Vulnerability of Sustainable Islamic Stock Returns to Implied Market Volatilities: An Asymmetric Approach

ere has been increasing interests in the sustainable way of investing as enjoined by several sustainability initiatives. However, investors require eective portfolio diversication at various market conditions (stress, benign, and boom) and would consider sustainable equities to the extent that they aid in the minimisation of portfolio risks. As a result, a better way investors can mitigate portfolio risk is by forming portfolios with relevant volatility indices as enshrined in extant literature. It becomes necessary to investigate the susceptibility of Islamic stocks in a sustainable way to shocks from volatility indices to enhance eective portfolio decisions. In this regard, we investigate the asymmetric eect of implied volatility indices on sustainable Islamic stocks across dierent market conditions. Hence, the quantile regression and quantile-on-quantile regression techniques are employed. e study discovered an asymmetric inuence of volatility on sustainable Islamic stock returns at various quantiles. Furthermore, most volatilities’ asymmetric eects were generally inversely associated to sustainable Islamic stock returns, implying diversication benets across market outcomes. Also, with the exception of the extreme quantiles, there is a causal eect of volatilities on Islamic stock returns for most quantiles. It seems to reason that ordinary market outcomes, rather than market stress or boom, have a greater impact on causal estimates for our quantile regression model.


Introduction
e popularity of Islamic stocks has heightened over the years to induce the attention of investors, policymakers, researchers, asset managers, etc. is is as a result of their increased market performance relative to the conventional way of investing, even in times of crises. Investing in Islamic stocks further grants the opportunity to channel ones religious belief [1,2]. Aside from this, the high levels of integration among most conventional assets (see [3][4][5]) requires that e ective portfolios are formed with Islamic stocks due to the latter's high extent of satisfying investors' risk tolerance in times of crises [2,6].
However, prior studies utilising Islamic stocks alone divulge that Islamic stocks exhibit similar patterns of high interactions [7,8] depicting low degrees of diversi cation in the future. is is not surprising because, although Islamic stocks are mostly insulated from existing crises, their similar response to shocks weaken diversi cation potentials at various investment horizons.
is has brought about many empirical studies to investigate diversi cation bene ts among conventional and Islamic assets simultaneously [2,6,[9][10][11][12]. Findings from these studies generally divulge some considerable levels of interactions or contagion (increased in correlations after the onset of crises) among conventional and Islamic equities.
Comparatively, conventional equities are found to exhibit more volatility spillovers of excessive interactions than their Islamic counterparts [2] during market stress. Insights from these studies are that it is better to diversify among conventional as well as Islamic equities rather than concentrating on a particular asset class.
is opens up a gap to further assess the asymmetric effect of implied market volatilities which are forwardlooking. Application of implied volatilities has gained massive attention with conventional stocks [13,14] and cryptocurrencies [15][16][17], as well as commodities [5,18,19]. It is normally found from these studies that negative shocks are mostly transmitted from the implied market volatilities to these assets demonstrating diversification, hedge, or safe haven benefits depending on the market conditions as a result of portfolio formation.
It becomes pertinent to examine the asymmetric effect of implied volatilities on Islamic stocks which have gained investors' attention over time [20][21][22]. is is particularly important because Islamic stocks are most likely than not susceptible to external shocks [22,23]. is empirical discourse would highlight the relevance of forming reliable portfolios among market volatility indices as external shocks transmitters and Islamic stocks. It would also give a chance to the existing investors of Islamic stocks to reconstruct or rebalance their portfolios to incorporate implied market volatilities. Also, observing the asymmetric effect of implied market volatilities provides existing investors of Islamic stocks the opportunity to hedge against shock transmission regarding contagion effect to either redeploy or scale up their investments.
Hence, a nascent and fledgling body of literature investigates the nexus between implied volatilities and Islamic stock returns. For instance, Karim and Masih [20] through the wavelet approach investigated the asymmetric impact of realised and implied crude oil volatility on Islamic stock returns. However, the study of Karim and Masih [20] was limited to the oil market, thereby creating a myopic view of the nexus. e closest study to ours is that of Chang et al. [1], but did not consider the influence of implied volatilities in the nexus.
Some of the implied volatilities that have spillover effects on most financial markets around the world include the US VIX as a significant measure of investor fear and expectations [14], implied volatility in the energy markets, emerging markets volatility, and developed markets volatility. ese implied volatilities have been touted to have ravaging impact on financial markets [5,13,16,18,24] from which Islamic stocks could be more sensitive as a result of contagion effect from markets interactions.
