The Nature of Islamic Banking and Solvency Stress Testing - Conceptual Considerations

Andreas Jobst; Juan Sole

doi:10.5089/9781513550886.001.A001

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The Nature of Islamic Banking and Solvency Stress Testing - Conceptual Considerations

Author: Andreas Jobst and Mr. Juan Sole

Contributor Notes

Author’s E-Mail Address: ajobst@imf.org; jsole@imf.org

Publication Date:: 07 Aug 2020

eISBN:: 9781513550886

Language:: English

Keywords:: WP; stress testing; Islamic banking; Islamic finance principles; capital adequacy; shari’ah compliance.; Islamic bank; rate of return; market risk; operating income; interest rate; deposit base; financial system; asset performance; liabilities consist; Market risk; Credit risk; Islamic finance; Global; Middle East and Central Asia; Southeast Asia; Africa

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This paper provides a conceptual overview of key aspects of the design and implementation of solvency stress testing of Islamic banks. Based on existing regulatory standards and prudential practice, the paper explains how Islamic finance principles and their impact on various risk drivers affect the capital assessment of asset-oriented financial intermediation under stress. The formal specification of these risk factors helps operationalize and integrate the stress testing of Islamic banks within established frameworks for financial stability analysis.

Abstract

I. Preface

This paper pre-dates the current COVID-19 crisis and does not reflect the Fund staffs evolving analysis of potential financial stability implications and advice on financial regulation (IMF, 2020c).² However, its general guidance on the conceptual foundations of stress testing remains highly relevant to articulate the capital impact of economic contraction on Islamic banks, which are likely to face rising capital and liquidity pressures due to shrinking profits, deteriorating asset quality, and adverse funding conditions similar to their conventional peers.

Evaluating the extent to which banks are resilient to the adverse impact of the current crisis puts significant emphasis on stress testing as an integral part of overall risk governance and market surveillance. Stress testing are traditionally prospective—they help banks and supervisors assess capital adequacy and liquidity risk under severe but plausible scenarios when there is time to remedy identified vulnerabilities. However, when shocks have already occurred, such as in the case of the current COVID-19 crisis, the role of stress tests changes. Findings from past stress test exercises on pre-existing vulnerabilities (if available) can help inform timely policy decisions as developments unfold—ideally in the form of scenario analyses of evolving shocks (potentially in combination with selective data updates), especially if the deterioration of economic conditions and their impact on the financial system remains highly uncertain.

The relevance of stress tests during the current crisis also applies to Islamic banks, which share many characteristics with their conventional peers but are also exposed to additional risks due to the specific nature of their business models (Chattha, 2020). Islamic banks are particularly affected by liquidity and commodity price shocks given the scarcity of short-term liquid assets and deep money markets as well as the comprehensive collateralization of all borrowing and lending activities, which is mostly done via precious metals or certain agricultural goods. Most Islamic banks also operate in emerging market and developing economies (EMDEs), for which the multi-faceted nature of the shock raises complex (and in many ways unprecedented) macro-financial challenges. Many EMDEs face acute strains from a sharp reversal of capital inflows due to a deterioration of investor sentiment, with the attendant pressure on exchange rates and credit spreads raising the likelihood of credit defaults, financial distress, and macroeconomic instability.³ For instance, the recent fall in oil prices is bound to result in a tightening of domestic liquidity conditions in oil-exporting countries and a rise in banks’ nonperforming exposures due to the deterioration of the balance sheets of the government, household, and nonfinancial corporate sectors (IMF, 2020b).

II. Introduction

Over the past two decades, Islamic finance has undergone a rapid expansion in many emerging market and developing economies (EMDEs) (Chart), where religious principles often favor the use of financial services and products that are compliant with Islamic finance principles (Imam and Kpodar, 2015). The key characteristics of Islamic finance —such as the concept of profit- and loss-sharing between lenders and borrowers, the focus on investments that are socially responsible, and the requirement of linking finance with real economic activities—have grown in popularity, especially since the global financial crisis, and provide an alternative to more traditional financial products (IMF, 2015). They define an asset-oriented system of ethical financial intermediation and investment built on the principles of risk-sharing in lawful activities (halal or ) rather than rent-seeking gains. In particular, the use of Islamic finance principles for infrastructure projects has provided significant stimulus for Islamic banking (with many institutions entering the Islamic finance field for the first time).⁴

Islamic finance already accounts for more than half of total financial assets in some EMDEs, and the Islamic financial services industry is estimated to amount to $2.6 trillion (or about 0.7 percent of total financial assets [Financial Stability Board {FSB}, 2019]). The potential for growth of this form of finance is nonetheless considerable, given that its penetration rate in large and populous economies, such as Indonesia and Turkey, is still below 20 percent.

Most Islamic finance assets are concentrated in the banking sector,⁵ which has grown in systemic importance. While Islamic banks account for only one percent (or $1.6 trillion) of global banking sector assets ($146.6 trillion) (Chart), they represent at least 15 percent of the total banking sector in 14 countries, of which Iran and Sudan are the only ones where the entire financial system operates in compliance with Islamic law (shari’ah or ).⁶ The market share of Islamic banks in most of these countries has continued to increase over the past few years, further deepening the penetration of Islamic finance principles. Islamic banking is also expanding in countries that have few Islamic banks despite substantial Muslim populations―in Africa (such as Algeria, Egypt, Mauretania, Mauritius, Nigeria, Senegal, Tanzania, and Tunisia), the Middle East and Central Asia (Afghanistan, Iraq, Kazakhstan, Lebanon, Pakistan, and Oman), and Southeast Asia (Indonesia and Singapore) (World Bank/Islamic Development Bank, 2017). During the last monitoring period by the Islamic Financial Services Board (IFSB, 2018), which tracks an expanded list of 36 countries, Islamic banks have increased their domestic market share in 19 countries while remaining constant in seven others (including Iran and Sudan, where they have a 100 percent market share by construction). Iran remains the largest jurisdiction for Islamic banking, accounting for a slightly increased 34.4 percent of the global Islamic banking industry at mid-2017, followed by Saudi Arabia (20.6 percent), UAE (9.6 percent), Malaysia (9.1 percent), and Kuwait (6.0 percent) (Chart).⁷

As Islamic finance helps raise financial inclusion in many EMDEs with substantial Muslim populations, its bank-centric structure places a premium on nurturing the rising demand in a safe and sound manner (Lagarde, 2015). The asset-backed, ring-fenced, and project-specific nature of many Islamic financial activities constitutes unique sources of risk that require a suitable supervisory and regulatory environment to preserve the stability of the financial system and its ability to support growth (Lopez and others, 2014). The IFSB issued several prudential standards and guidance notes for institutions that operate (and are supervised) under Islamic finance principles. However, some of these standards are not applied consistently across jurisdictions (Song and Oosthuizen, 2014), and continued efforts are needed to refine supervisory and regulatory frameworks in line with these recommendations while ensuring greater harmonization.⁸

Stress testing is fundamental to analyzing the financial stability implications of Islamic banking in countries where Islamic finance is growing in significance.⁹ Stress tests are designed to identify vulnerabilities to the impact of a rapidly deteriorating operational and market environment affecting the overall risk profile—from the financial system level down to individual banks and their different lending and trading portfolios (Jobst and others, 2013).¹⁰ Over the past decade, bank stress testing has rapidly evolved and has become a central aspect of the IMF’s financial sector surveillance—as a key component of the Financial Sector Assessment Program (FSAP)¹¹ assessments, which are now formally part of IMF Article IV consultations, and its use in crisis program work (Ong, 2014; Ong and Jobst, 2020). Stress testing has also grown in importance for many IMF member countries as a forward-looking technique for supervisors and macroprudential authorities. It enables them to identify any vulnerabilities that individual institutions or an entire financial system might have to adverse events that, while unlikely to happen, would have a significant economic impact if they were to occur.

The development of stress testing approaches has focused largely on conventional banks. While core principles and methods that determine the capital impact of risk factors apply universally, stress tests for Islamic banks would need to acknowledge the distinct characteristics of shari’ah-compliant financial intermediation. Many risk factors affecting both Islamic and conventional banks are similar in form but markedly different in substance.¹² Much like their conventional peers, Islamic banks face credit, market, and operational risks from maturity and liquidity transformation (by managing cash flows over different risk horizons to satisfy payments); however, the capital adequacy of shari’ah-compliant banking activities is also affected by risk-and-profit sharing, which implies some loss-bearing by investors and reduces capital intensity of equity-like financing. In particular, specific risk factors that are germane to Islamic banks involve:

Displaced commercial risk (DCR) if shareholders forgo some of their profits to provide competitive (and stable) earnings to unsecured depositors (which would otherwise need to absorb losses);
Project and counterparty risks stemming from partnership-like financing;
Rate of return risk from pricing frictions if Islamic banks need to adjust profit rates of investment accounts (outside actual underlying asset performance) to compete with conventional banks in response to changes in monetary policy; and
Operational risk from the failure to comply with Islamic finance principles.

The distinct risk profile of Islamic banks underscores the need for a coherent and consistent approach to the design and implementation of solvency stress testing. This paper establishes a common understanding of the unique properties of Islamic banking in line with relevant Islamic finance principles (IFSB, 2012b and 2013) and provides a conceptual overview of key risk factors affecting the capital adequacy of banks under stress.¹³,¹⁴ The identification and calibration of risk factors follow the functional components of conventional top-down stress testing model(s) and technique(s) of balance sheet-based methods (Jobst and others, 2013). This approach complements the IFSB’s evolving supervisory guidance on microprudential stress testing, building on its Technical Note on Stress Testing (IFSB, 2016) and the associated User Guide (IFSB, 2017),¹⁵ consistent with the high-level principles on stress testing issued by the IFSB (2012a) and the Basel Committee (BCBS, 2018).¹⁶ However, several process-oriented considerations (and the technical implementation of stress tests) remain outside the conceptual scope of the paper, such as the treatment of capital resources, the design of stress scenarios, the calculation of losses consistent with prevailing accounting standards, the definition of output measures, the validation of results, and dealing with the outcome of the stress tests.

The paper is structured as follows. The next two sections review the fundamental principles of Islamic finance and describe the nature of Islamic banking (Sections II and III). Section IV provides an overview of the main risks arising from Islamic banking activities. Section V defines the prevailing solvency requirement for Islamic banks, which forms the basis for assessing the combined impact of these risks under stress (Section VI). Section VII concludes.

III. Fundamentals of Islamic Finance

Islamic finance encompasses all transactions by two or more contractual parties whose actions are subject to prohibitory and permissible norms defined by shari’ah principles in keeping with the qu’ran (or ) and the sunnah (or ) as religious sources.¹⁷ These principles are often reduced to the simple notion of prohibited interest (riba or ); however, they instead should be characterized as a process-driven view of performance-based profits from financing real activities that create heterogeneous goods and/or services (“co-generation”) between two or more parties (see Appendix IV).¹⁸ Investment returns are not guaranteed but derive from transparent rights and obligations regarding the generation and distribution of profits arising from mutual contributions of transacting agents. Investors are entitled to receive commensurate state- or time-contingent payoffs from their direct participation in the performance of the funded asset (that is, payments can vary over time as conditions change). Payments are made in association with the temporary or permanent use of assets and generally not from the time value of money.¹⁹ In contrast, interest payments in conventional finance represent the contractible cost for funds tied to borrowing a certain amount of principal over a prespecified lending period, generating returns without economic conditionality regarding the use of funds. Thus, from the perspective of Islamic finance, interest income is not seen as the effect of business transactions, but as the result of an undesirable process by which such an effect is achieved (Jobst, 2007a; Jobst and others, 2008).²⁰

These overarching requirements distill several specific contractual conditions, which also pertain to shari’ah-compliant financial transactions:

Price certainty without manipulation of risk. While the fair value of an asset (and the return from investment) is inherently uncertain, Islamic finance principles prohibit transactions with payment obligations that are incalculable ex ante and divorced from (required) asset performance (and/or the rendering of a service). These transactions would be considered gambling (maisir or ) if they (i) generate returns from money as a store of value (rather than a medium of exchange to execute trade or shared investment to help create a lawful usufruct); and (ii) have the manipulation of risk (without commercial interest) as their primary (or sole) purpose. However, contracts that mitigate risks to facilitate trade (and enhance productivity) could be considered permissible.
Identifiable characteristics and certainty about delivery results (in terms of quantity and quality). Sales must be immediate and absolute to avoid being deemed gharar (“that with hidden consequences” or “that whose nature and consequences are unknown” or ) or jahl (ignorance or ), which requires that (i) the object of a bona fide transaction must exist (or come into existence based on demonstrated real capital input); and (ii) its characteristics are clearly identifiable before the transfer of title takes place.²¹ Exchanges involving asymmetric information between contracting agents imply the risk of delusion or deception (Al-Suwailem, 1999–2000), especially if payment obligations and delivery results differ from rational expectations. Such contractual uncertainty could lead to exploitation (Vogel and Hayes, 1998) if they generated unilateral (or zero-sum) gains from state- or time-contingent prices, resulting in divergent impacts on different agents.
Asset ownership and implicit avoidance of leverage (underfunding). Islamic finance principles align financial claims with investments in real assets, which marginalizes the possibility of underfunding through leverage and fosters equity ownership (in lieu of financial leverage from debt creation without underlying asset values). Thus, any reference asset is required to be in the (constructive) ownership and possession of the creditor (or, in the context of risk management, the protection seller) at the inception of a transaction. This ensures the asset-backing of financial obligations (which also “collateralizes” the performance of contractual obligations) and the risk and reward sharing that follows from it.

