Spillover Nexus among Green Cryptocurrency, Sectoral Renewable Energy Equity Stock and Agricultural Commodity: Implications for Portfolio Diversification

1 Introduction

At present, countries worldwide are consistently making efforts to attain a climate resilient or low carbon economy. Recent research has widely acknowledged the devastating effect of excess carbon accumulation on human health, living, and environment (Taghizadeh-Hesary; Kumar & Radulescu, 2024; Taghizadeh-Hesary & Taghizadeh-Hesary, 2020). Currently, excessive greenhouse gas (GHG) emissions in the environment are playing a destructive role in rising temperature and harming the ecosystem and life on earth (Fang et al., 2020; Kumar et al., 2024a; Radulescu et al., 2024). Further, as reported in the study by Wang et al. (2020), GHG emissions could potentially increase twofold from the preindustrial level till 2035. The alarming level of GHG in the atmosphere causes adverse effects on the world economy like disruptions of business, lower productivity, taking resilience and adaption measures, and transforming into a climate friendly economy (Kumar et al., 2024b; Rudebusch, 2021). Due to the challenges presented by climate change, a new area of finance, that is, climate finance, has emerged to lessen the detrimental effects of climate change. Green investment is chiefly a vital mechanism for climate finance aimed at addressing issues associated with climate change such as mitigating financial risks, stimulating economic growth, and improving public health (Guo et al., 2020). Moreover, investors recognize the risks associated with climate transition including anticipated decreases in asset prices, revenue, and profitability in sectors with high carbon emissions. Therefore, investment pullback tends to occur in carbon-dependent industries (Reboredo & Otero, 2021). Further, green investment project has garnered attention from both equity and bond investors as they mobilized a significant portion of the funds towards environmental friendly projects and facilitated the transition to net-zero carbon economy. The sustainable finance consistently attracts more interest from investors than conventional funds. The value of the global green finance market hits $5.8 trillion in 2022 despite unstable economic conditions including low market returns, high inflation, soaring interest rates, and looming threat of recession that impacted all the financial markets (UNCTAD Report, 2023)^[1]. Indeed, recent findings demonstrated that investors continued to focus on sustainable investment even during the COVID-19 pandemic and earned attractive returns by funds having strong sustainability ratings (Pastor & Vorsatz, 2020). On the stock market, FTSE Russell estimated the market value of global green equities to be $7.2 trillion in 2021, representing 7% of the total global stock market capitalization.^[2]

Among the green investment assets, sustainable cryptocurrency is a growing buzz term in a contemporary sustainable finance area. The eco-friendly crypto has become a prominent emerging asset for climate-aware investors. The mining process of traditional cryptocurrencies involves extensive energy usage for running algorithms, high-powered computer systems, and depletable resources like coal and fossil fuels. These non-renewable resources cause adverse effects on the environment and carbon footprints. To address such criticism, green cryptocurrency relies on renewable energy such as wind, hydroelectric, and solar for the mining process. For instance, Stellar (XLM) utilizes its own consensus protocol (SCP) for mining purposes. The personal SCP shortens the authentication cycle, resulting in a more energy-efficient and cost-effective crypto asset. Therefore, investors are leaning towards eco-friendly investment options as they minimize the carbon footprint of cryptocurrency.

Further, environment stewardship of green assets marked by its green nature is evident, yet its financial outcomes are still uncertain. Consequently, there arises a need to diversify and mitigate the risk associated with extreme financial market swings (Baur & Lucey, 2010). Especially during the recent COVID-19 pandemic, which instilled panic in investors and led to high market volatility (Cheng et al., 2022). Baker et al. (2020) argued that volatility shocks induced by COVID-19 surpassed earlier turmoil like global financial crisis (GFC) in 2008 and Great Depression in 1929. Indeed, there is empirical evidence of increasing co-movement among financial assets during periods of market uncertainty (Heil et al., 2022, Jiang et al., 2017). Hence, there is a growing interest among investors to comprise varied classes of assets in their portfolios for diversification benefits and hedging against the market risk. The literature is encountering a growing number of studies on the return and risk transmissions between the green markets and other markets. Essentially, most of the studies focused on the risk spillover of the green market with financial and energy market (Duan et al., 2023; Reboredo, 2018; Shahbaz et al., 2021). Nevertheless, the literature still offers limited research regarding the development of the relationship between green assets and other asset classes.

Further, studies on spillovers nexus in the financial markets have been increasing, driven by the need of investors and policy makers to comprehend the cross-market linkages. The findings of such studies have important significance for portfolio diversification and contagion risk affecting the market stability (Ngene et al., 2018). Financial analysts and portfolio managers often seek asset classes capable of providing diversification benefits during periods of significant volatility swings. In fact, the dynamics of connectedness among the assets are crucial for many facets of empirical finance including risk management, portfolio allocation, and asset pricing (Gardebroek et al., 2015). However, this led to the emergence of a new avenue of research of finding out the asset classes which are weakly connected with each other and hence offer maximum diversification potential in the portfolio. The existence of the spillover phenomenon indicates that one large amplifier increases the connectedness of returns not only in the own asset but also in their cross-assets. The portfolio and risk managers must comprehend the dynamics of asset price to deal with the spillover.

In this study, we aim to investigate the interconnectedness of green cryptocurrencies, green equity, and agricultural commodities to assist the portfolio managers in minimizing portfolio risk. With the financialization of commodities, investors and traders identify them as a potential tool to diversify the portfolio risk (Tang & Xiong, 2012). The commodity market depicts different returns and volatility and exhibits a low degree of correlation with financial markets, and especially when macroeconomics disruption tends to drive returns on commodity assets and investors’ portfolio in diverging directions (Kang et al., 2017). Further, agricultural commodity prices showed great resilience during the COVID pandemic and offset the accumulated losses from investment in the equity market (Rubbaniy et al., 2022). Hence, investors are specifically keen to observe potential hedging options offered by commodity class to mitigate price crash risk. Existing studies have empirically addressed the linkage of green assets with financial assets. However, the limited emphasis has been given to the interrelationship between green assets and agricultural commodities. This scarcity of studies in the latter area justifies the further study.

This article differs from the prior studies in the following ways: To the best of our knowledge, this article is probably the first attempt which examines the spillover nexus among green cryptocurrency, subsector renewable energy stock, and agriculture commodity. Our research enhances the existing body of literature by considering a wide set of environment-based assets and agricultural commodity for portfolio optimization. Second, there are research studies on the relationship between sustainable equity and agriculture commodities. This article extends the literature by focusing on the variation of spillover effects between different sub-sector of renewable energy and agricultural commodity. Third, this study conducts a comparative analysis of the diversification and hedging benefits of a portfolio composed of eco-friendly assets and agricultural commodities during and after the COVID period.

