Dynamic spillover effects among green bond, renewable energy stocks and carbon markets during COVID-19 pandemic: Implications for hedging and investments strategies

Abstract

This study has been inspired by the emergence of socially responsible investment practices in mainstream investment activity as it examines the transmission of return patterns between green bonds, carbon prices, and renewable energy stocks, using daily data spanning from 4th January 2015 to 22nd September 2020. In this study, our dataset comprises the price indices of S&P Green Bond, Solactive Global Solar, Solactive Global Wind, S&P Global Clean Energy and Carbon. We employ the TVP-VAR approach to investigate the return spillovers and connectedness, and various portfolio techniques including minimum variance portfolio, minimum correlation portfolio and the recently developed minimum connectedness portfolio to test portfolio performance. Additionally, a LASSO dynamic connectedness model is used for robustness purposes. The empirical results from the TVP-VAR indicate that the dynamic total connectedness across the assets is heterogeneous over time and economic event dependent. Moreover, our findings suggest that clean energy dominates all other markets and is seen to be the main net transmitter of shocks in the entire network with Green Bonds and Solactive Global Wind, emerging to be the major recipients of shocks in the system. Based on the hedging effectiveness, we show that bivariate and multivariate portfolios significantly reduce the risk of investing in a single asset except for Green Bonds. Finally, the minimum connectedness portfolio reaches the highest Sharpe ratio implying that information concerning the return transmission process is helpful for portfolio creation. The same pattern has been observed during the COVID-19 pandemic period.

1. Introduction

Climate change has received a lot of attention from policy makers owing to its widespread effects on firms, households, and economies. The physical risk of climate change to economic agents emanating from natural disasters leads to the destruction of capital stock, loss of human lives and the disruption of economic activities (International Monetary Fund, 2020). Indeed, Guo et al. (2021) project that by 2050, climate change will take away about 10% of global economic value if the rising temperature levels follow the current trajectory. For investors, particularly institutional investors with huge funds under their management, climate change poses high portfolio risks even though it also presents investment opportunities as well (Mercer, 2015). There are therefore renewed global commitments to cut global carbon emissions and reduce rising temperature levels to tackle climate change (Intergovernmental Panel on Climate Change, 2014). These commitments have focused on mitigation and adaptation strategies aimed at tackling climate change. Some of these strategies include renewable energy, issuance of green bonds, and carbon pricing.

The use of fossil fuels as a major source of energy over the decades has been the largest contributor to Green House Gas (GHG) emissions causing global warming and consequently increasing climate change. Renewable energy (RE) which includes wind, solar, water, biomass, and wave among others, presents an alternative to fossil fuels to significantly reduce carbon emissions towards a sustainable economy as indicated in the 2015 Paris Climate Agreement and the UN Sustainable Development Goals. This has driven a lot of investor attention on renewable energy market. BP (2021) for instance, show that investment in solar and wind capacity more than doubled after 2015 equating to an annual growth of 18%. The study projects wind capacity to continue to increase at an annual rate of about 14% and solar capacity to also increase at an annual growth rate of about 18%. If these growth rates can be achieved, there is the need for more green finance in this market which could translate into green economic growth (Zhang et al., 2021).

Hence, green finance in the form of green bonds is needed to finance new green projects and re-finance existing ones to help in the transition to low-carbon economy and progress towards a net-zero emission. Here, when the proceeds from a bond issuance are used to finance or re-finance green projects, this type of bond is classified as a green bond (International Capital Market Association, 2021). Since its first issuance in 2007 by the European Investment Bank, green bonds have gained attention as an alternative fixed-income asset especially for investors who want to be ‘responsible investors’, that is, investors who are environmentally conscious. This makes green bond a double-edged sword, that is, on one side, green bonds help to tackle climate change by financing green projects and on the other hand, green bonds present an opportunity for investors to diversify their portfolio and manage their risks. In fact, total green bond issuance reached a record US$258.9 billion in 2019 showing a 51% growth on 2018 (Climate Bonds Initiative, 2020). The largest share (38%) of the proceeds was used in the energy sector. This shows that most of the proceeds from green bonds are invested in renewable energy and to also improve energy efficiency. The question one may ask is: can green bonds be a hedge for renewable energy stocks?

To answer this question, the present study examines how green bonds can be used as a hedge for renewable energy stocks. As observed by Nguyen et al. (2021), green bonds have low and negative correlation with stocks and commodities no matter the period. Hence, the diversification property of green bonds may be useful as a hedge in a portfolio for renewable energy stocks. Quite compelling from their study is the observation that the positive correlation between stocks and commodities were even heightened due to the global financial crisis (GFC) of 2007/2009. In a similar global crisis, albeit a health pandemic (COVID-19) this time round, it would be interesting to know the connectedness between renewable energy stocks, and to know the role of green bonds in this relationship during the vestiges of the COVID-19 pandemic. This is because the energy sector has been seriously hit by the COVID-19 pandemic. As indicated by Hosseini (2020) in a perspective paper, the rapid growth seen in the global renewable energy sector is confronted with threats from the COVID-19 pandemic; hence, the pandemic threatens to slow and possibly reverse the progress made in the sector. What seems rather to be in dearth are empirical studies that focus on the effect of COVID-19 on renewable energy stocks. Indeed, there are emerging studies that identify this thematic gap and study this relationship. Liu et al. (2021b) found that the uncertainties caused by COVID-19 on the returns and volatilities of renewable energy stocks is more significant than spillovers of uncertainties from the Global Financial Crisis (GFC).

Even scarcer in the literature are studies on the role of green bonds as a hedge for renewable energy stocks, also taking into consideration the COVID-19 pandemic. The emerging studies on green bonds have been examined within the context of balanced fixed-income investment portfolio (Broadstock et al., 2020), connectedness with financial markets (Reboredo & Ugolini, 2020), as a hedge for carbon market risk (Jin et al., 2020), and finally as co-movement with conventional bonds and commodities (Chatziantoniou et al., 2020, Le et al., 2021, Nguyen et al., 2021) and other asset classes (Reboredo et al., 2020). Given its role in combating climate change, green bonds can act as a hedge for renewable energy stocks when the tides of global shocks like the COVID-19 pandemic blows against these stocks. This hedging property is particularly reinforcing given that investors in green bonds seem to be on a ‘mission’, to say the least, to save the environment as a worthy course.

On the flip side, the role of green bonds in promoting renewable energy stocks may be dampened if there is continuous investment in fossil fuels making renewable energy stocks unattractive and uncompetitive for investors. One may, therefore ask: what role should governments/regulators play on the opposite (fossil fuel) end of the continuum of renewable energy to create the needed balance or swing the pendulum of investment to renewable energy stocks? Carbon pricing can be an effective way to swing this pendulum to renewable energy stocks. Carbon pricing is intended to reduce global emissions making the production of coal and other fuels costly while making renewable energy attractive. Hence, one would expect more investment in the renewable energy sector and its stocks as carbon prices increase. Indeed, Hanif et al. (2021) in a study that examined the dependence and connectedness between carbon pricing and renewable energy stock observed high and strong spillover between carbon prices and renewable energy indices in the short run and long run, irrespective of the time horizon. Their study showed positive dependence between carbon prices and renewable energy stocks. What our study seeks to do is to introduce carbon pricing to the dynamic framework between green bond and renewable energy stocks so as to offer a bird's-eye view of these dynamic relationships.

Therefore, given the limited number of studies on green bonds and the emerging interest in the use of green bonds as a hedge against volatilities in stocks, commodities and other assets, there is the need to examine the hedging effect of green bonds for renewable energy stocks especially considering the COVID-19 pandemic and to able examine the role of carbon pricing in this relationship. The novelty of this paper lies in filling this gap. So far, no study has offered a comprehensive analysis of the dynamic connectedness between green bonds and renewable energy stocks especially taking into consideration the COVID-19 pandemic. Given the negative effect of COVID-19 on green finance, it is important to identify the investment strategies as well as policies in the form of carbon pricing that can be implemented to limit these negative effects going forward. Providing empirical results of this nature can help inform investors on the strategies they can use in their portfolio creation. Given the possibility of green bonds to help diversify renewable stocks and reduce portfolio risk as we show in our results, more investors can be attracted to invest in green bonds. The analysis of the connectedness between green bonds and renewable energy stocks can help identify the direction of shocks transmission which can help policy makers in formulating recovery policies, especially in times of crises like the COVID-19 pandemic.

We make four main contributions to the literature. First, we provide new evidence by examining the connectedness between green bonds and renewable energy stocks using the TVP-VAR and LASSO-DY approaches. Second, we use portfolio approaches by constructing dynamic weighting schemes including a novel minimum connectedness portfolio – to provide evidence on whether green bonds can act as a hedge for renewable energy stocks. Third, we examine the role of carbon pricing in this relationship. Fourth, we provide further robustness of these results during extreme market conditions like the COVID-19 pandemic. The results show heterogeneous dynamic connectedness across the assets over time which are also influenced by global events like the European governmental debt crisis, the Brexit vote in 2016, and the COVID-19 pandemic. We show that clean energy is the main net transmitter of shocks while green bonds and Solactive Global Wind are the major net recipients of shocks. We also show that information on the return transmission process is helpful for portfolio creation given that the highest Sharpe ratio reached its highest value. Particularly, the results show that even though green bonds are not a good hedge for renewable energy stocks, they help to reduce the investment risk of these stocks.