IV. Islamic Banks’ Balance Sheets and Implications for Stress Testing

The typical balance sheet of an Islamic bank resembles that of a conventional bank but implies a higher sensitivity to monetary dynamics (see Table 1).²² Much like in conventional financial intermediation, Islamic banks engage in maturity/liquidity transformation by accepting short-term deposits and issuing commoditized payment obligations (similar to debt securities) to fund longer term lending and investment. However, Islamic banks can only intermediate funds with shari’ah-compliant contracts and financial instruments, which tends to result in a larger (positive) duration gap than that of conventional banks.²³ While they generate mostly predefined returns (due to religious requirements), their cost of funding is largely variable,²⁴ making them generally more vulnerable to a higher (nominal) cost of capital under monetary tightening.²⁵

^{Table 1.}

Stylized Balance Sheet of an Islamic Bank

Source: authors. Note: ^1/ restricted investment accounts (RIAs) are often recorded as off-balance sheet items; ^2/ cost-plus sale-trade financing; ^3/ for trading, shares, and commodities; ^4/ Islamic collective investment schemes (ICIS) are a structured financial scheme that pools investors’ capital contributions in a fund that is established and managed in accordance with Islamic finance principles.

^{Table 1.}

Stylized Balance Sheet of an Islamic Bank

Assets	Liabilities
Cash and cash equivalents	Demand deposits: checking and savings accounts
Interbank deposits (short-term murabahah)	Investment accounts
Financing/lending portfolio Exchange-based contracts Ordinary sales ^2/ of which: murabahah (secured) of which: commodity murabahah (unsecured) Special sales (delayed settlement) of which: salam/istisna (delayed delivery) of which: bay bithaman ajil (delayed payment) Leases of which: ijara (operating lease) of which: ijara muntahia bittamleek (financing lease) Profit- and loss-sharing contracts of which: mudarabah of which: musharakah/diminishing musharakah	of which: profit- and loss-sharing contracts (musharakah/mudarabah) Restricted investment accounts (RIA) ^1/ Unrestricted investment accounts (UIA) of which: agency contracts (wakalah) Restricted investment accounts (RIA) Unrestricted investment accounts (UIA)
	Funding liabilities Exchange-based contracts Ordinary sales ^2/ of which: reverse murabahah (secured) of which: reverse commodity murabahah (unsecured) Special sales (delayed settlement) of which: parallel salam/istisna (delayed delivery) Profit- and loss-sharing contracts of which: investment certificates (sukuk) of which: Islamic collective investment schemes (ICIS) of which: equity securities
Investment/trading portfolio Inventory (commodities) of which: murabahah inventory—available for sale (AfS) of which: salam commodities of which: ijara assets—available for lease (AfL) of which: mudarabah/musharakah investments (cost basis) ^3/ of which: investment properties Profit- and loss-sharing contracts of which: investment certificates (sukuk) of which: Islamic collective investment schemes (ICIS) ^4/ of which: equity securities Net foreign exchange position	Reserves Profit equalization reserves (PER) of which: attributable to UIA (PER_UIA) of which: attributable to equity (PER_Equity) Investment risk reserve (IRR) of which: attributable to UIA (IRR_UIA) of which: attributable to RIA (IRR_RIA)
	Capital (equity)
Fixed assets	Long-term syndicated musharaka/mudarabah

^{Table 1.}

Stylized Balance Sheet of an Islamic Bank

Assets	Liabilities
Cash and cash equivalents	Demand deposits: checking and savings accounts
Interbank deposits (short-term murabahah)	Investment accounts
Financing/lending portfolio Exchange-based contracts Ordinary sales ^2/ of which: murabahah (secured) of which: commodity murabahah (unsecured) Special sales (delayed settlement) of which: salam/istisna (delayed delivery) of which: bay bithaman ajil (delayed payment) Leases of which: ijara (operating lease) of which: ijara muntahia bittamleek (financing lease) Profit- and loss-sharing contracts of which: mudarabah of which: musharakah/diminishing musharakah	of which: profit- and loss-sharing contracts (musharakah/mudarabah) Restricted investment accounts (RIA) ^1/ Unrestricted investment accounts (UIA) of which: agency contracts (wakalah) Restricted investment accounts (RIA) Unrestricted investment accounts (UIA)
	Funding liabilities Exchange-based contracts Ordinary sales ^2/ of which: reverse murabahah (secured) of which: reverse commodity murabahah (unsecured) Special sales (delayed settlement) of which: parallel salam/istisna (delayed delivery) Profit- and loss-sharing contracts of which: investment certificates (sukuk) of which: Islamic collective investment schemes (ICIS) of which: equity securities
Investment/trading portfolio Inventory (commodities) of which: murabahah inventory—available for sale (AfS) of which: salam commodities of which: ijara assets—available for lease (AfL) of which: mudarabah/musharakah investments (cost basis) ^3/ of which: investment properties Profit- and loss-sharing contracts of which: investment certificates (sukuk) of which: Islamic collective investment schemes (ICIS) ^4/ of which: equity securities Net foreign exchange position	Reserves Profit equalization reserves (PER) of which: attributable to UIA (PER_UIA) of which: attributable to equity (PER_Equity) Investment risk reserve (IRR) of which: attributable to UIA (IRR_UIA) of which: attributable to RIA (IRR_RIA)
	Capital (equity)
Fixed assets	Long-term syndicated musharaka/mudarabah

Islamic banks also exhibit a stronger connection between the sources and uses of funding. Shari’ah-compliant financial intermediation is characterized by pervasive risk sharing, which implies that (most) depositors enter into a wide range of profit- and loss-sharing (PLS) agreements that participate in the bank’s asset performance (at varying degrees), but rank senior to capital instruments.²⁶ There are four types of “Islamic deposits:” (i) restricted investment accounts (RIAs); (ii) unrestricted investment accounts (UIAs); (iii) exchange-based contracts using reverse sales, and (iv) current accounts (see Table 1). Many Islamic banks obtain a significant part of their funding from UIAs, which are typically commingled with the bank’s own funds and current accounts;²⁷ however, in some countries, reverse commodity murabahah sale contracts have become the main source of deposit funding (e.g., Malaysia) for Islamic banks. UIAs do not constrain the bank from using these funds (as long as investments are shari’ah compliant).²⁸ In contrast, funds from RIAs are separately managed funds (and often reported as off-balance sheet items) that can be invested only in a limited set of pre-agreed activities whose market and credit risk losses are fully borne by account holders (that is, loss-absorbing from a capital perspective).

Since checking accounts are interest-free loans (qard hasan or ) with guaranteed principal and exchange-based contracts are fully collateralized by design, their economic characteristics are akin to secured (conventional) deposits. However, investment accounts (IAs) are not liabilities of the bank but unsecured sources of funding. UIAs are viewed as puttable instruments (that is, investors have the right of withdrawal) under IAS 32,²⁹ whereas RIAs do not guarantee repayment of either principal or return.³⁰ This results in additional risk factors that impact the solvency and liquidity conditions of Islamic banks.

Consistent with the concept of permissible profits from risky capital investment, there are three basic forms of shari’ah-compliant uses of funds by Islamic banks without explicit interest:

Lending (debt-based contracts) through cost-plus sale-repurchase agreements (or back-to-back sales) of existing assets provided by the borrower (or a third party) through murabahah or ) (or reverse murabahah/tawarruq), which may contain deferred payment (bay bithaman ajil or ) and/or delivery (salam or /istisna’a or );
Leasing (asset-based contracts) through sale-leaseback agreements (operating leases) or the leases of third party-acquired assets with purchase obligation components (financing lease) (ijara or ); and
Profit-and loss-sharing (equity-based contracts) funding the production of future assets (musharakah or / mudarabah or ) through principal-agent relationships with a predetermined allocation of shared profits and full (or limited) risk-sharing.³¹ In contrast, lending and leasing contracts are “exchange based,” that is, they are initiated by a temporary (permanent) transfer of existing (future) assets from the borrower to the lender (for example, via the sale of commodities), or the acquisition of third-party assets by the lender on behalf of the borrower.

Islamic banks incur credit and market risks from exchange-based instruments (that is, sales and leases) on both the assets and liabilities sides of the balance sheet. These instruments are not exclusively financial transactions but involve the sale of an asset between the bank and the customer. The sale establishes a strong funding relation to real economic activity in lieu of indebtedness, irrespective of the use of funds. In a murabahah contract, the bank acquires an asset (typically a durable good) from a third party and then sells it to the borrower in exchange for future installments on the purchasing price and markup until the maturity date (cost-plus sale); in this manner, the bank is able to finance the purchase of the asset.³²,³³ If the asset is acquired from the borrower in return for funding but cannot be delivered at inception (salam/istisna’a), the bank pays an agreed price, and the customer obtains funds (or working capital) instantly in exchange for the promise of delivering a defined commodity (or rendering the specified service) at a future date. In an ijara contract, the bank buys an asset that is subsequently leased to a customer (who has the option but not the obligation to acquire the asset) for a prespecified rate of return.

In all exchange-based transactions, the bank incurs credit risk from nonperformance of the counterparty and/or asset impairment. Moreover, Islamic banks often carry on their balance sheets inventories of commodities and other physical assets, which pre-endow future sales-based transactions.³⁴ Consequently, market price deviations from the purchase price of the asset(s) that motivate the funding relation expose the bank to market risk in the form of potential losses (and also potential gains if the price of the asset(s) increases). This risk is often termed commodity or inventory risk, depending on the nature of the asset. Figures 1 to 3 illustrate the main features of both ordinary and special sales contracts and show the flows of assets and payments.

Equity-based instruments are equivalent to venture capital and project finance, which entail investment risks. In profit-sharing agreements (musharakah and mudarabah), the bank receives a payout in accordance with a pre-agreed disbursement ratio only if the investment project generates enough profit to repay the initial investment amount and the premium payment. Since the lender bears losses up to the total amount of investment (which determines the share capital),³⁵ equity-based contracts preclude any recourse in absence of enforceable collateral. Islamic banks may become exposed to two types of risks, depending on the accounting treatment of equity investment. If shares are held for trading purposes (that is, in the trading book of the bank) and marked-to-market, then their value is subject to the fluctuations in market price, which exposes the bank to market risk. Equity-based instruments held until maturity entail equity position risk, which is defined as the “risk arising from entering into a partnership for the purpose of undertaking or participating in a particular financing or general business activity” (IFSB, 2005a, p. 13).³⁶ According to the IFSB, the rating and the residual maturity of the specific investment position(s) determines the capital charges.

V. Risks and Their Capital Impact Within Islamic Banking

This section reviews the main risks associated with the balance sheet characteristics and financial products commonly found in Islamic banking activities. The strong asset linkage and “process-driven perspective” on profit generation have fundamental implications for the capital assessment of Islamic banks. This entrepreneurial approach underpinning many Islamic finance contracts and the high dependence on collateral also raises the search cost of financial intermediation and monitoring cost of counterparties (especially if repayment is influenced by the access and valuation of commodity prices).³⁷ In addition, the state-contingent nature of payouts from financial transactions complicates the design and implementation of hedging strategies and investor/depositor protection schemes (especially in financial systems where conventional and shari’ah-compliant banking coexist).

