Ṣukūk or Bond, Which Is More Sustainable during COVID-19? Global Evidence from the Wavelet Coherence Model

Abstract

Understanding the co-movement and lag–lead relations among indices is integral to financial decision making. These parameters show the reactiveness of the market towards new information. Understanding them helps to minimize risk and facilitates optimal portfolio diversification. By employing the wavelet coherence econometric model, the authors of this study analyzed the intricate relations among the Bond and Ṣukūk indices using global data belonging to the United States (US), the United Kingdom (UK), Middle East and North Africa (MENA), and Gulf Cooperation Council (GCC) countries. The findings indicated the presence of strong but similar implications of the initial shock of COVID-19 deaths on both Islamic and conventional markets’ volatilities, especially in long-term investment bands (64–128 days). The results oppose the general belief that Islamic finance is more sustainable and less volatile to crises than its traditional counterparts. Moreover, the authors of this study report diverse relationships among bond and Ṣukūk indices throughout the sample periods. We consistently found low correlations in short-term investment bands (4–16), leading to optimal diversification opportunities. However, high correlations were reported due to COVID-19 in the long-term investment bands (128–256), leading to low diversification opportunities for long-term investors.

1. Introduction

Due to the intricate nature of financial choices, investors are often at an impasse in deciding between their strategic position on capital appreciation or capital preservation. Especially during financial turbulence, investors seek to safeguard their capital rather than returns [1]. In this regard, diversification plays a vital role in capital preservation by allocating investments in various asset classes. Diversification helps investors optimize the portfolios not only when the returns are positive but also when the market faces diminishing returns. Historically, it is evident that investors with 100% equity-based portfolios often face poor returns. At the same time, investors who diversify their portfolios by investing in bonds, stocks, and hedge funds are more likely to enjoy higher returns. However, opt assets must have low correlations with one another. Thus, it is essential for adequate portfolio diversification that the asset returns negatively correlate with other assets. This condition is also applicable for fixed-income investments such as bonds [2]. A positive correlation between asset classes such as stock and bonds is due to the “spillover” effect. Research defines the spillover effect as a scenario in which the shock in the stock market influences the returns and volatility of the bond market. This eventually causes a decline in the prices of both assets.

Moreover, investors, who prefer to diversify their portfolios by combining different classes of assets, always appreciate the emergence of new financial options. That safeguards their investments and ensures overall capital preservation. In this regard, the Ṣukūk instrument provides an alternative mode of financing to investors compared to traditional bonds or commercial banks. Furthermore, due to its distinct structure and market dynamics, the Ṣukūk yield tends to correlate less with other fixed income markets [3]. Even though the researchers have thoroughly evaluated the diversification benefits of stock and bonds, e.g., [4,5,6,7,8], the reported literature on bond markets is highly diverse in terms of its findings. Some studies demonstrated a low correlation between global bond markets, suggesting that diversification benefits investors [9,10,11].

On the other hand, some researchers have argued the existence of a strong correlation among the same global bond market, leading to high diversification benefits [12,13,14]. It was also reported that these changing correlation patterns through time are due to varying levels of integration among the markets and the overall easiness of international capital transfers [15]. Similarly, very few studies have evaluated the correlation between the Ṣukūk and bond indices and how it benefits portfolio diversification, e.g., [1,16,17,18].

Moreover, it has been hypothesized that Islamic finance, given its strict and conservative shariah-based screening criteria, is less volatile to these crises than its traditional counterparts. Some studies have suggested that shariah-based companies may tend to underperform (decrease in revenue) due to the underlying shariah restrictions such as limited funding sources (debt), business procedures, and no-risk hedging through options [19]. However, conventional options are not subject to these screenings. Even though they have specific financial objectives, they are not near the level of shariah restrictions [20]. Therefore, it is believed that their performance tends to vary due to differences in criteria and underlying characteristics. For instance, as per Samia Nasreen, in Ṣukūk, the claim is on the ownership of the asset, and unlike bonds (which have fixed return rates), returns are based on the performance of their underlying asset. Similarly, Ṣukūk is not subject to speculation, interest, and other riskier aspects of the conventional market [21]. Accordingly, it may provide higher safeguards to investor’s capital than conventional instruments [22].

While both Sukuk and conventional bonds enable issuers with availability to liquidity through the public debt market, there have been inconsistent findings regarding the disparity between Sukuk and bonds. On the one hand, a set of studies demonstrated that bonds are considerably more vulnerable than Sukuk to changing global markets and that there are real distinctions between how the returns of Sukuk and bonds are computed [23,24]. On the other hand, another set of studies demonstrated that there are no discernible variations between the returns of Sukuk and bonds, alternatively referring to the identical handling of the two products by market players [25,26].

In the context of the GCC region, the authors of [27] evaluated the difference in the performance of conventional indices and their Islamic counterpart. Their findings suggested similar risk profiles of Islamic and conventional indices. Similarly, Cevik and Bugan analyzed the dynamic relationships between Islamic and conventional markets using the Markov-switching vector regression model. Their findings suggested that strong integration between these markets as a conventional counterpart highly influenced Islamic stocks in both bear and bull regimes. Hence, the authors rejected the notion of Islamic markets as a safe haven that provide diversification benefits during crises [28]. Moreover, while using the same Markov regime-switching model in the context of the US, Latin American, Europe, and Asian markets, Trabelsi reported findings that supported the study of Cevik as they demonstrated insignificant differences in the performance of conventional and Islamic indices across normal and crisis regimes [29].

