3.1. Data and sources

This research is aimed at exploring the dynamic asymmetric correlation between major thematic and major low carbon or carbon efficient indices since these indices could play key roles in technology transfer and digitalization globally. We use the daily closing prices for the eight thematic MSCI ACWI IMI indices: ATIII, CSI, DEI, FII, INI, NGIII, RBI and SCI. As measures of global carbon efficiency and environmental performance, we consider four low carbon or carbon efficient indices, i.e., the MSCI World Low Carbon Leaders Index (WLCLI), the MSCI World Low Carbon Target Index (WLCTI), the S&P 500 Carbon Efficient Index (S&P500CEI) and the S&P Global LargeMidCap Carbon Efficient Index (S&PGLMCEI), as well as two other environmentally/socially responsible indices, the MSCI ACWI Sustainable Impact Index (SII) and the World EGS Leader Index (WEGSLI). The sample covers the period from 10 January 2019 to 10 January 2023, and the data were sourced from the official websites of S&P Global https://www.spglobal.com/spdji/en/ and MSCI https://www.msci.com/our-solutions/indexes.

The key motivation for considering the current data is to highlight the possible dynamic asymmetric features when comparing tranquil and turbulent periods, which could provide a better understanding of the changes that occurred during the COVID-19 crisis. The daily data for thematic indices were available starting in 2019, which also restricts the coverage of the overall dataset. Based on the different daily prices, the daily returns were calculated as Rt = ln(pt)-ln(pt-1); i.e., they were calculated using the first log differences of the closing prices, and they represented a total of 1043 observations.

3.2. Preliminary analysis

Fig 1 presents the evolution of prices, showing a common pattern for all thematic and low carbon/energy efficient indices. The plot indicates that for all the indices, there is a notable decrease in prices, suggesting that the COVID-19 outbreak contributed to a decrease in prices during the last quarter of 2019. Similar behavior regarding the relative financial asset class has been reported in research covering the COVID-19 pandemic period [20]. The abrupt decline in prices was due to investment inflow, the loss of investor trust, and risk-averse behavior during the global health crisis (GHC). Following a subsequent abrupt decline, prices for all indices showed a rising trend in 2020. It is reported that enormous capital inflow injections into these classes fostered price and overall market capitalization; for example, FinTech investments increased from $87 billion in the first quarter of 2020 to $98 billion in the first quarter of 2021 [20]. Another explanation of the upward trend that followed 2020 and served as a turning point for all EGS investments in terms of social aspects suggests that the financial crisis triggered by COVID-19 led to a change in investor perception regarding social aspects [53]. Thus, the increase in investor demand, investment inflow, and investor perception explains these patterns. Later, prices came to follow a consistent descending trend, possibly due to slower global economic growth, lower inflation, and ongoing monetary tightening.

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Fig 1. Evolution of thematic and carbon efficiency indices.

https://doi.org/10.1371/journal.pone.0293929.g001

Fig 2 shows the evolution of daily return series for the indices under analysis, revealing an abrupt change that occurred at the beginning of the GHC. Additionally, compared to the tranquil phase, the fat tails and volatility clustering are larger in the turmoil phase, which implies that market volatility and daily price return dynamics were notably different before and after the GHC. The time-varying price returns displayed in Fig 2 could also indicate the existence of volatility clustering and fat tails, which could suggest some possible nonlinear process.

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Fig 2. Daily differenced returns.

https://doi.org/10.1371/journal.pone.0293929.g002

Table 1 reports the descriptive statistics for the daily returns, and Table 1 presents similar statistics for the price series. In general, the mean returns were positive for all indices. Among thematic (carbon efficient) returns, FII (WLCTI) demonstrated the highest average returns, while the lowest average returns were those of NGIII (S&P500CEI). Thematic returns were more volatile in low carbon indices, with INI (WEGSLI) showing the highest (lowest) standard deviation of 0.01758 (0.00968). Regarding skewness and kurtosis values, all of the return series present leptokurtic levels and are skewed left (i.e., the left tail was longer). The Jarque-Bera test confirms that these returns violate the properties of normal distribution, and finally, the augmented Dickey–Fuller (ADF) shows that return series were stationary during the period under analysis.

