h.

○

$\alpha and \beta$ are short-run dynamic coefficients in the model’s adjustment long-run equilibrium.

○

${\gamma }_{it}$ is the speed of adjustment parameter with a negative sign.

○

${ECT}_{t-h}$ is the error correction term with lagged value of t − h.

○

${\epsilon }_t$ is residuals.

▪

Step 5: Robustness check.

Finally, this paper uses the Breusch–Godfrey Lagrange Multiplier (LM) test [95,96] and tests for heteroscedasticity using the Breusch–Pagan Godfrey test [95] to determine serial correlation. Simultaneously, the Jarque–Bera test for normality and the LM test [95,96] are applied to check the model’s robustness and accuracy.

Secondly, in the case of evidence of a long-run relationship between the green bond index and spot carbon price, the hedging ratio for these two assets is calculated. In theory, a hedging ratio is a comparison of the green bond index purchased or sold to the value of the spot carbon price being hedged. Therefore, the optimal hedge ratio (h*) is used to minimize the variance of the position’s value. This ratio is calculated as follows:

$${h^{*}}_i={\rho }_{i, CP}\frac{{\sigma }_{CP}}{{\sigma }_i}$$

where

○

${\rho }_{i, CP}$ is the correlation coefficient between the green bond index i and the spot carbon price.

○

${\sigma }_{CP}$ is the standard deviation of the spot carbon price.

○

${\sigma }_i$ is the standard deviation of the green bond index i.

4. Empirical Results

4.1. Statistical Description

Table 2. Descriptive statistics of the return series of sample sequences.

CPR		GBR_EU	GBR_US	GBR_CN	COR	SIR_EU
Mean	0.000979	−0.000274	−0.000227	0.000163	0.000254	0.000311
Median	0.000000	−0.000238	−0.000162	0.000136	0.002844	0.000872
Maximum	0.128381	0.024001	0.011026	0.002648	0.081564	0.043134
Minimum	−0.170425	−0.021242	−0.013655	−0.003097	−0.133124	−0.037643
Std. Dev.	0.025676	0.005501	0.002906	0.000561	0.025066	0.009190
Skewness	−0.240002	0.260518	−0.002216	0.083118	−0.601112	−0.308899
Kurtosis	9.690770	4.716120	3.940862	6.566629	5.504545	5.237227
Jarque-Bera	1312.407	93.81591	25.81955	371.8306	225.1109	157.1167
Probability	0.000000	0.000000	0.000002	0.000000	0.000000	0.000000
Sum	0.685063	−0.192072	−0.159039	0.113808	0.178032	0.217393
Sum Sq. Dev.	0.460838	0.021154	0.005904	0.000220	0.439172	0.059039
Observations	700	700	700	700	700	700

Note: (i) This table gives the descriptive statistics of the return series of ECX EUA Carbon spot price, Crude oil daily return, EU stock index, and green bond indices of the EU, US, and China. (ii) The time period is from 18 February 2021 to 29 December 2023. Source: Extracted results from Eviews.

provides information about the descriptive statistics of the data. The CPR and COR demonstrate considerable standard deviations, indicating relatively large variations in comparison to other variables. Moreover, the positive skewness of the GBR_EU and GBR_CN distributions indicates a right-skewed distribution shape of the data, compared to a normal distribution, and the skewness values of GBR_EU and GBR_CN indicate a higher frequency of values on the left side of the distribution, with a long tail extending to the right. The kurtosis values of the sample sequence exceed 3, indicating heavier tails and sharper peaks than a normal distribution. Notably, the high Jarque–Bera values for all variables indicate non-normal distributions.

4.2. The Hedging Effect of Green Bonds in Carbon Market Risk

Table 3. Unit root test.

Variables	t-Statistic	Prob.	Level
CPR-EU	−24.75907	0.0000	I(0)
GBR-EU	−23.04010	0.0000	I(0)
GBR-US	−23.14812	0.0000	I(0)
GBR-CN	−23.61262	0.0000	I(0)
COR	−25.64648	0.0000	I(0)
SIR-EU	−26.54238	0.0000	I(0)

Source: Extracted results from Eviews.

gives evidence for the level differences in the ADF tests for all variables, showing the stationarity at level I(0) for all data. Thus, the p-values are all smaller than 5%, hence the null hypothesis is rejected.

