1. Introduction
Sustainability has established itself as a crucial factor in advanced societies, influencing the course towards a more balanced social, environmental and economic future. Global initiatives such as Directive (EU) 2022/2464 reflect the commitment to redirect capital towards sustainable investments and manage financial risks associated with climate change, promoting transparency in long-term economic activities.
The concept of sustainable development was introduced in 1987 by the Brundtland Report, which stressed the need to integrate environmental and development concerns to meet present needs without compromising future generations (Report of the World Commission on Environment and Development). This approach was consolidated with the Millennium Development Goals in 2001, which mobilized global efforts to address critical social priorities such as poverty, gender inequality, and environmental degradation (Fehling et al., Reference Fehling, Nelson and Venkatapuram2013; Sachs, Reference Sachs2012). In 2015, the Sustainable Development Goals (SDGs) expanded this framework, with 17 goals addressing complex global challenges, most notably SDG 8 on decent work and economic growth, which directly links corporate sustainability to financial performance.
The COVID-19 pandemic, which emerged in late 2019 and was declared a global pandemic in January 2020, has been one of the most significant crises of the century. Measures imposed to contain the virus, such as travel restrictions and quarantines, profoundly impacted economic stability and global health, reducing economic activities, affecting stock prices, and increasing inflation, unemployment, and energy prices (Martin et al., Reference Martin, Sánchez and Wilkinson2022). This crisis has led to a decline in GDP per capita in more than 90% of countries, a phenomenon not seen since the Great Depression (Yeyati & Filippini, Reference Yeyati and Filippini2021).
In The Lancet, Horton (Reference Horton2020) described COVID-19 not only as a pandemic but also as a syndemic. This concept, proposed by Singer (Reference Singer2000), refers to the interaction and co-occurrence of multiple diseases within a population, where social, economic, and environmental factors exacerbate these diseases. The idea of a syndemic goes beyond the mere existence of simultaneous epidemics; it emphasizes how systemic issues such as inequality, poverty, and access to healthcare contribute to the clustering and magnification of these diseases (Mendenhall & Singer, Reference Mendenhall and Singer2020). Understanding COVID-19 as a syndemic, therefore, suggests that its effects are far-reaching, potentially enduring, and impacting various sectors, including financial markets.
The significance of viewing COVID-19 as a syndemic lies in recognizing that its impact is not just immediate and health-related but also deeply intertwined with broader socio-economic disruptions. This perspective is crucial for analysing the effects of the pandemic on financial markets, particularly in understanding volatility asymmetry. Volatility asymmetry, where adverse shocks result in greater future volatility than positive ones, becomes a key indicator in evaluating how the syndemic nature of COVID-19 has influenced stock market indices, including those that prioritize sustainability (Beckaert & Wu, Reference Beckaert and Wu2000).
By comparing market behaviours before and after the outbreak of COVID-19, particularly within the polycrisis framework, we can gain insights into how deeply embedded social and economic factors have interacted with the pandemic to influence market dynamics. This approach helps in understanding the fluctuations experienced during the crisis and offers valuable tools for predicting future financial crises and business cycles, as Schwert (Reference Schwert1989) highlights. Additionally, studies like those of Pindyck (Reference Pindyck1983) illustrate how interactions between risk, inflation, and financial markets can explain the decline in stock values during periods of uncertainty, further underscoring the relevance of studying volatility asymmetry within the context of a polycrisis.
In conclusion, framing COVID-19 as a syndemic is not just a semantic choice but a critical analytical lens that allows us to appreciate the complexity of the pandemic's impact. It emphasizes the need to consider the broader socio-economic context when analysing financial markets and provides a foundation for comparing the pre-and post-pandemic periods to understand the long-term implications for market stability and sustainability.
Therefore, this study seeks to understand how various shocks, such as those triggered by COVID-19, impact price volatility and business cycles due to unfavourable changes in macroeconomic factors. This allows us to establish a connection between asymmetric effects on volatility, real price fluctuations, and business cycles. This knowledge is crucial not only for the general functioning of financial markets, including money, capital, foreign exchange and other regulated markets but also for regulators and investors operating in these markets.