Stress tests measure the capital impact of certain risk factors based on the sensitivity of various types of financial activities to negative shocks to economic and financial conditions. As with conventional banks, the most common risks affecting solvency conditions are credit risk (if a counterparty fails to perform its payment obligations), market risk (if market prices, for example, interest rates, foreign exchange, and stock prices, decline), and operational risk (see Figure 4).³⁸ However, the characteristics of these risk factors have different implications for Islamic banks across financial instruments, contractual agreements, and bank business models (IFSB, 2005b):

Credit risk of asset performance in all exchange-based contracts (murabahah, ijara) in the financing/lending portfolio;
Market risk of asset price fluctuations affecting the valuation of forward exchange-based contracts (salam, istisna, bay bithaman ajil), including inventory risk³⁹ in the investment/trading portfolio from significant commodities exposures and uncovered/parallel special sales contracts (parallel salam); and
(General) operational risk if the failure of systems, internal procedures, and controls (as well as external events, such as natural disasters) lead to financial losses.

Islamic banks also face unique risks, which are particularly relevant for their business model:

Counterparty and project risks from profit- and loss-sharing arrangements (mudarabah, musharakah) given the asset-based nature of contracts;
Indirect interest rate risk due to competition for deposits in mixed banking systems;
Displaced commercial risk, which implies a transfer of some shareholder value to unsecured depositors to fund reserves for smoothing profits from lending and investments (in case of lower-than-expected returns) and compensate for losses in excess of reserves; and⁴⁰
(Specific) operational risk from either the non-compliance with Islamic finance principles or the non-recognition of shari’ah -compliant business activities and methods under conventional jurisprudence.

Given the limited access of Islamic banks to high-quality shari’ah-compliant funding over short-term horizons, any stress testing approach would need to be flexible enough to also incorporate the interaction of solvency and liquidity risks (through higher funding costs and/or deleveraging needs). Liquidity and solvency risks of individual institutions are increasingly connected during times of stress and tend to be influenced by system-wide liquidity conditions associated with the interconnectedness and network effects within the financial system. Current stress testing models either contain liquidity and solvency interactions and/or network modules to consider contagion and systemic risk from a cross-functional perspective (Jobst and others, 2017). Empirical evidence suggests that (i) the interaction between solvency and funding costs is indeed statistically significant; and (ii) it might be economically relevant, especially during periods of stress. Stress tests that do not account for the interaction between solvency and liquidity shocks substantially underestimate the risk exposure of individual banks and banking sectors (Puhr and Schmitz, 2014; Schmitz and others, 2017).⁴¹

A. Displaced Commercial Risk

Islamic banks endogenize the mutual cost of depositor protection through an informal and non-binding self-insurance scheme covering IA holders as unsecured creditors (investors) without (re)payment guarantees. IAs contractually bear all losses from projects (investments and lending), where the bank acts as agent or mudarib ,⁴² and, thus, can help mitigate losses. However, some Islamic banks with a large share of funding from IAs smooth the returns paid to depositors over time (and absorb some or all losses if necessary) due to competitive pressures.⁴³ Similarly, they might also consider absorbing liquidity risk from assets managed on behalf of IA holders, who can withdraw their funds before the contractual maturity (for instance, when investment projects yield lower-than-expected rates of return).⁴⁴ In both cases, shareholders may forgo part (or all) of their pre-agreed mudarib profit share to offset a profitability shock affecting IA holders’ promised rate of return (as equity is subordinated to deposits) (Lukonga, 2015); this may affect a bank’s capital position if some retained earnings are transferred to IA holders (see Box 1).

This mechanism is referred to as displaced commercial risk (DCR) and varies with the impact of investment and lending performance. DCR is not derived from Islamic finance principles but has evolved as common practice among Islamic banks to maintain stable funding in situations when adherence to the loss-sharing of IAs would suggest otherwise. However, in some countries, profit smoothing is not practiced (such as in the case of Malaysia), and, thus, DCR does not apply to any form of investment account (BNM, 2017).

In absence of depositor protection, DCR normally applies only to unrestricted IAs (UIAs) since restricted IAs (RIAs) are considered fully loss-absorbing (and tend to be treated as off-balance sheet items). DCR covers any unexpected losses that are not absorbed by UIA holders, and thus need to be fully capitalized (that is, the share of IAs assumed to be affected by DCR (consistent with the traditional concept of credit and market risk-weighting). Banks also establish two types of provisions from which to draw funds to smooth the rate of return paid to IA holders and compensate for any expected losses; even though these reserves are outside the concept of DCR, they have an operational impact on the quantification of DCR (see Figure 5):⁴⁵

The profit equalization reserve (PER) is typically funded by the net income from mudarabah IAs. The bank (as agent or mudarib) is entitled to a pre-agreed fraction of profits from these equity-based contracts, so both IA holders and shareholders are beneficiaries of the PER. Islamic banks normally use PER to smooth the income of investors over time.⁴⁶
The investment risk reserve (IRR) is solely attributable to IA holders and is funded by income after the deduction of the bank’s share (that is, the mudarib’s share) and contribution to PER. Since the mudarib does not bear losses outside cases of negligence and/or misconduct, IRR is typically used to cover losses from investments financed with IAs.

^{Box 1.}

The Quantification of Displaced Commercial Risk

The cascading mechanism underpinning the creation of prudential reserves can also be expressed in terms of income flows and balance sheet identities of an Islamic bank. If the bank’s liabilities consist only of equity, E, and unrestricted IA accounts, UIA, general loan loss provisions and PER (which are expressed as shares l and p, respectively) are retained from estimated annual net income, ${\tilde{r}}_{A}$ (which is expressed as return from jointly funded total assets, A), so that the available return, $(1 - p) (1 - l) {\tilde{r}}_{A}$ , for disbursement and profit-sharing between investors and shareholders

(1 - p) (1 - l) {\tilde{r}}_{A} {\begin{cases} (\frac{E}{A}) (1 - p) (1 - l) {\tilde{r}}_{A} \to P E R \\ (\frac{U I A}{A}) (1 - p) (1 - l) {\tilde{r}}_{A} {\begin{matrix} e (\frac{U I A}{A}) (1 - p) (1 - l) {\tilde{r}}_{A} \\ (1 - e) (\frac{U I A}{A}) (1 - p) (1 - l) {\tilde{r}}_{A} {\begin{matrix} i (1 - e) (\frac{U I A}{A}) (1 - p) (1 - l) {\tilde{r}}_{A} \to I R R \\ (\begin{matrix} 1 - i \end{matrix}) (1 - e) (\frac{U I A}{A}) (1 - p) (1 - l) {\tilde{r}}_{A} \end{matrix} \end{matrix} \end{cases}

defines the amount of IRR, $i (1 - e) (1 - p) (1 - l) {\tilde{r}}_{A} (\frac{U I A}{A})$ , which is retained by the Islamic bank before attributing income to UIAs, where UIA/A represents the share of profits allocated to UIAs, e is the bank’s commission as mudarib for UIAs, and i is the proportion of returns appropriated to IRR. Capital is required to absorb displaced commercial risk (DCR) from unexpected losses (after accounting for reserves) when UIAs’ returns are negative, $\begin{matrix} {\tilde{r}}_{U I A} = (\begin{matrix} 1 - i \end{matrix}) (1 - e) (\frac{U I A}{A}) (1 - p) (1 - l) {\tilde{r}}_{A} < 0 \end{matrix}$ and exhaust available (accumulated) reserves so that $\begin{matrix} {\tilde{r}}_{U I A} A > P E R + I R R \end{matrix}$ .

We can determine the amount of capital required to cover unexpected losses by estimating the worst negative returns based on the historical cumulative distribution function of UIAs’ returns, ${\tilde{r}}_{U I A}$ , at a given level of statistical confidence, a ∈ (0,1), over time horizon t (consistent with bank’s prevailing solvency standards).¹ Let ${\tilde{r}}_{U I A}$ be a sample of observations drawn from identically distributed, independent random variables {X_t; t = 1,2,..., n} following the stochastic process

\begin{matrix} F (x) = μ_{{\tilde{r}}_{{U I A}_{t}}} + z_{t} σ_{{\tilde{r}}_{{U I A}_{t}}} z_{t} \sim i i d (0, 1), & (B 1.1) \end{matrix}

with conditional mean and standard deviation $\begin{matrix} μ_{{\tilde{r}}_{{U I A}_{t}}} = 𝔼 ({\tilde{r}}_{U I A}) a n d σ_{{\tilde{r}}_{{U I A}_{t}}} \end{matrix}$ respectively, where $σ_{{\tilde{r}}_{{U I A}_{t}}}^{2} = 𝔼 (z_{t}^{2} | Ω_{t - 1})$ , and z has the conditional c.d.f G(z) = Pr(z_t < z|Ω_t-1), based on the available information Ω_t-1 at time t – 1.

Thus, we can rewrite equation (B1.1) above as

\begin{matrix} V a R_{a, t} \equiv \inf (x_{t} | F (x \geq a)) = μ_{{\tilde{r}}_{{U I A}_{t}}} + N (1 - a) σ_{{\tilde{r}}_{{U I A}_{t}}}, & (B 1.2) \end{matrix}

which represents the point estimate of the (1 – a)-quantile of the probability distribution F(VaR_a,t) = Pr[x_t > VaR_a,t] = 1 – a, where $F (x) \sim N [μ_{{\tilde{r}}_{{U I A}_{t}}}, σ_{{\tilde{r}}_{{U I A}_{t}}}^{2}]$ converges to a normal distribution. The corresponding conditional tail expectation (CTE) (which represents a coherent risk measure of unexpected negative returns) with $\frac{1}{a} \int_{0}^{\infty} F_{t}^{\leftarrow} (x) ⅆ x = \frac{1}{1 - a} \int_{0}^{1} F_{t}^{- 1} (a)$ (a)da is defined as

\begin{matrix} C T E_{a, t} = 𝔼 [x_{t} | x_{t} \geq F_{t}^{- 1} (a) = V a R_{a, t}], & (B 1.3) \end{matrix}

based equation (B1.2), after accounting for available (accumulated) reserves, where

\begin{matrix} V a R_{a, t} = - \sup {F_{r}^{- 1} (a) | \Pr [({\tilde{r}}_{U I A} - \frac{P E R + I R R}{A}) > 0] \geq a} \\ = μ_{{\tilde{r}}_{{U I A}_{t}}} + N (1 - a) σ_{{\tilde{r}}_{U I A}} + \frac{P E R + I R R}{A} . (B 1.4) \end{matrix}

While the empirical diffusion process of returns might not necessarily converge to normality, this assumption makes it straightforward to derive point estimates of CTE_a,t based on the equivalency between the z-scores ø(Φ^-1) (1 – a))/(1 – a) (for CTE) and Φ^-1(a) (for Value-at-Risk [VaR]), where ø(.) and Φ^-1(.) are the standard normal probability distribution and quantile functions.² Appendix II shows how to determine CTE_a,t if the normality assumption is relaxed and the asymptotic tail properties are modeled using extreme value theory (EVT).

Multiplying the estimated value of CTE_a,t with the amount of total assets, A, determines the unexpected losses absorbed by shareholders in the absence of any risk-sharing between the Islamic bank and UIA holders, which would imply perfect DCR (and a so-called a-parameter equal to one, which is explained in Section V). DCR declines by any amount of unexpected losses that are absorbed by UIA holders (net of provisions), so that α < 1.

Note:

^1/ We ignore cases where returns are either smoothed by PER or absorbed by IRR if they fall below a benchmark return rate but are still positive. See Toumi and others (2011) for a detailed analytical treatment of these cases.^2/ For instance, we can approximate CTE at the statistical confidence level a = 99.7 percent via VaR at a = 99.9 percent.

B. Credit Risk

Like their conventional peers, Islamic banks face credit risk from counterparties failing to meet their obligations in investment or lending contracts (IFSB, 2005b). Both types of asset-based contracts, ordinary sales/leases (murabahah and ijara) and special sales (salam, istisna’a and bay bithaman ajil), imply credit risk.⁴⁷ In ordinary sales/leases and special sales with deferred payment (bay bithaman ajil), the credit risk stems from the uncertainty about the timely and full repayment (which in the case of the latter is amplified by the lack of collateral due to delayed settlement). In special sales with deferred delivery (salam and istisna’a), credit risk arises from (i) the failure to deliver the specified commodities; (ii) the late delivery of the commodities; or even (iii) the defective delivery of the commodities.

While equity-based contracts (mudarabah and musharakah) held in the banking book expose the bank primarily to so-called capital impairment risk, some of these investments may also imply credit risk.