Methodologically, we employed a time-varying parameter VAR (TVP-VAR) model, an extension of the spillover framework by Diebold and Yilmaz (2012), to examine the static and dynamic spillover effect among green cryptocurrencies, renewable energy stocks, and agriculture commodities. This model is superior to the Diebold-Yilmaz approach because it overcomes the problem of arbitrarily chosen rolling-window size, which may result in loss of observation and may produce excessively erratic or flattened parameters (Antonakakis et al., 2020; Korobilis & Yılmaz, 2018). Further, the TVP-VAR model is supposedly better than other GARCH models such as VAR-GARCH, BEKK-GARCH, and DCC-GARCH for at least two reasons. First, these competitive models only provide estimates of static spillovers between the assets. On the other hand, the TVP-VAR approach estimates dynamic spillovers in addition to the static spillovers. Second, these competitive GARCH models sometimes face the problem of data convergence (Yousaf & Ali, 2020). Further, the previous studies such as Gajardo and Kristjanpoller (2017) demonstrated the potential complex characteristics of financial time-series such as non-linearity, time-varying, and asymmetry features. The TVP-VAR model identifies non-linearity in the relationship and explore time-varying impact between the variables. Besides these advantages over the competing framework, the TVP-VAR model produces spillovers in various settings: (a) total spillovers, (b) from each market to system, (c) from system to each market, (d) net directional spillover in both static and dynamic fashions. In addition, we computed optimal portfolio weights, hedge ratios, and hedge effectiveness for the pairwise portfolios of green cryptocurrency-agriculture commodity and renewable energy stock-agriculture commodity using conditional variances and covariances from the DCC-GARCH model, proposed by Kroner and Ng (1998) and Kroner and Sultan (1993). It offers valuable information to investors and portfolio managers regarding optimal asset allocation and hedging, particularly in COVID and after COVID periods.

The rest of the article is structured as follows: Section 2 presents the literature review. Section 3 provides the methodology and data. Section 4 discusses the empirical results. Finally, Section 6 concludes this article.

2 Literature Review

A wide branch of literature has focused on green and sustainable finance in the recent years. This growing attention towards green investment is reflected in the investor’s preference towards green bonds, clean energy equity, and digital green cryptocurrency (Alessi et al., 2023). Further, existing studies have explored the potential diversification benefits associated with the green assets (Narayan et al., 2022, Rehman et al., 2023, Zhou et al., 2024) which could help investors not only in constructing efficient portfolio investment but also in facilitating the expansion of green financial markets. Therefore, the current research studies are focusing on evaluating the integration of traditional markets with sustainable financial markets. For instance, Naeem et al. (2022) examined the quantile connectedness between green bonds and traditional assets and revealed that green bonds offer diversification benefits particularly to the energy and agriculture assets. By using the cross-quantile approach, Arif et al. (2021) measured the safe-haven features of green assets under different market conditions and illustrated that green bond index appears as a significant diversifier to offset the risk of conventional financial assets. In the same vein, Ben Ameur et al. (2024) established that the inclusion of clean energy and green bond indices in conventional asset portfolio considerably reduces the extreme risk of portfolio. In the context of the Indian Stock Market, Dutta et al. (2021) illustrated higher risk transmission from energy and precious metal market to green stocks during bearish stock market periods and projected contagious shocks arising from energy and metal market destabilizing the equity market. Oliyide et al. (2023) somewhat oppose such findings and evidenced that green assets and commodities serve as a complementary to each other during a bearish market state and this relationship turned into a substitution stance during bullish market conditions. Likewise, Ramlall (2024) demonstrated that regardless of bearish or bullish market phases, green assets are capable of muting down portfolio tail risk. In addition, Sun et al. (2024) focused on the connectedness among green economy stocks, carbon, and energy market and indicated that green economy stocks have satisfactory hedging ability in the portfolio consisting of clean and dirty assets. Few recent studies have focused on analysing the pricing of renewable energy and fossil fuels companies during major climate-related events. For instance, Gong et al. (2024) evaluated the impact of the Paris Agreement on the performance of renewable and non-renewable energy companies. The findings highlight a significant increase in the TOPSIS score of renewable energy companies during the period of formal entry of the United States into the Paris Agreement. Similarly, Gong et al. (2023) measured the degree of climate risk using Notre Dame Global Adaptation Initiative and found an existence of climate risk premium in the pricing of fossil fuel companies.

Since 2009, the year when the first cryptocurrency, Bitcoin, was introduced, a new strand of literature has emerged, focusing on the relationship of cryptocurrency with other asset classes. In this respect, Rao et al. (2022) found that equity markets, green bond, and bitcoin are strongly linked and disapproved the notion of bitcoin being a good hedging instrument during and post-COVID period. Likewise, Ali et al. (2024) evidenced a significant surge in return and volatility connectedness between green cryptocurrency and G7 equity markets during the period of market stress and uncertainty. Rizvi et al. (2022) evaluated the safe-haven properties of Green Assets and Cryptocurrencies under different time periods. The findings refuted the expected role of green bonds as safe-haven while exhibiting investors’ preference towards cryptocurrency during bearish trends. In line with these findings, Umar et al. (2024) uncovered that eco-friendly cryptocurrencies do not move independently of conventional investment assets and thus counter the argument of green asset being standalone diversification measure in a portfolio. Similarly, Zeng et al. (2025) revealed the strong linkage of green bond with the metal market, particularly lead and aluminium, at medium- to long-term frequencies and cryptocurrency market, which is highly associated with the prices of copper and lead in the short term. Goodell et al. (2022) employed wavelet analysis and investigated the interconnectedness of green assets with Bitcoin. The findings deduced that there is a considerable cushion in green investment indices to offset the risk of Bitcoin. Similarly, Esparcia et al. (2024) assessed the potential diversification of different types of cryptocurrencies by including them in equity-based portfolios and documented the portfolio opportunity provided by traditional and green cryptocurrencies on short-term investment horizons. Taking this debate a step ahead, Wang et al. (2022) proposed an index to measure the environmental concerns of the cryptocurrency market by capturing media coverage on the negative impact of cryptocurrency on climate change and concluded that it has a positive relationship with uncertainty indices of cryptocurrency, VIX, Bitcoin, and Brent Crude oil and negative relationship with the industrial production in the long run.

