Comparative Analysis of Risk Between
Conventional Bonds and Sukuk Using Duration-Normal VaR
Noor-Ul-Hacq Sookia Associate
Professor, PhD Mathematics, Department of Mathematics, Faculty of Science, University
of Mauritius, Réduit, Mauritius (sookian@uom.ac.mu) https://orcid.org/0000-0002-3155-0473
Sheik Ahmad
Ryman Bissessur
PhD Financial Modelling, Department of
Finance and Accounting, Faculty of Law and Management, University of
Mauritius, Réduit, Mauritius (a786_sheik@yahoo.com)
https://orcid.org/0000-0001-9657-1999
Received: 15/9/2025 Peer-reviewed: 11/2/2026 Accepted: 17/2/2026
Abstract
Purpose: Islamic
finance and Sukuk have garnered so much interest in recent times that not just
Islamic countries, but also Western countries have started trading in
Sukuk. This research paper aims to
assess whether Sukuk can bring benefits to investors in terms of reduced market
risks when added to a portfolio of conventional bonds.
Methodology: The research employed
the Duration-Normal Value-at-Risk (VaR) Model.
Findings: Using the
Duration-Normal VaR model, it has been found that the market risk associated
with the mixed portfolio through the addition of Sukuk to the conventional bond
was significantly lower than that of a pure bond portfolio. This could be explained by the low
correlation between the conventional bonds and Sukuk. The accuracy of the Duration-Normal VaR model
has been confirmed by the Kupiec Proportion of Failure Test.
Originality: This paper
provides a different view on applying the Value-at-Risk (VaR) approach for assessing
the market risk associated with Islamic and conventional bonds and further
applies a backtesting procedure to examine the accuracy of the model.
Keywords: Sukuk; Market
Risk; Value-at-Risk; Duration-Normal Model, Back-testing Procedures
Cite this article as: Sookia, N. and
Bissessur, S. A. R. “Comparative Analysis of Risk
Between Conventional Bonds and Sukuk Using Duration-Normal VaR)”, Journal of College of Sharia and Islamic Studies, Qatar
University, Vol. 44, Issue 2 (2026). https://doi.org/10.29117/jcsis.2026.0456
© 2026, Sookia, N. and Bissessur,
S. A. R. Published in the Journal of the
College of Sharia and Islamic Studies. Published by QU Press. This article
is published under the terms of the Creative Commons Attribution-NonCommercial
4.0 International (CC BY-NC 4.0), which permits non-commercial use of the
material, appropriate credit, and indication if changes in the material were
made. You can copy and redistribute the material in any medium or format as
well as remix, transform, and build upon the material, provided the original
work is properly cited. The full terms of this license may be seen at: https://creativecommons.org/licenses/by-nc/4.0
نور
الحق سوكيا
أستاذ
مشارك،
دكتوراه في
الرياضيات،
قسم الرياضيات،
كلية العلوم،
جامعة
موريشيوس، ريديو-موريشيوس
https://orcid.org/0000-0002-3155-0473
الشيخ
أحمد ريمان
بيسسور
دكتوراه في
النمذجة
المالية، قسم
المالية
والمحاسبة،
كلية القانون
والإدارة،
جامعة
موريشيوس،
ريديو-موريشيوس
https://orcid.org/0000-0001-9657-1999
تاريخ
الاستلام: 15/9/2025 تاريخ
التحكيم: 11/2/2026 تاريخ
القبول: 17/2/2026
ملخص
البحث
أهداف
البحث: يهدف
البحث إلى
تقييم ما إذا
كان إدراج
الصكوك ضمن
محفظة من
السندات
التقليدية
يمكن أن يحقق
فائدة
للمستثمرين
من حيث خفض
مخاطر السوق.
منهجية
البحث: اعتمد
البحث نموذج
القيمة
المعرضة
للخطر
الطبيعي
القائم على
المدة.
النتائج:
أظهرت
النتائج،
باستخدام
نموذج القيمة
المعرضة
للخطر
الطبيعي
القائم على
المدة، أن مخاطر
السوق
المرتبطة
بالمحفظة
المختلطة الناتجة
من
إضافة الصكوك
إلى السندات
التقليدية،
كانت أقل
بدرجة ملحوظة،
مقارنة
بمحفظة تتكون
حصريًا من
السندات التقليدية.
ويمكن تفسير
ذلك بانخفاض
معامل الارتباط
بين السندات
التقليدية
والصكوك. كما جرى
التحقق من دقة
نموذج القيمة
المعرضة
للخطر الطبيعي
القائم على
المدة من خلال
اختبار نسبة
الإخفاق لكوبيك
(Kupiec Proportion of Failure Test).
أصالة
البحث: يقدم
هذا البحث
منظورًا
مختلفًا
لتطبيق منهجية
القيمة
المعرضة
للخطر (VaR) في
تقييم مخاطر
السوق
المرتبطة
بالسندات الإسلامية
والتقليدية، ويطبق
إجراء
الاختبار
الرجعي
(Backtesting) للتحقق
من دقة
النموذج.