C. Market Risk

Islamic banks are especially exposed to market risk due to the prevalence of asset-based financial contracts and transactions. Market risk arises from adverse movements in asset prices that affect the valuation of on- and off-balance sheet exposures. These exposures from inventory can be particularly large for Islamic banks, which tend to hold considerable inventories of commodities to pre-endow future sales contracts or fund trading in active (secondary) markets for equity-based transactions. For instance, selling a murabahah or salam contract exposes the bank to the risk of a decline in the future market price of the underlying asset, which would reduce the expected rate of return. Islamic banks aim to mitigate market risk by minimizing inventories of commodities on their balance sheets, completing transactions swiftly (so as to avoid any lapse of time causing differences in contractual and market prices), and enlisting various hedging techniques. The expediency of execution, however, is often subject to external constraints, especially in less developed economies where it may take longer to conclude trades due to the lack of automation. Similarly, Islamic banks that are heavily engaged in financing agricultural activities could also be exposed to greater commodity and inventory risk, depending on the volatility of the price of the agricultural products involved.

Credit and market risks interact if an Islamic bank limits inventory risk from special sales. Engaging in multiple salam contracts exposes the bank not only to credit risk from the first salam contract but also to market risk from any offsetting salam contract. After agreeing to a salam contract on a particular commodity, an Islamic bank would enter into a second (parallel) salam contract to sell forward the commodity received under the first salam contract; this reduces the bank’s net open position of a certain commodity and mitigates associated inventory risk. However, if the first salam contract fails, the bank would have to buy the commodity at the prevailing market price to meet its obligation under the parallel salam contract.⁴⁸ Since two salam contracts cannot be made contingent on each other, the bank cannot reduce the credit risk of the first contract by making the second agreement contingent on the fulfillment of the first. Thus, market risk amplifies potential losses from counterparty risk if the commodity price underlying the salam contract appreciates.⁴⁹

Moreover, since the parallel salam does not offset the credit exposure stemming from the first salam (IFSB, 2005a), it does not represent a genuine hedge but purely as an asset-liability/cash flow management tool.⁵⁰

D. Operational Risk

The concept of operational risk generally relates to potential losses stemming from failed internal processes and systems as well as human error and fraud (including legal risk). For an Islamic bank, failure to comply with religious norms under shari’ah principles governing its activities (or to enforce shari’ah principles under secular courts) represents an additional legal risk, which falls within the classification of operational risk.⁵¹ Such legal risk could lead to the de-recognition of income and resultant losses. Even in jurisdictions with a conventional solvency regime, an Islamic bank would be statutorily entitled to compensate customers in cases when a particular transaction is deemed non-compliant with shari’ah principles. The bank may also decide to forgo some of its profits that are attributable to non-compliant activities (and reduce shareholder value). Typically, these profits are donated to charity.

VI. Capital Requirement for Islamic Banks

The capital adequacy of Islamic banks is similar to that of conventional banks, but also accounts for the potential loss absorption by depositors. Unlike in conventional banking, the capital base of Islamic banks does not cover all unexpected losses, assuming that unsecured investors, such as IA holders, are not fully repaid if the bank becomes a gone concern. In keeping with the Basel Accord for conventional banks, the IFSB (2005a) introduced (and later refined; see IFSB [2012b]) the Capital Standard for Islamic Financial Institutions, which adjusts both the numerator (capital) and the denominator (risk-weighted assets) of the conventional capital adequacy ratio (CAR) to accommodate the business model of Islamic banks. This capital standard comprises a Standard Formula and a more elaborate Supervisory Discretion Formula (SDF), which differ from the capital standard defined in the Basel II/III framework for conventional banks (BCBS, 2010).

The Standard Formula does not explicitly recognize the potential the DCR banks face in practice (which can reduce capital), but all existing reserves are assumed to be available to absorb losses.

Thus, capital adequacy ratio (CAR_std) is defined as

\begin{matrix} C A R_{S t d} = \frac{\overset{c a p i t a l}{\overset{︷}{t o t a l (b o o k) e q u i t y}} {+ P E R_{e q u i t y} + I R R_{R I A}}}{O p R i s k + R W A_{t o t a l} - (R W A_{R I A} + R W A_{U I A})}, & (1) \end{matrix}

where the numerator defines the amount of eligible capital, OpRisk is the capital charge for operational risk, RWA_Total stands for total RWAs (related to market and credit risks). The RWAs are reduced by the amount of RWAs funded by IAs (IFSB, 2013).⁵² However, operational risk losses are attributable to the bank, and thus need to be capitalized.⁵³ Eligible capital is defined as total equity, which might—in some circumstances—also include the shareholders’ share of PER and (RIA’s share of) IRR.⁵⁴ This definition of capital is similar to that of Tier 1 under the revised Basel Accord (BCBS, 2010), which includes disclosed reserves from after-tax retained earnings. The consideration of PER for Islamic banks is consistent with this approach (Grais and Kulathunga, 2007).

The SDF adjusts the Standard Formula to account for the bank’s voluntary loss absorption through DCR (beyond existing reserves), but also recognizes that shari’ah-compliant banking does not cover all investor-specific losses from investments/lending funded by UIA holders.⁵⁵ The UIA holders’ share of reserves mitigating some of the DCR and any unexpected losses on investments financed by IAs (in the case of UIAs only beyond DCR) are subtracted from RWAs (IFSB, 2013; see Figure 6).⁵⁶ The eligible capital in the specification of CAR_SDF can also—in some circumstances^omprise the shareholders’ share in the PER, PER_equity, and IRR attributable to IAs (after accounting for the degree of DCR affecting UIAs), IRR_RIA.

Thus, the appropriate CAR is given by

\begin{matrix} C A R_{S D F} = \frac{\overset{c a p i t a l}{\overset{︷}{t o t a l (b o o k) e q u i t y}} {+ P E R_{e q u i t y} + I R R_{R I A} - α (P E R_{U I A} + I R R_{U I A})}}{O p R i s k + R W A_{t o t a l} - (R W A_{R I A} - (1 - α) R W A_{U J A}) - α \times \underset{R W A_{P E R, I R R}}{\underset{︸}{R W A f u n d e d b y r e s e r v e s (P E R_{U I A} a n d I R R_{U I A})}}}, & (2) \end{matrix}

where α ∈ [0,1] signifies the estimated degree of DCR, that is, the amount of unexpected losses from UIAs, which need to be capitalized. In practice, the supervisory authorities have relative discretion in setting the value of a (see Table 2).⁵⁷ RWA_RIA and RWA_UIA are the RWAs funded by the two types of loss-bearing investment accounts (RIA and UIA).

^{Table 2.}

Displaced Commercial Risk―Current Regulatory Implementation and Industry Practice

(ordered by global share of Islamic banking assets)*

Sources: Adewale and Archer (2019), Farooq and Vivek (2012), IFSB (2011), and authors. Note: */ no data available for Iran and Bangladesh;

^{^1/}Dubai.

^{Table 2.}

Displaced Commercial Risk―Current Regulatory Implementation and Industry Practice

(ordered by global share of Islamic banking assets)*

Country	Alpha-Value
Saudi-Arabia	1.00
UAE ^1/	0.35
Malaysia	0.00
Kuwait	0.50
Qatar	0.35
Turkey	0.70
Indonesia	0.00
Bahrain	0.30
Sudan	0.50
Kazakhstan	0.35
IFSB Example	0.30

Sources: Adewale and Archer (2019), Farooq and Vivek (2012), IFSB (2011), and authors. Note: */ no data available for Iran and Bangladesh;

^{^1/}Dubai.

^{Table 2.}

Displaced Commercial Risk―Current Regulatory Implementation and Industry Practice

(ordered by global share of Islamic banking assets)*

Country	Alpha-Value
Saudi-Arabia	1.00
UAE ^1/	0.35
Malaysia	0.00
Kuwait	0.50
Qatar	0.35
Turkey	0.70
Indonesia	0.00
Bahrain	0.30
Sudan	0.50
Kazakhstan	0.35
IFSB Example	0.30

Sources: Adewale and Archer (2019), Farooq and Vivek (2012), IFSB (2011), and authors. Note: */ no data available for Iran and Bangladesh;

^{^1/}Dubai.

Alternatively, when supervisory authorities have discretion in accounting for DCR and also for RIAs, the corresponding reserves would need to be made explicit in the capital adequacy formula by including PER_RIA and RWAs funded by PER_RIA. The deduction of RWAs would decline by aRWA_RIA and the diminished loss-absorbing impact of reserves on capital decreases by IRR_RIA and aPER_RIA, so that

\begin{matrix} C A R_{S D F} = \frac{\overset{c a p i t a l}{\overset{︷}{t o t a l (b o o k) e q u i t y}} {+ P E R_{e q u i t y} - α (P E R_{U I A} + P E R_{R I A} + R R_{U I A})}}{O p R i s k + R W A_{t o t a l} - (R W A_{R I A} - (1 - α) R W A_{U I A}) - α \times \underset{R W A_{P E R, I R R}}{\underset{︸}{R W A f u n d e d b y r e s e r v e s (P E R_{U I A}, P E R_{R I A} a n d I R R)}}}, & (3) \end{matrix}

However, for the remainder of the paper, we disregard this augmented definition of capital in equations (1) and (2), so that

\begin{matrix} C A R_{S D F} = \frac{c a p i t a l}{O p R i s k + R W A_{t o t a l} - R W A_{R I A} - (1 - α) R W A_{U I A} - α R W A_{P E R, I R R}} . & (4) \end{matrix}

For illustrative purposes (see Figure 6), we retain the IRR available to smooth returns of UIAs for a given degree of DCR (see Box 1) so that

\begin{matrix} C A R_{{S D F}_{a d j}} = \frac{c a p i t a l - α {I R R}_{U I A}}{O p R i s k + R W A_{t o t a l} - R W A_{R I A} - (1 - α) R W A_{U I A} - α R W A_{P E R, I R R}} . & (5) \end{matrix}

The share (1 – α) of RWAs associated with UIAs, (1 – α)RWA_UIA, is deemed unaffected by DCR (that is, it constitutes loss absorption by depositors), and, thus, is deducted from the denominator—just like RWA_RIA, which is often treated as an off-balance sheet item and need not be capitalized.⁵⁸,⁵⁹ Only the proportion of RWAs funded by reserves that cover expected losses incurred by UIAs, (1 – α)RWA_PERiIRR, is relevant for the denominator in the calculation of capital adequacy.

However, the predefined impact of DCR on loss absorption by UIAs in CAR_SDF entails conceptual challenges by commingling expected and unexpected losses. The loss-absorbing share of UIAs, (1 – α)RWA_UIA, is contingent on the adequate provisioning for expected losses to UIAs through IRR_UIA and the capitalization of unexpected losses up to αRWA_UIA. If earmarked capital and reserves are insufficient to cover a higher-than-expected DCR, the lower loss absorption by UIAs would decrease CAR_SDP. Also, CAR is likely to decline (all else being equal) if the bank does not generate enough profits to allocate retained earnings to keep the assumed loss-absorbing share of UIAs unchanged (which is likely in an adverse situation).⁶⁰

Figure 7 compares the conventional and Islamic specification of CAR based on equations (3) and (4) using the stylized balance sheet data of an Islamic bank (see Appendix I, Table A2). The first chart shows that the capital adequacy of the Islamic bank is strictly higher under the adjusted specification of CAR due to the loss absorption by IA holders. Considering that reserves covering expected losses of UIAs are deducted from capital, CAR_SDP can drop below the conventional CAR if low loss absorption by IAs implies high DCR, and RWAs of Islamic banks converge to those under the conventional assessment of capital adequacy as the α-parameter increases.

Based on the analytical determination of DCR in the previous section (Section IV. A), we can evaluate whether a certain choice of the α-parameter is consistent with the actual investment risk faced by UIAs, assuming that the bank capitalizes most (but not all) unexpected losses that are not absorbed by the loss-sharing arrangement with UIAs. Given that the loss-absorbing share of RWAs funded by UIAs, (1 – α)RWA_UIA, is subtracted from total RWAs in the denominator of CAR_SDF, an appropriate a-parameter for αRWA_UIA ≤ UL would need to satisfy

\begin{matrix} α^{*} \times \underset{R W A_{U I A}}{\underset{︸}{\frac{U I A}{A} \times \underset{R W A_{t o t a l}}{\underset{︸}{{\bar{R W}}_{t o t a l} \times A}}}} = C T E_{a, t} \times U I A, & (6) \end{matrix}

which simplifies to

\begin{matrix} α^{*} = C T E_{a, t} / {\bar{R W}}_{t o t a l}, & (7) \end{matrix}

where the conditional tail expectation CTE_a,t specifies the estimated share of UIA being lost with given level of statistical confidence, a ∈ (0,1), over time horizon t (consistent with bank’s prevailing solvency standards) (see Box 1), assuming that the average credit and market risk weights for assets funded by UIAs, ${\bar{R W}}_{U I A} = {\bar{R W}}_{t o t a l} = {R W A}_{t o t a l} / A$ , is the same as the one for all other balance sheet assets, where RWA_total = RWA_credit + RWA_market.