The main objective of this study is to analyse the differential impact of positive and negative shocks on sustainable and non-sustainable stock market indices during a syndemic such as COVID-19. This approach offers several significant contributions to the existing literature. First, it provides a deeper understanding of the resilience and stability of sustainable investments in times of crisis, which can influence investment decisions and risk management strategies. Second, it assesses the effectiveness of sustainability practices in mitigating the adverse effects of economic shocks. Third, it reveals how investor sentiment and market behaviour differ between sustainable and non-sustainable companies during a crisis, providing valuable information for policymakers and regulators. Finally, by understanding the asymmetric effects of shocks on volatility, this study provides tools to anticipate better and prepare for future crises, ensuring the long-term stability and sustainability of financial markets.
This paper addresses a significant gap in the existing literature, where research on volatility asymmetry in the context of sustainable investments during systemic crises is limited. While studies have been conducted on volatility asymmetry in general, few have explored how these dynamics manifest themselves specifically in sustainable versus non-sustainable indices in the context of a global polycrisis. This study seeks to fill that gap by providing detailed insights into how financial markets react differentially to shocks in a challenging economic environment.
The paper is structured as follows. In Section 2, we present the state of the art of the subject under study, then in Section 3, we present the data, the description, and the estimation techniques. In Section 4, we present the results of the time series analysis and the implied volatility study. Section 5 discuss our results and Section 6 shows our conclusions.
2. State of the Art
Research on volatility asymmetry in financial markets has been extensive. Volatility asymmetry, a phenomenon where financial markets exhibit greater sensitivity to adverse shocks than positive ones, has been widely studied in economic and financial literature. This concept, commonly known as the leverage effect, was first introduced by Black (Reference Black1976) and later expanded by Christie (Reference Christie1982) and French et al. (Reference French, Schwet and Stambaugh1987), who demonstrated that volatility in the U.S. stock market tends to increase more significantly following negative returns than after positive returns of the same magnitude. These findings highlight the critical importance of understanding how financial markets disproportionately react to bad news, a pattern consistently observed in both developed and emerging markets.
Beckaert and Wu (Reference Beckaert and Wu2000), extending this analysis to non-U.S. markets, found a significant inverse relationship between developed and emerging markets, indicating that shocks in one market can have opposite effects on other markets depending on their level of development. Similarly, Bates (Reference Bates2000) explored how international markets reflect this asymmetry, revealing that emerging markets are particularly vulnerable to adverse shocks, which amplify volatility more pronouncedly than in developed markets.
Interest in volatility asymmetry has grown markedly during global economic crises, such as the COVID-19 pandemic. Jebali et al. (Reference Jebali, Kouaissah and Arouri2022) analysed volatility behaviour during the pandemic. They concluded that stock markets experienced a significant increase in asymmetric volatility, exceeding the levels observed during the 2008 global financial crisis. This phenomenon highlights the need for more robust risk management strategies and a reassessment of how financial options are valued in times of crisis.
Nogueira and Madaleno (Reference Nogueira and Madaleno2022) delved into analysing volatility asymmetry in the context of sustainable indices, explicitly focusing on the EURO STOXX Sustainability Index, using MGARCH models. Their study, which spanned data from 2000 to 2022, revealed that the COVID-19 pandemic did not significantly alter the prior correlation patterns between sustainable and traditional indices. However, they emphasized the importance of policymakers and investors working together to promote greater independence of sustainable indices from macroeconomic disturbances.
The comparative analysis between traditional indices and those following environmental, social, and governance (ESG) criteria is essential for understanding volatility asymmetry in a broader context. Cunha et al. (Reference Cunha, de Oliveira and Orsato2020) investigated whether sustainable investments can outperform traditional benchmark indices regarding returns and stability. Their results indicated that, in some instances, ESG indices not only offer superior returns but also exhibit lower volatility asymmetry, making them particularly attractive during periods of crisis.
Additionally, Tiwari et al. (Reference Tiwari, Aikins Abakah, Gabauer and Dwumfour2022) analysed the volatility of sustainable stock indices and identified asymmetric behaviour in volatility, confirming that positive and negative shocks affect these indices differently. Their study also highlighted a significant impact of regime shifts on the volatility of sustainable indices, underscoring the importance of considering regime dynamics in the analysis of volatility asymmetry.
Zhang et al. (Reference Zhang, He and Hamori2022) employed a dynamic connectivity approach based on DCC-GARCH and a DCC-GARCH t-copula model to analyse the dynamic connectivity between sustainability-related financial indices and carbon futures. Their findings indicate that carbon futures act as transmitters of volatility. At the same time, green bonds serve as receivers, highlighting the complex relationships between different sustainable assets and their responses to shocks during times of crisis.