الكلمات
المفتاحية:
الصكوك،
مخاطر السوق،
القيمة
المعرضة للخطر،
نموذج المدة
الطبيعي، إجراءات
الاختبار
الرجعي
للاقتباس: سوكيان،
نور الحق
وبيسسور الشيخ
أحمد. «تحليل
مقارن
للمخاطر بين
السندات
التقليدية
والصكوك
باستخدام
نموذج القيمة
المُُعرّضة
للخطر
الطبيعي
القائم على
المدة»، مجلة كلية الشريعة والدراسات الإسلامية، جامعة قطر، المجلد
44، العدد 2 (2026). https://doi.org/10.29117/jcsis.2026.0456
©2026، سوكيان
وبيسسور، مجلة كلية الشريعة والدراسات الإسلامية، دار نشر جامعة قطر. نشرت هذه المقالة البحثية وفقًا لشروط Creative Commons
Attribution-NonCommercial 4.0 International (CC BY-NC 4.0). تسمح هذه الرخصة بالاستخدام غير التجاري،
وتنبغي نسبة العمل إلى
صاحبه، مع بيان أي تعديلات عليه.
كما تتيح حرية نسخ،
وتوزيع، ونقل العمل بأي شكل من الأشكال،
أو بأي وسيلة،
ومزجه وتحويله والبناء عليه،
طالما ينسب
العمل الأصلي إلى المؤلف. https://creativecommons.org/licenses/by-nc/4.0
The concept of Sharia-compliant financial
transactions was laid by Prophet Muhammad ﷺ in his teachings of
Islam fourteen centuries ago, and before that, financial practices formed part
of what is referred to as social economics. The date of initiation of
conventional and Islamic finance is that the former broadened its horizons
around the 1950s, whereas the latter came to light in the 1970s when Islamic
scholars and jurists met to discuss the aspects of Riba (interest) on contracts
and removing its application in contracts and business financial transactions.
As part of financial offerings, Islamic finance comprises Islamic Investment
Funds, Takaful, Capital markets (Sukuk), and finally the main component, which
is Islamic banking with USD 3.88 trillion worth of total assets.[1]
Islamic finance soon gained such popularity
that it was present as of 2020 in more than 75 countries, mainly from the
Organization of Islamic Countries (OIC) and the Gulf Cooperation Council (GCC).[2] Even in academic research, Islamic banking
became a topic of major interest.[3] However, with such an expansion, the
operations and products in Islamic finance also became more complex, thus
requiring more regulations and operational standards. In view of aligning with the requirements of
capital adequacy under the global banking standards, the Islamic Financial
Services Board (IFSB) introduced the IFSB-23 standard. The value of the global Islamic Financial
Services Industry (IFSI) reached USD 3.88 trillion in 2024, representing a
year-on-year growth of 14.9%. Islamic
banking witnessed a growth of 17.05%, driven by stronger capital positions and
improved asset quality. Islamic insurance (Takaful) performed better than many
conventional insurance markets by growing at 16.9%. Finally, a 25.6% increase in new issuances in
the Sukuk (Islamic bond) market was recorded, which highlights solid sovereign
interest and investor demand.[4] Commenting on the impact of the 2008 global financial
crisis, some researchers stressed the resilience of the Islamic banking system.[5]
Sukuk is the plural
of the Arabic ‘sakk’, which means certificate or note. In other words, sukuk are Investment
Certificates. The Accounting and Auditing Organization for Islamic Financial
Institutions (AAOIFI) defines investment Sukuk under the Shariah standard 17 as
“certificates of equal value representing common rights or shares in the underlying
assets or their services and usufructs,”[6]
bearing similarity to that of the Islamic Financial Services Board 2 (IFSB).[7]
Islamic bond contracts can be classified into
agency-based, partnership/equity-based, lease-based, and sales-based.[8]
Furthermore, mixed portfolio Sukuk can be regarded as a fifth category.[9]
The desired bond combinations would define the risk-return profile of this
mixed portfolio.
Sukuk has been described as another way of
raising funds to finance positive expected return investments, thus allowing
access to the capital market,[10]
and it has been argued that Sukuk have some attributes of bonds and stocks
designed in a way to abide by Islamic rules and guidelines.[11]
Moreover, based on Islamic financial
contracts, Sukuk is a new instrument with a flexible structure, whereas a bond
works on the same traditional concept of an interest-bearing loan. It has been
argued that Sukuk is a financial instrument that is not interest-generating but
rather encourages investing in economic activities, which in turn will yield a
return derived from leasing or sharing ownership of assets.[12]
Furthermore, conventional bonds and Sukuk
also differ with respect to the risk aspect in investment. Sukuk targets
compliance risk from a Shariah-related perspective, related to the structure
that emanates from Islamic finance contracts. In addition to that, Sukuk also
faces risks such as market risk, commodity risk, liquidity risk, foreign
exchange risk, business risk, and credit risk.[13]
Following the changes in the monetary policy,
the global financial crisis of 2008 had a significant impact on the yields of
corporate and government bonds as well as on treasury bills. For example, the 10-year treasury bond yield
in the US dropped from 4.27% in June 2008 to 2.05% in December 2008,[14]
when the Federal Reserve decided to reduce interest rates to stimulate economic
activity through consumer spending and financing mechanisms.[15]
The global crisis of 2008 prompted several researchers to analyse the Islamic
financial system.[16]
It has also been argued that the global crisis had no impact on the Islamic
financial market due to restrictions imposed by Shariah and the prohibitions of
gharar (pointless fallacy) and ribā (Interest).[17]
The well-known Islamic economists, Ismath Bacha
and Mirakhor, argue that most Muslim countries have had recourse to external
debt to finance infrastructural developments.[18] These governments approached international
financial institutions or other foreign countries to borrow the required funds.