The assumed DCR is not credible if the bank cannot absorb actual unexpected losses in addition to expected losses covered by available IRR. In case of UL* > UL, unexpected losses are insufficiently capitalized (that is, the assumed capital relief from UIAs in equation (2) is too high since α* > α,) and would require a transfer of shareholder wealth, (α* – α) RWA_UIA, to compensate for higher-than-expected loss absorption by UIA holders; this also implies that the bank would need to remain profitable to fund such a transfer during times of stress.

We construct a simple practical example of this approach by using the historical return performance of the MSCI World Islamic Equity Index⁶¹ as a proxy for the investment returns of UIAs and the stylized balance sheet of an Islamic bank (see Appendix I, Table A2). The amount of unexpected loss is determined as a point estimate (see equation (B1.4) in Box 1) for different levels of statistical confidence after accounting for the “cascading mechanism” of provisioning (PER and IRR) and the loss-mitigating effect of existing reserves. Figure 8 shows the sensitivity to VaR_ait to the historical return volatility. Under these conditions, we find that that choice of α = 0.3 would be insufficient since ${C T E}_{a, t} > α {\bar{R W}}_{t o t a l} = 0.15$ if the historical volatility doubles to a level of statistical confidence close (but below) the prudential requirement (99.9 percent).⁶²

VII. Stress Testing Islamic Banks

This section provides an overview of the calibration of shocks to specific risk factors and their impact on the determination of capital adequacy of Islamic banks. In general, the capital assessment under stress should capture all material risks affecting all operations and provide a total view of capital adequacy—on an aggregated or individual basis—of legal entities and/or across groups. Compared to conventional banks, Islamic banks require a more nuanced treatment of risk factors given the specificities of risk exposures, the influence of shari’ah compliance on the transmission of shocks, and the impact of potential risk mitigation. Thus, this section identifies the characteristics of these risk factors and illustrates how properties of Islamic banking shape the way in which shocks can be integrated into a standard specification of risk factors underlying the capital assessment.

A. Scope of Risk Factors

Like their conventional peers, Islamic banks are vulnerable to three key transmission channels of negative shocks to their balance sheets, albeit with different implications for the profit and loss (P&L) statement and the assessment of capital adequacy:

Changes in pre-impairment income from financing activities, including the capital impact of investment shortfall (which may entail DCR) due to lower-than-expected rates of return, indirect interest rate risk, and/or higher funding costs;
Changes in asset quality, including valuation changes of traded securities (mark-to-market [MtM] and available-for-sale [AfS]), asset impairment charges (credit losses and other losses) of held-to-maturity (HtM) assets,⁶³ and operational risk losses; and
Changes in risk intensity resulting from higher unexpected losses (due to deteriorating asset quality) of defaultable assets and traded securities (that is, credit and market RWAs), mitigated by the positive impact of charge-offs and net lending and investment, and lower loss absorption by IAs (including changes in assumptions about DCR).

Stress tests would include (as a minimum) both credit and market risks affecting the capital adequacy of Islamic banks: (i) declining lending and investment income due to a negative shock to the realized rate of return (and indirect interest rate risk in mixed banking systems); (ii) rising impairments due to increasing credit and counterparty risks in the lending and investment portfolios; and (iii) adverse changes in asset prices affecting the valuation of exposures to market risk.⁶⁴ The impact of these risk factors is measured as the change of CAR_SDP according to equation (iv) under the impact of stress after accounting for net operating losses and the change in RWAs (which also affects assets funded by reserves), so that

\begin{matrix} C A R_{S D F_{s t r e s s e d}} = C A R_{S D F} + \underset{r e t a i n e d e a r n i n g s}{\underset{︸}{n e t o p e r a t i n g i n c o m e - d i v i d e n d p a y o u t}} + Δ R W A_{t o t a l} + Δ 0 p R i s k = \frac{c a p i t a l + r e t a i n e d e a r n i n g s}{(\begin{matrix} 0 p R i s k + Δ 0 p R i s k \\ + R W A_{t o t a l} + Δ R W A_{t o t a l} - (R W A_{R I A} + + Δ R W A_{R I A}) \\ - (1 - α) (R W A_{U I A} + Δ R W A_{U I A}) - α (R W A_{P E R, I R R} + Δ R W A_{P E R, I R R} \end{matrix})}, & (8) \end{matrix}

where the net operating income (after taxes) comprises the implied rate of return from financing activities and investment less (i) the net effect of asset impairments and valuation losses (that is, credit and market risks); and (ii) the impact of changes in the rates of return and funding costs (including forgone return from impaired assets). The change of RWAs, ΔRWA_total, reflects the net change in unexpected losses from higher market and credit risks due to the deteriorating asset quality, after accounting for the substitution effect between higher RWAs of existing impaired assets and lower RWAs of new assets (unless renewals are excluded from the stress test). Operational risk losses reduce net operating income. but primarily change the capitalization of operational risk in the denominator.

These risk transmission channels of shocks from credit and market risks, as well as changes in profitability, can be modeled via so-called “satellite models” or expert judgment.⁶⁵

Satellite models define the historical sensitivity of bank performance to changes in macrofinancial conditions and commonly include a lagged term, GDP growth, rates of return, cost of capital, other macroeconomic variables, and firm-specific variables, such as leverage, loan-to-asset ratio, and the funding gap. Most satellite models are focused on changes in credit and market risks. Other risk factors, such as operational risk, require more qualitative approaches (and a discrete specification of the severity of shocks) due to a lack of sufficient empirical observations and/or difficulties estimating consistent macrofinancial scenarios. The results of stress tests and the interpretation of associated findings are heavily influenced by the scope and calibration of macrofinancial linkages and the assessment of vulnerabilities to these risks but depend on data availability/granularity.

The following section focuses on the practical implementation of these risk factors, with each considered a single-factor shock over a single time period (without the loss mitigation of net operating profits from investments and lending).

B. Displaced Commercial Risk

Analogous to the net interest income of conventional banks, the implied rate of return from lending and investments is the main determinant of the profitability of Islamic banks. However, the impact of changes in the rate of return on capital adequacy depends on the scope for DCR (that is, the extent to which reserves can be released to cover claims from investment deposits if realized profits fall below expectations and overall profitability of investments generate losses that exhaust provisions).

Three possible stress scenarios illustrate how shocks to the rate of return influence the scope for DCR:

Shock to asset returns. Suppose that the bank’s rate of return from investment/lending drops below the (non-guaranteed)⁶⁶ targeted profit rate offered to depositors (that is, the realized rate of return is lower than the expected rate of return). Islamic banks have a few options available to mitigate the effect of investment shortfall on the stability of the deposit base. While this investment shortfall should be passed on to IA holders in principle, they are fully (or partially) covered by provisions (PER and IRR); if they exceed provisions, shareholders tend to absorb part of this shortfall by accepting DCR to maintain the deposit base (“total accounts”). Therefore, the shortfall is given by

$i n v e s t m e n t s h o r t f a l l = (a c t u a l r e t u r n — e x p . r e t u r n_{I A}) \times t o t a l a c c o u n t s_{I A} . (9)$
Shock to availability of funding. Suppose that the bank’s lending and investments generate the expected rate of return but competitors offer higher returns, which threaten to erode the bank’s deposit base. If the bank is unable to increase the returns offered to its existing IA holders, it faces the risk of depositors withdrawing their funds, so that

$i n v e s t m e n t s h o r t f a l l = (\begin{matrix} t o t a l a c c o u n t s_{I A} \\ - e x p . t o t a l a c c o u n t s_{I A} \end{matrix}) \times a c t u a l r e t u r n_{I A} . (10)$
Shock to asset returns and funding. Suppose that there is a decline in the amount of funds available in the economy—that is, a generalized tightening in liquidity conditions, which reduces the amount of cash that depositors are willing to place in IAs and increases the rate of return demanded by depositors.⁶⁷ The net effect is the deterioration of investment performance due to an increasing funding cost. The shortfall is now given by

$i n v e s t m e n t s h o r t f a l l = (\begin{matrix} a c t u a l r e t u r n_{I A} \\ - r e v i s e d e x p . r e t u r n_{I A} \end{matrix}) \times (\begin{matrix} e x p . t o t a l a c c o u n t s_{I A} \\ - t o t a l a c c o u n t s_{I A} \end{matrix}) . (11)$

Once the amount of investment shortfall is known, the effect on CAR after considering retained earnings can be computed as⁶⁸

\begin{matrix} C A R_{D C R} = \frac{c a p i t a l + (\begin{matrix} r e t a i n e d e a r n i n g s \\ - i n v e s t m e n t s h o r t f a l l (1 - s h a r e cov e r e d b y P E R_{e q u i t y}) \end{matrix})}{(\begin{matrix} 0 p R i s k + R W A_{t o t a l} - R W A_{R I A} - (1 - α) R W A_{U I A} \\ (- α (\max R W A_{P E R, I R R} - R W A_{P E R, I R R} c o v e r i n g i n v e s t m e n t s h o r t f a l l, 0)) \end{matrix})}, & (12) \end{matrix}

which might involve a reduction of capital if the investment shortfall exceeds available provisions, PER_UIA and IRR, so that

R W A_{P E R, I R R} - R W A_{P E R, I R R} c o v e r i n g i n v e s t m e n t s h o r t f a l l < 0. (13)

PER is shared between both shareholders and depositors, whereas IRR can only be used for distributions to depositors. In practice, shareholders may decide to release some of PER_equity. If all reserves are exhausted, any transfer of shareholder value would diminish also retained earnings if (α* – a)RWA_UIA so that

\begin{matrix} i n v e s t m e n t s h o r t f a l l cov e r e d b y P E R_{e q u i t y} = \max (\begin{matrix} i n v e s t m e n t s h o r t f a l l - \\ i n v e s t m e n t s h o r t f a l l \\ c o v e r e d b y P E R_{U I A} a n d I R R, 0 \end{matrix}) . & (14) \end{matrix}

C. Indirect Interest Rate Risk

Additional risks could arise from changes in general interest rates if Islamic banks operate in a mixed financial system (that is, where conventional and Islamic financial service providers operate alongside each other). Islamic banks that choose to benchmark the return on their IAs to the deposit rate offered by conventional banks incur indirect interest rate risk.⁶⁹ A tightening of monetary conditions and the attendant increase of prevailing (maturity-matched) interest rates (by conventional banks) could result in Islamic banks loosing some of their deposits to conventional banks unless the expected return from investment matches the higher market rate. The economic effect of this scenario would be similar to that of DCR due to a shock to an Islamic bank’s rate of return from investment/lending, so that

int e r e s t r a t e g a p = (\begin{matrix} e x p . r e t u r n_{I A} \\ - η \times m a r k e t int e r e s t r a t e \end{matrix}) \times t o t a l a c c o u n t s_{I A}, (15)

whose magnitude is influenced by the degree of pass-through, η, from general interest rates to the expected returns of IAs.