The rest of the paper are organized as follows: Section 2 gives a brief review of the emerging studies on green bonds, renewable energy, and carbon pricing; Section 3 is dedicated to the methodology used to analyse the data; Section 4 describes the data used in the study; Section 5 presents and discusses the results while, Section 6 concludes the study and provides policy implications.

2. Literature review

The literature on renewable energy is gaining a lot of attention recently especially due to the renewed global calls to combat climate change. In the finance literature, studies on renewable energy stocks are gaining momentum especially on its relationship with other non-renewable energy stocks, energy commodities and crude oil prices.

On the relationship with non-renewable energy stocks and commodities, Asl et al. (2021) study the returns and volatilities spillovers between renewable energy index (S&P Global Clean Energy), the S&P Global Oil, along with natural gas and crude oil – both non-renewable energy commodities – and among other assets. The results showed that renewable energy index and the oil index have the highest optimal weights in their portfolio construction and that renewable energy stocks can be a good hedge for equity risks emanating from the oil and gas industries. On the crude oil prices, Ferrer et al. (2018), for instance, examined the dynamic connectedness between US clean energy stocks and crude oil prices using the time-frequency connectedness methodology developed by Baruník and Křehlík (2018). The study observed strong connectedness in the short-run but not in the long-run. However, the study did not find crude oil prices to drive the performance of clean energy stocks. These results confirm the findings of Henriques and Sadorsky (2008) who also found a weak relationship between crude oil prices and renewable energy stocks in a vector autoregression (VAR) framework. Reboredo (2015), on the contrary, found the existence of co-movement between crude oil prices and renewable energy stocks using a conditional Value-at-risk (CoVaR) approach. These results have implications for investors in the choice of their portfolios. Thus, depending on the risk profile of the investor in selection and allocation of portfolio assets, renewable energy remains an important asset that may have diversification advantages. These studies, however, differ from our current study in that we go a step further to look at the connectedness of green bonds with renewable energy stocks given the growing need for more investments in green projects to help tackle the issue of climate change. In this regard, we seek to understand whether green bonds and renewable energy stocks can form a good portfolio and whether green bonds can act as a hedge for renewable stocks especially in crisis periods like the COVID-19.

Meanwhile, given the ambiguous role of renewable energy stocks within a portfolio, empirical studies on green finance are gradually gaining momentum albeit scarcely dominant in the finance literature (Zhang et al., 2019). Few studies including Zhang et al. (2021) who examined the role of green finance in the public spending-green growth nexus; Taghizadeh-Hesary et al. (2021b) who examined the role of green finance in power purchasing agreements in financing green projects; Taghizadeh-Hesary and Yoshino (2019) who examined how private investors can be induced to invest into green finance; Lewis (2010) who examined the role of carbon finance in promoting renewable energy development in China; and Heinkel et al. (2001) who examined the impact of green investment on corporate behavior. Indeed, as pointed out by Zhang et al. (2019) in a comprehensive review of green finance literature, most of the empirical literature on green finance have focused on policy papers in relation to climate financing and investment in climate adaption with little attention in the finance mainstream literature. Particularly, these scholars recommend an urgent need to study green finance issues from finance perspectives and using techniques from finance especially on the role of green bonds, hence then need for the present study.

The finance literature is growing with studies identifying green bonds as an emerging alternative fixed-income asset that can act as a hedge for renewable stocks especially for climate-friendly investors. Sangiorgi and Schopohl (2021) through a survey of asset managers in European countries provide some insights into why these asset managers invest in green bonds. The study found that majority of investors are actively invested in the green bond market and that most of these investors prefer green bonds that are issued by sovereign countries and corporations. The major determining factors of investors’ choice of green bond are competitive pricing and the credentials of the green bond. These investors, however, prefer to invest in green bonds which have clear description of what green projects the proceeds would be used to finance. Hence, the attention of investors on the green bond market is likely to influence the investment flows to the sector. This projection is consistent with the study of Pham and Huynh (2020) who show that investor attention influences the return and volatility of green bonds. Taghizadeh-Hesary and Yoshino (2019), therefore, studied ways that can induce the private sector to participate in green finance and investment and suggest two ways to achieve this. First, by establishing green credit guarantee schemes (GCGSs), the risk of green projects can be reduced given that part of the risk will be alleviated by the government. Second, by returning a portion of the tax revenue originally generated from spillover effect of green energy supply to investors, the rate of return on green energy projects can increase. These would, therefore, incentivize investors to go into green finance.

Monk and Perkins (2020) interviewed conference participants and experts, reviewed relevant literature and trade publications, to understand how the growth or diffusion of green bonds can be accelerated. The study found that most of the processes and dynamics associated with introducing innovation inspired frameworks in literature also apply to the growing innovation of green bonds. These include, the participation of various market actors in the process; processes that reinforce self-learning and legitimacy and a broad-based development approach in the conceptualization of the product as part of fixed-income assets.

The growing investor interest in green bonds and the scale of innovation or growth in green bonds market is quite intriguing even given the evidence of ‘green premium’. Indeed, MacAskill et al. (2020) in a systematic literature review enquired whether green bonds have a ‘green premium’ or ‘greenium’ in their pricing. The study found consensus in the literature that show a consistent existence of green premium in about 56% of the studies in the primary market and around 70% of studies in the secondary market. This evidence is found especially for the type of green bonds that follow best practice and those that are issued by governments. Taghizadeh-Hesary et al. (2021a) also found that green bonds in Asia have higher returns but higher risks and higher heterogeneity. This presupposes that the non-pecuniary motive of environmentally responsible investors is strong and growing. These findings suggest the role that green bonds can play in promoting renewable energy stocks and in combating global climate change.

While the aforementioned studies focused on the drivers of green finance, our study departs from these previous studies in the sense that we examine the connectedness of green bonds to renewable energy stocks in order to identify whether green bonds per se can act as a hedge for renewable energy stocks. We also examine the implication of creating a portfolio with these two asset classes.

While the environmental impact of green bonds remains unequivocal through the financing of green projects, the empirical question of the role of green bonds in the portfolio or asset class of investors remains an emerging empirical issue. Nguyen et al. (2021) recently studied the co-movement among green bonds, conventional bonds, equities, commodities, and clean energy from 2008 to 2019 using the rolling window wavelet correlation approach. The study found low and negative correlation of green bonds with stocks and commodities making magnifying the diversification benefit of green bonds. Huynh (2020) also shows that there is contagion risk between green bonds and top-rated government bonds. This implies that a portfolio that includes top-rated government bonds and green bonds may experience extreme losses during periods of financial turbulence. Our study differs from these studies as we examine the connectedness between green bonds and an array of renewable energy stocks, and further examine the role of carbon pricing in this relationship. We further test the impact of the COVID-19 pandemic in this relationship. By so doing, we are able to provide empirical evidence on investment strategies that can be implemented by investors.

To analyze the hedging effect of green bonds, Jin et al. (2020) examined the role of green bonds as an effective hedging instrument for carbon market risk. The study used three dynamic hedge ratio models including the DCC-APGARCH, DCC-T-GARCH, and DCC-GJR-GARCH models as well as the constant hedge ratio model (OLS model). The study found the green bond index to be the best hedge for carbon futures and that this relationship is time invariant. An earlier study by Reboredo (2018) confirmed the large diversification benefits of green bonds for stocks and energy markets, and the negligible diversification benefit for corporate and treasury markets investors.

Reboredo et al. (2020) in a later study examined the connectedness between green bonds and different asset classes over different investment horizons in the EU and US asset markets. The study examined the dynamic correlations between green bonds and the asset classes using wavelet coherence while they examined connectedness using the forecast error variance decomposition of a multivariate VAR model. Unlike the earlier results of Reboredo (2018), the study found strong connectedness between green bonds and corporate and treasury bonds in the EU and US markets. The study found visible spillovers from corporate bonds and treasury bonds to green bonds but negligible transmission shocks from green bonds to the other bonds.

The literature on one hand shows the correlation and connectedness between crude oil, commodities, as well as renewable and non-renewable energy stocks. On the other hand, a strand of literature also examines the correlation and connectedness between green bonds, other bonds, energy markets and equities. What appears to be missing which our study addresses are the correlation and connectedness between green bonds and renewable energy stocks. Even more compelling to examine is the role of carbon pricing and COVID-19 pandemic in this relationship.