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Table 1. Descriptive statistics.

https://doi.org/10.1371/journal.pone.0293929.t001

Fig 3 and Table 2 display the unconditional correlation matrix for the daily return series for thematic and carbon efficient or low carbon indices. Those unconditional correlations were positive and weak except for the correlations with the S&P 500 CEI, which is generally weakly negative across the majority of price returns. Considering the unconditional correlations in the carbon efficient and low carbon indices, the coefficients ranged from 0.1599 for the WLCTI-SCI pair to -0.0165 for the S&P 500 CEI-SCI pair. The correlation among returns in the thematic indices was highly positive, with the same pattern occurred among low carbon or carbon efficient indices. Weak and negative unconditional correlations support the idea of possible diversification benefits, and further investigation is needed to explore the hedging benefits among thematic and low carbon investments.

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Fig 3. Unconditional correlation matrix.

https://doi.org/10.1371/journal.pone.0293929.g003

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Table 2. ADCC-GJR-GARCH estimates.

https://doi.org/10.1371/journal.pone.0293929.t002

4.1. ADCC-GJR-GARCH model

Previous multivariate GARCH models have enormous limitations and make many assumptions. For instance, the constant conditional correlation (CCC) GARCH model contains an assumption that the correlation will remain constant over time, which is an unrealistic assumption in the case of financial markets. Precedingly, Engle’s [2002] DCC-GARCH model considered conditional correlation as time-variant and introduced a more realistic econometric model. In previous studies, models of a similar nature as the multivariate GARCH model were introduced, such as the GO-GARC and EGARCH. Notably, these multivariate GARCH models could capture constant or dynamic correlations. However, the asymmetric impact of information or volatility clustering is ignored in these models.

As earlier indicated, we consider asymmetric dynamic conditional correlation through the Glosten-Jagannathan-Runkle–generalized autoregressive conditional heteroscedasticity (ADCC-GJR-GARCH) model of Cappiello, Engle [54] and Glosten, Jagannathan [55] to examine the possible hedging role of carbon-efficient assets across thematic indices. The ADCC-GARCH model of Cappiello, Engle [54] builds upon the Engle [56] standard dynamic conditional correlation (DCC-GARCH) model. We used the ADCC-GJR-GARCH model in this study due to its greater relevance and empirical significance. The choice of the ADCC-GJR-GARCH model provides greater relevance to the objectives of our study, as this study aims to explore hedging and safe-haven opportunities by estimating asymmetric dynamic correlations between thematic and carbon efficient indices. In terms of empirical significance, it is understood that bad news or negative shocks predict volatility with greater accuracy in financial markets than positive shocks or good news. In financial time series data, estimating the correlation of an asymmetric nature requires the application of the ADCC-GJR-GARCH (1, 1) model, which can be used to capture volatility clustering or to differentiate the impact of positive and negative news that is overlooked in the simple GARCH (1, 1) model [57]. Thus, our study employed the ADCC-GJR-GARCH model to uncover asymmetric conditional correlations over time.

Univariate GARCH models are fitted to the asset returns in the initial stage. Estimating the asymmetric conditional correlation for both positive and negative standardized returns occur in the second stage. The ADCC-GJR-GARCH model is applied in this study, based on a vector of asset returns where r_t is distributed normally with a mean equal to zero, as follows: (1) (2) (3) (4) where the time-varying conditional correlation matrix is denoted by R_t.H_t is a representation of the conditional covariance matrix of the r_t,r_t = [r_1tr_2t]′ vector of returns, which is itself a 2x1 vector of returns and includes returns on any thematic index (r_1t) and the corresponding carbon efficient or low carbon index (r_2t). The conditional standard deviations from the univariate GARCH models are represented by the diagonal matrix D_t. A 2×1 i.i.d. vector of the standardized residuals is represented by z_t, with the conditional correlation matrix of the standardized residuals being indicated by Q_t. Finally, ε_t = [ε_1t,ε_2t]^′ is a 2×1 vector of conditional residuals on the dataset at time t-1.

