ISLAMIC FINANCE

IN THE LIGHT OF MODERN ECONOMIC

THEORYSUREN BASOV AND

M. ISHAQ BHATTI

Islamic Finance in the Light of ModernEconomic Theory

Suren Basov • M. Ishaq Bhatti

Islamic Finance in theLight of ModernEconomic Theory

Suren BasovUniversity of Melbourne

and Deakin UniversityVictoria, Australia

M. Ishaq BhattiLa Trobe Business SchoolLa Trobe University, Departmentof Economics and Finance

Melbourne, Australia

ISBN 978-1-137-28661-1 ISBN 978-1-137-28662-8 (eBook)DOI 10.1057/978-1-137-28662-8

Library of Congress Control Number: 2016947038

© The Editor(s) (if applicable) and The Author(s) 2016The author(s) has/have asserted their right(s) to be identified as the author(s) of this work in accordancewith the Copyright, Designs and Patents Act 1988.This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whetherthe whole or part of the material is concerned, specifically the rights of translation, reprinting, reuseof illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, andtransmission or information storage and retrieval, electronic adaptation, computer software, or by similaror dissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoes not imply, even in the absence of a specific statement, that such names are exempt from the relevantprotective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in this bookare believed to be true and accurate at the date of publication. Neither the publisher nor the authors orthe editors give a warranty, express or implied, with respect to the material contained herein or for anyerrors or omissions that may have been made.

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Printed on acid-free paper

This Palgrave Macmillan imprint is published by Springer NatureThe registered company is Macmillan Publishers Ltd. London

Preface

This book provides the reader with an understanding of the basic legaltenets of the Islamic finance industry and studies the real economic effectsof those tenets using the tools of modern mechanism design theory. Itstarts by explaining the history and legal framework of Islamic banking,and describes typical Islamic financial products and the structure ofIslamic financial institutions. However, as every student of economicsknows, the ways in which the legal framework translates into real eco-nomic restrictions is subtle and is shaped by the reactions of economicactors. In the second part of the book we demonstrate this point bystudying the theory of tax incidence—which is not directly related tothe theory of Islamic finance, but is simple and illustrates the pointneatly—and by discussing the famous Miller–Modigliani theorem, whichis of direct relevance to Islamic banks, who are prohibited from charginginterest and often have to rely on profit–loss sharing agreements.

The third part of the book is the most formal and it introduces thereader to modern mechanism design theory. In particular it discussesoptimal contracting under hidden actions and hidden information. In thefinal part we apply the tools of mechanism design theory to understandthe real economic restrictions imposed by Islamic law and the perfor-mance of Islamic institutions.

The book can be used as an advanced textbook for graduate studentswho wish to specialize in the area; it includes exercises which makes it

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vi Preface

easier to use as an assigned text on a course. We hope that by collectingtogether in one volume a description of the legal framework of Islamicfinancial institutions and the necessary technical tools for analyzing theireconomic effects, together with some examples of their application, willfacilitate the use of the results by applied economists and help to improvethe design of Islamic financial institutions.

Melbourne, VIC, Australia Suren BasovMelbourne, VIC, Australia M. Ishaq Bhatti

Contents

Part I Islamic Finance: Rationale, History,Instruments and the Legal Framework 1

Reference 2

1 Introduction 31.1 Overview 31.2 The Two Worlds of Finance 41.3 The Rationale of Islamic Finance 6

1.3.1 The Development of IslamicBanking Worldwide 7

1.3.2 IBF in the Middle East 101.3.3 IBF in South Asia 181.3.4 IBF in the Southeast Asia 201.3.5 IBF in Africa: Sudan 231.3.6 IBF in European and Western