GARCH models are widely used in calculating stock market volatility because they can accurately model and predict the unique characteristics of financial data. This includes volatility clustering, where periods of high volatility tend to follow periods of high volatility, and asymmetry, where negative price changes tend to have a more significant impact on volatility than positive price changes of the same magnitude. GJR-GARCH and E-GARCH models are extensions of the basic GARCH model that specifically address asymmetry. GJR-GARCH does this by including a term that captures the asymmetric response of volatility to positive and negative shocks. At the same time, E-GARCH uses a logarithmic transformation to ensure that the conditional variance is positive and allows for asymmetric effects.
GJR-GARCH and E-GARCH models have proven to be essential tools for capturing volatility asymmetry in econometric modelling. The GJR-GARCH model, developed by Glosten et al. (Reference Glosten, Jagannathan and Runkle1993), is widely recognized for its ability to accurately predict asymmetric volatility across various assets and volatility regimes, as noted by Brownlees et al. (Reference Brownlees, Cipollini and Gallo2011). Similarly, the E-GARCH model, introduced by Nelson (Reference Nelson1991), has been highlighted by Lim and Sek (Reference Lim and Sek2013) as one of the most effective models for predicting volatility in markets with skewed return distributions.
In a recent study, Duttilo et al. (Reference Duttilo, Gattone and Iannone2023) applied advanced econometric models, such as mixtures of generalized normal distributions and the E-GARCH model, to analyse the returns and volatility of ESG investments compared to traditional ones. Their findings suggest that ESG factors can mitigate the impact of negative shocks, thereby reducing volatility asymmetry in these indices. This indicates that sustainable investments could offer greater resilience during economic crises, underscoring the need to promote the adoption of sustainable practices in financial markets.
Roy et al. (Reference Roy, Jaiswal and Gautam2024) analyse the risk profile of investment portfolios incorporating ESG factors in global financial markets, differentiating between developed and emerging markets. The study examines how these portfolios behave in terms of returns and volatility during different market regimes, specifically during and after the COVID-19 pandemic. Using daily data from representative ESG portfolios in countries such as the US, Japan, China, and India, the analysis focuses on fluctuations in volatility and returns using a GJR-GARCH model, which captures volatility asymmetry. The results reveal that ESG portfolios outperformed during the health crisis, showing lower risks and higher returns compared to the post-COVID-19 periods, suggesting that investors prefer sustainable assets in times of uncertainty.
Despite advancements in understanding volatility asymmetry, there remains a significant gap in the literature regarding how this phenomenon specifically affects sustainable indices during global economic crises. This study aims to fill this gap by comparing the behaviour of volatility asymmetry between ESG and traditional indices during the COVID-19 pandemic. By conducting this comparative analysis, this work seeks to make a significant contribution to the debate on the resilience and sustainability of investments during times of crisis, providing crucial insights for investors, regulators, and policymakers.
3. Methodology
3.1. Data
For this work, we study the asymmetry of the volatility of two international stock indexes (Standard & Poor’s [S&P500] and EU50) and their corresponding sustainability index (Dow Jones Sustainability World Index [DJSWI] and EURO STOXX Sustainability Index). The data collected ranges from November 18, 2016, to November 10, 2023, both inclusive. In this analysis, we use daily data to estimate volatility using the GARCH technique and implied volatility.
To analyse the impact of COVID-19 on volatility asymmetry and compare stock indices with sustainability indices, we differentiated two subperiods: pre-COVID-19 and post-COVID-19, referring to pre-COVID-19 at the time before the virus spread, and therefore, the post-COVID-19 period takes just time at the time when propagation began. We take the pre-COVID-19 period from November 2016 to December 2019. Consequently, the period after COVID-19 will be from January 2020 to November 2023.
The S&P500 Index, created in 1923, ranks the 500 largest companies globally by size, liquidity, and economic activity. It includes 400 industrial, transportation, utility, and financial firms. Unlike other indexes, it excludes small and medium-sized enterprises and does not account for dividend effects. The index’s value is calculated using an arithmetic mean.
The DJSWI comprises global sustainability leaders identified by S&P Global through the Corporate Sustainability Assessment. It represents the top 10% of the largest 2500 companies in the S&P Global BMI based on long-term economic, environmental, and social criteria.