The approaches and methodologies utilized in most of these studies may have significantly contributed to the literature’s disagreement regarding whether returns on Sukuk and conventional bonds are distinct. Furthermore, a number of these studies were concentrated on searching domestic markets or particular geographic markets, which confined the significance and appropriateness of such outcomes due to the sparsely populated nature of issuers and participants in such markets, as well as the particularly weak links with global markets in comparison to global financing. The authors of this comprehensive study corrected these shortcomings by exploring the co-movement patterns of the global bond and Sukuk markets. Furthermore, the authors of this study tested the decoupling assumption i.e., the decoupling hypothesis assumes fundamental differences between one class of assets from others in terms of their risk and returns characteristics along with low correlations, leading to diversification opportunities for investors. During the COVID-19 crisis, Islamic options have employed the wavelet model, and, in terms of the fixed income market (Ṣukūk and bonds), the authors of this study were some of the first to do so as well. Fourth, this study adds knowledge to the theoretical literature on the financial crisis by signifying how the non-economic and non-financial aspects of COVID-19 influence volatility in fixed income indices, i.e., Ṣukūk and bonds. Furthermore, the data obtained from indices belong to different regions and markets, allowing the study to have better generalizability and practical implications for investors composing their portfolios, i.e., hedge their assets belonging to different regions based on the given correlations during a financial crisis such as COVID-19.

2. Literature Review

Previous literature indicates diverse findings regarding the performance of Islamic assets during crises, e.g., the authors of [30,31,32,33] declared Islamic indices as more resilient against crises. However, the authors of [27,28,29,34,35] asserted that Islamic indices do not show lower volatility or significantly different performance than conventional indices during crises. Recent studies showed huge implications of COVID-19 on selected Islamic and conventional stock indices, i.e., [36,37,38]. However, the authors of [39] investigated the effect of COVID-19 on the co-movement relations between Ṣukūk and bond indices. By employing the wavelet econometric model, the authors of that study showed a similar effect of the pandemic on volatilities of conventional, e.g., Dow Jones and FTSE indices, and Islamic indices. Their findings opposed the idea of the decoupling effect of Islamic stocks. Hence, Islamic stocks do not provide a safe alternative during a crisis [40]. The influence of COVID-19-related announcements on the connectedness of a conventional stock market (Chinese) and Islamic stocks was also evaluated, and findings suggested that announcements related to COVID-infected cases and deaths impact the conditional correlations of Islamic and conventional stocks, though COVID-recovered cases have no such impact. In other words, researchers found high instability among the co-movement between Islamic and conventional stocks due to COVID announcements (death and new cases), especially in the short term. The above-described diverse findings suggest an exciting avenue for researchers to evaluate the volatilities/co-movement of Ṣukūk and bonds during crisis and non-crisis periods, such as how specific crisis events such as COVID-19 influence their volatilities.

In addition to co-movement, understanding the lag–lead relation shows the reactiveness of the market towards new information [16]. Based on the market lead–lag analysis, investors may use historical data to predict returns [41,42]. Moreover, due to a higher level of integration, contagion effects were found to be persistent among markets. Researchers have described the contagion effect as a general tendency of different assets to be similarly influenced by macroeconomic variables [1]. This leads to a positive correlation among markets. Previously, several researchers tried to understand the implication of contagion effect on financial markets, including [43,44,45,46]. Despite the recent growth in Ṣukūk literature, there have been very few studies evaluating the lead–lag relation between Ṣukūk and bond indices, e.g., [1,18,47]. Hence, this argument provides an appealing avenue to explore, especially regarding the direction of causality in Ṣukūk markets, which are supposed to be more resilient against the contagion effect (macroeconomic variables).

3. Research Methodology

3.1. Data

The data used in this study were obtained from the DataStream from 2005 to 2020. In the first step, to operationalize the data, we transformed the selected Ṣukūk and bond indices into market returns by taking the natural logarithmic difference between daily Ṣukūk and bond prices. The proposed bond and Ṣukūk indices were mainly taken from the United States (US), United Kingdom (UK), Middle East and North Africa (MENA), and Gulf Cooperation Council (GCC) countries. As the proxy for COVID-19, we used daily data of global death counts of COVID-19 (GDC) from 1 January 2020 to April 2021. COVID-related were obtained from governments’ official sources of the intended countries. As for the COVID-19 objective, the proposed model for analysis was the same, i.e., wavelet transform. Since the main objective was to analyze the influence of the crisis on the volatilities of conventional and Islamic indices, this method helped to simultaneously identify correlations under the time–frequency domain.

The rationale for selecting the Ṣukūk indices of MENA and GCC countries is that from 2001 to 2019, the MENA and GCC countries had the highest number of Ṣukūk issuance and ranked 1st with 58.28% of shares (amounting to USD 171,861 million) in total Ṣukūk issuance worldwide [48]. This shows that their markets are well-established and have a well-established investor base. Similarly, UK and US markets have a well-developed bond index, endowing our work with better generalizability by including a developed market perspective.

Table 1. Variables details.

No	Index Name	Ticker
1	Dow Jones Sukuk Index	DJSUKUK Index
2	The S&P Gulf Cooperation Council (GCC) Sukuk index	SPSUKHYT Index
3	US Generic Govt Bond 10 YR	USGG10YR Index
4	FTSE Sukuk Index	SBKU0P Index
5	S&P Middle East and North Africa (MENA) SUKUK	SPBDSMNT Index
6	Gulf Cooperation Council (GCC) Bond Index	H30738EU Index
7	Global Aggregate Bond Index	LEGATRUU Index
8	S&P Middle East and North Africa (MENA) Bond Index	SPMNAHY Index
9	Dow Jones Sukuk AP	DJSUKB Index
10	UK BOND	UK BOND
11	Global death counts of COVID-19	GDC

Sukuk and bons data were sourced from DataStream, while the GDC data were sourced from official government sources and the WHO.

presents details of variables used in this study.