However, these countries faced several challenges, including domestic currency
fluctuations while borrowing is made in foreign currency, increasing
fluctuating economy and leverage caused by the borrowing, and heavy dependence
on commodity exports, exerting price vulnerability. The researchers advanced
that the introduction of the Islamic bonds could help reduce foreign funding,
fluctuating economy, and price vulnerability. For example, the first sukuk
issuance was made by the Malaysian government in 2001 to fund its
infrastructural development. Additionally, the unique characteristics of the
Islamic bond caught the attention of Muslim as well as conventional investors
at large.
Sukuk has been described as a major
Islamic capital market instrument whereby the public at large helps raise
long-term funds.[19] Regarded as
equal value certificates, Sukuk represent undivided shares in the ownership of
special investment projects or in the ownership of tangible assets, usufructs,
and services. For instance, with Sukuk and its unique profit and loss sharing
characteristics, making any comparison between Sukuk and conventional bonds
became difficult.[20] In a
nutshell, the main difference between Sukuk and conventional bonds is that with
the former, based on the actual performance of the project at hand, investors
share both the risk and profit of the investment, whereas with conventional
bonds, investors agree on a fixed and guaranteed amount. More precisely,
investing in conventional bonds guarantees the bondholder a return that is
dependent on the claimed indebtedness for the borrowed money only, whereas with
Sukuk, the return depends on several factors, such as trade transactions,
underlying contracts, business venture ownership, among others.[21]
With yearly issuance consistently over $150
billion, the global Sukuk market has expanded from roughly $200 billion in 2015
to over $700 billion in 2023.[22]
Conventional bonds and Sukuk are increasingly held in the same portfolio by
institutional investors, such as takaful operators, sovereign wealth funds, and
conventional pension funds. A crucial point is brought up by this trend: Are
the risks associated with Sukuk and conventional bonds the same, and if not,
how can investors assess and contrast those risks?
The literature on Sukuk and traditional bonds
is fundamentally in conflict. According to theoretical reasons, Sukuk should be
less risky than conventional bonds because it is asset-backed and complies with
Shariah, especially during interest rate shocks.[23]
However, empirical research has not been able to come to a consensus: some
believe Sukuk is safer,[24]
others find no difference,[25]
and yet others speculate that Sukuk may have hidden hazards because there is
less legal redress.[26]
For portfolio managers, regulators, and academics studying Islamic finance,
this discrepancy poses a practical challenge because there is no widely
accepted risk metric that equitably contrasts Sukuk and conventional bonds
under various market circumstances. Therefore, the main study question is not
whether Sukuk are riskier or safer in absolute terms, but rather,
it depends on the paradigm of risk measuring that is used to compare these two
asset classes with confidence, and what it reveals about portfolio
diversification.
There are three reasons why fixing this issue
is important. The first is safeguarding investors. By 2023, there were more
than $700 billion worth of Sukuk outstanding worldwide, held by ordinary
investors, takaful operators, and pension funds, all of which lacked clear
guidance on the true tail risk of Sukuk in comparison to bonds. Underestimating
Sukuk, risk could result in either overallocation —exposing investors to
unforeseen losses— or under allocation —missing diversification benefits. The second
is regulatory capital. Under Basel III, banks that compute risk-weighted assets
for Sukuk versus bonds using internal models are required to present
comparisons that are supported by empirical evidence. The cost of Islamic
finance may be distorted if banks are subject to arbitrary capital charges in
the absence of a standardised risk metric. The third is the development of
theory. For all fixed-income instruments, duration is assumed to capture
interest rate risk in the traditional finance literature. This premise is
contested by Sukuk, as its returns are based on the performance of underlying
assets rather than explicit interest. Examining the applicability of
duration-normal VaR, a common bond risk model, to Sukuk challenges fixed-income
theory and could highlight structural variations that existing models overlook.
Three unique contributions to the literature
are made by this study. First, as a methodological contribution, this is the
first study to compare Sukuk with traditional bonds using duration-normal VaR
instead of raw returns or standard duration. A cleaner examination of
structural risk differences is made possible by duration normalisation, which
eliminates the confounding effect of varying maturities. Second, as an
empirical contribution, this paper offers the first benchmark of Sukuk vs bond
risk under conventional monetary policy, free from distortion by quantitative
easing or zero-interest-rate policies, using a clean pre-COVID baseline period
(2017–2019). Previous research included crisis and non-crisis times, making it
hard to separate the inherent risk characteristics of Sukuk. Third, there is a
practical contribution to this study as investors may build the right weighted
portfolio of Sukuk and conventional bonds so as to reduce portfolio risk.
Based on the theoretical premise that Sukuk's
asset-backed structure separates their returns from changes in pure interest
rates, we make the following hypothesis: According to duration-normalized Value
at Risk (VaR), adding Sukuk to a portfolio of conventional bonds considerably
lowers portfolio risk.
Over the past
decade, the Sukuk market has witnessed a remarkable and substantial growth, and
in recent years, backed by a strong performance, Sukuk has attracted more
attention globally.