Recently, the study of agriculture commodity pricing has gained attention primarily due to the food crisis occurring around the globe and GFC of 2007–08. The major agricultural commodities are cointegrated with the crude oil as it is one of the feedstocks used for biofuels. The existing literature reported the studies on the integration of agricultural commodities with financial markets and found evidence of potential diversification benefits of commodities. For instance, Hernandez et al. (2020) examined the spillovers between agricultural commodities and the equity market and found that agricultural investments are negatively correlated with global and regional equity markets which make them an attractive tool for hedging during market turbulent times. Likewise, Demiralay et al. (2018) supported the diversification effectiveness of agriculture and metal commodities and concluded that commodity futures enhance the benefit of diversification into equity portfolio. In addition, Iqbal et al. (2022) uncovered that agriculture future markets have the least volatility connectedness, making them suitable diversifier for other financial markets during normal periods. Similarly, Öztek and Öcal (2017) concluded that agricultural commodity indeed delivers diversification opportunities during calm periods. Cai et al. (2018) explored the time-scale relationship among crude oil, precious metal, and agricultural commodities by employing wavelet coherence measure and disclosed that the causality relationship fluctuates over time for different time horizons. Acikgoz et al. (2023) supported the notion that agricultural commodities exhibit a low degree of co-movement with financial assets and hence boost portfolio performance. In addition, Kyriazis (2022) established that agricultural commodities generate the best risk-return trade off in the portfolio consisting of exchange rate, cryptocurrencies, precious metals, and fuels. Conversely, there are studies which discarded the notion of agricultural commodities being good diversifiers. Bonato (2019) provided evidence of a prominent spillover effect between oil and commodities and found that diversification benefits of the commodity market have declined while hedging costs have increased. By applying wavelet-based copula, Mensi et al. (2017) illustrated time, tail, and horizon-dependent linkage among oil, wheat, and corn future market. In the same vein, Wen et al. (2021) demonstrated reducing hedging ability of commodity market against the risk arising from the Chinese stock market but suggested that precious metal and grain have relatively good risk reduction ability. Shah and Dar (2021) noted rapid transmission of spillover between agricultural commodities, and financial markets and hedging potential were relatively low during GFC, European Debt Crisis, and COVID-19 period. Kang et al. (2017) analysed spillover transmission among agricultural commodities (corn, wheat, and rice), precious metal (gold and silver), and WTI crude oil and concluded that bidirectional transmission of return and volatility exist among the commodities. Zhang and Wei (2024) argued that a portfolio consisting solely of energy and carbon assets delivers a better Sharpe ratio compared to a portfolio that includes agriculture and metal commodities.

For example, Naeem et al. (2021a) empirically evidenced insignificant correlation between agricultural commodities and green bonds and thereby indicating the effective diversification benefits offered by green bonds for the fluctuations in agricultural commodity prices. Similarly, Naeem et al. (2021a) documented that agricultural soft commodities (wheat and corn) have weak connectedness with the green bonds irrespective of investment horizon. Thus, combining wheat and corn with the green bonds will result in diversification strategy against the market shocks. Likewise, Niu and Zhang (2024) indicated that agricultural commodities can hedge green market risk in the long-term investment horizon under normal market circumstances. However, contagion risk is present during both bullish and bearish phases. Zeng et al. (2023) revealed short-term spillover between green and agricultural market exceeding long-term spillovers. Furthermore, during the COVID-19 epidemic, there was a notable increase in the connection between green markets and agricultural commodities including corn, wheat, and soybeans.

The market portfolio theory suggest that fragmented markets provide the potential of earning diversification gains and minimizing the risks in portfolios (Dunis & Shannon, 2005). Financial markets are no longer clearly separated due to the advent of globalisation and digitalisation. Market interdependencies and connectivity have increased as a result of it (Bernardi & Petrella, 2015). It further paves the way for future research to find out the interconnectedness between asset classes having low correlation and offering diversification potentials to investors and fund managers. Therefore, this article analyses the spillover effects between Green Cryptocurrency and Equity and Agricultural Commodity on a time-varying basis by considering pandemic and non-pandemic periods.

3 Methodology and Data

We employed daily data of four major green cryptocurrencies (Stellar, Nano, Cardona and IOTA), three sub-sectoral renewable energy stocks (NASDAQ Solar Index, NASDAQ Geothermal Index, and NASDAQ Wind Index), seven agricultural commodities (wheat, cocoa, coffee, corn, cotton, sugar, and soybean). The cryptocurrency data are collected from the coinmarket.cap website, whereas renewable energy stock and agricultural commodity data are gathered from the NASDAQ OMX and S&P Global website, respectively. The seven agricultural commodities are extracted from the S&P 500 based on the global industry classification standards. We chose only those agricultural commodities for which data are available from January 2, 2020. The commodities included in the study are significant in terms of their large production, distribution, and consumption worldwide. In fact, the select commodities constitute a substantial proportion of the S&P GSCI agriculture commodity index, which is a widely recognized instrument to measure the performance of the agriculture market. These commodities have a historically shown a negative correlation with stock markets, which can improve diversification benefits during market downturns (Hernandez et al., 2020: Zapata et al., 2012), Therefore, it is of interest to understand the extent to which these agricultural commodities are related to the prices of other financial assets. Further, the cryptocurrencies examined in this study were selected based on their dominance in the green cryptocurrency market, as measured by market capitalization and trading frequency.^[3] Three selected renewable energy sectors represent the broader clean energy industry. The solar energy is the most mature renewable energy source, followed by wind and geothermal energy, which have gained significant momentum in recent years. The selection of three different types of renewable energy stock allows the authors to present more focused conclusions based on the different characteristics of the renewable energy stocks. Data sample spanned from January 2, 2020, to June 7, 2024. To perform during and post COVID-19 analyses, we opted for two sub-sample periods: during COVID period (January 2, 2020, to May 4, 2023) and post-COVID period (May 5, 2023, to June 7, 2024). The cutoff date of the beginning of COVID-19 is selected on the following grounds: First, on January1, 2020, WHO had launched the IMST (Incident Management Support Team), activating the organization to deal with the virus outbreak. Second, on January 5, 2020, WHO announced the news of new virus outbreak to the world. Further, daily returns are calculated by taking natural logarithm between two successive days: r t = ln p t p t − 1 , where p t and p t − 1 denote asset price at t and t − 1, respectively.

Next, to perform the spillover analysis between eco-friendly cryptocurrencies and stock and commodity, we employed the TVP-VAR framework proposed by Antonakakis et al. (2020), which is an extension of connectedness work of Diebold and Yilmaz (2012, 2014). The TVP-VAR model is preferable to spillover analysis proposed by Diebold and Yilmaz (2012, 2014) due to its desirable attributes such as no loss of valuable observation and lesser dependence on outliers. The TVP-VAR model is estimated based on lag length of order one, which was selected by Bayesian information criterion (BIC).

The TVP-VAR (1) can be written as follows:

where Y t is a (N × 1) dimensional vector, Y t − 1 represents a (Np × 1) lagged vector of the dependent variables, and ϕ t denotes (N × Np) matrix of coefficients, which is assumed to be time varying. Error terms are represented by u t and v t (N × 1) vectors. S t and R t are (N × N) dimensional metrics representing time-varying variance–covariance metrics of the error terms u t and v t , respectively. The TVP-VAR model is estimated by the multivariate Kalman filter process with forgetting factors introduced by Koop and Korobilis (2014). The Kalman filter process is detailed in the study by Antonakakis et al. (2020).

The next step is to transform the TVP-VAR to its TVP-VMA (vector moving average). The vector moving average model’s dynamic coefficients are the fundament of the connectedness approach introduced by Diebold and Yilmaz (2012) through the generalized impulse response function (GIRF) and generalized forecast error variance decomposition (GFEVD) proposed by Koop et al. (1996) and Pesaran and Shin (1998). The transformed equation can be expressed as follows:

where A t = ( A 1 , t , A 2 , t , … A p , t ) is an (N × N) matrix of parameters. Therefore, GIRF can be interpreted as a response of total variables following a shock in variable i.

The pairwise directional connectedness from j to i is defined by GFEVD ψ j g , t (J). It presents the influence of variable j on variable i in terms of its forecast error variance share, which can be expressed as follows:

where ∏ j g , t (J) represents the variance share one variable has on others. ψ j , t g ( J ) = S j j , t − 1 / 2 A J , t S t u j , t , ∑ i , j = 1 N ∏ j , t N ( J ) = N .