Countries 231.3.7 IBF in Australia 26

1.4 Conclusions 27References 27

vii

viii Contents

2 Islamic Financial Instruments 312.1 Overview 312.2 Equity-Based Instruments 32

2.2.1 Musharakah 332.2.2 Mudarabah 35

2.3 Debt-Based Instruments 372.3.1 Murabahah 372.3.2 Salam 402.3.3 Istisna’ 422.3.4 Ijarah 44

2.4 Takaful 46References 47

3 The Historical Roots and Evolution of IslamicFinancial Thought 49

Part II The Law of Unexpected Consequences 53References 54

4 The Incidence of Taxation 554.1 Exercises 584.2 Bibliographic Notes 59Reference 59

5 The Basics of Corporate Finance:The Miller–Modigliani Theorem 615.1 The Miller–Modigliani Theorem 625.2 Hidden Information and the Breakdown of

the Miller–Modigliani Theorem 645.3 Prohibition of Riba in the Light

of the Miller–Modigliani Theorem 675.4 Exercises 685.5 Bibliographic Notes 69

Contents ix

5.6 Unexpected Consequences of the Provisionsof Islamic Law 69

References 71

Part III Game Theory and Mechanism Design 73References 74

6 Game Theory 756.1 The Normal Form and the Extensive Form 756.2 Mixed Strategies and Behavioral Strategies 776.3 Simultaneous-Move Games of Complete

Information 776.3.1 Dominant and Dominated

Strategies 776.4 The Nash Equilibrium 806.5 Simultaneous-Move Games of Incomplete

Information 806.5.1 Harsanyi’s Doctrine 81

7 The Revelation Principle 837.1 Bibliographic Notes 84Reference 84

8 Monopolistic Screening 858.1 The Monopolistic Screening Model

with Two Types 868.2 The Unidimensional Screening Model 888.3 The Spence–Mirrlees Condition and

Implementability 898.4 The Concept of the Information Rent 938.5 Three Approaches to the Unidimensional

Relaxed Problem 948.5.1 The Direct Approach 94

x Contents

8.5.2 The Dual Approach 958.5.3 The Hamiltonian Approach 96

8.6 The Hamiltonian Approach to theUnidimensional Complete Problem 98

References 100

9 The Multidimensional Screening Model 1039.1 The Hamiltonian Approach

and the First-Order Conditions 1059.2 An Example 1079.3 Exercises 109References 109

Part IV Mechanism Design Applications to Islamic Finance 111

10 Business Loans, Trust, and Contract RestrictionFaced by Islamic Banks 11310.1 Model 113

10.1.1 The Optimal Contractfor a Linear-Exponential Model 116

10.2 Comparing the Performanceof a Conventional and an Islamic Bank 123

10.3 Bibliographic Notes 124References 125

11 Loans Provision and Adverse Selection WithinOrthodox Religious Communities 12711.1 The Model 127References 132

12 Shariah Compliance and Risk-Incentive Trade-Offs 13312.1 A Simple Principal–Agent Model 13312.2 The Principal–Agent Model Under

a Mudarabah Contract 135

Contents xi

12.3 Social Norms and Risk-Incentive Trade-Offs 13712.4 Bibliographic Notes 142References 143

13 Shariah Compliance, Positive AssortativeMatching and the Performance of IFI’s 14513.1 Costs and Benefits of Asset Restrictions 14613.2 Positive Assortative Matching