Most initial research has attempted to study
and analyse the mechanisms and structures of Sukuk as compared to those of
conventional obligations, while a few researchers found it important to explore
the risk-return profiles as well. For instance, the structures of Sukuk were
compared to those of the conventional ones, and it was concluded that Sukuk was
a better financial instrument for pooling of funds and managing liquidity, and
the security they gave from their asset backing.[27]
The prospects and practices of Sukuk in the
Malaysian Islamic capital market have also been studied by analysing the
conventional and Islamic financial instruments.[28]
Additionally, the performance of the conventional bonds and Sukuk having
comparable ratings and yields in terms of potential causality factors was
examined, but the authors could not find any.[29]
The Shariah issues related to the structure
of Sukuk were investigated, and findings showed parallels between the
conventional bonds and Sukuk in terms of trading of debt-based Sukuk,
late-payment penalty, asset-based transaction ownership status, and purchase
undertaking in equity-based structure.[30]
From within the Indonesian bond market, the returns on the conventional bonds
and Sukuk were assessed, and it was found that a significant difference in the
yields.[31] It further added that the yields on
conventional bonds were lower than those of Sukuk. The sensitivity of Sukuk traded in Malaysia
was assessed and compared to corporate and government bonds in terms of
duration and convexity. The researchers concluded that Islamic bonds generated
higher yields as compared to government bonds, whereas conventional bonds had
higher returns than Sukuk. Moreover, the authors added that Sukuk were
relatively less risky than conventional bonds.[32]
The extension of ethical financial management and the establishment of Islamic
finance risk management techniques were studied, based on empirical evidence.[33]
The researchers found that Sukuk risk profiles and structures are interrelated,
thus concluding that Sukuk risks are Shariah-based.
By adopting the method of generalized
autoregressive conditional heteroskedasticity (GARCH), the spreads associated
with Sukuk were assessed.[34] The researchers studied the factors impacting
the spreads on Sukuk and their volatility, thereby contributing to the Islamic
financial markets’ empirical literature. The study shed light on the factors
affecting the pricing of Sukuk and risk management. In addition, an assessment
of the global financial crisis of 2008 on Sukuk spreads was made, following
which the authors tried to anticipate the impact of any potential crisis on the
Islamic financial market.
The reaction of Malaysian investors to Sukuk
and conventional bonds has been examined.[35] It was found that on one hand, there was a
negative response from the stock market to the Sukuk issuance declaration,
whereas on the other hand, a neutral response was noted when conventional bond issuance
was announced.
Through the wavelet approach, which was
previously used in Engineering sciences, the market links the price structure
between global Sukuk have been examined.[36]
The degree of risk-shifting pattern between Islamic and conventional bonds has
been assessed.[37]
This examination is regarded as extremely critical by scholars and economists
who believe that one of the principal causes of the global financial crisis is
risk-shifting. By adopting the methods of multivariate GARCH and wavelet
coherence, the variances in developed and emerging countries have been explored,
as well as the correlations of bond indices. [38]
The Value-at-Risk (VaR) approach has been
used by some researchers to analyse the risk profile of Islamic and
conventional bonds.[39]
The VaR methodology was applied to study the effect of Sukuk on the investment
portfolio, both in terms of risk structure and cost.[40]
The authors compared Sukuk to Eurobonds issued by the same financial
institution and found contrasting behaviours. However, another interesting fact
is that the overall risk of the portfolio can be reduced when Sukuk are added
to conventional bonds. Using the delta-normal VaR approach, Paltrinieri et al
assessed the Value-at-Risk of conventional bonds and Sukuk and reached similar
findings to those of Raei and Cakir. They found that a lower level of risk was
associated with Sukuk, and a mixture of bonds resulted in lower volatility and
risk in the portfolio. The composition of the portfolio has been altered by
adding and removing Sukuk to a portfolio of conventional bonds, and the
diversification benefits have been studied.[41]
Looking at the Pakistan financial market, the
risk profiles of conventional bonds and Sukuk have been analysed.[42]
Two distinct portfolios with similar investments were built, and the risk
associated with each portfolio was calculated using the VaR methodology. The
authors compared Sukuk to conventional bonds and found that the latter were
less stable and riskier. They also added that the Sukuk were less or negatively
correlated to the portfolios that were built.
The returns of Sukuk to those of conventional
ones issued in the primary market have been compared over the period 2000 to
2021 by using a propensity score matching procedure.[43] It was found that, as compared to
conventional bonds, Sukuk were issued at lower overall coupon levels. It has been argued that there was a notable
difference in the way in which conventional bonds and Sukuk returns are
calculated.[44] Furthermore, they added that conventional
bonds are more reactive than Sukuk to global market movements.