The total connectedness index (TCI), which illustrates the network’s interconnection, is constructed using the GFEVD. More specifically, it explains how a shock on one variable spill over to other variables:

We can compute the directional connectedness that “a variable i transmits its shock to all other variables j,” called total directional connectedness to others and defined as follows:

We also calculate the directional connectedness that a variable i receives from variables j, known as the total directional from others and defined as follows:

Finally, the net directional connectedness is defined as follows:

If H i , t g > 0 , then variable I transmits more shocks to the network than it receives from the network. On the contrary, if H i , t g < 0 , then variable i receives more shocks from the network than it transmits to the network.

Finally, by using the DCC-GARCH model, we estimated the conditional variance and covariance to determine the optimal weights for the pairwise portfolio. Using Kroner and Ng (1998), the optimal weights can be calculated as follows:

where w x y , t is the weight of asset y in a one-dollar portfolio at time t, h x y , t represents conditional variance between x and y, and h x , t and h y , t describe the conditional variance of asset x and y, respectively. By using Kroner and Ng (1993), we also computed the hedge ratio as follows:

where β x y , t denotes the hedge ratios, indicating that a long position in the asset x can be hedged by taking a short position in asset y.

Finally, we examined the efficacy of various portfolios by computing the hedge effectiveness score. Following Ku et al. (2007), hedge effectiveness can be computed as follows:

where variance_Unhedged denotes unhedged portfolio return’s variance and variance_hedged represents the variance of x and y asset-based portfolio’s returns.

3.1 Preliminary Analysis

Tables 1 and 2 collect the summary statistics for the seven agricultural commodities, three sectoral renewable energy stock, and four green cryptocurrencies for two different periods: during and post-COVID period. The average return for all variables over COVID period is positive, with the highest returns of Cardona and XRP. However, negative returns were seen in the post-COVID period by agricultural commodities such as wheat, corn, cotton, sugar, soybean, and renewable energy stocks like Geothermal and Wind. This indicates that the risk and return dynamics of agricultural commodities are dissimilar to those of green cryptocurrencies. The median values are different from the mean values implying series are not normally distributed in both the periods. Further, the results show significant fluctuations in all the variables as indicated by the maximum and minimum values. The maximum and minimum mean returns are recorded by Nano in the COVID period. XRP has the most positive return, and cocoa has the most negative mean return in the post-COVID period. The standard deviation ranges between 1 and 8%, showing the higher values during the pandemic sub-period, as that period was identified as a time of greater instability in the financial markets (Altig et al., 2020). The highest standard deviation was recorded by Nano followed by XRP during the COVID period. On skewness, it is noticed that half of the variables have negative skewness in the pandemic period, while few variables were observed to be negatively skewed in the post-pandemic period. For kurtosis, all the variables examined in the study recorded kurtosis which surpassed the threshold of 3, implying that the return series exhibit flatter tails compared to normally distributed series.

Table 1

Sample statistics during COVID

	Wheat	Cocoa	Coffee	Corn	Cotton	Sugar	Soyabean	Geothermal	WIND	Solar	Stellar	Nano	Iota	XRP	Cardona
Mean	0.000171	0.0001	0.0004	0.0004	0.000201	0.000765	0.00047	0.000268	0.000117	0.001037	0.000872	0.000204	0.000236	0.001037	0.00293
Median	−0.00112	0.0004	−0.00035	0.000537	0.000724	0	0.001105	0.00156	−0.00037	0.0009	0.002208	7.86 × 10−5	0.003239	0.001196	0.00186
Max	0.082832	0.0525	0.095552	0.069095	0.057979	0.058874	0.06382	0.14409	0.09154	0.120513	0.553585	0.639542	0.331964	0.622692	0.3175
Min	−0.10016	−0.050	−0.09026	−0.07038	−0.05798	−0.05356	−0.06975	−0.13391	−0.11828	−0.19333	−0.44031	−0.63019	−0.57146	−0.54101	−0.5372
Std. Dev.	0.021204	0.0155	0.022492	0.016212	0.019202	0.016356	0.013625	0.024348	0.021257	0.028572	0.066629	0.085738	0.070586	0.072412	0.06894
Skewness	0.164879	−0.077	0.238543	−0.19788	−0.15608	0.069953	−0.4186	0.073187	−0.04494	−0.57061	0.619638	1.003944	−1.07421	0.331211	−0.2599
Kurtosis	4.839211	3.1234	4.069922	5.502682	3.529545	3.4029	6.040013	7.742997	5.823483	7.499439	15.25154	19.02639	13.54028	18.92258	9.6360
Jarque-Bera	122.2003	1.3697	48.03203	224.7016	13.22512	6.366559	347.9903	788.1106	279.3047	754.1562	5307.263	9130.689	4049.962	8888.863	1550.75
Prob	0*	0.5041	0*	0*	0.00134*	0.041449**	0*	0*	0*	0*	0*	0*	0*	0*	0*
Obs	840	840	840	840	840	840	840	840	840	840	840	840	840	840	840
ADF	−28.165*	−28.0*	−28.172*	−28.182*	−26.820*	−29.0656*	−27.3448*	−30.6804*	−27.305*	−18.997*	−29.668*	−30.6626*	−30.4716*	−29.750*	−31.388*

* denotes level of significance at 1%; ** denotes level of significance at 5%.

Table 2

Sample statistics post-COVID

	Wheat	Cocoa	Coffee	Corn	Cotton	Sugar	Soybean	Geothermal	Wind	Solar	Stellar	Nano	Iota	XRP	Cardona
Mean	−7.49 × 10−5	0.004415	0.00075	−0.00098	−0.0003	−0.00108	−0.00068	−0.00092	−0.00043	0.000898	0.000252	0.001582	0.000419	0.000289	0.00054
Median	−0.00108	0.004302	0.000268	−0.00172	0.0001	−0.00111	−0.00038	−0.00178	0.000575	0.000233	−0.00169	0.00224	−0.00035	0	−0.00081
Max	0.082517	0.126351	0.067167	0.061634	0.0418	0.054781	0.059429	0.07696	0.052426	0.056824	0.479979	0.313867	0.390275	0.548118	0.209627
Min	−0.06654	−0.21568	−0.06009	−0.06921	−0.042	−0.08177	−0.0374	−0.04642	−0.09972	−0.05048	−0.14033	−0.17051	−0.17991	−0.1507	−0.15316
Std. Dev.	0.021566	0.031233	0.020875	0.016337	0.0155	0.017861	0.012822	0.015913	0.016595	0.018202	0.046659	0.049611	0.054161	0.048438	0.042822
Skewness	0.389122	−1.79343	0.094361	0.140963	0.0351	−0.28397	0.523693	0.427339	−1.01068	0.089623	4.014645	1.219568	1.851345	5.214049	0.574199
Kurtosis	4.16652	16.31315	3.302719	5.522968	3.4704	4.073928	4.705233	5.054348	8.833593	3.120854	43.25806	11.36382	16.57541	61.92868	6.479293
Jarque-Bera	22.53202	2178.291	1.458129	73.84725	2.5929	16.9111	45.88875	56.72814	436.7536	0.535503	19309.36	869.7198	2268.771	41036.12	153.8201
Prob	0.00001*	0*	0.48236	0*	0.2734	0.000213*	0*	0*	0*	0.765098	0*	0*	0*	0*	0*
Obs	275	275	275	275	275	275	275	275	275	275	275	275	275	275	275
Adf	−8.4813*	−17.354*	−18.982*	−15.930*	−15.3*	−16.8148*	−15.776*	−16.3157*	−16.604*	−16.494*	−19.0482*	−16.0825*	−16.6153*	−19.2252*	−16.468*

*denotes level of significance at 1%.

