Co-movement and lead–lag relationship between green bonds and renewable energy

7 Background: A recent study in Nature Climate Change shows that due to reduced human 8 activities during the Coronavirus disease 2019 (COVID-19) pandemics, daily global 9 emissions of carbon dioxide decreased by 17% from the average level in 2019. With the 10 gradual recovery of economic activity and human energy consumption, the emissions of 11 greenhouse gas and pollution would rise again. Green bonds are considered a crucial tool 12 to release climate finance. The green bond market can act as an essential bridge between 13 capital providers (i.e. institutional investors) and sustainable assets (i.e. renewable energy). 14 This study is the first attempt to examine co-movement and the lead–lag relationship 15 between green bonds and global and sector renewable energy stock markets in the time and 16 frequency horizons. We apply continuous wavelet, wavelet coherence, and line and non17 line causality approaches on data during the period 2010–2020, coincidentally including 18 the COVID-19 pandemic. 19 Results: (1) Green bonds and renewable energy markets show evidence of a similar pattern 20 based on the wavelet power spectrum, which shows high price volatility at small and 21 medium scales, especially during periods of turbulence and crisis. (2) The dynamic 22 connection between green bonds and renewable energy returns is weak (strong) on the short 23 (long) time-scale. However, on medium-term time scales, the dependence between them is 24 significant only during turbulent periods, such as the European Sovereign Debt Crisis 2012 25 (ESDC) and the COVID-19 pandemic. (3) With regard to causality, our results show 26 unidirectional and bidirectional linear (non-linear) causality at low and high frequencies. 27 Moreover, our finding reveals the fact regarding the lead–lag relationship that, most of 28 the time and frequencies, no one market necessarily dominates the other. 29 Conclusion: Our findings provide several remarkable policies and practical implications 30 for market regulators and investors. Institutional investors can benefit by including green 31 bonds in their portfolios to decrease their climate change risk and improve their 32 environmental, social, and corporate governance rating in the portfolio. Considering that 33 the dependence between green bonds and renewable energy stock prices varies over various 34 time scales, investors with different investment horizons should make diverse investment 35 portfolio and hedging choices. The finding is also relevant for formulating green finance 36 policies and supporting renewable energy investments. Policy decisions on the transition 37 of energy to a decarbonized economy should consider the consequences for green bonds, 38 which are also critical for the transition to a climate-resilient economy. 39

shorter investment maturities, such as day traders or hedge funds, are more interested in 98 the short-term actions of the market. Alternatively, other agents, such as large institutional 99 investors, are more concerned with long-term market behavior. Therefore, an appropriate 100 frequency band would help to understand better the co-movement of green bonds and 101 renewable energy stocks at different frequency levels. 102 What should the relationship between the renewable energy stock prices and green bond 103 yields be? There is a view that there should be a negative correlation using a present -value 104 model. For instance, an increase in the discount rate in the future is expected to lead to a 105 fall in share prices and an increase in long-term interest rates. However, there may also be 106 a positive correlation, as changes in long-term interest rates may be related to information 107 about the future dividend stream of the stock [18]. Several contradictory assumptions may 108 predict a co-movement between these two green assets. This hypothesis is closely related 109 to the theoretical arguments about the relationship between stock and conventional bonds 110 [19], although the issuance of green bonds is ostensibly driven by the "green bond (2) Risk hedging needs: when the price of an asset deviates too much from its real 116 value, hedgers will shift more of their positions to other safe assets to reach the target hedge 117 ratio level [21]; (3) Asset substitution: Assuming that stocks and bonds are two perfectly 118 competing assets, if the disclosure of relevant information helps increase the price of stocks, 119 investors will be incentivized to convert bonds into stocks in their portfolio; if the 120 information is more favorable to bonds, investors will replace their stock holdings with 121 bonds [22]. When hypothesis (1) is confirmed, the stock and bond markets exhibit a 122 "linkage effect"; when hypothesis (2) and hypothesis (3) are confirmed, there is usually a 123 "seesaw effect" between the two. The co-movement between the two markets can also be 124 explained by the above three hypotheses since the renewable energy stock and green bond 125 markets are subordinate to the stock and bond markets, respectively. We expect financial 126 contagion between the green bonds and renewable energy markets because, as an important 127 source of funding for renewable energy companies, when the overall green bond market 128 improves, investors expect the renewable energy markets to strengthen as well. 129 To this end, we analyze (i) dynamic co-movement and the lead-lag relationship between 130 cross time-scale by applying cross-wavelet coherence and phase analysis, and (ii) the 131 causality between green bonds and renewable energy returns by using (discrete) wavelet 132 methods combined with linear and non-linear causality tests. We find that the interaction 133 between green bonds and renewable energy returns is weak in the short time scale and that 134 this weakness persists throughout the sampling period. In the long run (512 days-), green 135 bonds are closely linked to the renewable energy market, despite differences between the 136 global and sectoral indices. However, on medium-term time scales, the degree of 137 dependence between these two markets is high only during turbulent periods. Concerning  This study investigates the idiosyncratic characteristics of return connections between 142 green bonds and renewable energy markets. We examine these linkages because they are 143 important for investment and risk management decisions. For example, portfolio managers 144 often transfer funds from stocks to bonds when they expect stock market returns to decline.