The asymmetric univariate GJR-GARCH (1,1) model of Cappiello, Engle [54] was used to estimate the component of H_t in line with the work of Glosten, Jagannathan [55] as follows: (5) where the conditional variance of the return series is represented by h_i,t, and the asymmetric or GJR term is noted as d_i. Additionally, the persistence of the volatility process (GARCH) is assessed by β_i, the ARCH effect is denoted by α_i, and ω_i denotes a constant term. If ε_i,t-1 < 0, then the indicator function I(ε_i,t-1) = 1 and if these conditions are satisfied, it is equal to zero. If the assumption or condition of α_i + β_i + d_i < 1 and α_i > 0 are satisfied, then steadiness and positivity are both confirmed.

The standardized residuals z_t are used to calculate the conditional correlation parameters after estimation by the univariate GARCH models. Based on the ADCC-GARCH model, Q_s dynamics are described as follows: (6)

The unconditional correlation matrix of η_t is written as , while z_t is written as ]. When the parameter is true, the indicator function is given by . The function η_t = I(zt,<0) ∘ z_t assumes that if the coefficient is equal to zero, the argument is false and that, if it is one, the argument is true. The parameter matrices are represented by θ₁,θ₂ and φ, while “∘” denotes the Hadamard product. If φ = 0, the AGDCC-GARCH model is reduced to the conventional DCC-GARCH model without an unequal influence on the conditional correlation.

The time-varying correlation matrix for the ADCC-GJR-GARCH model is shown as follows: (7) where the diagonal matrix is represented by , and has the square root of the ith diagonal of Q_t in the ith diagonal position.

4.2. Wavelet coherence approach

Empirical analysis was also conducted in this study using bivariate wavelet coherence analysis. Wavelet coherence is among the most widely recognized techniques for measuring the co-movements among financial and economic time series. In contrast to standard time series modeling, the underlying approach enables the estimation of the co-movements between any two time series across both time and frequency realms [58].

Following the wavelet coherency method of Torrence and Compo [59], the cross wavelet transform between two time series, x(t) and y(t), is defined as follows: (8) where W_x (a,b) and W_y (a,b) are the cross wavelet transforms of x(t) and y(t), respectively, and ’a’ and ’b’ are the scale and position index, respectively. Furthermore, * denotes a complex conjugate. The cross-wavelet transform can capture the local covariance between two time series, x(t) and y(t), at each scale.

After Torrence and Compo [59], we followed Goodell and Goutte [58] to define the wavelet coherence between any two time series as (9)

The squared wavelet coherence between x(t) and y(t) identifies notable co-movement through cross-wavelet power series at each scale, where R²(a,b) describes the localized correlation in a time-frequency domain in squared form, and its value falls between 0 and 1. Moreover, S denotes a smoothing operator for each scale 0 ≤ R² (u,s) ≤ 1. Since R²(a,b) is limited to only positive values, the wavelet coherence phase difference is introduced at this step of the methodology to reflect both positive and negative correlations. Thus, the wavelet coherence phase difference can be defined as: (10) where lm denotes the imaginary smoothed part, and Re represents the real part of the smoothed cross-wavelet transform.