For the optimal lag length,

Table 4. Lag length selection.

Variables	LR	FPE	AIC	SC	HQ
Model 1 for the EU	4	1	1	0	0
Model 2 for the US	3	2	2	0	1
Model 3 for China	8	1	1	0	0

Source: Extracted results from Eviews.

points out that in model 1, the benchmark LR suggests an optimal delay of 4, while 1 is the lag length proposed by FPE and AIC criteria, and the SC and HQ criteria propose 0. Therefore, a lag length of 1 for model 1 was chosen. For model 2, LR indicates a lag length of 3, while FPE and AIC suggest a lag length of 2; SC states that the optimal lag is 0 and HQ recommends 1. In conclusion, a lag length of 2 was chosen for model 2. Regarding model 3, the benchmark LR suggests an optimal delay of 8, while FPE and AIC propose 1; SC and HQ recommend 0. Hence, the lag length for model 3 is 1.

Then, the Trace and Max Eigenvalue statistical values of the Johansen cointegration test results are smaller than the 5% critical value, meaning the rejection of the null hypothesis at the 5% level across the 3 models. Hence, there is cointegration at the 5% significance level between carbon price volatility and green bond index in the three markets from 18 February 2021 to 29 December 2023 (

Table 5. Co-integration test.

Test	No. of CE(s)	Eigenvalue	Trace	Test 0.05	Prob.
Model 1 for EU	None *	0.324348	847.0746	47.85613	0.0000
	At most 1 *	0.295391	573.7967	29.79707	0.0000
	At most 2 *	0.223063	329.7687	15.49471	0.0000
	At most 3 *	0.198066	153.8485	3.841465	0.0000
Model 2 for US	None *	0.323798	846.4968	47.85613	0.0000
	At most 1 *	0.295606	573.7864	29.79707	0.0000
	At most 2 *	0.222231	329.5451	15.49471	0.0000
	At most 3 *	0.198667	154.3709	3.841465	0.0000
Model 3 for CN	None *	0.298093	820.7376	47.85613	0.0000
	At most 1 *	0.292945	574.0316	29.79707	0.0000
	At most 2 *	0.238506	332.4185	15.49471	0.0000
	At most 3 *	0.184908	142.5050	3.841465	0.0000

Notes: Trace test indicates four co-integrating equations at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level. Source: Results extracted from Eviews.

). Thus, the cointegration among variables in the three models is confirmed by the Johansen tests.

Concerning modeling co-integrated time series data (VECM), the relationship between variables in both the short and long run are presented in

Table 6. VECM.

	The EU				The US				CN
	Coefficient	t-Statistic	s.e.	Prob.	Coefficient	t-Statistic	s.e.	Prob.	Coefficient	t-Statistic	s.e.	Prob.
C(1)	−0.757427	−15.04322	0.050350	0.0000	−0.167628	−5.150445	0.032546	0.0000	−0.489653	−11.67142	0.041953	0.0000
C(2)	0.885123	4.414306	0.200512	0.0000	−1.243341	−2.022530	0.614746	0.0435	17.24785	8.153292	2.115446	0.0000
C(3)	−0.098153	−1.792353	0.054762	0.0735	−0.103424	−1.386948	0.074569	0.1659	−0.163848	−2.850560	0.057479	0.0045
C(4)	−0.125370	−3.279633	0.038227	0.0011	−0.566733	−13.99489	0.040496	0.0000	−0.258525	−6.966182	0.037111	0.0000
C(5)	−0.725454	−4.266991	0.170015	0.0000	−0.310735	−8.411965	0.036940	0.0000	−9.009760	−5.033565	1.789936	0.0000
C(6)	0.061153	1.525554	0.040086	0.1276	0.035761	0.071535	0.499908	0.9430	0.115957	2.784239	0.041648	0.0055
C(7)	−0.286319	−2.466455	0.116085	0.0139	0.330565	0.885445	0.373332	0.3762	−0.314664	−2.703928	0.116373	0.0070
C(8)	0.000158	0.157260	0.001003	0.8751	0.094656	1.588912	0.059573	0.1125	0.000160	0.151452	0.001059	0.8797
C(9)					0.009657	0.224050	0.043101	0.8228
C(10)					−0.586097	−3.383934	0.173200	0.0008
C(11)					−0.159293	−1.322362	0.120461	0.1865
C(12)					0.000187	0.176236	0.001062	0.8602

.