3.2. Wavelet Coherence

This study was intended to determine the co-movement and lead–lag relation between the bond and Ṣukūk indices at different investment frequencies and time scales. For this purpose, we applied a wavelet coherence approach to examine the correlation patterns between these series in the given time–frequency domains. Specifically, we applied the continuous wavelet transform approach employing a bivariate framework (Morlet set to 6). A technique used in [49,50] allows for various kinds of localization in data. Given its ability to decompose co-movements (time-varying) into various investment horizons, this technique allowed us to examine the correlational patterns among financial series without subdividing the data into different periods. Furthermore, it was also an attractive avenue for providing tailored fit strategies to investors with different investment horizons. Compared to standard econometric models, which separately analyze frequency and time components, the wavelet approach simultaneously provides a three-dimensional analysis, including of the frequency, time, and strength of correlation between these components.

In summation, the wavelet approach has four main advantages: (I) Instead of assuming static relationships between financial series, it allowed us to compute and analyze the dynamic relations [51]; (II) it allowed us to identify the structural breaks in financial series and total radical shift in correlation/frequencies; (III) it allowed us to determine the causal relations at different frequencies; and (IV) it is a model-free approach, so it is more flexible than methods that have restrictions due to the number of parameters and elected estimation model [52]. The model’s econometric equation is as follows [49]:

$$R_n^2\left(S\right)=\frac{|s \left(s^{-1}{W}_n^{XY}\left(S\right)\right){|}^2}{s(s^{-1}|W_n^X\left(S\right){|}^2. S(s^{-1}|W_n^Y\left(S\right){|}^2}$$

(1)

In this equation, ‘S’ is used as a smoothing operator. The smoothing is achieved by bringing convolution in scale and time. This is a necessary step. Without smoothing, the wavelet coherence will equal 1 at all estimated scales and times.

$$S\left(W\right)=S_{scale} \left(S_{time}\left(Wn\left(s\right)\right)\right)$$

(2)

The operators S_time and S_scale in the equation denote smoothing in the time and scale axes, respectively. These smoothing operators were obtained from the work of [53]. Usually, a smoothing operator is used based on the elected wavelet model. Here, we used the Morlet wavelet approach, so we opted for these operators as they have similar characteristics to the applied model.

$$S_{time} \left(W\right) {\displaystyle |}s=\left(Wn \left(s\right)\times c_1^{\frac{-t^2}{2s^2}}\right) ; S_{time} \left(W\right) {\displaystyle |}s=Wn \left(s\right)\times c2 \mathrm{\Pi }\left(0.6s\right)) {\displaystyle |}s$$

(3)

where C₁ and C₂ are normalization constants and the term Π denotes the rectangle function. As the applied model was the Morlet wavelet, the scale decorrelation length was 0.6 factors [54].

The coefficient in wavelet coherence is used to measure the linear correlation between two stationary series at each given scale, and it ranges from 0 ≤ $R_n^2$(S) ≤ 1. $W_n^{XY}$ is the cross-wavelet power, which helps to uncover regions in time-scale spaces that specifically have a high common power between time series. Below is the cross-wavelet power depiction of two time-series y (t) and x (t):

$$W_n^{XY}\left(S\right)=W_n^X\left(S\right)W_n^{*Y}\left(S\right)$$

(4)

The term * expresses the complex conjugate and $W_n^X$ (S) and $W_n^{*Y}$ denote the continuous wavelet transform of these two series y (t) and x (t), respectively.

$${\varphi }_n^{XY}=tan-1(\frac{I\left\{S\left(s^{-1}{W}_n^{XY}\left(s\right)\right)\right\}}{R\left\{S\left(s^{-1}{W}_n^{XY}\left(s\right)\right)\right\}}$$

(5)

Here, the terms ‘R’ and ‘I’ represent the real and imaginary parts of the smooth power spectrum, respectively.

4. Results and Discussion

4.1. Descriptive Analysis

Table 2. Descriptive statistics.

Dow Jones Sukuk	Dow Jones Sukuk	Global Aggregate Bond	US Bond	GCC Bond	SPMENA Bond	SPGCC Sukuk	FTSE Sukuk	SPMENA Sukuk	Dow Jones Sukuk AP	UK Bond
Mean	0.0000	0.0001	0.0003	0.0002	0.0002	0.0002	0.0004	0.0002	0.0000	0.0001
Standard Error	0.0001	0.0000	0.0004	0.0001	0.0003	0.0001	0.0002	0.0000	0.0000	0.0001
Median	0.0000	0.0002	0.0000	0.0002	0.0002	0.0003	0.0003	0.0002	0.0001	0.0000
Standard Deviation	0.0038	0.0032	0.0278	0.0037	0.0067	0.0029	0.0067	0.0012	0.0013	0.0056
Sample Variance	0.0000	0.0000	0.0008	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Kurtosis	812.9143	5.3573	36.7246	34.4013	24.5524	37.5656	31.0893	15.0393	18.8884	8.4814
Skewness	−14.6381	−0.0175	0.1715	−0.7949	−2.9852	−2.9764	0.6563	−1.2334	−1.8871	0.4653
Range	0.2320	0.0502	0.7500	0.0745	0.0942	0.0580	0.1383	0.0198	0.0211	0.0961
Minimum	−0.1566	−0.0220	−0.3435	−0.0401	−0.0605	−0.0365	−0.0522	−0.0117	−0.0138	−0.0330
Maximum	0.0754	0.0282	0.4065	0.0344	0.0337	0.0215	0.0861	0.0082	0.0073	0.0631
Sum	0.0910	0.5752	−1.1438	0.4735	−0.0895	0.4598	0.5139	0.3380	0.0205	0.3098

contains a descriptive analysis of different Sukuk and bond indices. As per the statistics, the maximum mean return was 0.0039%, which was obtained from the FTSE Sukuk index. Furthermore, a minimum return of 0.000009367% was given by Down Jones Sukuk AP. Moreover, these indices differed in their maximum and minimum daily yields, with the highest maximum daily yield offered by the US Bond of 0.4064% and the lowest daily yield of 0.007329% belonging to Do Jones Sukuk Ap. The standard deviation of these indices ranged from 0.02784% (highest: US Bond) to 0.001178% (lowest: SPMENA Sukuk).