is is because, recently, Islamic stocks are becoming linked to shocks from implied volatilities [22,24]. is can be traced from the behaviour of conventional investors and fund managers who seek to invest in Islamic stocks to minimise losses during crises. In times of crises, firms with a relatively huge indebtedness tend to receive most of the shocks, wherein, Sharia-compliant firms operate around a certain interest-bearing debt threshold of about 33% in accordance with the screening method of Dow Jones Sharia, to mention a few. is filtering criterion mitigates financial integration between Islamic stocks and implied volatilities to become less positively related to harness diversification benefits.
However, as found by Karim et al. [25], Islamic stocks are less exposed to implied volatility or fear index than their conventional counterparts due to the former's distinct screening features to be more decoupled from the risks facing conventional markets. Conversely, Tissaoui and Azibi [24] and Shahzad et al. [26] documented that both Islamic and conventional stocks are exposed to global risk factors similarly and achieving strong linkages with their conventional counterparts.
is leads to the rejection of the decoupling hypothesis of both Islamic and conventional stocks. ese inconsistencies render a further assessment of the susceptibility of most Islamic stocks (Sharia-compliant) to several relevant implied volatilities worthwhile of examination to enhance investors' understanding and confidence.
It is known that implied volatilities drive interconnectedness among financial markets including Islamic stocks during stressful times [22]. What is not known is the susceptibility of Islamic stock returns to implied volatilities at market conditions of stress, normal, and boom using the quantile regression approaches? at is, prior studies conducted on the susceptibility of Islamic equities to implied volatilities are mostly silent on the use of the quantile regression approaches (see [20][21][22][23][24]26]). However, the quantile regression approaches, quantile regression (QR), and quantile-on-quantile regression (QQR) offer the opportunity to capture the nonlinear, asymmetry, and nonstationary influence of changes in implied volatilities [13] and Islamic stock returns (see [27,28]), as well as the effect during bearish, normal, and bullish market situations. e traditional QR and regular least squares approaches alone do not display these properties as good as QQR does. Furthermore, the market condition of Shariah stocks may not be the same as volatility indices. us, Shariah stocks and volatility indices may witness different market conditions and, hence, analysing the asymmetric relationships between the two assets across their varied market conditions is important.
We  Discrete Dynamics in Nature and Society 3 firms around the globe to have a pivotal mandate to disclose their performance on sustainability issues while putting up a sustainable behaviour. However, since investors desire to form reliable portfolios, diversification benefits with other assets become their utmost flight to quality. Second, the asymmetric effect of implied market volatilities which have gained significant interest from a nascent and fledgling body of academic literature is utilised in tandem with the sustainability Islamic stocks. We select four relevant implied market volatilities to integrate shocks from developed market, emerging market, the US market, and energy market. Most of these volatilities have been touted to be significant risk transmitters in several conventional assets [5,13,14,18], but a few studies on Islamic stocks utilise specific or few implied volatility indices [20][21][22] to ensure a myopic view on the nexus. We do this to draw insights into effective portfolio reconstructions, redeployment, and rebalancing towards risk minimisation strategies.
ird, to examine the asymmetric effect of the implied market volatilities on Islamic stocks across market conditions (stress, benign, and boom) [29], the quantile regression as well as quantile-on-quantile regression techniques are employed. Moreover, the robustness of these estimates would hinge on the application of the causality in mean at various quantiles. ese are presented to clearly divulge the heterogeneous [30] behaviour of markets and their participants across market conditions of stressed, normal, or boom [11,[31][32][33][34].
We found asymmetric influence of volatility on sustainable Islamic stock returns at various quantiles. Furthermore, most volatilities' asymmetric effects were negatively related to sustainable Islamic stock returns, implying diversification benefits across markets conditions. Moreover, with the exception of the extreme quantiles, there was a causal effect of implied market volatilities on Islamic stock returns at most quantiles. e next of this section is arranged as follows. In Section 2, we present the study's methodology whereas Section 3 contains results and discussion. Section 4 concludes the study with some implications, recommendations, and suggestions for further studies. is makes the indices relevant to withstand shocks and support diversification with other financial assets. All the seven indices are needed for this current study because they would provide better information on most Islamic sustainability or Shariacompliant equities across different regional blocs to examine their susceptibility to shocks, while encouraging regional policy decisions.