as a Magnification Mechanism 14713.3 Bibliographic Notes 151References 151

14 Optimal Incentives for Takaful Operators 15314.1 Exercises 15514.2 Bibliographic Notes 155References 155

15 Can Short-Selling Prohibition Be Optimal? 15715.1 Stable Distributions 158References 163

16 Conclusions 165References 168

Bibliography 169

Index 171

List of Figures

Fig. 2.1 Mudarabah contract 36Fig. 2.2 Murabahah contract 38

xiii

Part IIslamic Finance: Rationale, History,

Instruments and the Legal Framework

In this part we discuss the rationale and history behind Islamic banking,and the legal framework of the Islamic financial industry. Siddiqi (1983,pp. 69–94) argues that: Islamic banking increases efficiency in the invest-ment sector; Islamic banking differentiates between consumer debt andpublic debt; the application of interest worsens the distribution of incomeand wealth; the control of wealth means the concentration of power;the interest-based system creates a tendency of banks to over-expandcredit that leads to inflation. Siddiqi also argues that Islamic banking:creates an alternative to interest by replacing it with the profit–loss sharingprinciple; stimulates efficiency in asset allocation; offers stability in thevalue of money; increases the volume of investments; provides justice andequity in distributions; provides reasonable finance for the governmentas well as finance for the customers; encourages the international flowof funds based on justice and cooperation; enhances the mobilization ofsavings and the profitability of investments. Many of these claims holdtrue historically. However, to understand to what degree they still hold inmodern times and what challenges Islamic finance faces in the modern

2 I Islamic Finance: Rationale, History, Instruments and the Legal Framework

world a rigorous economic modelling is required. In this book we willfamiliarize the reader with the main tools of economic modelling andshow how they can be applied to Islamic finance.

Reference

Siddiqi, M.N. 1983. Banking without interest. Leicester: The Islamic Foundation.

1Introduction

In this chapter we discuss our main rationale for writing this book andintroduce the reader to the two worlds of finance.

1.1 Overview

One of the main reasons we decided to write this book was because wehad observed a lack of texts that analyze Islamic finance using mathe-matical rigor. More specifically, we wanted to show how the discipline ofmechanism design could be applied to various cases in Islamic finance.It is understood that Islamic finance has differences from conventionalmethods of conducting finance today, but we think that the implica-tions of these differences are not well explored. We felt this choice ofmethodology was necessary because it helps to provide a solid theoreticalfoundation for performing any other sort of analysis in terms of testablehypotheses, simple comparative statics and basic policy implications. Wefirst introduce the subject matter by comparing the relevant differencesbetween the two “worlds” of finance. Subsequently, we familiarize thereader with the Islamic “world” of finance, and describe the available

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_1

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4 1 Introduction

instruments, ways of conducting financial engineering, and the operationof its financial system. Lastly, we introduce the reader to the main toolsof modern economic theory—game theory and mechanism design—toshow how they can be applied to Islamic finance.

1.2 The Two Worlds of Finance

We think that an extensive discussion of the differences between Islamicfinance and mainstream finance today is not necessary as it wouldencompass various other fields which are far beyond the scope of thisbook. The differences we consider important can be divided into twocategories, namely behavioral and operational. By behavioral we meanthe factors taken into account by economic agents in terms of theirmental accounting or, put another way, what they consider to be utilityand disutility. By operational we mean the available market mechanismsthrough which agents can maximize their utility.

In terms of behavioral differences, most of them stem from the fact thatIslam recognizes the existence of an all-superior being. The implicationsof this, which we would like to highlight, is that Islamic finance explicitlyacknowledges the limited rationality of given agents and that their utilityis subject to complying with the demands of the said being. However,Islam also acknowledges that the effect of this compliance also depends onagents’ levels of “trust” or “belief ”. One example of how these implicationscan affect the utility function and other behavioral aspects of decisionmaking concerns the Islamic concept of a “Day of Reckoning”. Thisturns agents’ utility maximization problems into amulti-period one whereevery action not only influences agents’ terminal utilities but also entersdirectly into their utilities in the final period. This is simply the ideathat if their actions comply with the demands of the all-superior being,they will receive an additional positive utility and vice versa in the finalperiod. Another way agents can be affected is that they can be consideredas dividing their resources between market activities and “faith-building”activities.

1.2 The Two Worlds of Finance 5

In terms of operational differences, the main ones can be drawn fromthe conditions of a valid sale according to Islamic law. Usmani (2007) liststen conditions:

1. The object of sale must be in existence at the time of sale.2. The object of sale must be in the ownership of the seller at the time

of sale.3. The object of sale must be in the physical or constructive possession

of the seller when it is sold to another person.4. The sale contract must be finalized on the spot.5. The object of sale must be a property of value.6. The object of sale should not be a thing that is used exclusively for

activities prohibited by Islamic law.7. The object of sale must be specifically known and identified to the

buyer.8. The delivery of the sold commodity to the buyer must be certain and

should not depend on a contingency or chance.9. The certainty of price is a necessary condition for the validity of a sale.10. The sale must be unconditional.