The EU50, representing the 50 largest companies in the Eurozone in market capitalization, was established on February 26, 1998. This index, known as the Euro Stoxx 50, reflects the performance of the largest companies across supersectors regarding market capitalization within Eurozone countries. It is a market capitalization-weighted index, meaning the constituent companies do not all carry the same weight.
The EURO STOXX Sustainability Index provides a reliable and investable representation of key sustainability leaders in the Eurozone, covering stocks from 11 countries. It uses Bank Sarasin’s proprietary research approach, focusing on ESG dimensions, and includes components from Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, Netherlands, Portugal, and Spain.
The indices analysed in the study differ mainly in their focus and inclusion criteria. The S&P 500 focuses on the 500 largest US companies by size and liquidity, disregarding dividends and small and medium-sized companies. In contrast, the DJSWI groups the top global companies in sustainability, selected by economic, environmental, and social criteria, representing the top 10% of the 2500 largest companies in the S&P Global BMI. The EURO STOXX 50 reflects the 50 largest companies in the Eurozone by market capitalization, covering various sectors, while the EURO STOXX Sustainability Index focuses on leading sustainability companies within the same region, assessed by ESG criteria, using a proprietary research approach.
3.2. Description of data
Figures 1–4 illustrate the evolution of each stock market index and implied volatility under study during the pre-COVID-19 and post-COVID-19 periods.
Figure 1. Pre-COVID-19 period.
Figure 2. Post-COVID-19 period.
Figure 3. Volatility in pre-COVID-19 period.
Figure 4. Volatility in post-COVID-19 period.
Figure 1 shows that all indices generally followed a similar pattern, with the EURO STOXX Sustainability Index displaying consistently lower values than the other indices. Notably, the DJSWI appeared more stable, while the S&P 500 exhibited greater fluctuations.
Figure 2 highlights the significant drop across all indices due to the onset of the COVID-19 pandemic. It is observed that sustainable indices experienced a milder and delayed decline compared to traditional indices. Additionally, the S&P 500 outperformed the EU50 index during the post-COVID-19 period, reversing the pre-COVID-19 trends.
Figures 3 and 4 depict the implied volatility trends. The S&P 500 consistently showed higher volatility compared to the other indices, particularly the EURO STOXX Sustainability Index, which had the second-highest levels. The spikes in volatility during the pandemic’s early stages in March 2020 underscore the significant impact of COVID-19 on market stability.
The descriptive statistics in Table 1 further support these observations, showing a higher mean return during the pre-COVID-19 period across all indices, with increased volatility and extreme values observed post-pandemic. This shift reflects the greater instability and uncertainty that characterized financial markets following the outbreak of COVID-19, with significant implications for both sustainable and traditional indices.
Table 1. Pre-COVID-19 and post-COVID-19 periods
3.3. Estimation techniques
Before delving into the techniques employed in the study, it’s important to highlight some inherent statistical properties commonly found in financial returns. These properties, often referred to as the three stylized facts of financial returns, significantly influence the method used for calculating volatility:
• Volatility clustering
• Fat tails
• Non-linear dependences
The first property, volatility clustering, notes that in financial returns, volatilities tend to group together, leading to periods of high volatility followed by periods of low volatility.
The second property, fat tails, highlights the occurrence of rare, extreme positive or negative returns in financial data, which would be improbable in a normally distributed dataset.
Lastly, non-linear dependences refers to the relationship between multivariate returns. Linear dependence is described by the correlation coefficient, indicating how returns move together. However, in cases of non-linear dependence, the correlation between different returns is influenced by the magnitudes of outcomes.
Certainly, one of the pivotal advancements in empirical finance has been centred around modelling and predicting volatility. Building upon the groundwork laid by Robles (Reference Robles2002), diverse approaches for modelling volatility have emerged, categorized into structured measured and other measured methods, as outlined in subsequent research.
We will emphasize on two GARCH type models which accommodate the asymmetry observed in market volatility: GJR-GARCH and E-GARCH.
For GJR-GARCH and E-GARCH, we start form GARCH in mean (or GARCH-M) (Engle et al., 1988):
\begin{equation}{r_t} = {y_0} + {y_1}{\sigma _t} + {e_t}\end{equation} where rt is the daily log return and where it is assumed 
${{\text{e}}_{\text{t}}}\sim {\text{N}}\left( {0,\sigma _t^2} \right)$). The GJR model for volatility is:
\begin{equation}\sigma _t^2 = {\alpha _0} + {\alpha _1}\sigma _{t - 1}^2 + {\alpha _2}e_{t - 1}^2 + {\alpha _3}e{\left( - \right)_{t - 1}}^2\end{equation}where e(-)t = et, if et < 0 and = 0 if et ≥ 0. If α 3 = 0, the GJR model collapses to the GARCH (1,1) model and the relation is symmetric.