Materials and Methodology
Also, we used four implied volatilities to gauge investors' fear into the Islamic market. e implied volatilities are the CBOE Emerging Markets Etf Volatility (EMV), Chicago Board Exchange Volatility Index (USVIX), Dorsey Wright Developed Market Momentum and Low Volatility (VDM), and CBOE Energy Sector Etf Volatility (EnergyV). e four implied volatilities would comprehensively give us the opportunity to investigate their heterogeneous as well as asymmetric impact on the seven selected Islamic stocks for effective portfolio reconstructions, redeployment, and rebalancing towards risk minimisation strategies. e daily data span 11 th January, 2017 to 11 th February, 2022, yielding up to 1264 observations. e suggested period was chosen based on the availability of consistent data at the start and the end locations. Regardless, this time period includes significant economic events such as the Brexit, crude oil price crash in history, and the COVID-19 pandemic. e data on sustainability Islamic equities were Note. * , * * , and * * * denote significance at 10%, 5%, and 1%, respectively.  Note. * , * * , and * * * denote significance at 10%, 5%, and 1%, respectively.
Discrete Dynamics in Nature and Society 5 obtained from RobecoSAM database. e volatility indices were obtained from investing.com. We utilised the natural logarithmic returns for each market indices.

Quantile-on-Quantile Regression (QQR).
e conditional quantile link between two or more variables is empirically justified using the QQR technique, which is a nonparametric variant of the traditional quantile regression (QR). e QQR is suited for studying bearish and/or bullish interrelations between the returns on Islamic stocks and volatility indices since quantiles can express asymmetry among high and low logarithmic price patterns. We show susceptibility of the Islamic stocks to volatility indices which are non-parametrically expressed as where SR t and VI t respectively, represent the returns of Islamic stock and volatility indices at period t, β θ (•) is the slope of the connection between the two assets at any Note. * , * * , and * * * denote significance at 10%, 5%, and 1%, respectively.  Note. * , * * , and * * * , * * * denote significance at 10%, 5%, and 1%, respectively. 6 Discrete Dynamics in Nature and Society conditional level, the θth quantile of SR t in equation (1) that is conditionally distributed is denoted by θ, and u θ t is the quantile in error which is made to have a θth conditional quantile.
Discrete Dynamics in Nature and Society Equation (2) can now be substituted into equation (1) to arrive at equation (4) as where ( * ) yields the conditional quantile of θth of returns on VI in equation (4). It additionally portrays the true susceptibility of the SR(τth) to shocks from the quantile of the VI(θth) in respect of equation (4), of the parameters β 0 and β 1 with indices represented by θ and τ. Similar to the case of OLS, we apply an analogous minimisation to produce the following equation where the quantile loss function, ρ θ (u), is represented as ρ θ (u) � u(θ − I(u < 0)), i is the function of indicator, the  Note. * , * * , and * * * denote significance at 10%, 5%, and 1%, respectively.  Note. * , * * , and * * * denote significance at 10%, 5%, and 1%, respectively. 8 Discrete Dynamics in Nature and Society kernel density function (KDF) is denoted as K(•), and h is the bandwidth parameter of the KDF. e observations of VI τ is weighted by the KDF where the minimal weights are inversely connected to the distribution of VI t in the form of F n (VI t ) � (1/n) n k�1 I(VI k < VI t ). Following the specifications of Sim and Zhou [35], the bandwidth for the quantiles we employ in this study for the QQ breakdown is defined as h � [0.05 to 0.95]. e smoothness of the estimated results is contingent on the bandwidth, which represents the divisions of the quantiles. Smaller bandwidths are recommended over larger bandwidths because larger bandwidths may lead to biased estimates of the coefficients.