3. Methodology

3.1. Time-varying parameter vector autoregression

To explore the time-varying linkages between clean energy, green bonds, wind, solar and carbon returns, we estimate a TVP-VAR model with heteroscedastic variance-covariances.1 Based upon the Bayesian information criterion (BIC), a TVP-VAR(1) model is selected which can be mathematically formulated as,

$$y_t=B_t{y}_{t-1}+{\epsilon }_t{\epsilon }_t\sim N(0,{\Sigma }_t)$$ (1)

$$\mathrm{vec}(B_t)=\mathrm{vec}(B_{t-1})+v_t{v}_t\sim N(0,S_t)$$ (2)

where y _t, y _t−1 and ε _t are K  × 1 dimensional vector and B _t and Σ _t are K  ×  K dimensional matrices. vec(B _t) and $v_t$ are K ²  × 1 dimensional vectors whereas S _t is a K ²  ×  K ² dimensional matrix. As the dynamic connectedness approach of Diebold and Yılmaz, 2012, Diebold and Yılmaz, 2014 rests on the Generalised Forecast Error Variance Decomposition (GFEVD) of (Koop et al., 1996, Pesaran and Shin, 1998), it is required to transform the TVP-VAR to its TVP-VMA representation by the Wold representation theorem: $y_t={\sum }_{h=0}^{\infty }{A}_{h,t}{\epsilon }_{t-i}$ where A ₀  =  I _K.

The H-step ahead GFEVD models the impact a shock in series j has on series i. This can be formulated as follows,

$${\phi }_{\mathrm{ij},t}^{\mathrm{gen}}(H)=\frac{\sum _{h=0}^{H-1}{(e_i^{\prime }{A}_{\mathrm{ht}}{\Sigma }_t{e}_j)}^2}{(e_j^{\prime }{\Sigma }_t{e}_j)\sum _{h=0}^{H-1}(e_i^{\prime }{A}_{\mathrm{ht}}{\Sigma }_t{A}_{\mathrm{ht}}^{\prime }{e}_i)}$$ (3)

$${\mathrm{gSOT}}_{\mathrm{ij},t}=\frac{{\phi }_{\mathrm{ij},t}^{\mathrm{gen}}(H)}{\sum _{k=1}^K{\phi }_{\mathrm{ik},t}^{\mathrm{gen}}(H)}$$ (4)

where e _i is a K  × 1 dimensional zero vector with unity on its ith position. As the ${\phi }_{\mathrm{ij},t}^{\mathrm{gen}}(H)$ stands for the unscaled GFEVD (${\sum }_{j=1}^K{\zeta }_{\mathrm{ij},t}^{\mathrm{gen}}(H)\ne 1$), Diebold and Yılmaz, 2009, Diebold and Yılmaz, 2012, Diebold and Yılmaz, 2014 suggested to normalize it by dividing ${\phi }_{\mathrm{ij},t}^{\mathrm{gen}}(H)$ by the row sums to obtain the scaled GFEVD, gSOT _ij,t.

The scaled GFEVD is at the center of the connectedness approach facilitating the computation of the total directional connectedness to (from) all series from (to) series i. While the TO total directional connectedness constitutes the effect series i has on all others, the FROM total directional connectedness illustrates the impact all series have on series i. These connectedness measures can be calculated by,

$$S_{i\to •,t}^{\mathrm{gen},\mathrm{to}}=\sum _{j=1,i\ne j}^K{\mathrm{gSOT}}_{\mathrm{ji},t}$$ (5)

$$S_{i\leftarrow •,t}^{\mathrm{gen},\mathrm{from}}=\sum _{j=1,i\ne j}^K{\mathrm{gSOT}}_{\mathrm{ij},t}.$$ (6)

Computing the difference between the TO and the FROM total directional connectedness results in the net total directional connectedness of series i:

$$S_{i,t}^{\mathrm{gen},\mathrm{net}}=S_{i\to •,t}^{\mathrm{gen},\mathrm{to}}-S_{i\leftarrow •,t}^{\mathrm{gen},\mathrm{from}}.$$ (7)

If $S_{i,t}^{\mathrm{gen},\mathrm{net}}>0$ ($S_{i,t}^{\mathrm{gen},\mathrm{net}}<0$), series i is influencing (influenced by) all others more than being influenced by (influencing) them and thus is considered to be a net transmitter (receiver) of shocks indicating that series i is driving (driven by) the network.

The connectedness approach also provides information on the bilateral level. The net pairwise directional connectedness shows the bilateral net transmission of shocks between series i and j,

$$S_{\mathrm{ij},t}^{\mathrm{gen},\mathrm{net}}={\mathrm{gSOT}}_{\mathrm{ji},t}-{\mathrm{gSOT}}_{\mathrm{ij},t}.$$ (8)

If $S_{\mathrm{ij},t}^{\mathrm{gen},\mathrm{net}}>0$ ($S_{\mathrm{ij},t}^{\mathrm{gen},\mathrm{net}}<0$), series i dominates (is dominated by) series j implying that series i influences (is influenced by) series j more than being influenced by (influencing) it.

The total connectedness index (TCI) is another relevant metric highlighting the degree of network interconnectedness and hence market risk. Considering that the TCI can be calculated as the average total directional connectedness to (from) others, it is equal to the average amount of spillovers one series transmits (receives) from all others. Chatziantoniou and Gabauer (2021) and Gabauer (2021) have shown that as the own variance shares are by construction always larger or equal to all cross variance shares the TCI is within $\left[0,\frac{K-1}{K}\right]$. To obtain a TCI which is within [0,1], we have to slightly adjust the TCI:

$${\mathrm{gSOI}}_t=\frac{1}{K-1}\sum _{i=1}^K{S}_{i\leftarrow •,t}^{\mathrm{gen},\mathrm{from}}=\frac{1}{K-1}\sum _{i=1}^K{S}_{i\to •,t}^{\mathrm{gen},\mathrm{to}},$$ (9)

A high (low) value indicates high (low) market risk.

Finally, we calculate the pairwise connectedness index (PCI) which can be seen as the TCI on the bilateral level illustrating the degree of interconnectedness between series i and j. This can be formulated as:

$${\mathrm{PCI}}_{\mathrm{ij},t}=2\left(\frac{{\mathrm{gSOT}}_{\mathrm{ij},t}+{\mathrm{gSOT}}_{\mathrm{ji},t}}{{\mathrm{gSOT}}_{\mathrm{ii},t}+{\mathrm{gSOT}}_{\mathrm{ij},t}+{\mathrm{gSOT}}_{\mathrm{ji},t}+{\mathrm{gSOT}}_{\mathrm{jj},t}}\right),0\le {\mathrm{PCI}}_{\mathrm{ij},t}\le 1.$$ (10)

3.2. Portfolio back-testing models

To shed fresh insights on the hedging potential of green bond against renewable energy stocks and its financial significance, we use portfolio back testing approach to examine the investment performance of assets under examination. We use varied estimation approaches used in portfolio construction comprising of conventional approaches and some recent connectedness oriented portfolios. A number of assumptions underlines our portfolio analysis. These include: the index can be purchased by the investor directly, market participants are interested only in green bond and renewable energy stock investment and are open to invest in both green bonds and renewable energy stocks. Even though these assumptions are narrow, we argue that these assumptions are sufficient in illustrating our objective. Outlined below are a brief summary of the portfolio estimation approaches adopted.

3.2.1. Bilateral hedge ratios and portfolio weights

The dynamic hedge ratio of Kroner and Sultan (1993) can be formulated as follows,

$${\beta }_{\mathrm{ij},t}={\Sigma }_{\mathrm{ij},t}/{\Sigma }_{\mathrm{jj},t},$$ (11)

where Σ _ij,t is the conditional covariance between series i and j at time t, and Σ _jj,t the conditional variance of series j at time t.

Kroner and Ng (1998) shows that the optimal bilateral portfolio weights between series i and j are calculated as,

$$w_{\mathrm{ij},t}=\frac{{\Sigma }_{\mathrm{ii},t}-{\Sigma }_{\mathrm{ij},t}}{{\Sigma }_{\mathrm{ii},t}-2{\Sigma }_{\mathrm{ij},t}+{\Sigma }_{\mathrm{jj},t}},$$ (12)

with

$$w_{\mathrm{ij},t}=\left\{\begin{array}{ccccc}0,\hfill & \hfill \mathrm{if}{w}_{\mathrm{ij},t}<0\hfill & \hfill & \hfill \hfill & \hfill \\ w_{\mathrm{ij},t},\hfill & \hfill \mathrm{if}0\le w_{\mathrm{ij},t}\le 1\hfill & \hfill & \hfill \hfill & \hfill \\ 1,\hfill & \hfill \mathrm{if}{w}_{\mathrm{ij},t}>1\hfill & \hfill & \hfill \hfill & \hfill \\ \hfill & \hfill \hfill & \hfill & \hfill \hfill & \hfill \end{array}\right)$$ (13)

where $w_{\mathrm{ij},t}$ is the weight of series i in a 1$ portfolio between series i and j at time t. Thus, $1-w_{\mathrm{ij},t}$ is the weight of series j at time t in the aforementioned portfolio.