The variance equation for the E-GARCH model is:
\begin{equation}\ln \left( {\sigma _t^2} \right) = {\beta _0} + {\beta _1}\ln \left( {\sigma _{t - 1}^2} \right) + {\beta _2}\left| {{e_{t - 1}} / {\sigma _{t - 1}}} \right| + {\beta _3}\left( {{e_{t - 1}} / {\sigma _{t - 1}}} \right)\end{equation}As previously mentioned, our exploration of asymmetry involves an examination of implied volatility. Implied volatility represents the level of volatility that traders implicitly negotiate within the options market. It closely aligns with the notion of perceived risk and serves as a measure that approximates the market’s consensus regarding volatility.
According to the Chicago Board Options Exchange, the calculation of the VIX, similar to the VSTOXX calculation, which are the implied volatility index for S&P 500 and EU50, respectively, incorporates stock indexes such as the S&P’s 500. These indexes are derived from the prices of the constituent stocks within them. Each index adheres to specific rules dictating the selection of component securities and utilizes a distinct formula to compute index values.
Due to the fact that we do not have the volatility indexes of sustainability, we estimated all volatility indexes following the logarithmic return method of cash flows (Pareja Vasseur et al., Reference Pareja Vasseur, Prada Sánchez and Moreno Escobar2019), in which at the moment of calculating the returns, its normality is assumed:
\begin{equation}{r_t} = \frac{{\left( {{S_t} - {S_{t - 1}}} \right)}}{{{S_{t - 1}}}}\end{equation}The volatility calculation is:
\begin{equation}{\hat \sigma _{{r_t}}} = \sqrt {\frac{1}{{T - 1}}\mathop \sum \limits_{t = 1}^T {{\left( {{r_t} - \bar r} \right)}^2}} \end{equation}To estimate the volatility for each day, we compute the first standard deviation using data from the initial 5 days. Subsequently, we calculate the remaining volatilities sequentially, using the data from subsequent days.
4. Results
4.1. Analysis of estimated volatility
In this subsection, we present the estimated volatility of the studied indexes before and after the COVID-19 pandemic. The following figures illustrate the evolution of estimated volatility for the S&P 500, DJSWI, EU50, and EURO STOXX Sustainability Index. These visual representations allow for a comparative analysis of how each index has responded to the macroeconomic shocks induced by the pandemic.
The volatility patterns observed in Figures 5 and 6 highlight the significant impact of COVID-19 on financial markets, with a pronounced spike in volatility during the early stages of the pandemic. Both the DJSWI and the S&P 500 experienced a substantial increase in volatility during the COVID-19 pandemic. However, the sustainability index appears to have exhibited slightly lower volatility overall, especially during the peak of the crisis and in the post-COVID period. This could be attributed to the resilience of companies with strong ESG practices and the sectoral composition of the index.
Figure 5. S&P500 pre-COVID-19 GJR-GARCH.
Figure 6. S&P500 post-COVID-19 GJR-GARCH.
The EU50 and EURO STOXX Sustainability indexes saw increased volatility during COVID-19, but the Sustainability index showed greater resilience, with a less pronounced spike and faster stabilization. This may be due to the strong ESG practices and favourable sectoral composition of companies in the Sustainability Index, which likely managed pandemic risks better. Companies with robust ESG practices could offer more stability during crises, making them attractive to risk-conscious investors.
4.2. Analysis of volatility asymmetry
The following tables show the analysis of asymmetry volatility to pre- and post-COVID-19 periods for the four indicators studied. Table 2 refers to the results obtained from the volatility analysis for the S&P 500, and Tables 3–5 refer to the results for the DJSWI, EU50, and EURO STOXX Sustainability Index, respectively.