▪

Model for the EU

In the case of the EU, the coefficient of ${CPR\_EU}_{t-1}$ equals to −0.125370, which means a negative relationship between carbon price returns in the EU on day t and the previous day. Furthermore, the coefficient of the EU green bond at lag t − 1 equals−0.725454, implying a negatvie influence of the EU’s green bonds on changes in carbon prices in the EU, meaning that H1 is accepted. The coefficient of oil prices at lag t − 1 equals 0.061153, which means a positive effect of oil prices on carbon price return, meaning H3 is rejected. By contrast, the stock price in the EU at lag t − 1 is 0.286319, showing a positive relationship between oil prices and carbon price returns. This means H4 is accepted. Regarding the permanent relationship between variables in the EU through error correction terms, the error correction terms (ECT) for model 1 is −0.757427, which is within the range of −1 and 0. In addition, the probability value is 0.0%, meaning a significance at the 5% level. This confirms a significant relationship between variables and indicates that it will take a 75% adjustment per day to reach long-term equilibrium in the EU.

▪

Model for the US

Regarding the case of the US, the coefficient of ${CPR\_EU}_{t-1}$ and ${CPR\_EU}_{t-2}$ equals −0.566733 and −0.310735, meaning a negative relationship between carbon price returns in the EU on day t and that of the previous days. Moreover, the coefficients of the US green bonds at lag t − 1 and t − 2 are 0.035761 and 0.330565, respectively, implying that in the short run, the fluctuation in the US’s green bonds positively affects changes in carbon price in the EU, meaning that H1 is accepted. The coefficient of the oil price at lag t − 1 and t − 2 is 0.094656 and 0.009657, meaning a positive impact of oil price on carbon price return or a rejection of H3. By contrast, the stock price in the EU at lag t − 1 and t − 2 is −0.586097 and −0.159293, indicating a negative relationship between oil price and carbon price return. This means H4 is rejected. In terms of the long-run relationship, the error correction term (ECT) for model 2 is −0.167628 with a probability value of 0.0%, meaning a relationship between the variables at the 5% level. Finally, this result indicates a daily adjustment of 16.7% for long-term equilibrium in the EU.

▪

Model for China

In the case of using Chinese green bonds, the coefficient of ${CPR\_EU}_{t-1}$ equals−0.258525, meaning a negative relationship between carbon price return in the EU on day t and that of the previous day. Moreover, the coefficient of Chinese green bonds at lag t − 1 is −9.009760, meaning a negative effect of green bonds on changes in carbon price in the EU, or an acceptance of H1. The coefficient of oil price at lag t − 1 is 0.115957, meaning there is a positive influence of oil price on carbon price return, or H3 is rejected. By contrast, the stock price in China at lag t − 1 is −0.314664, indicating a negative relationship between oil price and carbon price return. This means H4 is rejected. Pertaining to the long-run relationship, the error correction term (ECT) for model 3 is −0.489653 at a probability value of 0.0%, indicating a significant relationship between variables at the significant value of 5%. Additionally, it will take a 48.96% adjustment per day to reach long-term equilibrium in the EU.

Furthermore, lag length and coefficient values are completely different between the EU, US, and Chinese green bonds, implying that there are differences in the hedging effect of green bonds in the US market, EU market, and Chinese market on carbon price risk in EU ETS. In other words, H2 is accepted.

4.3. The Hedging Ratio of Green Bonds for Spot Carbon Price on EU ETS

From the outcome of standard deviation in Table 1 and correlation in

Table 7. Correlation between the return series of sample sequences.

COR		CPR_EU	GBR_CN	GBR_EU	GBR_US	SIR_EU
COR	1.000000	−0.082062	−0.027205	−0.010020	−0.050380	0.135933
CPR_EU	−0.082062	1.000000	−0.035373	0.062608	0.054734	0.075949
GBR_CN	−0.027205	−0.035373	1.000000	0.018541	−0.003575	−0.039040
GBR_EU	−0.010020	0.062608	0.018541	1.000000	0.682323	0.284340
GBR_US	−0.050380	0.054734	−0.003575	0.682323	1.000000	0.092096
SIR_EU	0.135933	0.075949	−0.039040	0.284340	0.092096	1.000000

Source: Extracted results from Eviews.