5.1. ADCC-GJR-GARCH estimates

The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) lag orders were used to select the best marginal model, i.e., those that maximize log-likelihood while minimizing AIC and BIC [57]. Table 2 reports the estimates for the ADCC-GJR-GARCH model. The parameters of the estimated model are statistically significant at the significance levels of 1% and 5%. The autoregression of the order-one coefficient is significant, except for ATIII and RBI, showing that the current return estimates are unaffected by the one-day price returns of ATIII and RBI. Considering the significance of the parameters for the majority of indices, this indicates that past price returns influence current returns, indicating possible market inefficiency. Moreover, there was evidence of statistically significant persistence in both short- and long-term volatility, as shown by coefficients α_i and β_i, respectively, suggesting that thematic and carbon efficient indices exhibit volatility clustering. Notably, long-term volatility persistence was greater than short-term volatility persistence, and the conditional volatility of indices tends to increase quickly because past conditional volatility has a greater impact than return innovations. These findings can give portfolio managers insights into the application of trading techniques based on long-run volatility persistence due to their potential explanatory power regarding present volatility.

Additionally, the parameter (d_i) indicates the asymmetric coefficient in the ADCC model, which is statistically significant for all returns series. The evidence for the significance of d_i demonstrates the influence of negative shocks (i.e., bad news) on conditional volatility dynamics. The leverage effect for all return series is positive, indicating that negative shocks tend to increase the conditional volatility to a greater degree than positive shocks of comparable magnitudes. The stability of our ADCC model was confirmed, as we noted that the total of the α_i (short-term), β_i (long-term) and d_i (asymmetric) volatility parameters was less than one (< 1). Notably, the impact of bad news (α_i + d_i) is greater in magnitude than that of good news (α_i). Hence, the positive leverage term parameters for the ADCC model are statistically significant and nonnegative, showing the appropriateness of using the ADCC-GJR-GARCH model. These results reveal that SCI (10.3975) has the highest estimated degree-of-freedom and CSI (9.8730) has the lowest degree-of-freedom (Df.). The degree of freedom or shape parameter of student-t distribution random errors is statistically significant and greater than two (> 2), confirming that the leptokurtic behavior of estimated residuals is captured by the degree of freedom (i.e., it is fat-tailed).

Regarding the asymmetric dynamic conditional correlation parameters, the estimates displayed in Table 2 show that the parameters of the ADCC model are statistically significant with positive signs across panels (Panel 1 to 8) and that the sum of ADCC parameters (α_i + β_i + d_i) is less than one (< 1). These findings indicate that the asymmetric dynamic conditional correlations between thematic and low carbon emissions were mean reverting. Moreover, the parameter (α_i) emphasizes the significance of shocks between the thematic and low carbon price returns, whereas β_i shows stronger persistence-of-volatility between markets, while the third parameter (d_i) indicates the asymmetric effect of price returns.

5.2. Asymmetric dynamic conditional correlations

The second stage of the ADCC-GJR-GARCH model is performed to obtain the average coefficients of asymmetric conditional correlation. Considering the panel-specific asymmetric conditional correlations, Table 3 demonstrates the asymmetric conditional correlation for each panel from Panel 1 to Panel 8.

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Table 3. Asymmetric dynamic conditional correlations.

https://doi.org/10.1371/journal.pone.0293929.t003

The outcome of Panel 1 illustrates the ADCCs of the Autonomous Technology & Industrial Innovation Index with major low carbon and sustainable indices (S&P and MSCI). The correlation coefficients among these pairs (ATIII-WEGSLI, ATIII-WLCTI, ATIII-WLCLI, ATIII-SII and ATIII-S&PGLMCEI) were negative and statistically nonsignificant. However, the ADCC coefficient sign was negative and statistically significant for the ATIII-S&P500CEI pair, suggesting an inverse relation between that pair. Similarly, the remaining panels (Panel 2 ∼ Panel 8) show asymmetric relationships among the returns of thematic and low carbon emission indices. These findings indicate that the returns of thematic or transformative indices (the Autonomous Technology & Industrial Innovation, Cybersecurity, Digital Economy, Fintech Innovation, Innovation, Next Generation internet Innovation, and Robotics and Smart Cities Indices) are uncorrelated with the carbon efficient indices (the MSCI World Low Carbon Leaders, MSCI World Low Carbon Target, S&P Global LargeMidCap Carbon Efficient, MSCI ACWI Sustainable Impact and World EGS Leader Indices. In contrast, the transformative indices reveal a negative asymmetric relationship with the S&P 500 Carbon Efficient Index across panels (Panel 2 ∼ Panel 8). In our case, the negative trajectory of ADCCs also validates the weak hedge (safe-haven) properties during both tranquil and tumultuous periods (represented by the global health crisis).