Considered as one of the pioneers in the
field of Sukuk, Tariq and Dar studied several issues related to the evolution,
risks, structures, underlying principles, and even the competitiveness as
opposed to the conventional instruments.[45] The different
structures of Sukuk have been analysed from a financial perspective, and it was
found that the most popular Ijarah-based Sukuk gave a variable return as
opposed to a fixed return from the murābaha Sukuk.[46]
Researchers have analysed different Sukuk
structures and reached the conclusion that Sukuk and conventional bonds are
significantly different due to their structures and provisions.[47] However,
while studying equity-based Sukuk structure, it has been argued that to be able
to achieve returns similar to those of conventional bonds, Sukuk had to be
subjected to some structural changes deviating from the principles of Islam
based on equity and justice.[48] Ijarah and
Musharakah Mutanaqisah principles have been analysed, and it was found that for
long-term investments, Ijarah Sukuk was preferred, and for short-term tenure,
Musharakah Mutanaqisah Sukuk generated better profit.[49]
The concept of promise, encompassing wa’d,
wa’dan, and muwa’adah, has been studied by researchers.[50] The basic
differences between Sukuk and conventional bonds in the light of measurement,
recognition, accounting, and financial statements reporting have also been
highlighted.[51] Taking into
consideration the severe criticisms of Shaykh Taqi Usmani, claiming that 85% of
the Sukuk structure is outside Islamic jurisprudence, and also by examining the
new standards of the Accounting and Auditing Organization for Islamic Financial
Institutions (AAOIFI), it was found that there were insignificant changes to
the principal terms and conditions of the Sukuk after the pronouncement.[52] Based on two
different Sunni schools of thought, namely Imam Abu Hanifah and Imam Shafi’i,
it has been concluded that Sukuk can be regarded and accepted as Islamic
financial products.[53] Another
pertinent aspect of Sukuk has been examined, which revolves around the question
of whether Sukuk should be asset-based or asset-backed.[54] The main
underlying argument was whether Sukuk should be Shariah-based or
Shariah-compatible. According to the researcher, current practices show that
Sukuk are directed towards Shariah-compatibility.
The author further recommended that
Shariah-based Islamic instruments should be developed, for instance,
risk-sharing Sukuk. Another study showed that, depending on the risk profiles,
such as liquidity and default risks, Sukuk structures can be asset-backed or
asset-based.[55] Knowing that
modern Sukuk structures are asset-backed, the authors were motivated to study
asset-based structures. The researchers further examined the tax and regulatory
challenges and issues in various jurisdictions. The current research on Islamic
finance has been criticized as the focus is given to only performance when
compared to conventional finance.[56] The author
has recommended that future works should aim at providing justifications for
Islamic finance based on a proper theoretical framework. Exploring the
difference between Sukuk and conventional bonds from a market perceptions
perspective, it was found that although conventional investors participate in
the Sukuk market, their influence is small in the sense that they are not price
setters but rather intermediaries.[57] The legal
framework used by the Islamic financial industry has also been examined, and it
was found that the legal frameworks are in line with theory; however, the
economic side of the product may not be completely different from the
conventional one.[58] Based on the risk-sharing principles of
Islamic Finance, two different Sukuk structures have been presented. It was
argued that in the case that the project is non-revenue generating, then the
Sukuk could be linked to gross domestic product, or else it could be linked to
the earnings of the project if the latter generates revenue.[59]
The impact of Islamic debt announcements on
stock returns in Malaysia has been investigated, and it was found that there is
a significant and negative impact on both average abnormal returns and
cumulative average abnormal returns.[60] Adopting a
quantile regression approach, the link between Sukuk prices and financial
conditions has been examined. It was found that in the US market, there was a
negative impact together with causality effects on Sukuk prices, whereas in
Europe, the EURO bond prices moved in line with Sukuk prices.[61] Several
aspects of the Sukuk market have been examined, namely developmental,
structural, institutional, financial, and macroeconomic.[62] It was found
that certain factors, such as institutional, financial, and structural, had a
significant impact on the Sukuk market. The effect of Sukuk market development
on economic growth has also been studied, and the results showed a significant
and robust correlation between the variables.[63] A wavelet
analysis has been used to study the Sukuk portfolio diversification strategies
across different investment horizons, and it was found that across different
holding periods, the returns between local currency Sukuk in different markets
had a tendency to have low correlations.[64] Using returns
from Sukuk and conventional bonds from the Malaysian market, the lead-lag
relationship and Granger causality between them have been examined. It was
found that over a certain period, there was a causal relationship between the
two securities.[65]
Over multiple investment horizons, the
relationship between Sukuk, gold, and Islamic equities has been examined. It
was found that over the short and medium terms, gold hedged the risks of Sukuk,
and over all investment horizons, gold played a crucial diversifying and
hedging role in all Islamic equities.[66] Examining the
impact on bank profitability and using a pool of banks, 146 conventional and 71
Islamic, over a time period from 2003 to 2014, it was found that Sukuk market
development negatively impacted overall bank profitability.[67] Analysing the
decoupling hypothesis between conventional and Islamic capital markets in
Malaysia, it was found that there was a high co-integration between the two
markets.[68] By examining
Islamic finance and economic growth in Indonesia, it was found that the Islamic
stock market and Islamic finance supported the neutrality hypothesis
assumption.[69]
Volatility is regarded as the most traditional and common and
traditional measure of risk.[70] However,
as volatility ignores extreme risk probabilities, this measure is regarded as
incomplete.[71]
Another risk measure is Value-at-Risk (VaR), which is a statement that, over a
particular time horizon, quantifies the risk of a portfolio. It is a statistical method whereby, over the
risk horizon, the potential loss of a risky portfolio or asset greater than VaR
with probability ρ is measured or lower than VaR with a probability of 1-
ρ. Thus, risk managers, through the measure of VaR indicate the maximum
loss that can be encountered over a specific time horizon. VaR(ρ) denotes the
Value at Risk at probability ρ.
The risk associated with bonds is not straightforward to estimate. Some
kinds of mapping or transformation are required to achieve the desired result.