Similarly, the maximum median yield of conventional bonds varied from the highest at 0.000250% (SPMENA Bond) to the lowest at 0.000009563% (UK Bond). Meanwhile, in Sukuk, the maximum median yield belonged to FTSE Sukuk (003087%) and the lowest median yield of 0.0000250% belonged to Dow Jones Sukuk. In detail, this analysis demonstrates an ambiguous image concerning these indices’ risk and return aspects. For instance, although FTSE Sukuk indices were found to offer the highest mean return and median yield, they also had the highest risk (standard deviation was assumed based on conventional bonds (US Bond)). These ambiguous findings illustrate the need for further thorough analysis.

Table 3. Correlation matrix.

Correlation Matrix	Dow Jones Sukuk	Global Aggregate Bond	US Bond	GCC Bond	SPMENA Bond	SPGCC Sukuk	FTSE Sukuk	SPMENA Sukuk	UK Bond
Dow Jones Sukuk	1
Global Aggregate Bond	0.0361	1
US Bond	−0.0131	−0.1030	1
GCC Bond	−0.0162	−0.0629	0.0621	1
SPMENA Bond	0.0241	0.0338	−0.0392	0.2755	1
SPGCC Sukuk	0.1844	0.0749	0.0126	0.0492	0.3058	1
FTSE Sukuk	0.0996	0.1407	0.0368	0.0720	−0.0766	0.1904	1
SPMENA Sukuk	0.2359	0.1095	−0.0453	0.0098	−0.0001	0.2350	0.2077	1
UK Bond	−0.0363	−0.0227	−0.0067	0.0651	0.0355	−0.0399	−0.0381	−0.0529	1

shows the results of a correlation analysis between the Sukuk and bond indices. Our analysis indicated the presence of the highest level of correlations between the SPMENA Bond and SPGCC Sukuk indices. However, the lowest correlation (negative) was found among Global Aggregate Bond and US Bond. Though this analysis provided an absolute reflection of the correlation pattern among these indices, it lacked frequency and time components. Thus, to provide more robust analysis, we analyzed the same patterns using the wavelet transform approach, as presented in a later section. The wavelet approach provided a three-dimensional analysis, including the frequency, time, and strength of correlation between these components.

To aid understanding of the relative co-movement/volatility between intended fixed income indices and COVID-19 deaths, Figure 1 demonstrates the wavelet coherency between each pair of selected variables. The colors depict the regions with high and low correlations among the series. The warmer colors (e.g., red) represent higher correlation regions, while the colder colors (e.g., blue) express a lower correlation or dependence between series.

In the 4–8-days frequency bands shown in Figure 1, we can detect the presence of minute but strong chunks of correlations between COVID-19 deaths and all given Ṣukūk and bond indices throughout the sample period. We can further detect the presence of small co-movement between COVID-19 and the Dow Jones Ṣukūk AP, SPGCC Ṣukūk, and Dow Ṣukūk indices during the Sep–Oct periods in the 16-day frequency band. Though there was considerable co-movement found in conventional bond indices (GCC Bond, SPMENA Bond, and Global Aggregate Bond indices) during the September–October period (16-day band), the intensity was lower in the mentioned indices. Furthermore, we noticed a consistent presence of a huge chunk of co-movement in 32–64 frequency bands for all indices. The dependence was shown to remain persistent from around mid-January to mid-September for most Ṣukūk indices (except for FTSE Ṣukūk). However, the in conventional bond indices, the co-movement ended around July–August. This prolonged correlation signifies the impact of COVID-19 on all low-frequency band (higher investment period, i.e., 32–64 days) indices. It also indicates the presence of similar strong implications of the initial shock of COVID-19 deaths on both Islamic and conventional markets. However, after the initial shock, the indices were able to mitigate the initial strong dependence (though slower in the case of Islamic indices).

Given its strict and conservative shariah-based screening criteria, it has been hypothesized that Islamic finance is less volatile to these crises than its traditional counterparts. However, in our study, the relative intensity of COVID-19 deaths was found to be more persistent for Ṣukūk indices than the bond indices. These findings contradict the results of [30,31,32,33], which declared Islamic indices more resilient against crises. This long-lasting impact of COVID-19 on Islamic indices can be attributed to the following facts. First, compared to other crises, the financial implications of COVID-19 on different sectors and assets, including shariah-based assets, were relatively critical [36]. Secondly, oil prices sharply plunged during the price war between Saudi Arabia and Russia in 2020, which coincided with COVID-19, as the oil demand further declined due to the global traveling ban. Moreover, since most of these oil companies belong to the Middle East and constituted a significant proportion of our sample size (Islamic indices), the huge impact of these COVID-19 crises on given Ṣukūk indices is understandable.

The results of several studies support our findings [27,28,29,34] that Islamic indices do not show lower volatility than conventional indices during crises. Recent studies also showed huge implications of COVID-19 on Islamic and conventional stock indices, e.g., [36,37,38].

In Figure 2, we examine the cross coherence between different combinations of Ṣukūk and bond indices. At first glance, most of these are shown to have had a lower level of correlations, with a few exceptions such as GCC Bond and FTSE Ṣukūk, Global Aggregate Bond and FTSE Ṣukūk, and GCC Bond and SPMENA Ṣukūk. In these cross-comparisons, we found a strong dependency among mentioned indices, specifically in trading periods of 64–256 days.

In Figure 2A, we evaluate the correlation between the US Bond and SPGCC Ṣukūk indices. Our analysis demonstrated a small dependency between given indices in most trading bands. This low level of correlation demonstrates a portfolio diversification opportunity for US bondholders in the GCC Ṣukūk market in low investment bands (4, 16, and 64). However, in the 128–256 frequency band during the year 2018–2020, there was a high correlation between given indices, which hindered the diversification opportunity for long-term investors. Concerning lead–lag relations, the arrows point towards the right and upward direction in the 128-frequency band, which signifies both a positive correlation between series and that GCC Ṣukūk was leading US Bond. However, in the 256-day band, the arrows point in the right downward direction, which shows positive relations. Nevertheless, the US Bond index was stronger than GCC Ṣukūk here.