, we have calculated the hedging ratio of the three green bond markets affecting the EU carbon market (

Table 8. Hedging ratio.

Markets	Hedging Ratio
h(CPREU/GBR_US)	−0.31254
h(CPREU/GBR_EU)	0.292228
h(CPREU/GBR_CN)	2.505122

Source: Extracted results from Eviews.

). With a positive optimal hedging ratio, a short position in the market index should be added to the portfolio and with a negative optimal hedging ratio, a long position in the market index should be added to the portfolio when the optimal ratio is negative. The hedging ratios of the US as well as China are −0.3.254 and 2.505122, respectively. This suggests that China’s hedging ratio is observed to be at the pinnacle, indicating the strongest defensive capability among the three markets. On the other hand, the US’s hedging ratio is in negative territory, reflecting the lack of effective defensive capacity of its green bonds. Furthermore, the standard deviations for EU green bonds are the highest followed by US green bonds, demonstrating that hedging ratios of these green bonds may not be stable over time. The standard deviation of the Chinese green bonds is observed to be the lowest, indicating a tighter probability distribution and consequently, a lower risk. This implies that a smaller standard deviation is associated with a lower dispersion of returns, thereby reducing the potential risk. Additionally, the hedging ratio for China is the highest, signifying the lowest risk among the considered options. These findings underscore the robustness of this investment strategy, which could be a significant consideration for investors in their decision-making processes.

5. Discussion

By using the VECM model, this paper provides evidence of the hedging effect of green bonds (the S&P Green Bond, Solactive Green Bond, and FTSE Chinese Green Bond on the US market, the EU market, and Chinese market, respectively) on carbon price risk in the EU ETS over the period from 2021 to 2023, despite differences between the impacts of these three green bonds. There are also significant impacts of stock indexes and oil prices on carbon price risk in the EU ETS.

Firstly, green bonds play a hedging role for carbon price risk in the EU ETS since there are both short-run and long-run relationships between carbon price risk and all three green bonds described above. This finding entirely supports signaling theory, confirming that firms can increasingly use green bonds for risk position mitigation, enabling them to communicate pro-environmental messages through the market. This research result is also consistent with the conclusions of Leitao et al. (2020) and Rannou et al. (2021) who also emphasized the close relationship between green bonds and the carbon market [49,50], particularly within the EU ETS, both in the short term and the long term. Furthermore, Jin et al. (2020) asserted that the S&P Green Bond return exhibits the highest connectedness with carbon futures returns compared to other indexes, thereby validating the effectiveness of green bonds as instruments for hedging against carbon price risks on a market scale [8]. Additionally, Li et al. (2022a) arrived at comparable conclusions regarding the positive effect of green bonds on carbon price returns in the US and Chinese markets simultaneously [51].

Secondly, divergences were observed within the hedging effects of green bonds in the US, EU, and Chinese markets on carbon price risk in the EU ETS in terms of lag length, coefficient values, and hedging ratios. To be precise, the optimal lag length of the EU and Chinese green bonds is one day, which shares a similar pattern with the findings of Zhang et al. (2021) [97], while the figure for the US green bonds is two days, which is in line with Amountzias et al. (2017) [98]. In other words, carbon prices in the EU will respond within one day if there are some changes in green bond indexes of the EU and China while it takes two days for the carbon prices in the EU to react with green bond indexes of the US. This finding highlights the dominant role of the US green bond market for spillover transmission to other green bond markets [32].

In addition, the highest coefficient was observable in the link between EU green bonds and carbon price in the EU ETS, which can be clearly and simply explained due to the fact that both instruments are exchanged within the same European Union market. In fact, the EU green bonds, which are closely aligned with the EU’s sustainability standards and green investment criteria, do indeed have a robust hedging effect on EU carbon prices, which underscores the pivotal role of EU green bonds in advancing the region’s shift towards a low-carbon economy and mitigating carbon price volatility. Hedging against carbon price risk in the EU ETS by using EU green bonds also allows investors to mitigate the risk associated with exchange rate fluctuations. Furthermore, although the Chinese green bond index experiences the lowest coefficient, it could potentially function as an effective hedging tool because of China’s commitment to environmental sustainability and the rapid expansion of its green bond market. A short position in the green bond index in China can serve as a hedge for a long position in carbon futures.