If realized profits fall below expectations, Islamic banks would have to offer a higher rate of return (or raise the profit-sharing ratio) on IAs above the (non-guaranteed) targeted return by releasing reserves to maintain their deposit base. If both PER_UIA and IRR are not sufficient to finance the “interest rate gap” to conventional banks, shareholders may decide to release some of PER_equity (as in equation (14) above for investment losses). Since some IA holders may be insensitive to (small) changes in the rate of return, the elasticity of deposits is captured by the fraction ø of IAs that would need to be compensated by the existing reserves and/or lower dividend payouts to shareholders.⁷⁰ Thus, the interest rate gap can be expressed as

int e r e s t r a t e g a p = (\begin{matrix} e x p . r e t u r n_{I A} \\ - η \times m a r k e t int e r e s t r a t e \end{matrix}) \times ϕ \times t o t a l a c c o u n t s_{I A}, (16)

whose effect on CAR can be written as⁷¹

\begin{matrix} C A R_{I R R} = \frac{c a p i t a l + (\begin{matrix} r e t a i n e d e a r n i n g s \\ - i n t e r e s t r a t e g a p (1 - s h a r e cov e r e d b y P E R_{e q u i t y}) \end{matrix})}{(\begin{matrix} 0 p R i s k + R W A_{t o t a l} - R W A_{R I A} - (1 - α) R W A_{U I A} \\ (- α (\max R W A_{P E R, I R R} - R W A_{P E R, I R R} c o v e r i n g i i n t e r e s t r a t e g a p, 0)) \end{matrix})}, & (17) \end{matrix}

where

\begin{matrix} i n t e r e s t r a t e g a p cov e r e d b y P E R_{e q u i t y} = \max (\begin{matrix} i n t e r e s t r a t e g a p - \\ i n t e r e s t r a t e g a p \\ c o v e r e d b y P E R_{U I A} a n d I R R, 0 \end{matrix}) . & (18) \end{matrix}

D. Credit Risk

Credit risk represents a key component of the capital assessment of Islamic banks under stress and can be specified in a way similar to that of conventional banking. Credit risk shocks affect the valuation of exchange-based contracts in the financing and lending portfolio (that is, ordinary sales [murabahah], special sales [salam, istisna’a, bay bithaman ajil], and leases [ijara]) as well as investment exposures in the banking book (that is, direct equity exposures, investment certificates [sukuk], and profit- and loss-sharing contracts [mudarabah, musharakah]). Some shocks that are typically considered in stress tests are:

a broad-based deterioration of economic conditions affecting multiple sectors,⁷² resulting in a general increase of nonperforming asset (NPA) balances and charge-offs;
a negative shock to a specific economic sector affecting the asset quality of all relevant exposures; and
deterioration of already existing NPAs by one or more “notches” in the distribution across subcategories (substandard, doubtful, and delinquent).⁷³

The first two shocks result in additional credit losses but also increase the level of unexpected losses (above the level of provisioned asset impairment reflected in pre-shock NPAs), which increase the estimates of RWAs. In contrast, the last shock would not increase credit losses but raise the level of required provisions due to higher expected losses overall. The credit risk-related losses from both lending and investment activities can be expressed as

\begin{matrix} c r e d i t r i s k l o s s = Δ N P A - s p e c i f i c p r o v i s i o n s + f o r e g o n e r e t u r n s, & (19) \end{matrix}

which reflects the amount of asset impairments ΔNPA (net of any specific provisions for expected losses)⁷⁴ and the forgone return from impaired lending (due to termination, default, or arrears)⁷⁵. Higher unexpected losses due to deteriorating asset quality can be specified as⁷⁶

\begin{matrix} Δ R W A_{c r e d i t} = Δ R W A_{c r e d i t_{Δ P D}} + Δ R W A_{c r e d i t_{Δ c o n c e n t r a t i o n}} - R W A_{c h \arg e} - R W A_{Δ c r e d i t}, & (20) \end{matrix}

due to a higher probability of default (PD), ΔRWA_{credit_ΔPD}, the change in portfolio concentration, f(ΔConcentration_portfolio), the impact of charge-offs, RWA_charge-off, and the net change of the RWAs of credit-related exposures, RWA_Δcredit, which captures the substitution effect between higher RWAs of impaired assets and lower RWAs of new investment/lending (assuming that renewals are included in the stress test in a non-static credit portfolio). However, recent developments in stress testing following the implementation of the IFRS 9 impairment model suggest a greater focus on modeling credit risk losses using an accounting approach,⁷⁷ which has also shifted the estimation of unexpected losses toward standardized approaches. Thus, equation (20) can be simplified to

\begin{matrix} Δ R W A_{c r e d i t} = - R W A_{c h \arg e - o f f s} - R W A_{Δ c r e d i t}, & (21) \end{matrix}

where the RWAs of defaulted exposures, RWA_charge-off, reduce the total RWA_credit, which can be approximated by taking 2.5 times the average RWAs for non-defaulted exposures (accounting for the fact that risk-weights for defaulted exposures were higher prior to default). Appendix V provides a detailed specification of the nonlinear effect of changes in PDs and the impact of concentration risk on RWAs for a more comprehensive implementation of credit risk (consistent with economic capital approaches).

Implementing the above formula in an Islamic banking context is complicated by the loss absorption of IA holders, which reduces the impact of credit risk shocks on both the level of capital (through net operating income) and unexpected losses (in the form of RWAs). Since IA holders absorb some losses associated with higher credit risk under stress, the CAR formula can be written as

C A R_{c r e d i t} = \frac{(\begin{matrix} c a p i t a l + r e t a i n e d e a r n i n g s \\ - c r e d i t r i s k l o s s \times \underset{s h a r e o f l o s s b o r n e b y U I A a n d R I A}{\underset{︸}{(\frac{{\tilde{R W A}}_{U I A} + {\tilde{R W A}}_{R I A}}{{\tilde{R W A}}_{t o t a l}})}} \end{matrix})}{(0 p R i s k + {\tilde{R W A}}_{t o t a l} - {\tilde{R W A}}_{R I A} - (1 - α) {\tilde{R W A}}_{U I A} - α {\tilde{R W A}}_{P E R, I R R} + Δ R W A_{c r e d i t} \times \underset{s h a r e o f l o s s b o r n e b y U I A a n d R I A}{\underset{︸}{(\frac{{\tilde{R W A}}_{U I A} + {\tilde{R W A}}_{R I A}}{{\tilde{R W A}}_{t o t a l}})}})}, (22)

assuming that all IAs (UIA and RIA) absorb credit risk-related losses in proportion to their share of total RWAs, with updated ${\tilde{R W A}}_{t o t a l}$ consistent with ΔRWA_credit, and corresponding changes in loss absorption and associated provisioning is ${\tilde{R W A}}_{R I A} = R W A_{R I A} + Δ R W A_{R I A}, {\tilde{R W A}}_{U I A} = R W A_{U I A} + Δ R W A_{U I A} and {\tilde{R W A}}_{P E R, I R R} = R W A_{P E R, I R R} + Δ R W A_{P E R, I R R}$ .⁷⁸ However, the attribution of losses according to equation (20) would further depend on whether losses stem from assets funded by either UIAs or RIAs (which is ignored in this expression). If data constraints limit a sufficiently detailed analysis of loss absorption by IA holders, the conservative implementation of credit risk under stress would result in

\begin{matrix} C A R_{c r e d i α t} = \frac{c a p i t a l + r e t a i n e d e a r n i n g s - c r e d i t r i s k l o s s}{(0 R i s k + {\tilde{R W A}}_{t o t a l} - {\tilde{R W A}}_{R I A} - (1 - α) {\tilde{R W A}}_{U I A} - α {\tilde{R W A}}_{P E R, I R R} + Δ R W A_{c r e d i t})}, & (23) \end{matrix}

which ignores the loss absorption by IAs, so that $\frac{{\tilde{R W A}}_{U I A} + {\tilde{R W A}}_{R I A}}{{\tilde{R W A}}_{t o t a l}} \to 0$ , and overstates the effective capital impact of credit risk-related losses.⁷⁹

Special sales (with delayed settlement) may involve additional credit risk. The counterparty risk of a bank increases if the asset price of a commodity (“collateral asset”) supporting a sales contract with deferred delivery (salam or istisna’a) increases until the maturity date of the contract; this applies conversely to asset price declines if the borrower’s payment to the bank is deferred (bay bithaman ajil). In the case of the former, for example, a negative supply shock to the agricultural sector (that is, output declines due to a drought or some other natural disaster) would increase the market price for agricultural goods if demand remained unchanged. In this situation, an agricultural salam contract (see Figure 2) would expose the bank to higher counterparty risk since the value of the to-be-delivered commodity (as the collateral asset) is likely to exceed the amount owed by the borrower in present value (PV) terms. The credit loss arises when the borrower fails to deliver the commodity or delivers a smaller amount than agreed in the salam contract ex ante. In a bay bithaman ajil contract, the depreciation of the collateral asset increases the borrower’s cost of repayment, resulting in a higher probability of default.

The credit risk losses from the borrower’s early determination or failure to fully repay a salam contract can be quantified as the ex post difference between the contractual and actual value of the commodity plus any forgone rate of return (if default occurs prior to the contractual maturity/delivery date).

c r e d i t r i s k l o s s_{s p e c \dot{ι} a l s a l e s_{d e l a y e d d e l i v e r y}} (1 + f o r e g o n e r e t u r n) (P V (c o l l a t e r a l a s s e t) - s p o t v a l u e (p a y m e n t o f a s s e t), (24)

where the discount factor to derive the PV of the collateral assets, PV {collateral asset), represents the “implied return” of the bank.

Conversely, for a contract with deferred payment (bay bithaman ajil), the depreciation of the collateral asset would have the same effect, so that

c r e d i t r i s k l o s s_{s p e c \dot{ι} a l s a l e s_{d e l a y e d p a y m e n t}} = (1 + f o r e g o n e r e t u r n) (P V (a s s e t r e p a y m e n t) - s p o t v a l u e (a s s e t d e l i v e r e d) . (25)

Combining both equations above for all exposures to special sales results in the net amount of credit risk-related losses under the assumption that the valuation of some contracts is influenced by the same change in asset prices so that

\begin{matrix} c r e d i t r i s k l o s s_{s p e c i a l s a l e s} = c r e d i t r i s k l o s s_{s p e c \dot{ι} a l s a l e s_{d e l a y e d d e l i v e r y}} + c r e d i t r i s k l o s s_{s p e c i a l s a l e s_{d e l a y e d p a y m e n t}} . & (26) \end{matrix}

Thus, equation (23) can be augmented by equation (26) so that

\begin{matrix} C A R_{c r e d i t} = \frac{(\begin{matrix} c a p i t a l + r e t a i n e d e a r n i n g s \\ - c r e d i t r i s k l o s s - c r e d i t r i s k l o s s_{s p e c ι a l s a l e s} \end{matrix})}{(0 p R i s k + {\tilde{R W A}}_{t o t a l} - {\tilde{R W A}}_{R I A} - (1 - α) {\tilde{R W A}}_{U I A} - α {\tilde{R W A}}_{P E R, I R R} + Δ R W A_{c r e d i t})} . & (27) \end{matrix}

E. Market Risk

Given the asset-based nature of Islamic banking, market risk (“inventory risk”) arises chiefly from price changes of net open positions of inventory. Islamic banks hold certain assets (for example, real estate or commodities) as collateral to different forms of exchange-based contracts, such as murabahah, salam, and ijara (see Table 1), which are recorded at fair value as available-for-lease (AfL).⁸⁰ The expected losses from these lending and investment activities are “bi-dimensional,” that is, they are defined by the probability of shortfall between the value of collateral and the total counterparty exposure. Thus, the risk that the value of the inventory owned by the bank diminishes and/or experiences greater price volatility is closely related to credit risk. If the market price declines, the bank would be forced to charge a lower sales price or adjust the lease value, unless it is willing to accept a lower degree of collateralization. Then the market-related loss is given by

\begin{matrix} m a r k e t r i s k l o s s_{o r d i n a r y s a l e s} = (1 + f o r e g o n e r e t u r n) (i n v e n t o r y_{n o m i n a l v a l u e} - i n v e n t o r y_{m a r k e t v a l u e}) . & (28) \end{matrix}

Market risk losses can also arise from the decline in the market values of profit- and loss-sharing investments held in the trading book, market risk loss_trading, such as investment certificates (sukuk), Islamic collective investment schemes (ICIS), and equity securities. If the change in market risk is associated with a change in price volatility, it will affect the risk-weighting of inventory assets held in the trading book, ΔRWA_market. Moreover, market risk exposures may involve some foreign exchange (FX) risk, which requires a different methodological treatment than in the context of conventional banking.⁸¹ There are two important differences between Islamic and conventional FX transactions: (i) under the rules of sarf, which govern currency exchanges consistent with Islamic finance principles, gold and silver are treated as foreign currency (and not as commodities); and (ii) the permissible use of currency derivatives in Islamic finance is restricted (Jobst, 2009; Jobst and Solé, 2012).