Tables 1 and 2 further report the diagnostic tests of all variable series. The Jarque-Bera test is used to examine the normality assumption in the variable series. The null hypothesis of normality failed to get rejected for coffee, cotton, solar (post-COVID), and cocoa (during COVID) as indicated by their p-value. The remaining variables are nonnormally distributed. Finally, the augmented the Dickey Fuller test reveals that series are stationary at 1% level of significance in both the periods. The null hypothesis of the presence of the unit root in the series is rejected for all the variables.

The time-varying returns of the variables under consideration are illustrated in Figures 1 and 2 for both the periods. First, the presence of volatility clustering is visible among green cryptocurrency and stock and commodities, particularly, during the COVID period. This signifies a certain degree of predictability in the market, as opposed to the conventional random walk. On the contrary, post-COVID, return series are relatively less clustered and exhibit lower peaks. Second, sharp price movements are recorded for cryptocurrencies, which is not surprising since cryptocurrencies are relatively volatile assets.

Figure 1

Return series (during COVID).

Figure 2

Return series (post-COVID).

The pairwise correlation between the variables and their overall distribution in both sub-sample periods are shown in Figures 3 and 4. It is evident that variables under examination are not normally distributed. Higher correlation among the variables is evident during the COVID period. On comparing variables across the assets, it is observed that agricultural commodities have an exceptionally low correlation with green cryptocurrencies and sectoral renewable equity stocks, which reveals the existence of portfolio diversification benefits among the assets. In all, relatively higher correlation is found between green cryptocurrencies and renewable energy stocks, which is not astonishing as they are related assets. Further, the highest correlation coefficient is found between XRP and Stellar (0.62) during COVID and between XRP and Stellar (0.59) in post-COVID. The lowest correlation coefficient during COVID is found between coffee and Nano (0.00) and between coffee and Iota (−0.08) in post-COVID.

Figure 3

Correlation (during COVID).

Figure 4

Correlation (post-COVID).

3.2 Static Spillover Analysis

The mean-based spillovers are displayed for the agricultural markets (cotton, wheat, soybean, sugar, corn, coffee, and cocoa), Green cryptocurrency (XRP, Stellar, Iota, Cardona, Nano), and renewable sectoral equity (wind, geothermal, and solar) in Table 3 (during COVID) and Table 4 (post-COVID).

Table 3

Static spillover (during COVID)

	Cotton	Wheat	Soybean	Sugar	Corn	Coffee	Cocoa	Wind	Geothermal	Solar	XRP	Stellar	Iota	Cardona	Nano	From
Cotton	56.96	3.11	4.12	6.07	5.85	2.13	1.81	2.81	3.07	4.81	1.24	2.00	2.18	2.42	1.41	43.04
Wheat	2.49	54.55	11.98	4.67	16.92	1.76	0.99	0.66	1.12	1.01	0.50	0.88	0.79	0.93	0.74	45.45
Soybean	2.81	10.51	51.32	3.47	17.44	2.97	0.92	0.59	1.18	2.00	1.12	1.29	1.58	1.83	0.97	48.68
Sugar	5.93	5.20	4.59	59.53	6.16	2.41	2.25	1.71	1.57	1.64	1.57	1.94	1.89	2.26	1.37	40.47
Corn	4.69	14.57	17.29	4.70	46.11	2.83	0.93	1.50	1.37	2.15	0.50	0.95	0.61	0.68	1.12	53.89
Coffee	3.00	2.65	4.98	3.37	3.31	69.96	3.29	1.23	1.37	1.47	1.18	1.16	1.15	1.02	0.86	30.04
Cocoa	2.06	1.95	2.58	2.82	1.48	3.75	69.68	1.56	2.26	2.47	1.97	1.48	1.78	2.15	2.03	30.32
Wind	2.36	0.96	1.28	1.41	1.75	0.88	1.27	57.62	6.81	11.97	1.89	2.74	3.23	2.89	2.95	42.38
Geothermal	2.05	0.74	0.97	1.21	0.87	0.73	1.88	6.08	57.11	9.07	3.09	4.74	4.62	4.12	2.71	42.89
Solar	3.18	1.05	2.35	1.50	1.31	1.03	1.33	9.43	8.34	51.72	2.96	3.79	4.18	4.28	3.55	48.28
XRP	0.64	0.70	1.77	0.85	0.51	0.61	0.71	1.05	1.81	2.21	30.1	19.2	14.6	14.62	10.1	69.49
Stellar	0.89	0.65	1.05	0.84	0.54	0.47	0.50	1.45	2.48	2.34	17.5	27.6	15.3	17.25	10.9	72.37
Iota	0.96	0.68	1.47	0.98	0.77	0.61	0.73	1.57	2.39	2.63	13.7	15.9	28.8	17.01	11.6	71.12
Cardona	0.98	0.61	1.05	1.00	0.56	0.47	0.75	1.47	2.23	2.74	13.7	17.9	16.9	29.00	10.5	71.00
Nano	0.78	0.67	0.77	0.75	0.69	0.43	0.87	1.64	1.95	2.69	11.5	13.8	14.1	13.00	36.2	63.80
To	32.82	44.06	56.25	33.66	58.17	21.07	18.20	32.76	37.96	49.18	72.6	87.9	83	84.47	61	773.22
Inc. Own	89.78	98.62	107.57	93.18	104.2	91.03	87.88	90.38	95.38	100.9	103	115	111	113.47	97.2	TCI
NET	−10.22	−1.38	7.57	−6.82	4.28	−8.97	−12.1	−9.62	−4.93	0.90	3.14	15.55	11.9	13.47	−2.8	51.55

Table 4

Static spillover (post-COVID)