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Reducing risk through this transfer depends on the linkages between the stock and bond 146 markets. If cross-market asset returns are highly correlated, bonds would not provide the 147 risk aversion that investors need. And if cross-market asset returns are negatively correlated, 148 the possibility exists for long-term asset portfolios. Exploring the dynamics of the 149 correlation between stock and bonds markets can provide theoretical support for the 150 practice of asset allocation by institutional investors such as investment funds and 151 insurance funds. Linkages between markets should also be taken into account when 152 formulating regulatory policy, for example, market regulators would consider these 153 linkages when assessing the effects of proposed policy changes.

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This work provides a novel insight into green investment from a new perspective and 155 contains at least four contributions on green bonds and renewable energy research. First, 156 we use a continuous wavelet transformation method to distinguish between short-and long-157 term investor behavior in green bonds and renewable energy stocks. This aspect is 158 important for investors who act at different time scales and over different periods. Indeed, 159 from the perspective of portfolio diversification, green portfolio managers are more 160 interested in higher frequency asset price linkages. In other words, they are concerned 161 about short-term movement. However, others are more interested in lower frequencies (i.e., 162 longer-term time scale). Second, using the frequency domain to understand the two main 163 green assets better and choose the incentive policy that suits them is useful for 164 policymakers. Third, a non-linear Granger causality model is applied to analyze further the 165 relationship between green bonds and renewable energy over different time horizons. 166 Fourth, we also use the most recent dataset, which happens to include the COVID-19 167 epidemic period, resulting in extreme market volatility. As a result, we add an interesting 168 period for the green bond and renewable energy markets.

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The rest of the paper is organized as follows. Section 2 reviews the literature on green 170 bonds and renewable energy. Section 3 introduces the data and reports a preliminary 171 analysis. Section 4 outlines the methodology. Section 5 presents the empirical results.

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Section 6 offers primary conclusions and implications. Index. In a comparable study, Bachelet et al. [24]confirmed that green bonds issued by 178 institutional issuers have higher liquidity than gray bonds. Reboredo [25] investigated the 179 co-movement between green bonds and financial markets. This finding suggested a strong 180 linkage between the treasury and corporate bond markets, and a weak connection between 181 stock and energy commodity markets. Likewise, Reboredo and Ugolini [26] employed the 182 value-at-risk (VaR) approach and discovered the price correlation between green bonds and 183 financial markets. This study provided evidence that the green bond market is closely 184 related to the fixed income and currency markets, resulting in a considerable price spillover 185 effect and a negligible reverse effect. However, the green bonds market is weakly linked to 186 these markets, such as stock, energy, and high-yield corporate bond markets. The research 187 of Reboredo et al. [27] further provided a similar result to that of Reboredo and Ugolini 188 [26] by using wavelet coherence methods; their finding suggested a strong connectedness  Given that green bonds offer significant funding for renewable energy projects [31], the 218 intrinsic connection between green bonds and the renewable energy market deserves 219 further exploration. This study is the first attempt to examined the co-movement and lead-220 lag relationship between green bonds and renewable energy markets across different time 221 horizons by applying (discrete) wavelet methods, and linear and non-linear causality tests.

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It would fill in the gaps for the empirical research of green bonds and renewable energy.

Data
We conduct an empirical analysis of co-movement and lead-lag relationship between 225 green bonds and renewable energy stock prices on a range of time scale. In this case, we  The wavelet is a function constructed from a single wavelet known as the mother wavelet,  Table 1 here which is a real-valued squared productive function given by the following:

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where − 1 4 is the standardized factor that ensures that the wavelet has a unit of energy, as a Gaussian envelope with unit standard deviation, and 0 denote a complicated 300 sinusoidal curve. In the present study, we set 0 = 6 to represent the appropriate 301 compromise between time and frequency localization.

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The CWT ( ) is a useful tool that enables to analyze time evolution along with 303 the frequency and is described as follows:

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where * denotes complex conjugation and the proportionality parameter determines 307 whether the wavelet can detect a higher or lower component of the sequence ( ), which 308 is possible when the tolerance condition is satisfied.  The cross-wavelet transform explores the interdependence between green bonds x(t) 315 and renewable energy y(t) in a different frequency space, which can be formulated as where ( , ) and ( , ) denote CWT of x(s) and y(s) , respectively and 319 represents the complex conjugate.