Special sales (see Table 1) may result in additional market risk if they occur together with a reverse transaction. Islamic banks typically take offsetting short positions through parallel special sales to minimize the carry cost of holding inventory as collateral (such as commodities) for contracts with deferred delivery (salam or istisna’a). In the case of a parallel salam, the bank receives a certain amount of cash from a third party and delivers the collateral asset upon maturity, which coincides with the delayed receipt of the collateral asset from the original sale (see Figure 3). The market risk of a parallel salam contract arises if the collateral asset appreciates. The bank would lose

\begin{matrix} m a r k e t r i s k l o s s_{s p e c i a l s a l e s} = F V (c o l l a t e r a l a s s e t_{s p o t v a l u e}) - c o l l a t e r a l a s s e t_{m a r k e t v a l u e} . & (29) \end{matrix}

if the market value of the collateral asset to be delivered to the counterparty of the parallel salam at maturity is higher than the future value (FV) of the spot payment for the collateral assets the bank is due to receive under the initial salam contract.⁸²

Similar to the consideration of unexpected losses from credit risk, price volatility and/or changes in the composition of listed exposures (sales and profit- and loss-sharing contracts) in the trading and investment portfolios change the amount of unexpected losses from market risk (see Table 1), which is specified as

\begin{matrix} Δ R W A_{m a r k e t} = \underset{Δ R W A_{m a r k e t_{Δ p r i c e}}}{\underset{︸}{f (Δ V a R_{p o r t f o l i o})}} - R W A_{Δ m a r k e t}, & (30) \end{matrix}

where f(ΔVaR_portfolio) reflects the change in the VaR and RWA_Δmarket represents the net change in portfolio allocation affecting RWAs, based on investment and trading behavior under stress. Since most stress tests focus on standardized approaches (assuming that higher price volatility is associated with a decline in credit quality), the expression above simplifies to ΔRWA_market = – RWA_Δmar, while the impact of valuation changes on the capital intensity is determined by predefined changes in risk weights. Appendix V explains how equation (30) can be derived based on an economic valuation approach.

Islamic banks absorb market risk losses through net operating income or, in the case of insufficiency, in its common equity. So the CAR after a shock to market risk from ordinary and parallel special sales, as well as assets in the trading portfolio, would be

\begin{matrix} C A R_{m a r k e t} = \frac{(\begin{matrix} c a p i t a l + r e t a i n e d e a r n i n g s \\ - m a r k e t r i s k l o s s_{o r d ι n a r y s a l e s} \\ - m a r k e t r i s k l o s s_{s p e c ι a l s a l e s} \\ - m a r k e t r i s k l o s s_{t r a d i n g} \end{matrix})}{(0 p R i s k + {\tilde{R W A}}_{t o t a l} - {\tilde{R W A}}_{R I A} - (1 - α) {\tilde{R W A}}_{U I A} - α {\tilde{R W A}}_{P E R, I R R} + Δ R W A_{m a r k e t})}, & (31) \end{matrix}

with updated ${\tilde{R W A}}_{t o t a l}$ consistent with ΔRWA_market. The scope of impact can also be made conditional on the source of funding. One could assume that the total amount of sukuk and the ICIS portfolio were exclusively funded by UIAs (IFSB, 2015); alternatively, in the case of commingling with other sources of funding for these investments, the respective shares would need to be taken into account. The impact on the net income of Islamic banks would then depend on the degree of loss absorption by UIAs (subject to the degree of DCR).

F. Operational Risk

Operational risk of Islamic banks is explicitly recognized in the capital assessment but could encompass a wide range of activities that might be outside the scope of stress tests. The one-off nature of large operational risk events frequently eludes purely quantitative models and warrants a qualitative overlay that explains the causality of operational risk events and the sensitivity of their financial impact.⁸³ Given the pervasiveness of operational risk from shari’ah compliance in Islamic banking, potential areas of overlap with other sources of risk are significant, suggesting an integrated (and possibly more qualitative) stress testing approach for this risk factor.⁸⁴ Thus, shocks to operational risk are not exclusive to the failure to comply with shari’ah principles, and their impact might differ from that implied by simple quantitative approaches, such as the BIA. For the purposes of a methodological treatment consistent with the quantitative assessment of other risk factors, the impact of shocks to operational risk above the regulatory minimum, ΔOpRisk, on capital adequacy under stress is defined as

\begin{matrix} C A R_{o p e r a t i o n a l} = \frac{c a p i t a l + r e t a i n e d e a r n i n g s - o p e r a t i o n a l r i s k l o s s}{(O p R i s k + Δ O p R i s k + {\tilde{R W A}}_{t o t a l} - {\tilde{R W A}}_{R I A} - (1 - α) {\tilde{R W A}}_{U I A} - α {\tilde{R W A}}_{P E R, I R R})} . & (32) \end{matrix}

G. Combination of Risk Factors and Organization of Risk Drivers

The aggregate impact of shocks to these risk factors should be considered without diversification benefits. Assuming that risk factors are not fully correlated, it is reasonable to account for their dependence structure and combinations of stress testing parameters in which the individual impact of each risk is lower than the risk in isolation. However, combining multiple risk factors with diversification effects tends to complicate the reliable capital assessment. Instead, the capital impacts CAR_DCR, CAR_IRR, CAR_credit, CAR_market, and CAR_operational of the various risk factor in equations (12), (17), (27), (31) and (32) are combined so that CAR_{SDF_stressed} in equation (8) above can be rewritten as⁸⁵

\begin{matrix} C A R_{S D F_{s t r e s s e d}} = \frac{(\begin{matrix} c a p i t a l + r e t a i n e d e a r n i n g s \\ - i n v e s t m e n t s h o r t f a l l (1 - s h a r e cov e r e d b y P E R_{e q u i t y}) \\ - int e r e s t r a t e g a p (1 - s h a r e cov e r e d b y P E R_{e q u i t y}) \\ \begin{array}{l} - c r e d i t r i s k l o s s - c r e d i t r i s k l o s s_{s p e c i a l s a l e s} \\ \begin{matrix} - m a r k e t r i s k l o s s_{o r d i n a r y s a l e s} - m a r k e t r i s k l o s s_{s p e c i a l s a l e s} \\ - m a r k e t r i s k l o s s_{t r a d i n g} - o p e r a t i o n a l r i s k l o s s \end{matrix} \end{array} \end{matrix})}{(\begin{matrix} O p R i s k - Δ O p R i s k + {\tilde{R W A}}_{t o t a l} \\ - {\tilde{R W A}}_{R I A} - (1 - α) {\tilde{R W A}}_{U I A} - α {\tilde{R W A}}_{P E R, I R R} \\ - α (\max (\begin{matrix} R W A_{P E R, I R R} \\ - R W A_{P E R, I R R} cov e r i n g i n v e s t m e n t s h o r t f a l l \\ - R W A_{P E R, I R R} cov e r i n g int e r e s t r a t e g a p, 0 \end{matrix})) \end{matrix})} & (33) \end{matrix}

with ${\tilde{R W A}}_{t o t a l}$ consistent with ΔRWA_credit and ΔRWA_market, which simplifies to

\begin{matrix} C A R_{S t d_{s t r e s s e d}} = \begin{matrix} c a p i t a l + r e t a i n e d e a r n i n g s \\ - (1 - s h a r e cov e r e d b y P E R_{e q u i t y}) (i n v e s t m e n t s h o r t f a l l + int e r e s t r a t e g a p) \\ \frac{- c r e d i t r i s k l o s s_{t o t a l} - m a r k e t r i s k l o s s_{t o t a l} - o p e r a t i o n a l r i s k l o s s}{0 p R i s k - Δ 0 p R i s k + {\tilde{R W A}}_{t o t a l} - {\tilde{R W A}}_{R I A}} \end{matrix}, & (34) \end{matrix}

under the standard formula (without DCR; see equation (4)), where credit risk loss_total = credit risk loss – credit risk loss_{special sales} and market risk loss_total = market risk loss_{ordinary sales} – market risk loss_{special sales} – market risk loss_trading. Both equations include balance sheet dynamics related to changes in RWAs due to new lending and investment (with retained earnings reflecting the impact of changes in net profitability (after income and taxes) as well as dividend policy and the managerial capital buffer). Adapting this approach would result in a stylized output template for a multiperiod stress test to accommodate the main results, risk drivers, balance sheet information, and stress testing parameters (see Appendix I, Table A3).

The specification of these risk factors also depends on the nature, scale, and complexity of the relevant banking activities and their interaction with the design of stress scenarios and the choice of the methodological framework:

The selection of risk factors needs to be sufficiently flexible to accommodate the evolving nature of banks’ business models and their susceptibility to certain shocks. The calibration of risk factors is premised on how the performance of banks and the dynamics of business strategies are affected by changes in macrofinancial conditions. However, their relevance and macrofinancial sensitivity is invariably bound to change over time and influenced by the constant evolution of practices and innovations in Islamic banking (conditional on the prevailing interpretation of the legal tradition and principles of Islamic jurisprudence [usul al-fiqh or ).
Additional measures can reveal a more comprehensive perspective on the full impact of different stress scenarios. Accounting measures (for example, net income and other profitability indicators) support an enhanced understanding of the dynamics of capital buffers, as they would affect the decision to pay out dividends to shareholders or bonuses to policyholders. Changes in the loss absorption of IA holders for different scenario severities illustrate how the capital assessment during times of stress is impacted by assumptions about DCR. Also, incorporating liquidity measures could provide useful insights, especially when investment assets become more illiquid (BCBS, 2013).
The extension of single-period shocks to multiperiod scenarios could help identify medium- and long-term vulnerabilities. Extending the stress test horizon and applying multiyear scenarios would also help identify medium- and long-term vulnerabilities from a gradual erosion of the solvency position, which would inform suitable remedial actions and recovery plans.
Secondary impacts and feedback effects emanating from a deteriorating financial position can be material in stress conditions. For instance, the degrading of the solvency position can result in a higher cost of capital, which might drain reserves for DCR and limit the ability of Islamic banks to attract sufficient deposits. The design of stress tests tends to be sufficiently flexible to accommodate differences in banks’ business models, their role in the domestic financial sector, and increasingly, their cross-border linkages with other financial institutions. Spillover effects from a general deterioration of asset prices and associated feedback effects between one or more banks under duress from the macrofinancial conditions are important considerations in a comprehensive assessment (see Appendix V).

The risk factors can be integrated into a conventional stress testing framework, such as the IMF Workbox Solvency Tool (Leika and others, forthcoming), which has been developed to conduct solvency stress tests based on current regulatory requirements and accounting standards. The tool allows stress testers to (i) project (or make assumptions about) the dynamic evolution of banks’ balance sheets using balance sheet information; and (ii) assess capital adequacy under stress.⁸⁶

VIII. Conclusion

In this paper, we presented a simple conceptual framework for the design and implementation of top-down solvency stress testing of Islamic banks. While the general mechanics and core principles of stress testing apply universally, the distinct characteristics of Islamic banking require a differentiated treatment of several risk factors, including (i) DCR (due to some transfer of shareholder value to unsecured depositors); (ii) indirect interest rate risk (due to competition for deposits in mixed banking systems); (iii) counterparty and project risk (if a counterparty fails to perform its payment obligations); (iv) market risk from inventories of commodities and parallel special sales contracts as natural hedges; and (v) operational risk from non-compliance with Islamic finance principles. Based on existing capital standards for Islamic banks (IFSB, 2012b and 2013), we developed a general understanding of how Islamic finance principles influence the capital impact of key risk drivers under stress. Whenever possible, we applied common stress testing model(s) and technique(s) for conventional banks to integrate the formal specification of risk factors-consistent with the evolving prudential guidance from the IFSB (2012a and 2016). However, several process-oriented considerations (and the technical implementation) remained outside the conceptual scope of the paper, such as the treatment of capital resources, the design of stress scenarios, the validation of results, and dealing with the outcome of the stress tests (Jobst and others, 2013). The operationalization of this conceptual approach would require a detailed analysis of (i) the nature, scale, and complexity of the relevant banking activities as well as (ii) secondary impacts and feedback effects emanating from a deteriorating solvency in multiperiod scenarios. Ong (2014) and Ong and Jobst (2020) provide an overview of relevant stress testing methodologies, which cover these aspects and complement this paper.⁸⁷

This would also involve incorporating a cross-functional perspective of solvency and liquidity risks consistent with Islamic finance principles. Liquidity and solvency risks of individual institutions are increasingly connected during times of stress and tend to be influenced by system-wide liquidity conditions associated with the interconnectedness and network effects within the financial system. Moreover, understanding the structural implications of differences in business models, behavioral characteristics under stress, and the interaction between solvency and liquidity conditions are fundamental to the application of this approach for financial stability analysis and macroprudential surveillance. This places more emphasis on qualitative analysis, such as the reputational risk of individual firms, the competitive environment, and existing risk controls that influence the gross impact of risks.