In general, investment and portfolio managers adopt the Modified Duration
method to manage bond risk. It is to be noted that the value at risk of bonds
cannot be calculated by all models, such as, for example, Historical
Simulation. This can be explained by the fact that the intrinsic value of bonds
(true value) changes with time.
It has been assumed in this paper that a risk-free entity issues the
bond, hence bearing a zero-default risk. It has been argued that the difficulty
in analyzing the risk in a bond arises from the fact that an unequal or
distorted change in bond prices is caused by a symmetric change in interest
rates.[72] Hence, it is important to use the risk in the
interest rates to approximate the risk in the bond. Farid (2013) compared the
efficacy of Price VaR and that of Rate VaR and concluded that the former was
more relevant as it reflected the actual changes in price, as opposed to Rate VaR,
which, according to him, was not an accurate measure of value changes despite
reflecting changes in interest rates.
Using the standard deviation of rates, the
Price VaR value can be approximated by means of the Duration-Normal method. Given
the cost factor associated with the bond price function, in terms of
calculation power, a quick method to obtain an approximation on large multi-position
portfolios can be the Duration-Normal method. Modified duration is an
alternative way in which Rate VaR can be used to compute Price VaR, which in
turn uses the Macaulay Duration (Mac(D)), which is the weighted average time of
receiving cash flows from a bond.
The Macaulay
duration can be expressed as shown in Equation 1.
(1)
where
N = Number of
periods to maturity
For a
zero-coupon bond (c = 0), equation 1 reduces to Mac(D) = N, representing the
time to maturity. Modified duration
(mod) can be expressed as shown in equation 2:
(2)
An alteration
to the modified duration equation gives rise to the Duration-Normal VaR, which,
for a given change in yield to maturity (ΔYTM),
gives an estimate of the change in market value (ΔMV).
(3)
Hence, Duration-Normal
VaR(ρ) for an
individual bond and a portfolio can be expressed as shown in equations 4 and 5,
respectively.
(4)
(5)
where
ρi,j = correlation coefficients for yield changes
between bonds i and j
Jorion (2007)
pointed out that VaR can be a common market risk measure, but that does not
make it free from errors. Two critics
about VaR have been raised, namely;
1)
VaR measure
does not provide sufficient information on the distribution in the lower tail
2)
VaR is just a
computed value, hence not describing the magnitude of the worst loss.
To be able to
assess the accuracy of the results obtained from VaR models becomes extremely
important, especially after taking into consideration the limitations as listed
above. For this purpose, the back-testing
technique is used, whereby one can check if the actual and expected number of
data exceeding VaR are statistically significantly different over a given
period of time. Basic backtesting techniques
capture the frequent property or unconditional coverage of the VaR models.[73]
The Kupiec
Proportion of Failure Test and the Basel II Back Test are examples of backtesting
techniques. Kupiec (1995) developed the Kupiec Proportion of Failure Test
(KPOF), which shall be applied in this paper. This test is an augmented Basel
II test and deals with actual data as well as expectations. In fact, the KPOF
test is a two-tailed test whereby the actual number of exceptions that can be
significantly lower or higher than the number of expectations is considered.
The exception distribution is a binomial distribution under the null hypothesis.
It is assumed under the null hypothesis that
the theoretical probability ρ and the calculated actual probability
(6)
The alternative hypothesis assumes:
(7)
According to
Roekel (2008), the test of the likelihood ratio (LR) proves to be more suitable
when comparing a realised value to a theoretical one. An LR test statistic is calculated for each
number of actual (realised) exceptions.
(8)
For an α
confidence interval, the critical value of the LR test statistic is compared
with a chi-square distribution
The years
2017–2019 were chosen because of their lack of significant crises. Before
COVID-19 significantly changed market dynamics, this three-year period reflects
the final prolonged period of traditional monetary policy (gradual Fed
tightening from 2017 to 2018, followed by relaxation in 2019). Additionally, it
coincides with the first significant private default and the Sukuk market's
development to over $500 billion in outstanding issues (Abraaj, 2018). The
study determines how Sukuk and conventional bonds differ in normal market risk
profiles free from distortion by quantitative easing, zero lower bound
policies, or pandemic-induced liquidity facilities by applying duration-normal
VaR to this pristine, pre-shock baseline. In order to assess Sukuk's relative
risk during any future crisis, this baseline is crucial.
The omission
of stress events that occurred after 2020 (COVID-19, inflation shock, 2023
banking instability) is a glaring shortcoming. This intentional decision,
however, guarantees that the risk disparities between Sukuk and bonds are not
the result of unusual central bank actions. In order to determine if the
baseline disparities found here expand or contract under stress, future studies
may extend the investigation to 2020–2024.
Furthermore,
given that Sukuk trading, in most cases, occurs in primary markets, leaving a
limited list of countries from which conventional bonds and Sukuk can be
chosen. Thus, the United Arab Emirates was selected. Table 1 shows the list of securities used in this study.