These conditions directly shape the securities available in an Islamicfinance world, which will be discussed in the next chapter, but alsoprovide subtle, environmental constraints that pervade all dealings relatedto Islamic finance. While they are more of interest to legal professionals,some of them cannot be excluded from more complex models such asthose related to financial engineering. For example, in application tothe asset market, provisions 1–3 will prohibit short sales without thepermission of the actual owner of the asset. Under the assumption thatasset returns follow a joint normal distribution, such a restriction will beunnecessarily restrictive and will prevent the traders from efficient risksharing. However, as we will argue in this book, if returns to the assets havea maximally skewed stable distribution, a rational trader facing unlimitedliability will choose not to engage in short-selling behavior. Under theseconditions, these provisions can be seen as improving the welfare of

6 1 Introduction

boundedly rational traders. In relation to the fifth condition, money isnot recognized as having intrinsic value and so does not enjoy the statusof a valid commodity. One of the restrictions it has compared to com-modities is that it can only be traded at spot. This effectively removes theconventional idea of bonds and derivatives from one’s permissible choiceof assets and limits one’s choice of conventional liquidity managementinstruments. As we will discuss later, assuming perfect capital markets, theunavailability of bonds is irrelevant, since the Modigliani–Miller theoremguarantees the equivalence of debt and equity contracts. The equivalence,however, breaks in the presence of private information. Provisions 4–8 aredesigned to exclude trading in hot air and pyramid schemes and they playan important role in societies with a weak legal system and where thereis uncertainty concerning contract enforcement. However, they excludethe possibility of contingent commodities, which play an important rolein achieving efficient risk sharing in the face of uncertainty in Arrow–Debreu markets.

1.3 The Rationale of Islamic Finance

If we consider the ten conditions of sale above, we can infer thatIslamic law places a heavy emphasis on the soundness of the contract.For example, seven of the aforementioned conditions basically ensurethat the seller actually has something worth the buyer’s money, whereasthe other three facilitate the soundness and upholding of the contract.More generally, scholars have recognized that one of the objectives ofIslamic law is in fact the preservation of wealth. This is not to say thatIslamic law prescribes economic stagnation and autarky, rather that one’swealth should increase through gains from trade and not economicallyinsubstantial market maneuvers such as hoarding. To explain this interms more relevant to finance, the literature often consolidates the tenconditions into more substantial principles, such as in Kettell (2010).We find that these conditions can be summarized into three principles,namely the prohibition of riba (excess interest), the prohibition of gharar(contractual uncertainty) and the prohibition of maysir (insubstantialeconomic activity).

1.3 The Rationale of Islamic Finance 7

1.3.1 The Development of Islamic Banking Worldwide

Islamic Banking and Finance (IBF) is the fastest growing industry of thefinancial arena and has been experiencing exponential growth in threeparts of the world, including the Middle East, South Asia and SoutheastAsia. In the African region, Sudan has been the torchbearer of IBF affairsover the past three decades. IBF practices have also been making headwayin North America, Europe and Australia. This section will provide ageneral review of the recent developments of IBF in terms of products, sys-tems, infrastructure andmarkets across the globe (Khan and Bhatti 2008).

The development of IBF reflects the persistent efforts made by Islamicscholars and institutions to find shariah-compliant means and mea-sures for eliminating interest in economic and financial dealing in theMuslim world. Islamic scholars such as Qureshi (1946); Siddiqi (1948)and Ahmad (1952) pioneered the idea of practicing Islamic banking inmodern times. Uzair (1955) made a major breakthrough by developinga more accomplished IBF model that explained the depositer–bankerand the banker–entrepreneur relationship under themudarabah principle.His work laid the foundation for the development and growth of thesystem along modern lines. Meanwhile, the Kuwait Investment Houseproject and subsequent literature contributed by Huda (1964), Mannan(1970) and Udovitch (1970) elaborated and presented a mechanism whichthoroughly replaced the conventional model with the Islamic banking one(Khan and Bhatti 2008). However, as we will explain later in this book,mudarabah imposes a constraint on possible principal–agent contracts,which limits the possibilities for the optimal trade-off between risk-sharing and incentives.