Figure 2B shows an evaluation of the co-movements between US Bond and FTSE Ṣukūk. An initial glance suggests a lower correlation between indices. Specifically, during 2015–2017 in the short-term investment bands (4–16 days), there were no signs of correlations between them. Hence, they offered a great diversification opportunity for US bondholders in the FTSE Ṣukūk market. However, from mid-2018 to 2020, there was a visible sign of high correlations between these indices in all given bands. Finally, for long-term investors, i.e., 256-day investment band, there was no global diversification opportunity in these markets. Throughout the sample periods, the US and UK indices were highly correlated with each other (evidently due to the existing high co-integration between the US and UK financial markets). Regarding the lead–lag relations, during the mid-2018-to-2020 high-correlation periods, they were inversely correlated with one another (16–32–64 bands), and FTSE Ṣukūk was leading US Bond. However, in the 256-days long-term investment band, the series was in-phase (positive correlations), and US Bond was leading FTSE Ṣukūk.

Figure 2C,D shows an examination of the correlation and lead–lag relation between (1) US Bond and Dow Jones Ṣukūk and (2) SPMENA Ṣukūk and UK Bond, respectively. In the first figure, one can observe a high correlation between US Bond and Dow Jones Ṣukūk at the investment bands of 32–64–256 days. The arrow sign between these indices points towards the left downward side, which means these indices were negatively correlated. Consequently, they still offer diversification benefits to long-term US investors in the Dow Jones Ṣukūk market. Moreover, Dow Jones Ṣukūk is shown to have been leading US Bond here. Additionally, in short-term investment horizons (4–16 days), there was a very minute sign of the correlation. Therefore, for a short-term investment, this market offers an appropriate diversification strategy for investors.

Similarly, Figure 2D illustrates the co-movement of SPMENA Ṣukūk and UK Bond. Based on the given analysis, there were overall low correlations between them. However, at 64- and 256-day investment bands, there were some red islands of correlations throughout the sample, as the arrows point towards the left side. Hence, they were inversely correlated with one another. So overall, these two series offer appropriate opportunities for SPMNEA Ṣukūk holders to diversify in UK Bond.

Figure 2E–H presents an analysis of the following indices: (1) SPGCC Ṣukūk and UK Bond, (2) Global Aggregate Bond and Dow Jones Ṣukūk AP, (3) Global Aggregate Bond and SPMENA Ṣukūk, and (4) Global Aggregate Bond and SPGCC Ṣukūk. In Figure 2E, due to the low correlations, one can observe a high possibility of diversification benefits for GCC Ṣukūk holders in the UK Bond market except for in 2013, where there was a small sign of high correlation in investment band 32–64–128. Similarly, in the 256-day investment band, from 2018 to 2020, SPGCC Ṣukūk holders were not able to obtain diversification benefits from the UK Bond market. Additionally, these two markets were found to offer an exceptional opportunity for risk-averse investors. Both series were in phase (positive correlations) in the given correlations, and SPGCC Ṣukūk was found to lead UK Bond. Likewise, Figure 2F shows the same relation in the context of Global Aggregate Bond and Dow Jones Ṣukūk indices. In this analysis, the relationships were found to be relatively more rigorous and provide fewer chances for Global Aggregate bondholders to diversify in Dow Ṣukūk due to strong correlations. Except in low investment horizons (4–16 bands), there were consistently high correlations in all given high investment bands (64–128–256) for all sample periods, which signifies lower diversification benefits in the market. In established correlations, the series was in phase (positive correlations), with Dow Ṣukūk leading global bonds most of the time.

Similarly, Figure 2G shows the correlation between the Global Aggregate Bond and SPMENA Ṣukūk. The analysis demonstrated some signs of strong correlations in medium-to-high investment bands (64–256) throughout the period. Moreover, the arrows point in the right direction in these chunks of strong correlations. Hence, there was a positive correlation, with SPMENA Ṣukūk leading Global Aggregate Bond here. Thus, there were no globalized diversification benefits for global bondholders in the SPMENA Ṣukūk markets. However, in short-term horizons (4–16), investors could still obtain the diversification benefits here due to low correlations. Figure 2H illustrates the co-dependency between the Global Aggregate Bond and SPGCC Ṣukūk. In this figure, except in the year 2013 (64-day investment band with a rightly pointed arrow (positive correlation)) and the year 2019–2020 (16–64–256 investment bands with the rightly pointed arrow (positive correlation), we found low correlations in all bands and periods. Therefore, overall Global Aggregate bondholders could obtain diversification benefits from the SPGCC Ṣukūk market.

Figure 2I–L shows the following indices: (1) Global Aggregate Bond and FTSE Ṣukūk, (2) GCC Bond and SPMENA Ṣukūk, (3) GCC Bond and SPGCC Ṣukūk, and (4) GCC Bond and FTSE Ṣukūk. Figure 2I presents an exploration of the correlations between global bonds and FTSE Ṣukūk. The prevailing low correlations indicate the possibility of diversification benefits for global bondholders in the FTSE Ṣukūk market. Our analysis also demonstrates that for 2018–2020, there was a high correlation in the 16–64–128 investment band. Therefore, in these years, investors were not able to gain diversification benefits as the direction of their correlations was also positive, with FTSE Ṣukūk leading Global Aggregate Bond.