Table 2. GJR and E-GARCH models (S&P500)
Table 3. GJR and E-GARCH models (Dow Jones Sustainability World Index)
Table 4. GJR and E-GARCH models (EU50)
Table 5. GJR and E-GARCH models (EURO STOXX sustainability index)
Before turning to the analysis, we note that not all coefficients are statistically significant at a confidence interval of 95%. In the case of the S&P 500 for GJR-GARCH models, all coefficients are highly significant. This means that the variable associated with the coefficient is having a significant impact on volatility. Along these lines, in the E-GARCH model, in the pre-COVID-19 period, the coefficient is highly significant in a normal distribution, the same as the Student’s t distribution for the post-COVID-19 period. However, for this period, the coefficient for normal distribution is not significant. This implies that we do not have enough evidence to affirm a relationship between this variable and the asymmetry of volatility.
For the DJSWI, all contrasts are highly significant unless the E-GARCH model for the post-COVID-19 period for normal distribution.
Jointly with the EU50 index, we could see that the contrast is not significant in the pre-COVID-19 period for the GJR-GARCH model for Students’ t distribution; however, for the E-GARCH model, none of the coefficients are statistically significant.
Eventually, the contrast is not statistically significant when analysing the EURO STOXX Sustainability Index using the GJR-GARCH model in the pre-COVID-19 period with a normal distribution. Thus, we lack adequate evidence to assert a relationship between this variable and the volatility asymmetry. Similarly, the same conclusion holds for the E-GARCH model with a normal distribution for both periods under investigation.
Table 2 shows the coefficient estimates for the GJR-GARCH and E-GARCH models on the S&P 500 index, revealing changes in conditional volatility dynamics before and after the COVID-19 pandemic. The GJR-GARCH model showed significant coefficients of α and γ in the pre-COVID-19 period, indicating asymmetry and reaction to shocks. However, the β coefficient changed in the post-COVID-19 period, suggesting an alteration in volatility contribution. The E-GARCH model also showed significant coefficients during the pre-COVID-19 period, indicating asymmetry and past volatility influence. The lack of significance of certain parameters in the post-COVID-19 period suggests a possible simplification of the model.
Table 3 shows that the coefficients of the DJSWI show significant variations between the pre- and post-COVID-19 periods. The GJR-GARCH model shows stable values of α and γ, but a change in the β component indicates volatility influence. In the post-COVID-19 period, the constant decreases, suggesting a reduction in conditional volatility. The statistical significance of coefficients varies between Normal and Student-t models, indicating differences in conditional returns distribution. The E-GARCH model’s non-significance of certain parameters during the post-COVID-19 period provides valuable information on returns dynamics.
Table 4 shows that the GJR-GARCH and E-GARCH methods’ coefficients show no clear pattern, indicating differences in parameter estimation and statistical significance. The β component shows a change in volatility influence, while the E-GARCH model’s non-significance in specific parameters during the post-COVID-19 period provides valuable insights into returns dynamics. The constant’s non-significance suggests greater stability, while the β’s non-significance suggests past volatility’s contribution lacks statistical significance. The E-GARCH component plays a dominant role in explaining conditional volatility.
Table 5 shows how the GJR-GARCH and E-GARCH models have been applied to the EURO STOXX Sustainability Index, providing information on the dynamics of conditional volatility during the pre- and post-COVID-19 periods. The GJR-GARCH model shows stable values of α and γ, while changes in the β component suggest changes in volatility contribution. The constant decreases in the post-COVID-19 period, suggesting a possible reduction in conditional volatility. The E-GARCH model shows no significance of the constant and β during the post-COVID-19 period, suggesting a reduced influence on conditional volatility and greater stability. The presence of significant coefficients in the Student-t model emphasizes the importance of considering the distribution of returns in the analysis.
In Figures 5−12, we could observe asymmetric time-series GJR-GARCH model estimates (normal distribution) of the impact of a surprise return shock on U.S. and European markets volatility. Eventually, the contrast is not statistically significant when analysing the EURO STOXX Sustainability Index using the GJR-GARCH model in the pre-COVID-19 period with a normal distribution.
In the S&P500 case (Figures 5 and 6), the impact is more significant in the post-COVID-19 period than in the pre-COVID-19 period. In fact, in the pre-COVID-19 period, the effect is higher when the surprise return is negative.
In its sustainable index (Figures 7 and 8), the DJSWI, the impact is more significant in the post-COVID-19 period when the surprise return is positive. But when it is negative, the effect is higher in the pre-COVID-19 period.
Figure 7. Dow Jones Sustainability pre-COVID-19 GJR-GARCH.
Figure 8. Dow Jones Sustainability post-COVID-19 GJR-GARCH.