3.2.2. Minimum variance portfolio (MVP)

A commonly used approach in portfolio analysis is the MVP method which attempts to create the portfolio with the least volatility founded on multiple assets as documented by Markovitz (1959). The portfolio weights are estimated using the following formula:

$$w_{{\Sigma }_t}=\frac{{\Sigma }_t^{-1}I}{I{\Sigma }_t^{-1}I}$$ (14)

where $w_{{\Sigma }_t}$ denotes the K  × 1 dimensioanl portfolio weight vector, I represents the K-dimensional vector of ones and Σ _t depicts the K  ×  K dimensional conditional variance-covariance matrix in period t.

3.2.3. Minimum correlation portfolio (MCP)

In recent times, another procedure in the construction of portfolios emerged, namely the MCP that has been introduced by Christoffersen et al. (2014). This approach is similar to the MVP, however, in this case the portfolio weights are obtained byminimizing the conditional correlations and not the conditional covariances. This can be outlined as follows,

$$R_t=\mathrm{diag}{({\Sigma }_t)}^{-0.5}{H}_t\mathrm{diag}{({\Sigma }_t)}^{-0.5}$$ (15)

$$w_{R_t}=\frac{R_t^{-1}I}{I{R}_t^{-1}I}$$ (16)

3.2.4. Minimum connectedness portfolio (MCoP)

Following the construction of the MVP and MCP portfolio techniques, we next generate MCoP by using the pairwise connectedness indices rather than the correlations or variances (Broadstock et al., 2020). The minimization of bilateral interconnectedness offer a portfolio procedure that is not affected heavily by network shocks. Thus, assets that are not influencing others and are not influenced by others are allocated with a higher weight in the constructed portfolio. This is expressed as shown below:

$$w_{C_t}=\frac{{\mathrm{PCI}}_t^{-1}I}{I{\mathrm{PCI}}_t^{-1}I}$$ (17)

PCI _t denotes the pairwise connectedness index matrix while the identity matrix is represented by I.

3.2.5. Portfolio evaluation

To ascertain the performance of the portfolios, we rely on two metrics, the Sharpe ratio (Sharpe, 1994) and the hedging effectiveness (Ederington, 1979).

On the one hand, the Sharpe ratio (SR), also called the reward to volatility ratio, is computed as follows:

$$\mathrm{SR}=\frac{{\overline{r}}_p}{\sqrt{\mathrm{var}(r_p)}}$$ (18)

where r _p represents the portfolio returns assuming that the risk-free rate is equal to zero. As higher SR values connotes higher returns relative to the level of risk in the portfolio, the SR allows us to compare various portfolios with each other as it informs us which portfolio has the highest return given the same volatility.

The second metric is called Hedging Effectiveness (HE), which informs us about the risk percentage reduction the portfolio over investing in a single asset i. To know whether the reduction is significant we calculate the HE test statistics of Antonakakis et al. (2020b). The HE can be computed by,

$${\mathrm{HE}}_i=1-\frac{\mathrm{var}(r_p)}{\mathrm{var}(r_i)}$$ (19)

where var(r _p) denotes the portfolio variance and varr _i represents the variance of asset i's. The HE _i index shows the percentage reduction in the variance of the unhedged position of asset i. A high (low) HE index denotes a high (low) risk reduction.

4. Data

In this study, we examine the hedging and safe-haven properties of green bonds against renewable energy stocks by examining the return transmission and hedging effectiveness across numerous assets for the period of 4th January 2015 to 22nd September 2020. In more detail, we use certificate prices of CO2 emissions (European Energy Exchange EU emissions trading system), S&P Green Bond Price Index (SPGRBND), and the following renewable energy stock indices: Solactive Global Solar (SOGLSOE), Solactive Global Wind (SOGLWIE), and S&P Global Clean Energy (SPGCLE$). All series are obtained from Datastream. Daily returns are presented in log form. Figs. 1 and 2 report the time series plots of standardized raw series and returns, respectively. In Fig. 1, we observe intense fluctuations in the price series of all assets under examination throughout the period. Interestingly, variations in prices and returns were even more pronounced during economic events such as the recent COVID-19 outbreak, the European governmental debt crisis, and the Brexit vote in 2016. Fig. 2 reveals that multiple volatility clusters exist for all series except for green bond.

Fig. 1.

Standardized raw series.

Fig. 2.

Returns.

Table 1 presents the summary statistics of the daily returns. Focusing on the mean returns, we note that the daily mean is positive for all series. The highest mean is recorded for carbon price (0.12) followed by global wind (0.10), global solar (0.073), clean energy (0.049) and green bond (0.005). Thus, green bond recorded the lowest mean estimate whereas its standard deviation is also the lowest among all employed series. We find that all series are significantly left skewed and leptokurtic distributed which in turn leads to the fact that all series are statistically non-normally distributed on the 1% significance level. Furthermore, all series appear to be stationary, autocorrelated and exhibit ARCH/GARCH error on the 1% significance level. Interestingly, CO2 and green bonds seem to be uncorrelated with solar, wind and clean energy which is preferred for risk and portfolio management. This result is in-line with Reboredo (2018) and Jin et al. (2020). In addition, the highest correlations are observed between solar and clean energy followed by wind and clean energy. All those statistics support our choice to model the interrelationship among those variables using a TVP-VAR approach with time-varying variance-covariances.

Table 1.

Summary statistics.

	CO2	Solar	Wind	Clean Energy	Green
Mean	0.12	0.073	0.102	0.049	0.005
Variance	10.697	3.158	1.879	1.642	0.026
Skewness	−0.419***	−0.855***	−0.170***	−0.791***	−1.281***
	(0.000)	(0.000)	(0.002)	(0.000)	(0.000)
Kurtosis	11.886***	15.452***	4.792***	13.961***	13.251***
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
JB	11948.980***	20343.073***	1942.665***	16614.814***	15331.672***
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
ERS	−4.028***	−6.271***	−2.460**	−3.569***	−9.820***
	(0.000)	(0.000)	(0.014)	(0.000)	(0.000)
Q(20)	36.727***	78.728***	25.878***	85.520***	83.680***
	(0.000)	(0.000)	(0.001)	(0.000)	(0.000)
Q2(20)	180.342***	26.131***	861.534***	1626.783***	1171.520***
	(0.000)	(0.001)	(0.000)	(0.000)	(0.000)

	Unconditional correlations
	CO2	Solar	Wind	Clean Energy	Green
CO2	1.000	0.043	0.055	0.070	−0.0004
Solar	0.043	1.000	0.301	0.507	−0.042
Wind	0.055	0.301	1.000	0.427	0.005
Clean Energy	0.070	0.507	0.427	1.000	−0.019
Green	−0.0004	−0.042	0.005	−0.019	1.000

Notes: ***, **, * denote significance at 1%, 5% and 10% significance level; Skewness: D’Agostino (1970) test; Kurtosis: Anscombe and Glynn (1983) test; JB: Jarque and Bera (1980) normality test; ERS: Stock et al. (1996) unit-root test with constant; Q(10) and Q²(10): Fisher and Gallagher (2012) weighted portmanteau test.

5. Empirical results

In this section, we discuss the averaged and dynamic results obtained from the employed TVP-VAR based connectedness approach which examines the return transmission mechanism between green bonds, carbon price and renewable energy stocks.

5.1. Averaged connectedness measures

Table 2 reports results for the TVP-VAR and the LASSO-VAR based connectedness approach. We note substantial variations in the magnitude of return shocks transmitted across variables. For the entire sample of variables under examination, we find green bonds transmit the lowest value of shocks to other markets (2.246%) followed by carbon price index returns (5.724%). The highest shock spillovers originate from clean energy to global solar (27.609%) followed by the propagation from global solar to clean energy (24.475%).

Table 2.

Averaged dynamic connectedness table.

	CO2	Solar	Wind	Clean Energy	Green	FROM others
CO2	92.270 (92.264)	2.230 (2.071)	2.204 (2.280)	2.523 (2.655)	0.772 (0.730)	7.730 (7.736)
Solar	1.625 (1.412)	59.850 (59.189)	10.398 (10.689)	27.609 (28.034)	0.518 (0.675)	40.150 (40.811)
Wind	1.412 (1.340)	11.574 (11.744)	61.971 (62.019)	24.589 (24.510)	0.453 (0.386)	38.029 (37.981)
Clean Energy	1.618 (1.498)	24.475 (25.250)	20.254 (20.371)	53.151 (52.236)	0.502 (0.645)	46.849 (47.764)
Green	1.070 (0.948)	1.515 (1.385)	1.356 (1.107)	1.855 (1.519)	94.204 (95.040)	5.796 (4.960)
TO	5.724 (5.199)	39.795 (40.450)	34.212 (34.447)	56.577 (56.719)	2.246 (2.436)	TCI
NET	−2.005 (−2.537)	−0.355 (−0.361)	−3.817 (−3.534)	9.728 (8.955)	−3.550 (−2.523)	34.639 (34.813)

Notes: Results are based on a TVP-VAR model with lag length of order 1 (BIC) and a 20-step-ahead forecast. Values in parentheses represents the measures based upon the LASSO results of Gabauer et al. (2020) while the others demonstrates measures of the Antonakakis et al. (2020a) approach.