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Solé, Juan, 2008. “Introducing Islamic Banks into Conventional Banking Systems,” Journal of Islamic Economics, Banking and Finance, Vol. 4, No. 2. Also published as IMF Working Paper 07/175 (Washington, D.C.: International Monetary Fund).
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Song, Inwon, and Carel Oosthuizen, 2014. “Islamic Banking Regulation and Supervision: Survey Results and Challenges,” IMF Working Paper No. 14/220 (Washington, D.C.: International Monetary Fund), Available at http://www.imf.org/external/pubs/ft/wp/2014/wp14220.pdf.
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Subhani, Azeemuddin, 2011. “Wither Islamic Finance? ‘… Allah Permitteth Bay’ and Forbiddeth Riba …’,” New Horizon, No. 178 (January–March), 15–8.
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Toumi, Kaouther, Jean-Laurent Viviani, and Lotfi Belkacem, 2011. “Actual Risk Sharing Measurement in Islamic Banks,” Critical Studies on Corporate Responsibility, Governance and Sustainability, Vol. 2, 325–47.
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Uberoi, Priya, 2010. “An Introduction to Islamic Derivatives,” Practice Note, Practice Law Company, March 25, Available at http://us.practicallaw.com/8-501-6191.
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Vogel, Frank E., and Samuel L. Hayes III, 1998. Islamic Law and Finance: Religion, Risk and Return (The Hague and Boston: Kluwer Law International).
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World Bank Group/Islamic Development Bank Group, 2017. “The Islamic Banking Sector,” Global Report on Islamic Finance (“Islamic Finance―A Catalyst for Shared Prosperity?”), Chapter 3, February 20 (Washington, D.C.: World Bank Group/Islamic Development Bank Group), 47–67.
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Appendix I. Additional Tables

^{Table A1.}

Glossary of Islamic Finance Terms for Banking

Sources: authors, Errico and Farrahbaksh (1998), El-Hawary and others (2004), IFSB (2005a and 2005b), and ISRA (2010).

^{Table A1.}

Glossary of Islamic Finance Terms for Banking

Term	Explanation
bay mu’ajal or bay bithaman ajil (predelivery, deferred payment)	The seller can sell a product on the basis of a deferred payment, in installments or in a lump sum. The price of the product is agreed upon between the buyer and the seller at the time of the sale and cannot include any charges for deferring payment. In a BBA contract, the lender is not compelled to disclose the profit margin.
ijāra (or ijārah) (lease, lease purchase)	A party leases a particular product for a specific sum and a specific time period. In the case of a lease purchase, each payment includes a portion that goes toward the final purchase and transfer of ownership of the product. The contract commences with a promise to lease that is binding on the part of the potential lessee prior to entering the contract. An ijara muntahia bittamleek (or ijara wa iqtina) contract offers the lessee the option to own the asset at the end of the lease period either by purchase of the asset through a token consideration or payment of the market value, or by means of a gift contract.
Investment risk reserve (IRR)	Reserves (after disbursement of the mudarib’s share), which are used to cover (some or all) losses of investment account (IA) holders.
istisna (or istisna’a) (deferred payment and delivery)	Agreement to sell to a customer a non-existent asset, which is to be manufactured or built according to the buyer’s specifications and is to be delivered on a specified future date at a predetermined selling price. A manufacturer (contractor) agrees to produce (build) and to deliver a certain good (or premise) at a given price on a given date in the future. The price does not have to be paid in advance (in contrast to bay salam). It may be paid in installments or part may be paid in advance with the balance to be paid later on, based on the preferences of the parties. A parallel istisna is a second istisna contract where a third party will be manufacturing for the bank an asset that corresponds to the properties of the asset underlying the first istisna contract.
mudaraba (or mudarabah) (trust-based contract)	Contract between the capital provider and a skilled entrepreneur whereby the capital provider contributes capital to an enterprise or activity that is managed by the entrepreneur as the mudarib. Profits are shared in accordance with the terms of the mudarabah agreement while losses are borne solely by the capital provider unless the losses are due to the mudarib’s misconduct, negligence, or breach of contracted terms.
murābaha (or murābahah) (mark-up/cost-plus sale)	Sales contract whereby the bank sells to a client at an agreed profit margin plus cost (selling price) a specified asset (which may have been purchased and acquired based on a binding or non-binding promise of purchase, for instance, in the case of a purchase order).
mushāraka (or mushārakah) (equity participation or “sweat capital finance”)	The bank enters into an equity partnership agreement with one or more partners to jointly finance an investment project. Profits (and losses) are shared in accordance with the terms of the musharakah agreement while losses are shared in proportion to each partner’s capital share. Diminishing musharakah is a form of partnership in which one of the partners promises to buy the equity share of the other partner gradually until the title to the equity is completely transferred to the buying partner. The “buying and selling” is independent of the partnership contract and should not be stipulated in the partnership contract since the buying partner is only allowed to give a promise to buy. It is also not permitted that one contract be entered into as a condition for concluding the other.
Profit equalization reserve (PER)	Reserve funded by mudarabah income (after disbursement of the mudarib’s share), which are used to cover (some or all) losses of investment account holders and smooth earnings of shareholders.
qard hasan (benevolent loans)	Non-interest-bearing loan intended to allow the borrower to use the loaned funds for a period with the understanding that the same amount of the loaned funds would be repaid at the end of the period. Banks are allowed to charge borrowers a service fee to cover the administrative expenses of handling the loan. The fee should not be related to the loan amount or maturity.
Restricted investment accounts (RIA)	Investment account holders authorize the bank to invest their funds based on mudarabah/mushāraka (profit- and loss-sharing) or wakalah (agency) contracts with certain restrictions as to where, how, and for what purpose these funds are to be invested.
salam (prepayment, deferred delivery)	The buyer pays the seller the full negotiated purchase price of a commodity that the seller promises to deliver at a future date (prepayment). A parallel salam contract with a third party stipulates that the buyer acquires the same commodity specified in the first salam contract.
sukuk (investment certificates)	These certificates confer ownership in an undivided part of an underlying asset where the holder assumes all rights and obligations to such asset.
tawarruq (or reverse murabahah)	Tawarruq defines the purchase of a commodity in the possession and owned by the seller on a deferred basis, which the buyer resells to a third party (other than the original seller) to acquire cash (al-wariq).
Unrestricted investment accounts (UIA)	Investment account holders authorize the bank to invest their funds based on mudarabah/mushāraka (profit- and loss-sharing) or wakalah (agency) contracts without any restriction. The bank can commingle these funds with their own funds and invest them in a pooled portfolio.
wakalah (agency)	In a wakalah contract, the principal (muwakkel) appoints an agent (wakil) to undertake transactions on his/her behalf in non-binding contract for a fixed fee, similar to a power of attorney agreement in conventional legal terms. Services under wakalah include all exchange-based and profit- and loss-sharing contracts.

Sources: authors, Errico and Farrahbaksh (1998), El-Hawary and others (2004), IFSB (2005a and 2005b), and ISRA (2010).

^{Table A1.}

Glossary of Islamic Finance Terms for Banking

Term	Explanation
bay mu’ajal or bay bithaman ajil (predelivery, deferred payment)	The seller can sell a product on the basis of a deferred payment, in installments or in a lump sum. The price of the product is agreed upon between the buyer and the seller at the time of the sale and cannot include any charges for deferring payment. In a BBA contract, the lender is not compelled to disclose the profit margin.
ijāra (or ijārah) (lease, lease purchase)	A party leases a particular product for a specific sum and a specific time period. In the case of a lease purchase, each payment includes a portion that goes toward the final purchase and transfer of ownership of the product. The contract commences with a promise to lease that is binding on the part of the potential lessee prior to entering the contract. An ijara muntahia bittamleek (or ijara wa iqtina) contract offers the lessee the option to own the asset at the end of the lease period either by purchase of the asset through a token consideration or payment of the market value, or by means of a gift contract.
Investment risk reserve (IRR)	Reserves (after disbursement of the mudarib’s share), which are used to cover (some or all) losses of investment account (IA) holders.
istisna (or istisna’a) (deferred payment and delivery)	Agreement to sell to a customer a non-existent asset, which is to be manufactured or built according to the buyer’s specifications and is to be delivered on a specified future date at a predetermined selling price. A manufacturer (contractor) agrees to produce (build) and to deliver a certain good (or premise) at a given price on a given date in the future. The price does not have to be paid in advance (in contrast to bay salam). It may be paid in installments or part may be paid in advance with the balance to be paid later on, based on the preferences of the parties. A parallel istisna is a second istisna contract where a third party will be manufacturing for the bank an asset that corresponds to the properties of the asset underlying the first istisna contract.
mudaraba (or mudarabah) (trust-based contract)	Contract between the capital provider and a skilled entrepreneur whereby the capital provider contributes capital to an enterprise or activity that is managed by the entrepreneur as the mudarib. Profits are shared in accordance with the terms of the mudarabah agreement while losses are borne solely by the capital provider unless the losses are due to the mudarib’s misconduct, negligence, or breach of contracted terms.
murābaha (or murābahah) (mark-up/cost-plus sale)	Sales contract whereby the bank sells to a client at an agreed profit margin plus cost (selling price) a specified asset (which may have been purchased and acquired based on a binding or non-binding promise of purchase, for instance, in the case of a purchase order).
mushāraka (or mushārakah) (equity participation or “sweat capital finance”)	The bank enters into an equity partnership agreement with one or more partners to jointly finance an investment project. Profits (and losses) are shared in accordance with the terms of the musharakah agreement while losses are shared in proportion to each partner’s capital share. Diminishing musharakah is a form of partnership in which one of the partners promises to buy the equity share of the other partner gradually until the title to the equity is completely transferred to the buying partner. The “buying and selling” is independent of the partnership contract and should not be stipulated in the partnership contract since the buying partner is only allowed to give a promise to buy. It is also not permitted that one contract be entered into as a condition for concluding the other.
Profit equalization reserve (PER)	Reserve funded by mudarabah income (after disbursement of the mudarib’s share), which are used to cover (some or all) losses of investment account holders and smooth earnings of shareholders.
qard hasan (benevolent loans)	Non-interest-bearing loan intended to allow the borrower to use the loaned funds for a period with the understanding that the same amount of the loaned funds would be repaid at the end of the period. Banks are allowed to charge borrowers a service fee to cover the administrative expenses of handling the loan. The fee should not be related to the loan amount or maturity.
Restricted investment accounts (RIA)	Investment account holders authorize the bank to invest their funds based on mudarabah/mushāraka (profit- and loss-sharing) or wakalah (agency) contracts with certain restrictions as to where, how, and for what purpose these funds are to be invested.
salam (prepayment, deferred delivery)	The buyer pays the seller the full negotiated purchase price of a commodity that the seller promises to deliver at a future date (prepayment). A parallel salam contract with a third party stipulates that the buyer acquires the same commodity specified in the first salam contract.
sukuk (investment certificates)	These certificates confer ownership in an undivided part of an underlying asset where the holder assumes all rights and obligations to such asset.
tawarruq (or reverse murabahah)	Tawarruq defines the purchase of a commodity in the possession and owned by the seller on a deferred basis, which the buyer resells to a third party (other than the original seller) to acquire cash (al-wariq).
Unrestricted investment accounts (UIA)	Investment account holders authorize the bank to invest their funds based on mudarabah/mushāraka (profit- and loss-sharing) or wakalah (agency) contracts without any restriction. The bank can commingle these funds with their own funds and invest them in a pooled portfolio.
wakalah (agency)	In a wakalah contract, the principal (muwakkel) appoints an agent (wakil) to undertake transactions on his/her behalf in non-binding contract for a fixed fee, similar to a power of attorney agreement in conventional legal terms. Services under wakalah include all exchange-based and profit- and loss-sharing contracts.

Sources: authors, Errico and Farrahbaksh (1998), El-Hawary and others (2004), IFSB (2005a and 2005b), and ISRA (2010).

^{Table A2.}

Stylized Balance Sheet of an Islamic Bank (with internally consistent values, in monetary units)

Topics

Countries

Series

About

Resources

Contributor Notes

Abstract

I. Preface

II. Introduction

III. Fundamentals of Islamic Finance

IV. Islamic Banks’ Balance Sheets and Implications for Stress Testing

V. Risks and Their Capital Impact Within Islamic Banking

A. Displaced Commercial Risk

B. Credit Risk

C. Market Risk

D. Operational Risk

VI. Capital Requirement for Islamic Banks

VII. Stress Testing Islamic Banks

A. Scope of Risk Factors

B. Displaced Commercial Risk

C. Indirect Interest Rate Risk

D. Credit Risk

E. Market Risk

F. Operational Risk

G. Combination of Risk Factors and Organization of Risk Drivers

VIII. Conclusion

References

Appendix I. Additional Tables