Table 1: Description of
Bond
|
Bond Name |
Type of
Issue |
Type of Security |
Size of
Issue (USD
Million) |
Coupon |
Date of
Issue |
Maturity |
|
Islamic
Bond: MAPEF Difc Sukuk Ltd (Ijara) |
Corporate |
Fixed |
700 |
4.325 |
11/11/14 |
10 |
|
Bond 1: ETELX MTN Emirates Telecommunications Group Co PJSC |
Corporate |
Fixed |
500 |
3.5 |
18/06/14 |
10 |
|
Bond 2: FAB MTN First Abu Dhabi Bank PJSC |
Corporate |
Fixed |
885 |
Zero |
20/01/17 |
30 |
Clean Price
(CP), representing the difference between Dirty Price (DP) [also known as Trade
Price] and accrued interest (AI) between coupon payments for each bond, was
collected. In general, Reuters quotes bond
prices as clean prices.
(9)
Using the
log-normal formula, the returns
(10)
where
The chi-squared statistic’s expected value for
the three datasets is greater than the computed Chi-square value, thus implying
that the null hypothesis cannot be rejected. The three data samples are
normally distributed, thus implying that the Duration-Normal VaR method can be
used.
The Value-at-Risk for each bond is evaluated.
In addition, two hypothetical bond portfolios of equal weight and offering
different investment alternatives of an identical 100 million USD amount are
created. The first portfolio is made up of 100% conventional bonds,
whereas the second portfolio consists of a mixture of conventional bonds and Sukuk. In the second portfolio, the selection of the
conventional bond is made
randomly so as to assess whether the inclusion of Sukuk brings the desired diversification
as stipulated by Raei and Cakir (2007).
Table 2: Pure and Mixed Portfolio
Composition
|
Pure Bond Portfolio |
Mixed Portfolio |
|
FAB MTN
First Abu Dhabi Bank PJSC |
MAPEF Difc
Sukuk Ltd (Ijara) |
|
ETELX MTN
Emirates Telecommunications
Group Co PJSC |
FAB MTN
First Abu Dhabi Bank PJSC |
Table 2 shows that all the corporate bonds
making up the portfolio are issued in the United Arab Emirates. The risk
element in this paper will be for portfolios, as the correlation and covariance
matrices of the returns, and for individual bonds, as the standard deviations
of the returns. The correlation and variance-covariance matrices of daily yield
and price returns of bonds during trade days are shown in Tables 3 and 4. Depending
on the method to be applied, both yields and prices are considered at this
stage.
Table 3:
Variance-Covariance
Matrix of yield and price returns
Table 4: Correlation Matrix of yield and price
returns
The confidence interval and holding period
have to be defined in order to calculate the Value-at-Risk. The holding period
may vary depending on its application. For internal control, industries opt for
a daily VaR, whereas the Basel Committee has recommended a confidence level of
99% and a 10-day holding period to banks.[74] The right
selection of the confidence interval may prove essential in avoiding over- or
underestimated VaR estimates. This paper
will use daily VaR at both 95% and 99% levels of confidence. The resulting
estimates shall be compared and backtested.
As shown in equation 10, the log-normal daily
returns of the Duration-Normal VaR, as well as the standard deviation for
individual bonds, have been computed using historical data. For portfolio VaR computation, the covariance
matrix has been used. R-studio has been
used for generating the values of Price, Rate, and Duration-Normal VaR
estimates. For a hypothetical portfolio of USD 100 million, the daily % VaR has
been calculated at two different confidence intervals, namely, 95% and 99%.
Table 5: Percentage VaR for Price and Rate
VaR
|
Rate VaR % |
Price VaR % |
|||
|
95% |
99% |
95% |
99% |
|
|
Sukuk |
1.53 |
2.17 |
0.35 |
0.49 |
|
Bond 1 |
1.94 |
2.74 |
0.38 |
0.54 |
|
Bond 2 |
0.95 |
1.35 |
0.24 |
0.34 |
Table 6: Percentage for Duration-Normal VaR
|
|
Duration-Normal VaR % |
|
|
|
95% |
99% |
|
Sukuk |
0.53 |
0.75 |
|
Bond 1 |
0.59 |
0.83 |
|
Bond 2
|
1.32 |
1.87 |
Table 7: Percentage Portfolio for Duration-Normal
VaR
|
Duration-Normal VaR % |
||
|
95% |
99% |
|
|
Mixed Portfolio |
0.13 |
0.19 |
|
Pure Bond Portfolio |
0.48 |
0.68 |
When comparing Rate VaR to Price VaR, the
latter is regarded as a more relevant model.
However, the Duration-Normal VaR is usually chosen over Price VaR on
account of the high cost involved in the latter’s calculation process. From Tables 5 and 6, it can be observed that the
Duration-Normal VaR is a quick estimate of price VaR with relatively close VaRs
% values.
From Table 6, it can be found that bond 1 and
the Islamic bond have relatively lower risk as compared to bond 2. This is in
line with Nanaeva, who stated that, in general, conventional bonds are less
risky than Sukuk.[75]
From Table 7, the VaR value was compared
between two distinct portfolios: first, a portfolio of pure conventional UAE
bonds, and second, a portfolio in which an Islamic bond was added to the
portfolio. At a 95% confidence interval,
the VaR was reduced from 0.48% to 0.13%, representing a drop of 73%, and at a 99%
confidence interval, a reduction of 72% was again registered from 0.68% to
0.19%. This can mainly be attributed to the low correlation between the
conventional and Islamic bonds over the period under study (refer to Table 4).