Overall, Table 3 illustrates the results of asymmetric nature conditional correlation for Panels 1∼8, which are time variant. Regarding the sign of the correlation coefficients, the average coefficients were predominantly negative across all panels (1∼8). Of equal importance, the correlation coefficients of thematic indices with returns of carbon efficient indices were statistically nonsignificant aside from the S&P 500 carbon efficient index (S&P500CEI), as shown in Panels 1∼8. Based on the strong (weak) hedge or safe-haven definitions of Baur and Lucey [60], Bouri, Jalkh [61], Bouri, Molnár [62], Gustafsson, Dutta [63], assets that are uncorrelated (negatively correlated) can on average serve as a weak (strong) hedge instrument. In our case, the nonsignificant correlation suggests that the majority of thematic indices are uncorrelated with carbon efficient indices, which validates the role of carbon efficient indices as weak hedges for thematic indices. Among all carbon efficient indices, the S&P 500 CEI shows negative significant correlation coefficients with the thematic indices across Panels 1∼8; hence, the S&P 500 carbon efficient index possesses rich properties of a strong hedge (safe-haven). These findings corroborate the results of Apostolou and Papaioannou [51], who emphasized that low carbon indices such as the S&P 500 CEI could present hedging or diversification opportunities for investors aiming to rebalance their portfolios away from brown assets due to the high risk associated with brown investments.

Similarly, employing a rolling window multiple correlation technique, Fareed, Abbas [29] reported a positive relationship between the S&P 500 carbon efficient index and the COVID-19 pandemic, suggesting safe-haven properties of S&PCEI during this period. Koçak, Bulut [34] also reported a positive impact of COVID-19 on the S&P 500 CEI during the global health crisis. The strong hedge or safe-haven can also be supported by the fact that the S&P 500 Carbon Efficient Index weights companies based on carbon intensity, while the Carbon Efficient Select Index weights companies based on their overall carbon footprint [13]. The S&P 500 carbon efficient index gains considerably in the recent turmoil period (global health crisis), as evidenced by earlier research [34] supporting the safe-haven role of S&PCEI. In general, financial investors trust low-carbon companies more than companies or financial assets in other sectors, resulting in investing in such company shares even during a health crisis. Our findings are consistent with earlier studies that reported the S&P 500 carbon efficient index as a hedging or safe-haven tool and investment opportunity for mitigating the economic fragility (global health crisis) and risks of thematic investments.