Similarly, for the maximum investment period (256 bands), there was a continuous high correlation throughout the period, which also negates any long-term diversification benefits for global bond investors in the FTSE Ṣukūk market. Additionally, both series showed low correlations. Figure 2J shows the co-movements between GCC Bond and SPMENA Ṣukūk. Our analysis indicated the presence of a relatively high correlation compared to previous indices. Due to these high correlations in medium-to-long investment bands (16–64–256), there was a low possibility of diversification benefits for GCC bondholders in SPMENA Ṣukūk markets. The lead–lag relations were found to be dynamic here, as there changed throughout time. In the 32 frequency bands, they were in anti-phase (negative correlations). However, in the 64 and 256 bands, the relationship between series was positive. However, there were no correlations in short-term investment periods (4–16), so short-term investors could still gain diversification benefits.

Likewise, Figure 2K shows the correlations between the GCC Bond and SPGCC Ṣukūk indices. In this series, we observed high correlations in the long investment horizon (256 days) band from 2017 to 2020. Then, from mid-2019 to 2020, we again found high correlations in medium-to-long investment (64–128–256) bands. So, in these mentioned bands, GCC Bond investors obtained no diversification benefits in the SPGCC Ṣukūk market. Other than these mentioned bands and periods, there was a low correlation, so they provided diversification benefits for investors.

Moreover, concerning lead–lag relations, in all the mentioned high-correlation bands, the series was in phase, and SPGCC Ṣukūk led the GCC Bond as the arrows point in the upward right direction. Next, Figure 2L illustrates the analysis of GCC Bond and FTSE Ṣukūk. During 2016–17 and mid-2018, GCC bondholders had diversification opportunities in the FTSE Ṣukūk market at all investment horizons. Nevertheless, after 2018–2020, there was a high correlation between GCC Bond and FTSE Ṣukūk, thus offering no diversification benefits for investors during that time. In this high-correlation period, the arrows point towards the right but in an upward direction. Hence, the series were in phase, and FTSE Ṣukūk indices were leading GCC Bond.

In most analyses, the long-term investment bands tended to be highly correlated, which signified lower diversification opportunities. Nevertheless, in short-term bands (4–16), most comparisons indicated the presence of low correlation among indices, leading to diversification opportunities. Our findings are somewhat supported by [55,56,57], which also showed the Ṣukūk market to be an appropriate venue for portfolio diversification in short-term investment horizons.

4.2. Comparison among Bond Indices

For Figure 3, we thoroughly analyzed the co-movement and lead–lag tendencies between the following bond indices: (1) US Bond and UK Bond, (2) Global Aggregate Bond and US Bond, (3) Global Aggregate Bond and GCC Bond, (4) GCC Bond and UK Bond, (5) US Bond and GCC Bond, and (6) GCC Bond and SPMENA Bond. Figure 3A, illustrating the analysis of US Bond and UK Bond, depicts a strong correlation between the given indices for almost all investment bands (16–64–256–1024) throughout the sample period. However, the arrows in the given correlations point towards the left side, which signifies a negative correlation between the US Bond and UK Bond indices. Therefore, despite the high correlation, the UK Bond market still offered superior diversification opportunities for US bondholders. Similarly, Figure 3B illustrates a similar analysis in the context of the Global Aggregate Bond market and US Bond. Based on the analysis, the US Bond offered a suitable diversification strategy for Global Aggregate bondholders, as the correlation between the indices was mostly minimal for different investment bands. Even in high-correlation segments such as the 64–256 investment band during 2006–2009 and 16–64–256 bands during 2011–2019, the arrows are in opposite directions. The opposite arrows signify the negative correlation between indices. Thus, these indices still offered diversification opportunities. In terms of lead–lag relation, the direction of arrows is left and upwards, demonstrating that the Global Aggregate Bond led US Bond.

Figure 3C illustrates the relationship between Global Aggregate Bond and GCC Bond. In this figure, some small islands are shown to have had high correlations such as in investment band 16–64–128 during the year 2015–18. Moreover, during 2020 at investment band 16–64, there was a high correlation among these indices. So, in these bands and periods, the global bondholders were not able to obtain diversification benefits from the GCC Bond indices. Concerning the lead–lag relations, the given arrows point in the right downward direction, which suggests a positive correlation between indices and that global bonds led GCC bonds here. Additionally, both markets complemented each other and offered suitable diversification opportunities for investors. Figure 3D illustrates an analysis of the GCC Bond and UK Bond indices. Based on the graphic illustration, the low-correlation part (yellowish area) overwhelmed the high-correlation portion (red area), suggesting that GCC bondholders had an enhanced opportunity to safeguard their investment through diversification in UK Bond markets. However, some portions of high correlations were found in the medium investment band (128) from 2015 to 2017 and short investment bands (16–32 days) during 2019. Therefore, the markets did not offer diversification opportunities in these bands and periods. Furthermore, the arrows point in the downward right direction, which signifies that the GCC Bond index led the UK Bond index and that there was a positive correlation between them.

Finally, Figure 3E illustrates an analysis of the same relations in the context of GCC Bond and SPMENA Bond. In this analysis, we found a high correlation between indices, and the nature of their lead–lag relations was dynamic. During the low/medium investment band (4–16–32–64), the arrows point in the right upward direction, suggesting a positive correlation between SPMENA Bond led GCC Bond. In long investment band 128, the arrows point in the right downward direction, which again suggests a positive correlation, but GCC Bond led SPMENA Bond here. Due to the positive and high correlation between indices, we cannot assume that SPMENA Bond indices were a lucrative diversification option for GCC bondholders.

In most cases, the reported correlation was low, with more diversification opportunities for investors, while the level of integration was higher in long-term investment horizons compared to short ones; these results are also supported by previous studies [58]. Moreover, the overlapping entities in both indices could have caused the high correlations (GCC Bond and SPMENA Bond). Similarly, correlations between the US Bond and UK Bond might have been due to the proximity of their economies.