Preliminary Analysis.
e time series plots of both price and returns for sustainable Islamic stocks (in black) and volatility indices (in red) are presented in Figure 1. Most of the Islamic stocks trend upwards prior to mid-2020, plunge in the mid-2020, and skyrocketed afterwards. It can be observed that markets rebound after the COVID-19 pandemic, demonstrating high market performance, supersede that of prior to the pandemic. Accordingly, we find prospects of extreme markets rebound after the onset of a shock within the sustainable Islamic stock markets. Conversely, except for the developed market volatility index, the remaining volatility indices are inversely related to the Islamic stock market, indicating a potential hotspot for portfolio diversification, hedge, or safe haven. Also, the plunge in prices at the COVID-19 pandemic is shown as shocks in the returns plots of the sustainability Islamic stocks. Generally, all the returns series exhibit volatility clustering.
We present Table 1 to examine the behaviour of individual financial time series over the sampled period. It can be seen that all the variables have positive mean suggesting potential for increased market performance. Also, there are fewer variations in the data and tendency for more negative values than higher values in addition to a leptokurtic distribution. We confirm that the data distribution of all financial time series demonstrates non-normality from the Jarque-Bera statistics.
Additionally, we observe from the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test that all the returns series are stationary with a failure to reject the null hypothesis of stationarity (p-value > 0.05). However, since all the returns series are not normally distributed, it accentuates the relevance of employing an asymmetric statistical tool capable of revealing relationships across market situations. In assessing the linearity of the financial time series, the Teraesvirta's Neural Network (TRS) test with a null hypothesis of linearity is employed. e TRS test suggests that the original returns series are nonlinear (p-value < 0.05). is further addresses the need for employing the QQR technique which is able to effectively deal with issues of asymmetry and nonlinearity relative to the traditional QR and OLS (see, e.g., [36] and references therein).
Moreover, the unconditional correlation coefficients between two time series are shown in Table 2. It is clear that the correlation of all the financial time series are almost significant at the 1% level. We notice a mixture of positive and negative correlations ranging from small to large magnitudes. e negative relationships between the variables have high likelihood for diversification, and this can be found between the Islamic stock returns and most of the volatility indices. is implies that portfolio diversification  Note. * , * * , and * * * denote significance at 10%, 5%, and 1%, respectively.    among the sustainability Islamic stocks would do more harm than good to potential investors. Tables 3-9 present the asymmetric effect of implied market volatilities on sustainable Islamic equities. We find a significant effect of implied market volatilities on Islamic stock returns across quantiles at varying levels of significance. e susceptibilities of Islamic stock returns to market volatilities across market conditions (stressed, benign, and boom) are mostly negative, except for volatilities from developed markets. Surprising, the effect of developed market volatilities on Islamic stocks have large magnitude, and considered to be positive except for S.PGS from Table 9. e similar asymmetric coefficients at most markets conditions demonstrate the persistence of Islamic stocks to external shocks. is explains that it takes a while for Islamic stocks to respond to changes in shocks from external shocks.

Quantile Regression.
Comparatively, all volatility indices but developed market volatility demonstrate reduction in magnitudes from the lower quantile to the upper quantile. Suggesting that negative shocks are more prominent at stressed market outcome, whereas positive shocks are stronger at market boom for all Islamic equities. It can therefore be concluded that most sustainable Islamic stocks are vulnerable to implied market volatilities.
is is partly in line with the assertion made by Haddad et al. [23] that Islamic equities are susceptible to international shocks. e significant negative effect of implied volatility from the energy market concurs with the findings of Karim and Masih [20] and Lin and Su [21]. Conversely, Lin and Su [21] found that negative shocks between implied volatility from crude oil and Islamic stocks are more prominent at higher quantiles. Moreover, outcomes generated from the current study do not absolutely deviate from the ones generated by prior studies on conventional assets as well as commodities [5,13,14,18].
It is relevant that investors of Islamic stocks form a well diversifiable portfolio with market volatilities. Also, existing investors of sustainable Islamic stocks should hedge against fluctuations in Islamic stocks having in mind the behaviour of market volatilities or redistribute their existing Islamic stock portfolios.