In the case of renewable energy stocks to green bond returns, we note that clean energy is the largest transmitter of shocks to green bond returns (1.855%) followed by global solar (1.515%) and wind (1.356%). The evidence of connectedness between green bonds and renewable energy markets is in consonance with the findings of Liu et al. (2021a), who observed significant dependence and risk spillovers between green bond and sectoral renewable energy markets. In a related study. Additionally, in the case of the shock transmission from green bond prices to renewable energy stocks, we note that green bonds transmits 0.518% of shocks to solar, 0.520% of shocks to clean energy and 0.453% of shocks to wind. Thus, global wind receives the least shocks from green bond price returns. In particular we notice that renewable energy stocks transmit more shocks to green bonds compared to the amount of shocks green bonds transmits to renewable energy stocks. On the other hand, CO2 is also seen to transmit more shocks to green bond (1.070%) than it receives from green bond (0.772%). These findings are in agreement with the conclusion of Hammoudeh et al. (2020) who found a significant link running from CO2 emission allowances price to green bond price returns. In all, we find that the average TCI is equal to 34.639% indicating that on average 34.639% of a shock in one variable spills to all others.

Focusing on the contribution to other assets, the gross directional return spillovers transmitted to other assets from each of the individual assets returns under examination ranges from 2.246% for green bonds to 56.577% for clean energy. This estimate shows that about 56.719% of all others’ forecast error variance can be explained by clean energy. It is also seen that 39.795% and 34.212% of the forecast error variance is caused by solar and wind, respectively, while Green Bonds transmit only about 2.246% of the forecast error variance to other markets. Clearly, it can be seen that Green Bond has only a marginal effect on other markets similar to the findings of Hammoudeh et al. (2020) who found no significant causality running from green bonds to other assets including clean energy. The range of the directional return shocks transferred from all other assets to one specific market ranges from 5.796% to 46.849%. We find that Green Bonds receive more shocks from other markets than it transmits to them. The same is seen for CO2, solar and wind. For example, solar receives 40.150% of its forecast error variance from other markets and transmits only 39.795% to others.

This leads us to the net directional connectedness measures which illustrate whether a series transmits more than it receives and hence be a net transmitter or vice versa a net receiver of shocks. Alternatively, we could indicate positive net spillover value as series that are spillover contributor while negative spillovers suggest that series are absorbing spillovers from others. Using estimates from the TVP-VAR, we find that green bonds, global solar, global wind, and carbon price are all net receivers of shocks with values equal to –3.550%, -0.355%, –3.817%, and –2.007%, respectively. This indicates that clean energy is dominating all others and hence the main net transmitter of shocks (9.728%) which again confirms the dominance of clean energy in the renewable energy market. For robustness purposes, we use the LASSO-VAR connectedness values which depict a qualitatively similar picture concerning the networks transmission mechanism behavior.

With the results reported in Table 2, it is worth noting that the elements of the main diagonal of Table 2 correspond to own-variable shocks (i.e., idiosyncratic), while all other elements, relate to the various interactions between the different markets. We note from the diagonal element that, in the case of green bond price returns, 94.204% of index evolution is driven by within index shocks/behavior, with only 5.796% index movement attributed to network connections. In the case of the renewable energy stocks, it can be seen that 59.850% of global solar, 61.791% of global wind and 53.151% of clean energy index revolution is driven by within index shocks. This suggests that index movement across renewable energy stocks driven by network connections is high compared to movement in green bond prices and carbon price driven by network connections. We find that 92.270% of index evolution in the case of carbon price is driven by within shocks. Our finding that only 5.7906% of index movement in green bonds price returns is driven by the other markets differs from the findings of Broadstock et al. (2020) who found that about 40% of US green bond price measured by (S&P Green Bond Index) is driven by network connections.

Overall, we hypothesize that the green bonds market is marginally integrated with renewable energy stocks in terms of the return transmission mechanism. We establish that renewable energy stocks and carbon price have a significant effect on green bond market. However, it appears the effect of renewable stocks including global wind, global solar and clean energy on green bond returns is stronger compared to the effect of carbon price on green bond returns. On the other hand, the influence of green bond on carbon market is stronger compared to its effect on renewable energy stocks. We attribute the dominance of renewable energy stocks over green bond to the conclusion of Tolliver et al. (2020), who note that green bond markets are expanding precipitously and proceeds are increasingly being allocated to renewable energy. Thus, the dominance of renewable energy stock could be attributed to growing trend in renewable energy investments driven by a number of policy supports. For example, the IEA Sustainable Development Scenario (SDS) instructs to reduce the fossil fuel share of energy supply investment by 40% through 2030 and to increase the share of renewable power in total energy supply to 60% by 2040 to achieve the three energy-related United Nations Sustainable Development Goals (UN SDGs). It also supports the Paris Agreement mandate to restrict global average temperature rises over the 21st century to well below 2^∘C (International Energy Agency, 2018).

For robustness purposes, we provide additional analysis on the magnitude of connectedness among the assets examined in the study during the COVID-19 period. Table 3 contains the COVID-19 connectedness results. We established several exciting results. For example, during the COVID-19 period, global solar emerged as a net transmitter of shock and not a receiver of shock (Table 2). We further note that the element in the main diagonal of Table 3 which correspond to own-variable shocks (idiosyncratic) reduced significantly compared to what we obtained in Table 2. This connotes that during the outbreak of COVID-19, a greater percentage of index movement in green bond, renewable energy stocks and carbon price were driven by network connections. It is noteworthy to mention that the magnitude of shocks transmitted across assets in Table 3 appear to the larger than what we observed in Table 2. Thus, the outbreak of coronavirus fuelled intense volatility.

Table 3.

COVID-19 averaged dynamic connectedness table (01.01.2020 – 22.09.2020).

	CO2	Solar	Wind	Clean Energy	Green	FROM others
CO2	68.711 (69.655)	10.722 (9.863)	6.930 (7.107)	11.128 (9.967)	2.508 (3.408)	31.289 (30.345)
Solar	6.579 (6.058)	42.965 (44.188)	17.765 (17.258)	31.921 (32.089)	0.770 (0.407)	57.035 (55.812)
Wind	4.213 (3.790)	19.575 (18.650)	47.746 (48.900)	27.651 (28.023)	0.816 (0.637)	52.254 (51.100)
Clean Energy	6.031 (5.210)	29.594 (29.666)	23.465 (23.866)	40.362 (40.867)	0.549 (0.391)	59.638 (59.133)
Green	0.984 (1.420)	2.567 (1.640)	2.733 (1.942)	2.456 (1.707)	91.260 (93.291)	8.740 (6.709)
TO	17.807 (16.478)	62.457 (59.819)	50.893 (50.173)	73.155 (71.786)	4.643 (4.843)	TCI
NET	-13.482 (-13.866)	5.422 (4.007)	-1.361 (-0.927)	13.517 (12.653)	-4.097 (-1.866)	41.791 (40.620)

Notes: Results are based on a TVP-VAR model with lag length of order 1 (BIC) and a 20-step-ahead forecast. Values in parentheses represents the measures based upon the LASSO results of Gabauer et al. (2020) while the others demonstrates measures of the Antonakakis et al. (2020a) approach.

5.2. Dynamic total connectedness

In this study, higher levels of the total connectedness index (TCI) connote strong connectedness among assets under examination. In other words, strong connectedness may suggest that the supposed risk relating to the green bond and renewable energy stocks and CO2 is increasingly equivalent indicating comparable market confidence. Fig. 3 illustrates the total connectedness index which reveal the evolution of the total co-movement using TVP-VAR and LASSO VAR. The shaded region denotes three crisis periods. First, European government debt crisis which ended in July 2014 following Ireland and Portugal exist bailouts. Second, the Brexit referendum period from 23rd June 2016 to 23rd July, 2016, and finally COVID-19 outbreak running from 1st January 2020. Focusing first on the connectedness using TVP-VAR, we note that the magnitude of connectedness among assets under examination considerably varies over time and ranges from 25% (lowest) to about 62% (highest). This indicates that the magnitude of connectedness across the markets examined not only react to events associated with green bonds, renewable energy stocks and CO2 but may swiftly do so and by material amounts. Next, we examine the extent of connectedness under three crisis periods including European government debt crisis, the Brexit referendum period and COVID-19 outbreak. Comparing these three volatile periods to normal periods, we observe the magnitude of connectedness is high during volatile markets states compared to normal markets states which is similar to the findings of Liu and Liu (2020) who documented that the dynamic connection between green bonds and renewable energy returns is significant only during turbulent periods, such as the European Sovereign Debt Crisis 2012 (ESDC) and the COVID-19 pandemic. A critical look at the TCI suggests that it assumed its lowest values in the beginning of 2018 and its highest values towards the end of 2020. Comparing the extent of connectedness, the existed during volatile markets states, we note high levels of connectedness during the COVID-19 period in 2020 compared to the level of connectedness that existed during the European governmental debt crisis and the Brexit vote in 2016. We make this claim because, the magnitude of connectedness reached its highest levels of about 62% during the COVID-19 in 2020 compared to TCI values of about 51% recorded in 2016. Comparing the TCI values obtained during bearish, normal, and bullish markets states show that, markets examined are not highly connected during normal markets states as seen for the period running from 2018–2019.