	Cotton	Wheat	Soybean	Sugar	Corn	Coffee	Cocoa	Wind	Geothermal	Solar	XRP	Stellar	Iota	Cardona	Nano	From
Cotton	66.24	1.50	2.04	5.31	1.61	2.88	4.00	2.18	1.60	2.15	1.46	1.70	2.33	2.36	2.64	33.76
Wheat	1.60	48.05	11.50	1.92	21.54	1.76	1.01	1.09	3.69	1.20	0.85	1.44	2.22	0.96	1.17	51.95
Soybean	0.59	10.00	49.56	2.62	17.90	2.28	1.01	0.50	3.22	3.41	1.30	2.57	2.46	1.48	1.10	50.44
Sugar	3.87	1.72	4.07	66.81	2.86	5.52	1.86	1.69	2.45	0.93	0.79	1.35	2.68	1.75	1.64	33.19
Corn	0.85	18.52	16.60	2.89	43.64	2.61	2.00	1.32	2.70	1.33	1.17	1.82	2.25	1.48	0.82	56.36
Coffee	1.27	2.03	1.67	5.25	2.60	66.89	3.06	1.51	3.94	1.53	0.81	1.22	4.23	1.81	2.18	33.11
Cocoa	1.95	1.58	1.06	1.84	2.84	2.88	71.88	1.30	1.46	3.11	2.36	1.73	2.39	2.68	0.94	28.12
Wind	1.90	1.99	3.24	1.13	1.21	4.28	0.94	63.88	6.34	7.77	0.83	1.55	2.35	0.96	1.63	36.12
Geothermal	1.11	1.51	2.94	1.96	1.53	3.43	1.43	5.71	61.62	9.96	0.71	1.47	2.38	1.87	2.36	38.38
Solar	1.92	0.95	4.16	1.00	1.58	1.83	2.44	8.34	9.88	58.83	1.14	1.58	2.43	2.78	1.12	41.17
XRP	0.59	0.46	0.66	0.99	0.43	0.72	1.24	0.82	1.32	0.90	36.41	25.99	7.88	16.35	5.22	63.59
Stellar	0.43	0.52	1.70	0.71	0.51	0.63	0.59	1.01	0.84	0.68	26.78	38.26	7.29	15.10	4.95	61.74
Iota	0.67	1.00	0.94	2.54	0.82	1.26	1.10	1.32	1.88	1.06	9.82	9.22	46.23	14.34	7.82	53.77
Cardona	1.17	0.63	0.80	1.76	1.01	1.17	1.29	0.93	1.77	1.49	16.40	15.10	11.38	34.81	10.28	65.19
Nano	1.73	0.70	1.34	2.94	0.83	2.24	1.54	1.52	1.51	1.47	7.18	6.85	8.17	13.42	48.56	51.44
To	19.64	43.11	52.72	32.86	57.26	33.49	23.52	29.25	42.60	36.99	71.61	73.58	60.45	77.36	43.88	698.32
Inc. Own	85.88	91.16	102.29	99.67	100.9	100.39	95.40	93.13	104.22	95.82	108.02	111.84	106.68	112.17	92.44	TCI
NET	−14.12	−8.84	2.29	−0.33	0.90	0.39	−4.60	−6.87	4.22	−4.18	8.02	11.84	6.68	12.17	−07.5	46.55

The estimates show substantial connectedness in all the periods. More precisely, the value of TCI is 51.55% during the COVID period and 46.55% in the post-COVID period. The spillovers are highest during the period of economic turmoil which aligns with the findings of Umar et al. (2021) and Yousaf and Ali (2020). Further, the diagonal numbers depict the return connectedness within each market, whereas off-diagonal numbers represent the direction of return spillovers among the assets.

First, the static connectedness during the COVID period is discussed (Table 3). The “FROM” column shows the spillovers from the system to each market. The results revealed that highest return spillovers are received by green cryptocurrencies from the network during this sub-period. This finding aligns with the conclusion of the study by Umar et al. (2023), which revealed that cryptocurrency receives sizeable high contribution in the times of economic turbulence. On the other hand, lowest return spillover from the network is dominated by the commodity market particularly coffee (30.04%) and cocoa (30.32%). Among the sub-sectoral clean energy markets, wind (42.38%) is least connected with the system during COVID. In agricultural markets, wheat and corn are experiencing the least spillover from the cryptocurrency market, while cotton and sugar are experiencing the most spillover. As far as the spillover effect from renewable energy stock is concerned, wheat is receiving lowest spillover effects, whereas cotton is receiving highest spillover effects from renewable energy. Moreover, we found that the spillover effect is stronger from the cryptocurrency market to the commodity market than in the reverse market, which suggests that investors should allocate their financial resources more on cryptocurrency. Similarly, renewable energy stocks are transmitting a slightly higher spillover effect than they are receiving from the commodity market, aligning with the findings of the study by Reboredo et al. (2021). This implies that investors should quickly rebalance and hedge their position when renewable energy stocks exhibit a declining trend. Further, connectedness from each market to the system is exhibited by “TO” bottom third row. From the findings, green cryptocurrencies are seen to be the highest transmitters of return to the system during this sub-period. On the contrary, the agricultural market transmits lowest return spillovers followed by wind. Specifically, in the agriculture market, cocoa (18.20%) and corn (21.07%) emerged as the least return transmitter to the system. Finally, the bottom row of Table 3 depicts the contribution of each asset as a net transmitter/receiver of spillovers. The results disclosed that all cryptocurrency (except for Nano) dominated their position as major transmitters of spillovers, whereas agricultural markets (except for soybean and corn) are major net recipients of spillovers.

Finally, as far as the connectedness measures in the post-COVID period are concerned (Table 4), the results are somewhat similar to the previous findings. In the estimate values of the FROM measures, again green cryptocurrencies are receiving the highest return effects from the system, although the magnitude is slightly less than during the COVID period. Further, Cardona (77.36%), Stellar (73.58%), and XRP (71.61%) also exhibit the highest spillovers to the network, while the markets with the lowest spillovers towards the system are cotton (19.64%), cocoa (23.52%), and wind (29.25%). In this sub-period, sugar and coffee emerged as the least receivers of spillover effects from cryptocurrency, while coffee and cocoa emerged as the highest receiver of spillover. Like the COVID period, the spillover effect is stronger from the cryptocurrency market and renewable energy stock to the commodity market than in the reverse direction. Finally, with regard to net connectedness values, the findings seemed to be similar to the COVID period. Likewise, Cardona, Stellar, and Iota are showing positive values (net transmitter), whereas cotton and wheat are depicting highest negative values (net receivers) in agricultural markets and wind and solar in the sub-sectoral energy market.

Further, Figures 5 and 6 depict a network diagram of connectedness to examine the pair-wise connectedness among green cryptocurrency, agricultural market, and renewable energy stock market. Within the network graph, one can determine the centrality of a particular variable in the system by analysing the number of arrows originating from that variable and vice versa. The yellow nodes depict the recipient variable, whereas blue nodes represent the transmitter variable demonstrating spillover dynamics among the markets. During the COVID period, Cardona and Stellar are the main primary transmitters to all other markets and cocoa and wind are the main recipients from all other markets. However, post-COVID, connectedness between pairs seems to be less pronounced. The graph exhibits corn and Cardona as the key transmitters and Solar and Nano as the major recipients of spillovers. Cotton and Cocoa as the least recipients of spillovers could be used to hedge against the downside spillover risk (Billah et al., 2024, Bouri et al., 2021). Both cotton and cocoa have specialized end-use markets unlike wheat, corn, and sugar, which influence multiple industries. This distinction may explain their low integration with the other markets. The findings are in line with the previous evidence found in Tables 3 and 4.

Figure 5

Network diagram of net pairwise spillovers (during COVID).

Figure 6

Network diagram of net pairwise spillovers (post-COVID).