Furthermore, the optimal hedging ratio for US green bonds is negative, while positive ratios can be seen for the EU and China’s green bonds. This means that, in the case of US green bonds, a long position of one dollar in respect of spot EUA carbon prices can be diversified by a long position in the US green bond market. In contrast, regarding the EU and China’s green bonds market, a long position of one dollar in respect of spot EUA carbon prices can be hedged by a short position in the respective green bonds market. This can be explained by differences in regulatory frameworks and market dynamics between the United States and the European Union, notably in terms of environmental policies and carbon pricing mechanisms. In fact, both the EU ETS and the Chinese carbon trading market possess the fundamental characteristics of trading markets, and the operation of the markets can be measured. The potential types of mutual impact between the EU and Chinese carbon trading market are as follows: (i) The Chinese carbon trading market’s sale of carbon allowances to the world influences the EU ETS. As an important trading counterpart, China sells carbon credit to the international markets annually, which means that any alterations or volatility in the Chinese carbon prices affect the EU ETS; (ii) China’s carbon trading market, being in its nascent stages of development, and its pricing and trading process is highly responsive to the influences from the EU carbon trading market. The EU carbon trading market, which has developed over many years, may influence the activities of China’s carbon trading market. Moreover, the Chinese industry sector is predominantly composed of heavy chemicals and fossil fuels, influencing China’s carbon trading market through the efficiency and activity of foreign carbon trading markets. By contrast, the carbon allowance market in the US is characterized by distinct attributes and follows different procedures for price determination compared to the EU market. The only contract-based market on carbon credit in the US operates on a voluntary participation basis, while the carbon allowance market under the EU ETS is a mandatory system. Under the EU ETS, emission allowances are allocated to installations emitting CO₂ by the governments and can be negotiated on exchanges as well as over the counter. The US stands as the only country that, despite signing, opted not to approve the Kyoto Protocol; several separate initiatives have started at the state level, and a voluntary cap-and-trade system was implemented in 2003 [99] (Kim and Koo; 2010).

Thirdly, this paper confirms the important role of oil prices and stock indexes for the stability of the carbon spot price in EU ETS, which entirely supports the conclusions given by Zhang and Umair (2023) [15] regarding dynamic spillovers among crude oil, stocks, green bonds, and carbon markets on a global scale. Oil prices exert a consistently positive influence on carbon price risk in the EU ETS. This finding is consistent with the conclusions of Yufei (2023) [67] but is different from research results from Vellachami et al. (2023), who show that in the European context, uncertainties in the crude oil and coal markets have a substantial and negative impact on carbon market returns [66]. However, this study reveals insights into the interplay between stock prices and carbon price risk when considering different types of green bonds. Models for US and Chinese green bonds show a negative impact of the stock index on carbon price risks, while the opposite effect can be seen in the model for the EU market. The positive impact of the stock market on the risk of carbon price is already confirmed by Zhou and Li (2019), Duan et al. (2023), and Yufei (2023) [67,73,74]. By contrast, Zhou and Li (2019) gave evidence of the negative impact of the Shanghai and Shenzhen 300 Index on China’s carbon emission prices [73].

6. Conclusions

This research provides evidence for the hedging role of green bonds for carbon price risk in the EU ETS, although green bonds in the US, EU, and Chinese markets impact carbon price risk in different ways and to differing degrees. This study shows that there is connectedness between crude oil, stock indexes, green bonds, and carbon price. Therefore, this working paper provides contributions in terms of theory and practice.

Regarding theories, the research results contribute to enriching the literature about the important role of green bonds for alternative green products, like carbon credit, as well as support the existence of dynamic spillovers among crude oil, stocks, green bonds, and carbon markets. In terms of practical implications, firms can consider green bonds as a hedging tool to protect themselves against the fluctuations of carbon prices. Alongside green bonds, crude oil price and stock indexes should be considered when firms examine the risks of carbon prices since they are closely correlated. Policy makers can utilize findings like these to develop green bond markets in their countries to promote national sustainable development.

However, this research does have some limitations. First, due to the unavailability of data about carbon prices and green bond indexes, the research sample is quite limited, running only from 2021 to 2023. In addition, since this sample period includes the COVID-19 pandemic, the findings may be typical in this context. Second, difficulties in collecting data led to the fact that this research only considers some determinants, such as oil price and stock indexes, without considering other factors like economic policy uncertainty or commodity prices. Future research could potentially resolve these limitations.