Fig. 3.

Dynamic total connectedness. Notes: Results are based on a TVP-VAR model with lag length of order 1 (BIC) and a 20-step-ahead forecast. The black area represents the measures based upon the Antonakakis et al. (2020a) approach while the red line demonstrates the LASSO results of Gabauer et al. (2020) results.

In all, the level of connectedness during crisis-free period among these markets is minimal compared to crisis period. On the other hand, the TCI is seen to fluctuate considerably over time and not stable for the entire period. Its levels increased marginally from about 25% in 2014 to about 40% in 2015 to 52% in 2016 before dropping sharply to around 25% in 2018 after which we witnessed a gradual increase in levels up to the beginning of 2020 of about 32%. The largest TCI is observed in January 2020 when the COVID-19 pandemic started reaching slightly more than 60%. For robustness purposes, we also report the TCI using LASSO results advanced by Gabauer et al. (2020) by the red line in Fig. 3 which illustrates a similar pattern compared to the TVP-VAR approach.

5.3. Net total directional connectedness

In this section, we focus on the discussion on the net total directional connectedness. A key feature of the main estimation technique used in this paper is its ability to establish and distinguish whether a specific market in the entire system is a net transmitter or net receiver of shocks. Reported in Fig. 4 is the net total directional connectedness index. The net spillovers are the difference between an asset's shocks contribution to others and the contribution of shocks an individual asset receives from other assets. Succinctly, a negative and positive net value indicates the individual asset is a net receiver of shocks and net transmitter of shocks respectively. For easy interpretation of Fig. 4, an asset in the system is a net transmitter of shock to the system if the shaded area is in the positive region while an asset is regarded as a net receiver of shocks if the shaded area lies in the negative region. From Fig. 4, we find that throughout the period, clean energy acts a transmitter of shock to other markets. In the case of green bonds, we find that green bond acts as shock transmitters at some point and receivers of shocks at some stretches of time. We record same for solar, wind and carbon price. During the COVID-19 period, green bonds seem to be a receiver of shocks together with wind and carbon price. However, clean energy and solar acted as transmitters of shocks during the COVID-19 period. Overall, the variation observed in each asset over time suggest a constantly evolving intensity attached to each market's role.

Fig. 4.

Net total directional connectedness. Notes: Results are based on a TVP-VAR model with lag length of order 1 (BIC) and a 20-step-ahead forecast. The black area represents the measures based upon the Antonakakis et al. (2020a) approach while the red line demonstrates the LASSO results of Gabauer et al. (2020) results.

5.4. Net pairwise directional connectedness

Next, we focus on the net pairwise directional connectedness to establish the exact role each market play with respect to other markets in the entire system. It is noteworthy to mention that the net total directional connectedness reported in Fig. 4 is very useful in classifying which specific market in the system is a net transmitter or receiver of shocks. However, from the net pairwise directional connectedness reported in Fig. 5 , we may establish how one specific market impacts another market in the entire system. Focusing on the pairwise directional connectedness between CO2 and renewable energy stocks including solar, wind and clean energy suggest that CO2 is predominantly receives high levels of spillovers from renewable energy markets during volatile market states in 2016 and 2020. Hanif et al. (2021) in a study that examined the dependence and connectedness between carbon pricing and renewable energy stock found strong spillover between carbon prices and renewable energy indices. In the case of CO2-Solar and CO2-Clean energy we note there are stretches of time where CO2 transmits shocks to solar and clean energy in small quantities during normal markets states. In the case of CO2 and green bonds, we note that the CO2 receives shocks from green bonds from 2017 through to 2018 and some months in 2019 even though transmission in the initial periods in 2017 was marginal. CO2 however transmitted relatively similar shocks in later months of 2019 as it received in the beginning of 2020. For all other periods, CO2 transmits large volume of shocks to green bond price returns. Concerning the pairwise spillovers between solar and other assets, we find that solar predominantly receives large quantity of shocks from clean energy for most periods and only transmits a minute quantity of shocks to clean energy around 2015. For solar-wind, solar-green, it is evident that wind and green bonds are net recipient of shocks from solar. Solar transmits more shocks to these assets than it receives from wind and green bond. Regarding the net pairwise directional connectedness between wind-clean energy and wind-green energy, we note some exciting outcomes.

Fig. 5.

Net pairwise directional connectedness. Notes: Results are based on a TVP-VAR model with lag length of order 1 (BIC) and a 20-step-ahead forecast. The black area represents the measures based upon the Antonakakis et al. (2020a) approach while the red line demonstrates the LASSO results of Gabauer et al. (2020) results.

While wind is a net recipient of spillovers from clean energy for the entire period, green energy is also seen to be a recipient of shocks from wind. There only time green bond transmits shocks to wind occurred in 2018 and 2019 which is even in smaller volume. Finally, we turn our attention to clean energy-green bond. As expected, clean energy transmits a great number of shocks to green bond for the entire period except in 2018 where green bond is seen to transmit some amount of shocks to clean energy. Overall, the key information we obtain from Fig. 5 is the transmission of net pairwise spillovers between CO2, Green Bonds and renewable energy markets and how they vary with time. The pattern of net pairwise spillovers reveals production and complementary relationships between green bonds and other assets.

5.5. Dynamic pairwise connectedness

This section provides a brief overview on the magnitude of connectedness across the paired markets discussed in Fig. 5. Succinctly, Fig. 6 reports the dynamic pairwise connectedness which addresses the question: how connected are paired markets? Thus, is green bond highly connected to renewable energy markets and CO2? This analysis is very significant and revealing since it expounds the level of connectedness among paired markets in the system and not connectedness among assets in the entire system. First, we focus on connectedness between CO2 and other assets in the system. We note that the magnitude of connectedness between CO2-Solar, CO2-Wind and CO2-Clean energy is minimal and follows the same pattern. We note that the level of connectedness increased tremendously during 2016 and 2020 periods. Thus, during bearish markets conditions, the connections between CO2 and renewable energy market increases. In the case of CO2-Green bond, the evidence of co-movement is extremely minimal. These two assets are predominantly not connected in most periods except in 2020 where we witnessed some form of connections. Second, we address the connectedness between solar and other assets in the network. Solar is seen to be highly connected with clean energy and wind. However, level of connectedness between Solar-Clean energy is higher compared to Solar-wind. Connectedness between Solar-Green bonds is marginal at all periods. Thirdly, wind-clean energy level of connectedness is extremely high at all periods. Finally, connectedness between wind-green bond and clean energy-green bond is seen to be less than 20% for the entire period. Thus, overall green bond is marginally connectedness to renewable energy market and CO2. This shows the diversification potential of green bond markets.

Fig. 6.

Dynamic pairwise connectedness. Notes: Results are based on a TVP-VAR model with lag length of order 1 (BIC) and a 20-step-ahead forecast. The black area represents the measures based upon the Antonakakis et al. (2020a) approach while the red line demonstrates the LASSO results of Gabauer et al. (2020) results.

5.6. Portfolio and hedging strategies analysis

5.6.1. Bilateral hedge ratios and portfolio weights

Table 4 contains the summary statistics of hedge ratios and hedging effectiveness between the first assets to the second asset. The table reports that a $1 long position in the first asset can be hedged with the average value of hedge ratio percentage of short position in the second assets. For example, hedge ratio estimates for the case of solar/ wind which is 0.54$ reveal that a $1 long position in solar can be hedged for 0.54$ investment in wind. It is noteworthy to mention that the mean values of the solar/green bonds are negative. This arises when the asset pairs are correlated negatively. Thus, green bond can act as a good hedge against solar. Following Kroner and Sultan (1993), we report in Fig. 7 the time-varying hedge ratios. The blue line reports the conditional hedge ratios while the dark blue line denotes conventional hedge ratios. It can be seen that for conditional hedge ratios are clearly changing as new information arrives at the market for CO2/Green Bond, Solar/Green Bond, Wind/Green Bond, Clean Energy/Green Bond. A critical look at the hedge ratios between other assets and green bond suggest the hedge ratios varies in a time-varying framework and event dependent. For instance, during the COVID-19 outbreak, we find stretches of time where the hedge ratios appear to be positive and negative at different point in time for the same period. Focusing on the hedging effectiveness of paired assets, it can be seen that investment in Wind/Solar, Clean Energy/Solar, Solar/Wind, Clean Energy/Wind, CO2/Clean energy, Solar/Clean energy and wind/clean energy will reduce asset volatility evidenced by their positive HE values. Interestingly, these reductions in volatility are statistically significant at 1% level of significance indicating the reductions are financially meaningful. Fig. 7 illustrates the bilateral hedge ratios summarized in Table 4. It can be observed that bilateral hedge ratios between assets under examination and green bond returns is insignificant as displayed in Fig. 7.

Table 4.

Bilateral hedge ratios.