In both European indexes (Figures 9–12), we can observe how, in the post-COVID-19 period, the GJR-GARCH model does not follow a linear function as in the others. Therefore, it is important to highlight the similarity between the two indexes in the two periods under study. This similitude between the European index and the sustainable index can lead us to think that both indexes share many companies.
Figure 9. EU50 pre-COVID-19 GJR-GARCH.
Figure 10. EU50 post-COVID-19 GJR-GARCH.
Figure 11. EURO STOXX Sustainability pre-COVID-19 GJR-GARCH.
Figure 12. EURO STOXX Sustainability post-COVID-19 GJR-GARCH.
4.3. Analysis of implied volatility
Tables 6 and 7 explore the impact of 1-day return shocks on implied volatility for the indexes under study. We segment returns into 12 intervals, calculating the average return and volatility change for the S&P 500, DJSW, EU50, and ESSI.
Table 6. Impact of 1-day return shock on implied volatility (pre-COVID-19 period)
Table 7. Impact of 1-day return shock on implied volatility (post-COVID-19 period)
Table 6 shows that positive values suggest an increase in implied volatility, while negative values indicate a decrease. The magnitude of the index return varies across different return bins. The number of observations for each return bin is also indicated. The EU50 Index has a mix of positive and negative values, with positive values suggesting an increase in implied volatility. The Dow Jones Index has positive values suggesting an increase in implied volatility, while negative values indicate a decrease. The SP500 Index has a mix of positive and negative values, with positive values suggesting an increase and negative values suggesting a decrease. The day t return ranges for daily returns are also provided. This table offers insights into the relationship between 1-day return shocks and implied volatility for various sustainability and market indices during the pre-COVID-19 period.
Table 7 indicates that negative values suggest a decrease in implied volatility, with magnitude varying across different return bins. The mean log change in V EURO Sustainability indicates a decrease in implied volatility, while negative values indicate a decrease in the index for different return bins. The mean 1 day Index return (ESSI) shows a decrease in the index for different return bins, while the magnitude of the index return varies. The Dow Jones also shows a decrease in implied volatility, with negative values indicating a decrease in the index for different return bins. The SP500 Index shows a decrease in the index for different return bins, with varying magnitudes. The day t return ranges for daily returns from ≤−0.025 to ≥0.025.
In Figures 13 and 14, we visually confirm the trends observed in Tables 6 and 7. The noticeable disparity between the two analysed periods is evident, mainly when the day t return is ≥0.025. Also, it is essential to underline that in the pre-COVID-19 period; we do not have enough data to calculate the mean log change in sustainability indexes when day t return is >−0.025 and when it is >0.015.
Figure 13. Impact of day t return in pre-COVID-19 period.
Figure 14. Impact of day t return in pre-COVID-19 period.
5. Discussion
This research highlights the substantial impact of the COVID-19 pandemic on observed volatility patterns, as evidenced by a sharp increase in volatility during the initial phase of the pandemic. Compared to traditional indices, sustainable indices are characterized by a less pronounced volatility spike and a more rapid stabilization. Previous studies have explored the link between sustainability and traditional indices and the more robust reaction to positive or negative news (the fundamental pillar of sustainability).
Previous results have demonstrated that traditional indices are more sensitive to negative shocks. In contrast, sustainable indices, particularly those incorporating ESG criteria, offer greater resilience and lower volatility asymmetry during crises.
In the current study, we go beyond previous results by disproving the lower impact of negative news on sustainable indices and, in addition, being able to capture and link asymmetry with faster stabilization. This issue has yet to be analysed in depth. Moreover, the current study, in addition to working on European and non-European indices, something that was already done in previous studies, works with models with two advanced econometric models at the same time, such as GJR-GARCH and E-GARCH, completing a demand widely requested by previous scientific studies to date.
The observed differences in volatility between sustainable and traditional indices could be explained by several factors. First, although the models used capture the dynamics of volatility and return asymmetry, they are not sufficient to establish causality. The sustainable indices showed lower volatility and rapid stabilization, but this could be the result of the inherent characteristics of the companies that make up these indices, which tend to be more resilient to shocks due to their strong sustainability fundamentals.
To establish whether index design is the cause of these differences, it would be necessary to apply additional models, such as Granger causality tests, to help determine whether index design and composition have a direct impact on observed volatility or whether there is only a correlation. On the other hand, investor motivations could be a relevant factor. Investors in sustainable indices may have a more long-term sustainability mindset, which could influence their behaviour during crises and hence the lower volatility observed in these indices.