The Mit-Ghamar Sosial Bank, established in Egypt in 1963, may beregarded as a pioneer of contemporary investment. The operations of thisbank were in trade and industry on a profit and loss (PLS) basis, withthe bank appearing to be very successful due to increasing communitysupport. Within a short time it developed nine branches, managing fundsto the value of 1:8 million Egyptian pounds, held for more than 250; 000depositors. The experiment, however, was abandoned in 1967 for politicalreasons. The Pilgrimage Management Fund Board undertook a similarexperiment by establishing Tabung Haji in Malaysia in 1963 with a total

8 1 Introduction

deposits of RM46,600 (US$12,000). The shareholders of Tabung Hajipooled their funds to invest in business and trade activities on the basisof risk-sharing. The core objective of the creation of Tabung Haji was toprovide financial assistance to its members so they couldmake pilgrimagesto Mecca (Khan and Bhatti 2008). In addition to this, Tabung Haji hasplayed a significant role for savings purposes among Muslim people inMalaysia. Up till now, it has served as one of the biggest Islamic financialinstitutions in Malaysia. For example, the value of the total savings forTabung Haji was RM10.5 billion in 2001, RM13.3 billion in 2006 andso on in 2016 it reach to RM60 billion with average annual increaseof RM4.5 billions. The total of its financial resources also went up by32:9%, increasing from RM900 million in 1999 to more than RM60billion in 2016 with more than 100 branches.

The practice of IBF acquired significant shape and momentum by theend of the 1970s due to increases in the general economic prosperity ofMiddle Eastern countries, primarily from the influx of petrodollars intothe region. The Middle East Islamic financial institutions (IFIs) systemreceived increasing sociopolitical and economic support for the growthand prosperity of many reputable banks which came into being, includingtheNasser Social Bank Cairo (1971–1972), the IslamicDevelopment Bank(1975), Dubai Islamic bank (1975), Kuwait Finance House (1977), FaisalIslamic bank of Sudan (1977) and Dar-Al-Maal Al-Islami (1980).

The development of Islamic finance activities is mainly crowdedaround three regions of the world, which include the Middle East,Southeast Asia and South Asia. In the Middle East, there are threecountries, Kuwait, Bahrain and the UAE, which are actively involved inIBF activities. Recently, the crowd has been broadened as IBF started togain momentum in Australia, the USA and European countries, especiallyin the UK (Khan and Bhatti 2008).

A number of Western market players, including ABN AMRO,Citibank and HSBC, have established their own Islamic window orsubsidiaries to attract petrodollar deposits from Gulf CooperationCouncil (GCC) countries in the1 Middle East and Muslim clientele

1There are 6 GCC member countries; Bahrain – or Kingdom of Bahrain, Kuwait, Oman – orSultanate of Oman, Qatar, Saudi Arabia – or Kingdom of Saudi Arabia (KSA), UAE – United ArabEmirates.

1.3 The Rationale of Islamic Finance 9

worldwide. Up until 2015, there were approximately 1,143 Islamicfinance institutions worldwide including 436 Islamic banks or windows,308 takaful (Shariah-compliant insurance) institutions and 399 Islamicfinancial and investment companies and will capture 40–50% of thetotal savings of the 1.3 billion Muslims worldwide by 2017.