	Mean	Std.Dev.	5%	95%	HE	p-value
Solar/CO2	0.04	0.11	−0.07	0.30	0.04	0.34
Wind/CO2	0.05	0.07	−0.02	0.22	0.03	0.46
Clean Energy/CO2	0.06	0.10	0.00	0.32	0.04	0.30
Green/CO2	0.00	0.00	−0.01	0.01	0.02	0.72
CO2/Solar	0.06	0.28	−0.39	0.66	0.05	0.22
Wind/Solar	0.33	0.16	0.16	0.62	0.25	0.00
Clean Energy/Solar	0.46	0.21	0.20	1.00	0.53	0.00
Green/Solar	0.00	0.01	−0.02	0.01	0.02	0.67
CO2/Wind	0.24	0.21	−0.08	0.60	0.05	0.25
Solar/Wind	0.54	0.14	0.32	0.89	0.29	0.00
Clean Energy/Wind	0.55	0.20	0.32	1.13	0.48	0.00
Green/Wind	0.00	0.01	−0.02	0.02	0.02	0.62
CO2/Clean Energy	0.23	0.23	−0.07	0.70	0.12	0.01
Solar/Clean Energy	1.05	0.21	0.74	1.41	0.64	0.00
Wind/Clean Energy	0.74	0.15	0.51	0.96	0.53	0.00
Green/Clean Energy	0.00	0.01	−0.01	0.02	0.03	0.51
CO2/Green	0.01	1.87	−2.44	3.48	0.03	0.55
Solar/Green	−0.36	0.99	−2.26	1.23	0.02	0.63
Wind/Green	0.02	0.61	−1.19	0.88	0.02	0.57
Clean Energy/Green	0.05	0.57	−1.03	1.08	0.02	0.59

Notes: Results are based on Kroner and Sultan (1993).

Fig. 7.

Dynamic hedge ratios. Notes: Results are based on Kroner and Sultan (1993).

To deepen our understanding further on the investment implications of our study, we report in Table 5 the summary statistics of the bilateral portfolio weights and hedging effectiveness with the graphical outlook of Table 5 reported in Fig. 8 . We note that with the exception of the bilateral portfolio weights between green bonds and other assets under examination, investment in the portfolio weights of all paired assets reduce volatility per the statistical significance of the HE indexes for each paired asset. Fig. 8 confirms the insignificance of the hedging effectiveness for green bond and other assets. Interestingly, notwithstanding the fact that even no asset is helpful to hedge green bonds, green bonds are significantly reducing the investment risk of all other series.

Table 5.

Bilateral portfolio weights.

	Mean	Std.Dev.	5%	95%	HE	p-value
CO2/Solar	0.23	0.13	0.10	0.57	0.78	0.00
CO2/Wind	0.15	0.14	0.04	0.56	0.85	0.00
CO2/Clean Energy	0.11	0.11	0.03	0.38	0.86	0.00
CO2/Green	0.00	0.00	0.00	0.01	1.00	0.00
Solar/CO2	0.77	0.13	0.43	0.90	0.26	0.00
Solar/Wind	0.28	0.12	0.13	0.59	0.49	0.00
Solar/Clean Energy	0.11	0.26	0.00	1.00	0.53	0.00
Solar/Green	0.01	0.01	0.00	0.03	0.99	0.00
Wind/CO2	0.85	0.14	0.44	0.96	0.16	0.00
Wind/Solar	0.72	0.12	0.41	0.87	0.14	0.00
Wind/Clean Energy	0.31	0.26	0.04	1.00	0.34	0.00
Wind/Green	0.02	0.02	0.00	0.05	0.99	0.00
Clean Energy/CO2	0.89	0.11	0.62	0.97	0.10	0.02
Clean Energy/Solar	0.89	0.26	0.00	1.00	0.10	0.02
Clean Energy/Wind	0.69	0.26	0.00	0.96	0.24	0.00
Clean Energy/Green	0.02	0.01	0.00	0.04	0.99	0.00
Green/CO2	1.00	0.00	0.99	1.00	0.01	0.79
Green/Solar	0.99	0.01	0.97	1.00	0.05	0.27
Green/Wind	0.98	0.02	0.95	1.00	0.06	0.19
Green/Clean Energy	0.98	0.01	0.96	1.00	0.05	0.23

Notes: Results are based on Kroner and Ng (1998).

Fig. 8.

Dynamic bilateral portfolio weights. Notes: Results are based on Kroner and Ng (1998).

5.6.2. Multivariate portfolio analysis

In this section we discuss the constructed multivariate investment portfolios based on the three approaches including MVP, MCP and MCoP approaches, together with the hedging effectiveness discussed in Section 3.2. We provide the dynamic portfolio weights reported in Fig. 9 to shed further insights on the individual asset's portfolio weights with the aim of providing more solid understanding on the composition of individual portfolio. From a closer look, it can be seen that the portfolio weights of MCP and MCoP differ only marginally while MVP nearly solely selects a single asset, namely green bonds.

Fig. 9.

Dynamic multivariate portfolio weights. Notes: Results of MVP, MCP and MCoP are based on Markovitz (1959), Christoffersen et al. (2014) and Broadstock et al. (2020), respectively.

Focusing on the specific asset weights, in the case of green bonds, we observe intense fluctuation in the dynamic portfolio weights for all three approaches during COVID-19 period. We observe for MCoP, that there was a sharp change during the start of COVID19 outbreak during the early days of 2020. However, during the peak of the pandemic, some assets reached portfolio weight record high. We also find intense nose diving in portfolio weights for green bond during the Brexit and the European governmental debt crisis. Similar results are obtained for the renewable energy stocks during the COVID19 pandemic under MCoP. Regarding weights from MVP and MCP, we further note significant marginal differences comparing individual portfolio weights under MVP and MCP approaches. In all, we find significant qualitative differences in portfolio weights among the three approaches. Comparing the portfolio weights during bearish and bullish market conditions, we note portfolio weight during the COVID-19 period and other crisis period dropped and appreciated at some point in time compared to normal market states period.

After establishing that there exist marginal differences between the portfolio weights of MCP and MCoP, we next delve deeper focusing on the implications of our findings for portfolio and risk management purposes. Thus, we contrast and compare the conventional portfolio analysis approaches including MVP and MCP as well as recent approaches such as the MCoP by exploring the hedging effectiveness reported in Table 6 for MVP, MCP and MCoP portfolios, respectively. Among these three competing portfolio construction approaches, the MVP procedure aims to minimize portfolio volatility by definition. The MCP techniques, on the other hand, center on reducing correlations across assets. Finally, the MCoP procedure minimizes pairwise connectedness or the bilateral return spillovers across assets.

Table 6.

Multivariate portfolio weights.

	Minimum variance portfolio
	Mean	Std.Dev.	5%	95%	HE	p-value
CO2	0.00	0.00	0.00	0.01	1.00	0.00
Solar	0.01	0.01	0.00	0.04	0.99	0.00
Wind	0.01	0.02	0.00	0.05	0.99	0.00
Clean Energy	0.01	0.01	0.00	0.03	0.98	0.00
Green	0.97	0.03	0.90	0.99	0.02	0.38

	Minimum correlation portfolio
	Mean	Std.Dev.	5%	95%	HE	p-value
CO2	0.27	0.03	0.20	0.30	0.89	0.00
Solar	0.22	0.03	0.17	0.28	0.62	0.00
Wind	0.18	0.05	0.10	0.27	0.37	0.00
Clean Energy	0.03	0.04	0.00	0.11	0.28	0.00
Green	0.30	0.03	0.26	0.35	-44.88	0.00

	Minimum connectedness portfolio
	Mean	Std.Dev.	5%	95%	HE	p-value
CO2	0.27	0.02	0.25	0.30	0.89	0.00
Solar	0.20	0.02	0.17	0.23	0.62	0.00
Wind	0.21	0.02	0.16	0.24	0.36	0.00
Clean Energy	0.04	0.04	0.00	0.11	0.27	0.01
Green	0.28	0.02	0.26	0.32	-45.39	0.00

Notes: Results of MVP, MCP and MCoP are based on Markovitz (1959), Christoffersen et al. (2014) and Broadstock et al. (2020), respectively.

To commence our analysis on the investment implications of our study, we first discuss briefly the average portfolio weights. It is evident from Table 6 following the average portfolio weights that green bond contributes significantly in a portfolio containing renewable energy stocks. This is because the portfolio weights for green bond ranges from about 30% of the allocated portfolio under MCP and MCoP approaches and approximately 97% for MVP for the entire period. Focusing on the renewable energy stocks, we observe some nuances, with global solar emerging as the asset with the largest portfolio weight among the renewable energy stocks in the case of MCP with average portfolio weight of 22% while global wind emerged as the renewable energy asset with largest portfolio weights under MCoP with portfolio weight of 21%. Interestingly, even though clean energy emerged as major transmitter of shock in the return transmission analysis, it can be seen here that its contribution is trivial since clean energy recorded the least portfolio weight for both MCP and MCoP. This highlights the optimisation of MCP and MCoP as clean energy highly correlates with all others (Table 1) and is receiving and transmitting to others substantially (Table 2). The role of carbon price is also seen to be paramount under MCP (27%) and MCoP (27%). It is worth mentioning that the largest single weight in the constructed portfolio is also from the green bond. This finding is in consonance with the work of Broadstock et al. (2020) who examined minimum connectedness portfolios among green and black bonds around the world.