QQR and QR Comparison.
In this section, we investigate the relevance for a non-parametric asymmetric distribution among the sustainable Islamic stock returns and volatilities returns. It also gives the opportunity to infer how significant the QQR estimates are, having the knowledge of the QR estimates. Figure 2 presents the combined plots for both QQR and QR. A look at Figure 1 indicates that although   [21,27,28]). Nonetheless, to some extent, the line graphs confirm the QQR except for the extreme quantiles of most relationships. It is worth noting that relative to the QR, the QQR projects a better view of the asymmetric linkages among the dependent and independent variables at varied quantiles of both variables. Hence, given that majority of the QQR estimates are confirmed by their QR counterparts, we emphasise the relevance of the chosen methodological framework. We present the three-dimensional QQR estimates in the next subsection to further address the asymmetric and nonlinear dynamics of the employed financial time series.

Quantile-on-Quantile Regression.
e three-dimensional asymmetric dependent nexus among Islamic stock returns and implied market volatilities is shown in Figure 3. It can be observed that lower values leading to negative values relative to higher ones are persistent with emerging market volatility and the US VIX. is implies that considering the quantile dependence structure of both Islamic stocks and implied market volatilities, it is better to diversify with the emerging market volatility and the US VIX. Accordingly, having in mind of the quantile dependence structure of the possible combinations of this study, portfolio rebalancing or redeployment is pertinent with volatilities from the energy and developed markets.

Robustness.
e causality in mean, as proposed by Jeong et al. [37] and advanced by Balcilar et al. [38] is employed in this study to confirm if sustainability Islamic stock returns are significantly driven by volatilities at varying levels of market conditions. Prior empirical research investigating the resilience of quantile regression has used this approach (see [13,39]). Figure 4 shows that, with the exception of the S&P Africa Frontier Shariah Index, volatility indexes have a strong causal impact on sustainable Islamic stock returns. From the lower mid quantiles to the upper mid quantiles, the causation grows stronger.
is means that typical market outcomes influence causal estimates for our quantile regression model more than market stress and boom.

Conclusion
We contribute to the asymmetric relationship among sustainability Islamic stock returns and volatility returns across market conditions. Hence, the quantile regression and quantile-on-quantile regression techniques were employed.
e causality in mean technique at various quantiles was further utilised to examine the robustness of our quantile estimates.
Findings from the study revealed asymmetric effect of volatilities on sustainability Islamic stock returns at various quantiles. In addition, the asymmetric effects of most volatilities were mostly inversely related with sustainability Islamic stock returns, suggesting diversification benefits at various markets outcome. Also, we document causality from volatility to Islamic stocks at various quantiles, except for the extreme quantiles. It goes to reason that typical market outcomes influence causal estimates for our quantile regression model more than market stress or boom. Particularly for each volatility indexes, volatility index from developed markets transmits positive shocks to sustainability equity indices, except for the S&P Global 1200 Shariah (S.PGS). Hence, diversification benefit would manifest only with the S.PGS index from shocks from the developed market volatility index. On the other hand, the remaining volatility indices transmit negative shocks at various quantiles indicating the need to diversify, hedge, or seek safe haven from them. e significant asymmetric relationship among Islamic stock returns and implied market volatilities across quantiles demonstrates inefficient market dynamics exacerbated by the irrational behaviour of investors to accentuate the heterogeneous and adaptive market hypotheses.
It is recommended that existing and potential investors of sustainable Islamic stocks be mindful of the heterogeneous susceptibilities of these stocks to market volatilities. It is important that they study the market at various markets condition, having in mind the potency of market volatilities. It is necessary that optimal policy interventions from these sustainable Islamic regional blocs are deployed to revamp vulnerable Islamic markets to external shocks. Further studies can assess frequency-dependent asymmetric impact of market volatilities on sustainability stocks at various investment horizons and market outcomes [12,40,41].

Data Availability
e data used to support this study are available upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.