The asymmetric conditional correlation coefficients for thematic and carbon efficient indices using the GJR-GARCH model are depicted in Fig 4. Overall, as indicated in subfigures (a∼h), we see inconsistent negative and larger negligible positive correlation jumps among all thematic and carbon efficient indices. The heterogeneous negligible positive/negative trajectory of the correlation ranging from January 1^st 2019 to November 30^th 2019 refers to the pre-COVID or tranquil period, where low carbon indices show weak hedges or diversifier characteristics with thematic indices (see subfigures a∼h), aside from the S&P 500 carbon efficient index, which serves as a strong hedge against thematic indices. Notably, the asymmetric correlation graphs also exhibited time-variant and heterogeneous behavior during COVID-19. Negative shifts were not intensive and stable, referring to the global health crisis where nonsignificant negative correlations (uncorrelated) confirm the claim that carbon efficient indices acted as weak safe-havens during the turmoil period. However, the magnitude of the negative shocks, except for the S&P 500 carbon efficient index, was not intensive during the turmoil period of COVID-19 (see subfigures a∼h). All thematic indices revealed a negative significant asymmetric correlation with the S&P 500 carbon efficient index throughout the sample period, validating that the S&P 500 carbon efficient index acts as the most consistent strong hedge and safe-haven for thematic indices during both tranquil and tumultuous periods. When deciding on future portfolios, sustainable investors need to be more willing to invest in green enterprises when combined with long-term sustainable development goals, which would advance carbon efficiency and decarbonization [8,43,64]. These findings are a result of the quick rise in COVID-19 transmission and the widespread implementation of lockdown measures that occurred at the beginning of the pandemic. Later, lockdown resulted in the closure of almost every sector worldwide, including industrial and service sectors, which is the main reason for S&PCEI stock returns to have experienced a significant fluctuation and negative correlation during the global health crisis. Moreover, the increased use of digital and innovative technologies during lockdown fostered social, financial, and economic transformation. However, the majority of thematic indices failed to exert carbon efficiency, although these thematic indices are innovative, highly technology focused and reach every part of human lives. In summary, this implies that the S&PCEI and other low carbon indices are strong (weak) hedges or safe-havens for thematic investors in both tranquil and tumultuous periods (COVID-19 pandemic). Thematic investors should diversify their risk by building a portfolio and preferably investing in S&PCEI rather than in other carbon efficient indices due to their weak hedging or safe-haven power. These results are consistent with those of earlier research [9,27], which recommends pursuing socially responsible assets to earn social and financial rewards.

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Fig 4. Asymmetric DCCs among the thematic and carbon efficient indices.

https://doi.org/10.1371/journal.pone.0293929.g004

5.3. Wavelet coherence evidence

This section presents the results of wavelet coherence analysis between thematic and carbon efficiency indices. Fig 5 represents the co-movement across both time and frequency. In addition, it also reveals the lead-lag-centered phase difference. Each subfigure displayed in Fig 5 has five key outputs. First, the horizontal axes (vertical axes) represent the time (frequency) domain. The component of frequency is decomposed into seven scales, where the shortest scale (2–4 days) represents the highest frequency band, and the longest level (128–256 days) denotes the lowest frequency band. Furthermore, we classified these frequency scales into three timeframes relative to investment horizons, i.e., short-term horizon (2–4, 4–8, 8–16, 16–32 days), medium-term horizon (32–64 and 64–128 days) and long-term horizon (128–256 days). Second, the magnitude of the co-movement is indicated by a color band where warmer colors (red and yellow) indicate higher co-movement or interlinkages, whereas colder colors (blue and green) highlight lower co-movement or coherence. Third, the black contour represents significance at the 0.05 or 5% level as calculated with the Monte Carlo simulation technique. Fourth, the curved dense line indicates the cone of influence, which shows the area impacted by edge effects. Additionally, the area beyond the cone of influence represents nonsignificant interlinkages. Finally, the directed arrows toward eight different directions signify the lead-lag-based phase difference and co-movement directions (positive or negative where zero phase difference indicates a precisely aligned co-movement of series; arrows pointing to the right (left) side → (←) represents that time series are in-phase (out-phase). The in-phase (out-phase) status depicted by the arrows denotes positive (negative) co-movement between thematic and carbon efficient indices. Arrows directing to the right-up or left-down (↗ and ↙) denote that innovation-themed indices lead the outcomes over carbon efficient indices. In contrast, right-down or left-up arrows (↘ and ↖) suggest that carbon-efficient indices lead the outcomes over innovation-themed indices. To conclude, straight up or straight down arrows (↑,↓) indicate that carbon efficient indices are leading or lagging, respectively.