4.3. Comparison among Ṣukūk Indices Image

For Figure 4, we examined the co-dependencies and lead–lag relations among the following Ṣukūk indices: (1) SPGCC Ṣukūk and SPMENA Ṣukūk, (2) SPGCC Ṣukūk and FTSE Ṣukūk, (3) FTSE Ṣukūk and SPMENA Ṣukūk, (4) Dow Jones Ṣukūk and SPMENA Ṣukūk, (5) Dow Jones Ṣukūk and Dow Jones Ṣukūk AP (aggregate), and (6) Dow Jones Ṣukūk and FTSE Ṣukūk. Figure 4D,E show that the nexuses between Dow Ṣukūk and SPMENA Ṣukūk and between Dow Ṣukūk and Dow Ṣukūk AP showed the highest levels of correlation. Therefore, in these indices, investors could not develop an effective diversification strategy. However, Figure 4A illustrates the analysis of SPGCC Ṣukūk and SPMENA Ṣukūk, showing that they offered diversification opportunities for short-term GCC Ṣukūk investors (4–16 investment bands) in the SPMENA Ṣukūk market. Nevertheless, in the long-term investment band (256), our analysis showed extremely high correlations in the given indices throughout sample periods (2014–2020) and, consequently, no diversification opportunity for long-term investors. The arrows in the given correlations point in the right downward direction (except in 16–64 bands during 2019, when arrows point in the upward direction), which suggests a positive correlation among indices, along with an indication of SPGCC Ṣukūk leading SPMENA Ṣukūk.

Likewise, Figure 4B illustrates the co-movement relations among the SPGCC Ṣukūk and FTSE Ṣukūk indices. In this figure, most of the parts are shown to have had low correlations. Overall, this indicates an effective diversification opportunity for GCC Ṣukūk holders in the FTSE Ṣukūk market. However, in 128 investment bands during 2016–2017 and investment bands 16–64–256 during 2018–2020, we found evidence of high correlations and thus the possibility of no diversification benefits. In these high-correlation bands, the arrows are mostly pointing in the right downward direction, which signifies the presence of strong positive correlations among series and that SPGCC Ṣukūk led the FTSE Ṣukūk market. Figure 4C specifies the same relations in the context of the FTSE Ṣukūk and SPMENA Ṣukūk indices. In the 16–64–256 investment bands during 2017–2020, we found signs of high correlations among the FTSE Ṣukūk and MENA Ṣukūk indices. Therefore, in these periods, investors could not gain diversification benefits in these markets. The arrows shown in the given correlations are pointing in the right-downward direction (positive correlations, with FTSE Ṣukūk leading SPMENA Ṣukūk) in high investment bands (128–256). In low investment horizons (16–32–64), the arrows are pointing in the right upward direction (positive correlation, with SPMENA Ṣukūk leading FTSE Ṣukūk), which suggests the signs of dynamic lead–lag relations among indices.

The reported high correlations between different Ṣukūk indices negate the argument established in [59,60,61] that the unique characteristic of Islamic markets and instruments may lessen overall co-integration between these Islamic markets. Instead, these unique features, i.e., prevention of cross hedging, speculations, and arbitrage opportunities, have no significant influence on the overall co-movement tendencies of these Islamic indices [21].

5. Conclusions and Policy Implications

The authors of this study explored the lead–lag relation and co-movement between the conventional and Islamic bond (also called Ṣukūk) indices. Understanding the lead–lag relations and co-movements among indices is essential for financial decision making, as it demonstrates the reactiveness of the market towards new information. Furthermore, it helps to minimize risk exposure and facilitates optimal portfolio diversification. We studied the mentioned linkages between bond and Ṣukūk indices belonging to the United States (US), United Kingdom (UK), Middle East and North Africa (MENA), and Gulf Cooperation Council (GCC) countries by applying the wavelet coherence model.

The findings indicated the presence of strong but similar implications of the initial shock of COVID-19 deaths on both Islamic and conventional markets, especially in long-term investment bands (64–128 investment frequencies). However, after the initial shock, the indices were able to mitigate the initial strong dependence from mid-2020 to mid-2021; we found no dependency between indices and COVID-19 deaths. However, the intensity of this co-movement with COVID-19 deaths was longer in Ṣukūk indices than in the bond indices. These results oppose the general belief that Islamic finance is less volatile to crises than its traditional counterparts. Moreover, our findings oppose conclusion presented in [30,31,32,33] that Islamic indices are more resilient against crises. Instead, in this study, the relative intensity of COVID deaths was more persistent for Ṣukūk indices than bonds, which was supported by the result of [27,28,29] suggesting that Islamic stock indices do not show a lower volatility than conventional indices during crises. Thus, given the similar volatilities of Islamic and conventional bonds in distress periods, our findings provide valuable insights to investors by opposing the general proposition about the Islamic instruments as a safe haven for investment during a crisis.

In this study, we found diverse relationships among indices regarding global diversification opportunities for different markets at numerous investment horizons. Especially in short-term investment bands (4–16), we consistently found the presence of low correlations, leading to optimal diversification opportunities. However, in the medium-to-long investment bands, the results varied based on the time. For instance, in most high investment bands (128–256), we found some occurrence of low correlations. Hence, the markets provided diversification opportunities for investors, e.g., US Bond and Dow Jones Ṣukūk, FTSE Ṣukūk and UK Bond, and SPMENA Ṣukūk and UK Bond. Our findings are supported by [55,56,57], which also showed the Ṣukūk market to be an appropriate venue for portfolio diversification. However, in recent times (2019–2020), we observed continuous high correlations (i.e., Global Aggregate Bond and SPGCC Ṣukūk, US Bond and SPGCC Ṣukūk, GCC Bond and SPGCC Ṣukūk, and SPGCC Ṣukūk and UK Bond), which may have resulted from the recent COVID-19 crisis.