3.3 Dynamic Analysis

Figure 7 presents time-varying spillovers during and post-COVID period. As expected, the total connectedness varies over time. Specifically, the total spillover index shows a peak in the initial quarters of 2020 which coincides with the sudden outbreak of COVID (Ali et al., 2023). The peaked connectedness could be attributed to the COVID-19 pandemic which had affected business operations and capital flows across the global. As a result, new markets emerged, and market participants are likely to adapt these structural changes as proposed by the heterogenous market hypothesis (Agyei & Bossman, 2023). However, spillover index diminishes gradually afterwards till the mid of 2023. There is a slight increase in the spillover value in 2023 followed by the phase of dramatic fall in the return spillover in the year 2024. The total connectedness varies with values ranging between 45 and 90% signifying the necessity of dynamic spillovers. This time-varying connectedness findings align with the study by Antonakakis et al. (2020), showing strikingly high interdependence among the markets in the period of economic disruption. Further, the results demonstrated that portfolio diversification opportunities among the select market can be explored in the period of economic stability when markets appeared to be less connected with each other.

Figure 7

Total return spillover.

Next, Figures 8 and 9 reveal the time-varying net spillover during and post-COVID period, respectively. The rolling net return spillovers of assets illustrates that net connectedness index changes over time, while its position shifts from transmitter to recipient and vice-versa over the period. Above zero (below zero) value of the connectedness index indicates the sender (receiver) position of the assest in net terms. In Figure 8, three green cryptocurrency remains major transmitter over the sample period. Iota, Cardona, and Stellar exhibit a significant role of transmitter over the sub-period except in the initial phase of COVID-19 pandemic. XRP and Nano exhibit alternate patterns with frequent switching taking place over the period. Following the onset of COVID, geothermal and solar exhibit positive value indicating the characteristics of net transmitter of spillover. This finding differs from those of Alrweili and Ben-Salha (2024), which reported the contrasting results. Subsequently, geothermal reversed its position from net transmitter to receiver afterwards. Interestingly, wind has been predominantly the major recipient of spillovers throughout the sample period. This result aligns with the findings of Dogan et al. (2022), Yousfi and Bouzgarrou (2024), and Zhang et al. (2023). The diverse behaviour of the sectoral equity clearly shows that the impact of the pandemic has varied significantly across the sectors and therefore underlining the significance of analysing them as unique assets. Among agricultural commodities, cotton, cocoa, and coffee have shown consistently the net recipient profile over the entire period except at the beginning of the pandemic. However, soybean and corn exhibit an alternate pattern with net transmitter profile being shown over the period. It is interesting to note that soybean and corn are the primary resources for the biodiesel and biofuel which are the most suitable substitute of the crude oil. During the COVID-19 period, crude oil experienced a substantial decline in the prices that may have contributed lower demand for soybean and corn, which eventually leads to increased spillover among agricultural commodities. These results complement the findings of Dahl et al. (2020) and Pal and Mitra (2017). Further, wheat has shown the status of net transmitter as well net recipient underscoring the dynamic role of commodity in the portfolio.

Figure 8

Time-varying net connectedness (during COVID).

Figure 9

Time-varying net connectedness (post-COVID).

Figure 9 shows net dynamic total connectedness of cryptocurrency, sectorol equity, and agricultural commodity in the post-COVID period. It is clearly evident from the visualizations of net connectedness graphs that spillover effects have drastically reduced compared to the COVID period. Among green cryptocurrency, Iota, Cardona, Stellar, and XRP have positioned themselves as net transmitter during Q3 of the year 2023. The intense spillover from the cryptocurrency during this period coincided with the legislation introduced by both European and US governments aimed at regulating the crypto industry, which might have boosted the total connectedness (Kellerman & Seddon, 2024). Further, solar and geothermal markets are predominantly net receiver and net transmitter over the entire period, respectively, underscoring the heterogeneity in the behaviour of the sectoral renewable energy market. Among the agricultural markets, cotton and wheat displayed the role of net recipient during the post-pandemic subperiod. The results align with the conclusion of the studies by Balcilar and Bekun (2020) and Tiwari et al. (2022) who documented that spillover shocks from these commodities are absorbed and not transmitted to the other assets. The remaining commodities, namely, coffee, cocoa, soybean, and sugar, exhibit the intervals of net transmission of spillovers at some point and receivers of spillovers at some stretches of time. The results reveal that the status of net recipient or transmitter varies over time and inclusion of cryptocurrency, agricultural commodity, and renewable energy stock could act as hedging assets or safe-haven assets in the investment portfolio. Therefore, a discussion of the implications for portfolio management may be necessary here.

4 Portfolio Implications

This section focuses on calculating minimum risk portfolio weights, hedge ratios, and hedge effectiveness in static setting, generating significant implications for portfolios consisting of agricultural commodity, renewable equity, and green cryptocurrency. Our hypothesis postulate that portfolio investors should consider including green assets in their portfolios to obtain diversification benefits (Akhtaruzzaman et al., 2023, Lalwani, 2024, Naqvi et al., 2022). The optimal portfolio weights and hedge ratios provide an idea on how hedges are constructed to improve the risk management (Chemkha et al., 2021).

Table 5 present optimal weights, ratios, and effectiveness for two periods: during COVID and post-COVID. The optimal weight is 0.5570 for the cotton/wind pair, implying that, for a $1 portfolio consisting of cotton and wind stock, investors should invest 55.70 cent in cotton and 54.7 cent in wind energy stock during COVID. The highest optimal weights are observed for soybean/Nano (98.54), cocoa/XRP (98.38), and cocoa/Nano (98.38) during the COVID period. On the other hand, cotton/Nano (96.46) and soybean/Stellar (96.29) have the first and second highest weights, respectively, in the post-COVID period. Further, all agricultural commodity exhibits greater weights in the pandemic period than that of the post-pandemic period. The expansion of weights of agricultural commodities during disease period underscore the benefit of diversified portfolio consisting of agriculture and green assets. The lowest optimal weights is seen for the coffee/wind (47.39) (during COVID) and cocoa/wind (21.97) (post-COVID) proposing that investors should allocate their 46.39 cents and 78.03 cents in the wind stock, respectively. Notably, wind emerges as the green token with the highest weights implying that investors should incorporate this asset in their portfolio. Conversely, Nano displays the lowest weights among all the agricultural green assets pairs, indicating that investors should avoid inclusion of such assets in their portfolio. Overall, the optimal weights for all pairs remains positive (or less than 1) across both the periods, indicating that portfolio managers should include renewable energy stock and green cryptocurrency in the portfolio of agricultural commodity to achieve effective diversification.

In addition, hedge ratios are calculated to provide further implication for portfolio management decisions. During COVID period, the largest hedge ratio of 0.1343 is found for the cotton/solar, showing that investor should take a short position of 13.43 cent in solar stock to hedge a $1 worth long investment in cotton stock. The hedge ratio is very low and ranges between 0.0002 and 0.1343, showing the lower cost of hedging the risk of commodity through green assets during the pandemic. Similarly, the highest ratio is observed for the cotton/solar in the post-COVID period where $1 worth long investment in cotton stock can be hedged with 16.87 cents short position in the solar stock. The hedge ratios range from −0.1106 to 0.1687 in this sub-period. The pairs show positive hedge ratios during the COVID period, but few pairs exhibit negative (below zero) hedge ratios over the post-COVID window. This indicate reverse investments (long for short and vice versa) are required to hedge against the risk of each asset.