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Fig 5. Wavelet coherence among thematic and carbon efficient indices.

https://doi.org/10.1371/journal.pone.0293929.g005

Following these key chunks of wavelet coherence graphs, we discuss the wavelet coherence analysis between thematic and carbon efficient indices across short-term, medium-term, and long-term investment horizons. In the case of Fig 5 (Panel 1 ∼ Panel 8), we observe low coherence dominating the entire sample period, as Fig 5 (Panel 1 ∼ Panel 8) appears to be mostly blue across the 2-4- and 4-8-day scales. However, it can be noted that the power spectrum shows high coherence (in red) at the 8-16- and 16-32-day scales with left-directed arrows (←). These results suggest that the underlying markets are out-phase in the short term, which indicates weak and negative co-movement in the short-term horizon. The out-phase or negative co-movements suggest short-lived weak (2–4, 4–8 days) and strong (8–16 and 16–32 days) hedging or safe-haven opportunities. In addition, right-down or left-up arrows (↘ and ↖) in the short run suggest that carbon efficient indices are leading the thematic indices in the short-term investment horizon.

In contrast, we noted high coherence power in red across the 32-64- and 64-128-day scales (Panel 1 Panel 8), and the majority of the arrows are right-directed (→). The black line contours are more noticeable on 32-64- and 64-128-day scales, and they are significant at the 5% level. These results also specify that underlying indices are in-phase in the medium-term investment horizon, which indicates strong positive co-movement across the subsequent investment horizon. In addition, the in-phase or strong positive co-movement implies minimal or no diversification opportunities in underlying asset classes in medium-term and long-term investment horizons during this period. Moreover, right-up or left-down (↗ and ↙) arrows in the underlying frequency scale suggest that thematic indices are leading the outcomes over carbon efficient indices in the medium-term investment horizon.

Similar to the medium-term investment horizon, high coherence can be noted beginning in 2019 to 2020 on a 128–256-day scale as noted in red (Panel 1 ∼ Panel 8). Thick black line contours in red areas during the respective period imply high co-movement significance at the 5% level. From 2019 to the end of 2020, the right directions arrows (→) denote in-phase and positive co-movement of the thematic and carbon efficient indices in the long-term investment horizon (Panel 1 ∼ Panel 8). Moreover, right-up or left-down arrows (↗ and ↙) on the 128–256-day scale suggest that thematic indices lead the outcomes in carbon efficient indices in the long-term investment horizon during the early sample period. Noticeably, a persistent yellow spot can be observed from 2021 to the end of the sample in the long-term horizon for each pair of thematic carbon-efficient indices, which indicates weak coherence during the COVID-19 pandemic. These findings imply minimal diversification properties in 2019 and 2020; however, carbon-efficient investments hold weak safe-haven properties.

Overall, it is determined in this discussion that the co-movements between underlying asset classes are out-phase (in phase) in the short term (medium term and long term), which indicates negative co-movement in the short term and positive co-movement in medium-term and long-term investment horizons. In addition, thematic investments lead (lag) the outcomes in carbon efficient assets in the medium run and long run (short run). Considering the hedging perspective, carbon-efficient investments are hedges or safe-havens for thematic investments in the short run, but they are limited to weak hedges or safe-havens in the long run. These results also corroborate our ADCC-GJR-GARCH findings, as the DCC-GJR-GARCH results show that the asymmetric correlation between thematic and carbon efficient indices is weak or uncorrelated (negative but nonsignificant estimates) and negative (in the case of the S&P 500 Carbon Efficient Index). However, in the case of the wavelet coherence approach, the findings reveal notable positive co-movement between thematic and carbon efficient indices in medium-term and long-term investment horizons. These findings also support the idea of considering innovative technologies [11,18,65] to mitigate CO₂ and stimulate carbon efficiency. As a notion that CO₂ and carbon efficiency are inversely correlated across multiple horizons was developed in earlier research [66], the role of thematic investments following the use of digitalization, urbanization, and innovative technology can support the fight against rising carbon emissions to ensure carbon efficiency. In addition, stringent environmental policies and green technological development [67] can be leveraged to pave the way for environmental quality and climate challenges.