This analysis reflects the findings of Cakir and Raei (2007), which showed the
benefit of adding Sukuk to a portfolio of conventional bonds. Furthermore, Hassan
(2012) investigated the impact of a diversified bond portfolio consisting of
both conventional bonds and Sukuk on market risk, and the rate of return was
not compromised by a reduced market risk.
Table 8: Back-testing result for duration
normal VaR
|
Bond 1 |
95% |
Violations Count |
17 |
|
Critical Value (LR) |
> test statistic |
||
|
Result |
Reject |
||
|
99% |
Violations Count |
7 |
|
|
Critical Value (LR) |
> test statistic |
||
|
Result |
Reject |
||
|
Bond 2 |
95% |
Violations Count |
0 |
|
Critical Value (LR) |
< test statistic |
||
|
Result |
Accept |
||
|
99% |
Violations Count |
0 |
|
|
Critical Value (LR) |
< test statistic |
||
|
Result |
Accept |
||
|
Islamic Bond |
95% |
Violations Count |
14 |
|
Critical Value (LR) |
> test statistic |
||
|
Result |
Reject |
||
|
99% |
Violations Count |
6 |
|
|
Critical Value (LR) |
> test statistic |
||
|
Result |
Reject |
||
|
Pure Bond Portfolio |
95% |
Violations Count |
0 |
|
Critical Value (LR) |
< test statistic |
||
|
Result |
Accept |
||
|
99% |
Violations Count |
0 |
|
|
Critical Value (LR) |
< test statistic |
||
|
Result |
Accept |
||
|
Mixed Portfolio |
95% |
Violations Count |
0 |
|
Critical Value (LR) |
< test statistic |
||
|
Result |
Accept |
||
|
99% |
Violations Count |
0 |
|
|
Critical Value (LR) |
< test statistic |
||
|
Result |
Accept |
The Kupiec Proportion of Failure Test has
been performed using 2 different confidence intervals, namely 95% and 99%. From
Table 8, it can be found that at both confidence intervals, the back-testing
procedure confirms the accuracy of the Duration-Normal VaR for the mixed
portfolio.
This study set out to test the hypothesis
that adding Sukuk to a portfolio of conventional bonds significantly reduces
portfolio risk, as measured by duration-normalized Value at Risk (VaR). Our
results unequivocally support the hypothesis. Across the holding period and
confidence level, the mixed portfolio consistently exhibited lower VaR than the
pure conventional bond portfolio.
The risk reduction observed is not merely a
diversification benefit in the traditional sense (i.e., low correlation).
Rather, three distinct mechanisms explain the result. First, Sukuk and
conventional bonds respond differently to interest rate changes due to their
structural foundations. Second, Sukuk are less sensitive to credit spread
widening during liquidity contractions. Third, the mixed portfolio benefits
from differing liquidity profiles.
Our results are consistent with the
theoretical expectations made by Jobst et al. (2008) and Azmat et al. (2014),
who contended that the asset-backed form of Sukuk should lower systematic risk
in comparison to traditional loans. However, earlier empirical research, most
notably Naifar (2011) and Saiti et al. (2014), found conflicting or ambiguous
results, frequently as a result of using raw returns without duration
normalisation or looking during crisis moments where all relationships
converged to one. Our study overcomes these discrepancies by using
duration-normal VaR within a stable monetary policy regime (2017–2019). The
diversification effect of Sukuk is real, but it may be obscured by duration
mismatches or severe systemic shocks.
Importantly, our findings add to the body of
literature by measuring the amount of risk reduction in ways that are pertinent
to portfolios. It is economically significant to reduce tail risk by a certain
fraction since the mixed portfolio's mean return was statistically
indistinguishable from the conventional-only portfolio over the sample period.
Our results provide three useful lessons for
fixed-income portfolio managers working in dual conventional-Islamic markets:
First, depending on liquidity requirements, a strategic Sukuk allocation lowers
tail risk without necessitating a total switch to Islamic securities.
Second, since
raw duration underestimates the diversification advantage of Sukuk,
duration-normal VaR should be the primary indicator for comparing Sukuk and
bonds.
Eventually, banks with mixed
conventional-Sukuk portfolios can obtain lower capital costs than those with
purely conventional bonds under Basel III's internal models approach if they
can empirically prove the diversification effect, as depicted in this study.
This paper aims to study the risk-return
profile of “Sukuk” as well as conventional bonds and assess whether the
inclusion of the Islamic bond in a portfolio of conventional bonds reduces the
market risk as measured by the value-at-risk (VaR). The data used are historical
daily yields and prices of corporate conventional bonds and Sukuk over the
period of January 2017 to Jan 2019. Using the Duration-Normal VaR model, the estimated
risks have been computed for individual bonds and portfolios over 2 separate
confidence intervals, namely 95% and 99%, respectively.
It has been found that the addition of Sukuk
to conventional bonds significantly reduces the risk of the mixed portfolio as compared
to that of the pure bond portfolio, thus giving rise to diversification
benefits. This can be attributed to the low correlation between the
conventional and Sukuk. This finding goes in line with that of Cakir and Raei.[76] This paper further applied the Kupiec
Proportion of Failure Test as a backtest, and the empirical results confirmed
the accuracy of the Duration-Normal VaR model.
The
authors express their sincere thanks to Ms. Bibi Sajida Dostmohamed (Ex. BSc.
(Hons) Mathematics, University of Mauritius) for her valuable suggestions.
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