Finally, Table 5 presents hedge effectiveness for the pairs. The hedge effectiveness scores are highest for the pair of cotton/solar (3.49%) and lowest for the coffee/Nano (−0.0001%) pair in the COVID period. On the other hand, hedge effectiveness is highest for the cotton/solar (3.37%) pair and lowest for the cotton/geothermal (−0.12%) pair in the post-COVID period. The hedging effectiveness score is more than zero for (55/56) pairs in the COVID window and (43/56) pairs in the post-COVID period. The positive hedge effectiveness implies that investors and portfolio managers can attain maximum benefit of diversification by adding these green assets in their undiversified portfolio of agricultural commodity, particularly, during the COVID period.

5 Robustness Analysis

This section checks the robustness of our results by employing alternate variables in the system. This process is important as it confirms the effectiveness of our proposed approach in investigating the relationship between the variables considered in the study. First, we replaced three green cryptocurrencies such as Stellar, Iota, and Nano with other green cryptocurrencies such as EOS, Tezos, and Tron to check the validity of our findings. We re-estimated the TVP-VAR model, and the results are reported in Tables A1 and A2. Overall, green cryptocurrencies are the major receiver and transmitter of the return spillovers to the system during COVID, which is highly consistent with the previous results. In the post-COVID period, all green cryptocurrencies except Tron are receiving the highest return effects and sending highest spillovers to the system which again align with the initial findings (Tables 3 and 4). In the second alternative setting, we excluded three agricultural commodities (corn, coffee, and cocoa) to examine whether the previous results would vary (Tables A3 and A4). First, the results reported cryptocurrency market sending stronger spillover to commodity market than in the reverse direction. Second, wheat is receiving least spillover and cotton and sugar are receiving the most spillover from the cryptocurrency. Overall, the relationship between the variables does not vary much from the findings observed in Tables 3 and 4. Similar results in the alternative setting of the variables confirm that our results are robust.

6 Conclusions

The extant literature has not established the linkage between newly emerged green cryptocurrency, sectoral renewable energy stocks, and agricultural commodities. In this article, we aim to explore the spillover of returns between four major green cryptocurrencies (Stellar, Nano, Cardona, and IOTA), three sub-sectoral renewable energy stocks (NASDAQ Solar Index, NASDAQ geothermal index, and NASDAQ wind index), and seven agricultural commodities (wheat, cocoa, coffee, corn, cotton, sugar, and soybean) in static and dynamic settings employing a TVP-VAR methodology. We examined this connectedness across two distinct sub-samples: during COVID-19 and post-COVID-19 time. The network analysis depicts spillover received or sent by each of the 14 assets during the sample period. In addition, we presented a comparative analysis of the diversification and hedging benefits of a portfolio composed of eco-friendly assets and agricultural commodities during and after the COVID period offering novel empirical evidence for investors and portfolio managers.

First, we noticed that spillovers are higher during period of economic turmoil, i.e. COVID period, underscoring the close monitoring of investment portfolios during such periods (Rizvi et al., 2020). The findings documented that environment friendly cryptocurrencies are the major shock transmitters and recipients in all asset systems. Similar results hold in the post-COVID period also. Cardona and Stellar particularly exhibit highest spillovers to the network. On the contrary, agricultural commodities reveal the lowest spillover indices with other markets, thus implying that on a system-wide basis, agricultural markets are decoupled from rest of the markets (Naeem et al., 2021b). In the renewable energy stock, wind stock has the least connectedness with other markets. The network graphs confirm that post-COVID connectedness between pairs seems to be less pronounced.

Second, dynamic spillover varies over time, exhibiting a peak in the initial quarters of 2020, which coincides with the sudden outbreak of COVID (Ali et al., 2023). The results imply that portfolio diversification opportunities among the select market can be explored in the period of economic stability when markets appeared to be less connected with each other.

Third, the dynamic NET spillover indices reveal that cotton, cocoa, and coffee are consistently net receiver over the entire period except at the beginning of the pandemic. On the contrary, Cardona and Stelllar exhibit the transmitter profile over the sub-period except in the initial phase of COVID-19 pandemic. Further, renewable energy stocks exhibit diverse positions implying that the impact of the pandemic has varied significantly across the sectors and therefore underlining the significance of analysing them as separate assets. Finally, in the post-COVID period, it is illustrated that the status of net recipient or transmitter of asset varies over time and inclusion of cryptocurrency, agricultural commodity, and renewable energy stock could act as hedging assets or safe-haven assets in the investment portfolio.

Finally, as far as, portfolio implications are concerned, the optimal weights, hedge ratios, and hedge effectiveness depict comparable values for during COVID and post-COVID periods. Notably, all agricultural commodities exhibit greater weights in the pandemic period than that in the post-pandemic period. The expansion of weights of agricultural commodities during the disease period underscores the benefit of diversified portfolio consisting of agriculture and green assets. In the post-pandemic period, increasing the allocation of green assets in the portfolio could enhance diversification benefits. In addition, hedge ratios are very low indicating the lower cost of hedging the risk of commodity through green assets during and post-pandemic. Finally, higher pairs having positive hedge effectiveness scores in the COVID window imply that investors and portfolio managers can attain the maximum benefit of diversification by adding those green assets in their undiversified portfolio of agricultural commodity, particularly, during the COVID period.

The issue of the climate change has posed threats to all nations irrespective of their geographic location, which necessitates the introduction of green finance instruments as corrective measures. Consequently, it is crucial for investors and portfolio managers to analyse the risks and opportunities associated with the green assets. Therefore, the findings of this article have significant implications for investors, portfolio managers, and policymakers. The study provides useful information regarding asset allocation, hedging, diversification, and portfolio management during pandemic and non-pandemic periods. By using this information, investors can make more informed decision while making investment in eco-friendly assets and possibly minimizing their exposure to non-renewable energy investments. For instance, we found that green assets proved to be a good hedge against the risk of commodity. The hedge is more effective particularly during the COVID period. Moreover, renewable energy stocks such as solar and wind offer better hedging compared to other green assets. As mentioned earlier, investors can have a diversified portfolio that comprises green stock and commodities, and it may be beneficial to periodically revise the asset allocations. In terms of policymakers, the commercialization of assets such as agricultural, forestry products, and industrial metal will facilitate the development of green assets, as these assets may provide diversification benefits against the investment risk of eco-friendly assets. In addition, private participation in green financing can be encouraged through government programme such as green credit guarantee schemes (Yoshino et al., 2021), which can further contribute to the development of these markets. Also, the existence of efficient legal framework for green cryptocurrencies is a key factor in strengthening the green cryptocurrency market (Tu et al., 2020). An efficient market will enable greater participation from investors for the investment purpose. Hence, policymakers can play a pivotal role in adoption of environmental friendly assets which could help in addressing the environmental responsibility of the financial industry and reduce their carbon footprint.