At the level of future research, it would be useful to explore all these limitations by incorporating causality models to examine whether the observed differences in volatility are causal or simply correlated with other factors. Also, the analysis of investors’ behaviour and motivations could be further explored through qualitative tools, such as interviews or surveys, to explore how their approach to sustainable investments influences the behaviour of indices during crises.
Importantly, our study takes the volatility work a step further by investigating, in addition, the impact of 1-day return shocks on implied volatility. This study is critical in providing a more granular and in-depth view of market dynamics. This information is invaluable to various market players, from risk managers and traders to regulators and academics, contributing to a more efficient and resilient financial system. However, while we can observe an increase in implied volatility concerning positive values and a decrease concerning negative ones and highlight an apparent disparity between pre- and post-COVID-19 periods, there is a limitation relating to the data in not being able to calculate the mean log change in sustainability indices when the t-day return was more significant than −0.025 or greater than 0.015. Future research can work on and deepen this intra-day study by incorporating a more extensive data set. The use of more advanced econometric models is also proposed.
6. Conclusions
Government policies are considered to have a crucial role in promoting environmental, social, and economic sustainability. Their effectiveness is seen to depend on the integration of environmental policies, sustainable economic development, social inclusion, participatory governance, and a holistic vision.
In addition to the government, private companies are recognized as critical players in implementing sustainable practices. Constant evaluation and monitoring of these practices are deemed essential to ensure their correct direction. Stock market indices, including those focused on sustainable companies, serve as indicators of business dynamics in this area.
The COVID-19 pandemic negatively impacted sustainability and other psychosocial factors, creating a polycrisis. Analysing stock market indices during the pandemic allows us to understand the importance of sustainability both before and after this disruptive event.
It can be observed that sustainable indices show an apparent harmony in stock prices before and after COVID-19, indicating greater stability in aggregate stock prices than traditional indices. This conclusion is partly refuted in previous research; now, with this study and the use of advanced econometric models GJR-GARCH and E-GARCH, greater price stabilization can be confirmed. That is, not only are shocks more harmonious in sustainable indices, but stabilization is also earlier.
As a consequence of the above, we can speak of greater confidence for investors as they encounter lower volatility, offering lower perceived risk and feeling more comfortable investing in markets with more significant signs of stability, as this suggests that they are less likely to experience abrupt losses.
Our study, in addition to being a pioneer in terms of the ability to contrast-sustainable and non-sustainable indices in their aggregate form, works on implied volatility by having a more significant impact, in relation to the performance of the specific day, on the logarithmic change with respect to the risk profile of the index. This is also consistent with the greater stability of investors in sustainable markets.
Although with the current research we manage to establish a positive link between sustainability, shocks and early price stabilization, it’s important to appreciate the inherent limitation to investment capacity as this depends on markets which can be unpredictable and that past stability is no guarantee of future stability. Investors often consider various factors, not just index stability, when making investment decisions. Additionally, prolonged stability can sometimes mask underlying risks or trigger market complacency, which could lead to exaggerated reactions when disruptive events finally occur. Future studies can also advance on companies that incorporate each of the indicators, sustainable and non-sustainable, since the detail of the companies that only appear in the sustainable indicator is relevant. Furthermore, future research can explore and work on the realized volatility of these indices.
Acknowledgements
This research is part of the International Chair Project on Trustworthy Artificial Intelligence and Demographic Challenge within the National Strategy for Artificial Intelligence (ENIA), in the framework of the European Recovery, Transformation and Resilience Plan. Reference: TSI-100933-2023-0001. This project is funded by the Secretary of State for Digitalization and Artificial Intelligence and by the European Union (Next Generation).
Author contributions
Sanz-Martín, L.: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing. Parra-Domínguez, J.: Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing. Corchado, J.M.: Funding acquisition, Investigation, Supervision, Validation, Writing – review & editing.
Funding statement
This research is part of the International Chair Project on Trustworthy Artificial Intelligence and Demographic Challenge within the National Strategy for Artificial Intelligence (ENIA), in the framework of the European Recovery, Transformation and Resilience Plan. Reference: TSI-100933-2023-0001. This project is funded by the Secretary of State for Digitalization and Artificial Intelligence and by the European Union (Next Generation).
Competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Research transparency and reproducibility
All data sources are available in the manuscript.
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