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As opposed to the power wavelet, crossed wavelet power (XWP) represents the local 321 covariance in time and frequency for each sequence, and the formula is as follows: Wavelet coherence 2 ( ) is also an important method for assessing the common 324 movement between green bonds and renewable energy in the time-frequency space. It 325 generates a quantity between 0 and 1 (a correlation coefficient), where 0 denotes a weak 326 inter-correlation and 1 means a strong interaction. 2 ( ) is given by:  However, the CWT will create redundant information, which leads to inefficient analysis.

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Therefore, the DWT is performed to account for specific time-frequency conditions 345 adequately.

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Parameters s and τ are discretized as s = 2 − ,τ = 2 − , , ∈ , and the definition of 347 the wavelet function becomes the following: where X and Y are stable time series, and n and q are the lag lengths of X and Y, respectively.

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The null hypothesis in the Granger causality test is that y does not cause x, which is 378 indicated by 0 : 1 = ⋯ = = 0. The contrast hypothesis is 1 : ≠ 0 for at least one 379 j. The test statistic has a standard F distribution, in which the degrees of freedom are (n, T-380 n-q-1) and T is the number of observations.    to be the same as that of Z given Y = y. Thus, we redefined the Eq.14 as follows: Moreover, the wavelet coherence and phase difference are applied to detect the lead-lag 495 relationship of green bond-renewable energy pairs. In the wavelet coherence diagram (Fig.   496 6), the color grade orders from warmer (higher cohesion) to cooler (lower cohesion). The 497 lowest coherence is close to 0 (dark blue), implying a perfect negative cohesion, whereas 498 the highest cohesion is close to +1 (dark red), which means a perfect positive cohesion.

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The horizontal axis shows time, and the vertical represents the period, converting it to units 500 of time (days).

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The visual inspection of Fig. 6 reveals several interesting findings. We have identified 502 that these markets share the same pattern over the long-term horizon. Green bond and Nonetheless, for the ERIX and TECH markets, which are exceptions, we do not find linear 555 causality between green bonds and TECH on short-run time scales.

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However, on medium time scales D2-D7 (more than one week and less than one year, 557 excluding non-working days), the linear Granger test results support that, in most cases, 558 the two markets are linearly correlated at the 5% significance level. Using the linear 559 Granger causality test, bidirectional Granger causality is observed between green bonds The non-linear Granger causality tests are performed on VAR models to detect the non-585 linear relationship between the green bonds and renewable energy markets at original and 586 decomposition data. Table 5 gives the values of the statistics T and P. According to the 587 research of Diks and Panchenko [51], the parameter C of the bandwidth is 8, and the 588 theoretical optimal rate of is 2/7, and with reference to Yu et al. [54], we set the optimal 589 bandwidth to 1.5 based on our sample size.

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For the original data, we discovered that the Granger causality was rejected at a 5% 591 significance level on the return sequence, that is, bidirectional non-linear Granger causality 592 is observed between the green bonds and the renewable energy market. This observation is   Table 5). This result is quite different from the linear Granger 620 causality test, which identifies the linear bidirectional Granger causality over a long period.

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The primary explanation could be attributed to the simple, linear, and low-level complexity 622 characteristic of the two long-term market trends. Given that the two series move slowly 623 on a smooth curve without significant structural breaks, the connection mechanism 624 between them may be following a simple linear relationship rather than a complex non-625 linear relationship. In general, our findings reveal that the green bond market is closely 626 associated with the renewable energy market.  two markets and design appropriate portfolio ratios to reduce and diversify portfolio risk. 673 We found evidence that green bonds and clean energy markets are positively correlated 674 and co-moved on long time scales. Moreover, the results of the Granger test indicate 675 bidirectional Granger causality between green bonds and renewable energy stocks, which 676 prevents investors from taking advantage of hedging. However, investors could design 677 their portfolios using the evidence of linear and non-linear causality because these two 678 markets would use each other for useful information in determining their future values.

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Particularly, information from other markets should be carefully considered when 680 forecasting market prices for green bonds or renewable energy.

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Our finding is also relevant for formulating green finance policies and supporting 682 renewable energy investments. In particular, when renewable energy and green bond prices 683 move up (down) together, public clean energy funding can have an impact on renewable 684 energy companies. This influence may result in a price externality for green bonds.

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Likewise, the removal of supportive policies (e.g., subsidies) for renewable energy would 686 negatively affect the price of renewable energy stocks, which may transmit to the price of 687 green bond assets. Therefore, policy decisions on the transition of energy to a decarbonized 688 economy should consider the consequences for green bonds, which are also critical for the 689 transition to a climate-resilient economy.

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For future work, we would further combine the wavelet correlation and dynamic hedging 691 models to examine the dynamic correlation and volatility spillover between green bonds 692 and renewable energy returns to help hold optimal portfolio weights and hedge ratios 693 especially in times of crisis and under different market conditions.  respectively. Corr. is the Pearson correlation for each renewable energy index with green 1094 bonds. As usual, ***，**and * denote significance at 1%, 5% and 10%, respectively.