With reference to the hedging effectiveness ratios reported in Table 6, we note from the MVP procedure that if we invested on average 0% in carbon price, 1% in global solar, global wind and clean energy and 97% in green bonds, then each asset volatility in the portfolio would be reduced by 1% for carbon price, 99% for global solar, global wind and clean energy and 2% for green bond. Interestingly, these reductions in volatility with the exception of green bond are statistically significant at 1% level of significance indicating the reductions are from a financial perspective meaningful.

Next, we focus on the portfolios from the MCP procedure. Findings suggest that investing 27% in carbon price, 22% in global solar, 18% in global wind, 3% in clean energy and 30% in green bond would reduce volatility of each asset by 89% for carbon price, 62% for solar, 37% for wind and 28% for clean energy while increasing asset volatility by -44.88% for green bond. Interestingly, all these reductions and increase in each asset's volatility are seen to be significant at 1% level.

Finally, we document concerning the MCoP approach that with the exception of green bond, investment of about 27% in carbon price, 20% in global solar, 21% in global wind, 4% in clean energy reduces increases asset volatility evidenced by the hedging effectiveness ratios. Thus, green bond is seen to increase asset volatility by 45% under MCoP. Comparing the weights under the three alternative portfolios show that the portfolio weights in the case MVP is less compared to MCP and MCoP. In all, we provide evidence through the portfolio analysis the existence of some level of dynamic network which permits for diversification benefits.

Finally, we report in Table 7 , the Sharpe ratio for our three portfolios with results indicating that MCoP is the best performing portfolio with SR of 0.067 followed by MCP with SR of 0.065. The fact that the MVP has only a SR of 0.050 is of major interest for risk and portfolio managers, as initially it appears to be superior compared to MCP and MCoP as the volatility reduction has been much higher. However, the fact that the MVP heavily invested in green bonds leads to the case that the portfolio returns are also much smaller compared to all other portfolio techniques by nearly the factor ten.

Table 7.

Sharpe ratio.

	MVP	MCP	MCoP
Mean	0.008	0.071	0.073
Std.Dev.	0.159	1.090	1.097
SR	0.050	0.065	0.067

Notes: Results are based on Sharpe (1994).

In this section we discuss the constructed investment portfolios based on the three approaches including MVP, MCP and MCoP approaches. Fig. 10 illustrates the alternative three constructed portfolios. Among the three portfolios, it can be seen that the performance of MCP and MCoP are identical sharing the same underpinning dynamic pattern recording a dip during the peak of COVID-19 in March-May 2020 before recording a sustained upward trajectory. Thus, MCP and MCoP perform better than MVP approach.

Fig. 10.

Equity line. Notes: The series illustrate the cumulative sum of portfolio returns. MCoP denotes the minimum connectedness portfolio, MVP stands for minimum variance portfolio, and MCP for minimum correlation portfolio.

5.6.3. Performance of multivariate portfolios during COVID-19 period

We note from Fig. 11 the performance of all three multivariate portfolios for the COVID-19 period. As can be seen, MCoP outperforms all other portfolios again. It is evident that during the peak of the pandemic, the performance of the portfolios declined marginally. However, the decline was only for a short period since the portfolios saw a sustained upward trajectory in their performance.

Fig. 11.

Equity line after COVID-19 shock (19.03.2020). Notes: The series illustrate the cumulative sum of portfolio returns. MCoP denotes the minimum connectedness portfolio, MVP stands for minimum variance portfolio, and MCP for minimum correlation portfolio.

6. Conclusion and policy implications

This paper examines the transmission of risk patterns between green bond and renewable energy stocks taking into consideration the role of carbon price. To achieve this, we use S&P Green Bond Price Index as a measure of green bond market and different renewable energy stocks indices: Solactive Global Solar, Solactive Global Wind, and S&P Global Clean Energy. In addition, we include the certificate prices for CO2 emissions (European Energy Exchange EU emissions trading system) as a measure of carbon prices. The employed dataset runs from 4th January 2015 to 22nd September 2020. More specifically, we use TVP-VAR and LASSO VAR based dynamic connectedness approach to model the interconnectedness of our predetermined network and construct numerous bivariate and multivariate portfolios that informs us about the hedging effectiveness of all series and potential financial gains.

Regarding our question on the role of renewable energy stock to the green bond market and vice versa, we document several findings. On transmission from one market to another market, we find that green bonds transmit the lowest value of shocks to other markets followed by carbon price index returns. The highest spillovers are transmitted from clean energy to global solar (27.609%). In the case of return transmission from renewable energy stocks to green bond, we note that clean energy is the largest transmitter of shocks to green bond. In other words, renewable energy shocks transmit more shocks to green bonds compared to the amount of shocks green bonds transmits to renewable energy stocks. Focusing on the contribution to other assets, about 56.577% of the GFEVD of clean energy spilled to other assets under examination while 39.795% and 34.212% of the GFEVD of solar and wind respectively are transmitted to other markets. Green Bonds have marginal effects on renewable energy stocks since it only accounts for 2.246% of shocks to other markets. Concerning the range of the directional shocks transferred from all other assets to one specific market, we find the range to be wider from 7.730% to 46.849% for green bonds and clean energy, respectively. We find that green bonds receive more shocks from other markets compared to what it transmits to other markets. The same is seen for all the other assets. Overall, we note that green bonds, global solar, global wind and carbon price have negative net spillover values which indicates these assets are net receivers of shocks with global wind emerging to be the largest receiver of shocks in our entire sample followed by green bonds. The largest net transmitter in terms of magnitude in our sample is clean energy which again confirms the dominance of clean energy in the renewable energy markets.

On the performance of the investment portfolios constructed using MVP, MCP and MCoP strategies, we again note several interesting findings. In general, we find suggestive evidence that the investment risk of all assets can be significantly reduced by creating portfolios. The only exception has been green bonds which in combination with others significantly reduced their investment risk, however, barely any combination has been found that significantly reduced the green bond investment risk. Notably, a lot of combinations have shown a higher reward to volatility ratio compared to green bonds. Regarding the dynamic portfolio weights, we establish that MCP and MCoP portfolio weights differ marginally from each other while MVP strongly focuses on green bonds nearly excluding all others from being part in the portfolio. Interestingly, we find that green bonds are difficult to hedge and also not helpful to hedge other assets when it comes to hedge ratios, however, creating bilateral portfolios has shown that green bonds help to significantly reduce the investment risk of other assets. However, barely any evidence has been found that carbon price or renewable energy stocks can reduce the risk of green bonds. Finally, in the multivariate portfolio setting, we have shown that all assets except for green bonds have been significantly reduced in their investment risk. Finally, our analysis shows that the MCoP portfolio reached the best performance.

The findings in this study proffer several implications. Our finding is also relevant for formulating green finance policies and supporting renewable energy investments. In particular, when renewable energy and green bond prices move up (down) together due to the magnitude of connectedness, public clean energy funding can have an impact on renewable energy companies. This influence may result in a price externality for green bonds. Likewise, the removal of supportive policies (e.g., subsidies) for renewable energy would negatively affect the price of renewable energy stocks, which may transmit to the price of green bond assets. Therefore, policy decisions on the transition of energy to a decarbonized economy should consider the consequences for green bonds, which are also critical for the transition to a climate-resilient economy. Additionally, to the policymakers tasked to develop policies for the advancement of green bond markets, our findings on shock transmission from the green bond markets can help to enact policies that can ensure a smooth recovery process during different market conditions. With green bond receiving most shocks from renewable energy stocks, policy makers should consider green bonds and clean energy stocks to be interrelated assets in their policy framework. For market participants, our results can help in their portfolio composition since we show the diversification potential of green bonds to renewable energy stock returns.

For future studies, we suggest that further studies be carried out to examine the effect of liquidity variations, economic policy uncertainty and geopolitical risk, since these factors can directly impact the portfolio investors demand for green bonds and renewable energy stocks. Moreover, further studies could contribute to the literature on the policies driving green bond finance for renewable energy through empirical assessments of other financial policy supports including tax credits (Nesta et al., 2014), direct public infrastructure investments which spur renewable energy deployment Polzin et al. (2015). Investigations into how these and other policy supports affect demand for (even supplemental) green bond finance for renewable energy would provide welcomed contributions to the literature discourse. On the estimation techniques, future research may also consider other robust estimation techniques such as the DCC-GARCH connectedness (Gabauer, 2020), Markov-switching dependence model (Abakah et al., 2021a, Tiwari et al., 2021), joint connectedness (Balcilar et al., 2021, Lastrapes and Wiesen, 2021), as well as, fractional integration analysis techniques (Abakah et al., 2021b, Abakah et al., 2021b, Gil-Alana et al., 2020) and quantile VAR (Jena et al., 2021).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.