Similarly, high correlations found in 2014 (global oil prices dropped in June) and 2020 could have originated from the oil price war between Saudi Arabia and Russia, influencing the whole MENA and GCC region (which constituted a massive part of our sample size). However, the rationale for these high correlations was out of the scope of this study and may be an attractive avenue for future researchers. Moreover, we noticed a dynamic relationship concerning the lead–lag relations among the indices, which were shown to change over time and investment horizons. Furthermore, owing to the rapid growth of the Ṣukūk sector in the GCC and MENA regions, along with the ever-growing interest from non-Muslim countries (e.g., the US and the UK), these findings provide valuable insights for the Ṣukūk issuers and policymakers. Thus, understanding the changing pricing patterns, volatilities, lead–lag relations, and other intricacies of this relatively new market is essential for investors who want to design their optimum portfolios through globalized diversification strategies. Furthermore,

Table A1. Global diversification opportunities in Ṣukūk and bond indices.

Does the Market Provide Diversification Opportunities for Investors?
Investment Bands	4 Days	16 Days	64 Days	128 Days	256 Days
US Bond and SPGCC Ṣukūk	Yes: due to low correlations	Yes: due to low correlations	Yes: due to low correlations	Note: during recent years, 2018–2020	Note: during recent years, 2018–2020
US Bond and FTSE Ṣukūk	Yes: during 2015–2017	Yes: during 2015–2017	Yes: during 2018–2020 due to inverse correlations	Yes: no correlations were found throughout the periods	No: due to high positive correlations
US Bond and Dow Jones Ṣukūk	Yes: due to low correlations	Yes: due to low correlations	Yes: high but inverse correlations	Yes: High but inverse correlations	Yes: high but inverse correlations
SPMENA Ṣukūk and UK Bond	Yes: due to low correlations	Yes: due to low correlations	Some small islands of high but inverse correlations	Yes: due to low correlations	Yes: due to Some small islands of high but inverse correlations
SPGCC Ṣukūk and UK Bond	Yes: due to low correlations	Yes: due to low correlations	Yes: except in 2013	Overall, yes: except in 2013	Overall, yes: except in 2018–2020
Global Aggregate Bond and Dow Jones Ṣukūk AP	Yes: due to low correlations	Yes: due to low correlations	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period
Global Aggregate Bond and SPMENA Ṣukūk	Yes: due to low correlations	Yes: due to low correlations	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period
Global Aggregate Bond and SPGCC Ṣukūk	Yes: due to low correlations	Yes: except during 2019–2020	Yes: except during 2013 and 2019–2020	Yes: except during 2019–2020	Yes: except during 2019–2020
Global Aggregate Bond and FTSE Ṣukūk	Yes: due to low correlations	Overall, yes: except during 2018–2020	Overall, yes: except during 2018–2020	Overall, yes: except during 2018–2020	No: due to high correlations throughout the sample period
GCC Bond and SPMENA Ṣukūk	Yes: due to low correlations	Yes: due to low correlations	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period
GCC Bond and SPGCC Ṣukūk	Yes: due to low correlations	Yes: due to low correlations	Overall, yes: except in 2019–2020	Overall, yes: except in 2019–2020	Overall, yes: except in 2017–2020
GCC Bond and FTSE Ṣukūk	Yes: due to low correlations	Yes: but only during 2016–17 and mid-2018	Yes: but only during 2016–17 and mid-2018	Yes: but only during 2016–17 and mid-2018	Yes: but only during 2016–17 and mid-2018
GCC Bond and Dow Jones Ṣukūk AP	Yes: due to low correlations	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period	No: due to high correlations throughout the sample period
FTSE Ṣukūk and UK Bond	Yes: due to low correlations	Yes: due to low correlations	Yes: due to low correlations	Yes: due to low correlations	Yes: due to low correlations, except in 2020
Dow Jones Ṣukūk and UK Bond	Yes: due to low correlations	Yes: due to low correlations	No: due to frequent chunks of high correlations	Overall, yes: except during 2013–2015	No: during 2013 to 2015 and 2017 to 2020
US Bond and SPMENA Ṣukūk	Yes: due to low correlations	Yes: due to low correlations	Yes: except during the year 2014–2015, 2016–2017, and 2019	Yes: due to low correlations	Overall, yes: except from 2014 to 2020

in Appendix A summarizes different diversification opportunities for investors in global bond and Sukuk markets based on their given correlations at different periods.

Additionally, the recent financial crises and the inability of conventional instruments such as bonds to cope with them have caused a huge demand for innovative alternatives in financial instruments. In this regard, Ṣukūk can provide an effective/unique option for both kinds of investors (Islamic and non-Islamic fund holders). Until now, Ṣukūk has operated on a niche market, but through effective policymaking, it has the potential to become a thriving avenue for global investors due to its unique risk-sharing and other characteristics. Thus, the findings of this study provide valuable insights for the regulators and policymakers regarding the importance of this tool in imminent markets.

Additionally, since diversification benefits are entirely dependent on these changing correlation patterns at different investment horizons and time scales, this study provides a thorough roadmap to investors for their hedging strategies based on their specific investment needs. As a theoretical contribution, this study adds knowledge to the literature on the financial crisis by signifying how non-economic and non-financial factors (such as COVID-19) influence the level of volatility in fixed income indices. Furthermore, this study also adds new knowledge about the nexus between sovereign Ṣukūk and bonds, as well as their level of integration.

Moreover, to bring sustainability to this emerging market, the authors of this study would like to propose some suggestions. For instance, the emergence of this COVID-19 pandemic demonstrates the necessity for digitalization, e.g., it critical for institutions to have the ability to perform their functions online. We believe that the current trends present an enormous opportunity for Islamic/conventional institutions to have a presence in untouched markets through sophisticated fintech collaboration to digitalize all core functions. Additionally, we firmly believe in the inclusivity of this industry throughout the world, especially regarding the legal and shariah framework in the standardization process. There should not be any ambiguity or concerns regarding the legality and compliance of shariah rules in issued Islamic instruments (i.e., Sukuk) in different markets.