The IBF industry is the fastest growing segment of global finance andoffers viable and ethical solutions in the retail and corporate sectors. IBFstarted with retail base lending and investment operation and after adecade or so made progress into corporate financing and syndication,equity and leasing. Since 2001, the Islamic capital market has maintainedannual growth as high as 15–20% due to rapidly growing trading insukuk2 amongst Islamic businesses and finance organizations. Malaysiais the largest issuer of sukuk. Investment in it exceeds US$32 billion,which constitutes about 85:5% of the Middle Eastern capital market.Takaful,3 has experienced annual growth of 20% in recent years. Thereare more than 250 takaful companies managing premiums worth US$2billion in 2005 and which are expected to grow to US$7.5 billion by2015. Takaful instruments have added much-needed risk cover for IBFand provided long term investment opportunities for Islamic investorsand institutions. Other growing areas of IBF include assets and wealthmanagement, hedge funds, and treasury and risk instruments. In sum,estimates of the current size of IBF industry range from $1.88 Trillionto $2.1 Trillion with expectations of market size to be $3.4 Trillion byend of 2018.4 Yet considerable scope remains for Islamic solutions inthe derivatives, swaps, options and futures market. The growing of IBFdiscipline invites common ground for collaboration and partnership withconventional finance institutions. The aim of players from both Islamicand conventional sectors would be to pool their expertise and resources todevise more ethical and efficient solutions in business and in the financesystem (Khan and Bhatti 2008, pp. 39–40).

2Sukuk is a shariah compliant bond, which constitutes partial ownership in a debt and is based onthe principle of profit/loss sharing.3Takaful is a form of Islamic insurance, which we will discuss later.4https://www.islamicfinance.com/2015/05/size-islamic-finance-industry/

10 1 Introduction

1.3.2 IBF in the Middle East

The Middle East, which is overwhelmingly populated by Muslims, isthe motherland of IBF. Middle Eastern economies are very promising,featuring stable currencies and lower interest and inflationary rates overthe years. Having gone through radical restructuring in recent times,these markets are now more regulated, transparent and integrated atboth the regional and international levels. The GCC countries in theMiddle Eastern region enjoys great political stability, law and order, andtherefore emerges as a hot spot for international business, finance andinvestment. Despite the uncertainty and likely contraction in 2016, theGCC region will continue to offer US$2 trillion worth of opportunitiesand be an attractive market for businesses anywhere in the world andhence IBF to continue grow. GCC countries have huge ambitions forinfrastructure development, which exceeded US$171 billion for the year2014. The planned projects in the GCC as of May 2016 amounts toUS$2 trillion, with Saudi Arabia and the UAE as the market leaders,and with construction and transport being the two leading sectors withshares of 52% and 19%, respectively for infrastructure developments overthe next five years. Price water coper house (PWC) reports that morethan 60% of the worldwide infrastructure spending will be done in bothAsia and Middle East region due to complementation of oil producingGCC’s economy and Chinese double digit growing which will reach to$6 trillion per year by 2025.5 Middle Eastern markets still offer verylucrative opportunities for international trade, business and investment.The present sociopolitical and economic conditions offer very fertilegrounds for continued growth and the development of IBF.

There is increasing support for IFIs in the Middle East from wealthyindividuals, state institutions, market players, governments and othercommunity groups. Most countries in the region have allowed IFIs towork as distinctive entities in conventional regulatory environments,wherethey appear to be more versatile and resourceful in successfully deal-

5https://www.pwc.com/gx/en/capital-projects-infrastructure/publications/cpi-outlook/assets/cpi-outlook-to-2025.pdf

1.3 The Rationale of Islamic Finance 11

ing with emerging challenges and opportunities. Large IFIs are makingindividual and collective efforts to develop a full spectrum of innovative,customer-oriented and competitive products and services, and IFIs ingeneral are tightening their grip on the petrodollars that have a historyof slipping away into European and other Western financial markets.There is a strong and persistent boom inMiddle Eastern economies due tosoaring oil prices which doubled from 2002 to 2016 with 5 years movingaverage oil prices reaching to $60 per barrel. If this trend persists, it couldbring additional revenues which might find its way to shariah-compliantbanking and investments (Graham 2006).Bahrain is the biggest hub of IBF affairs worldwide, with the country

hosting 33 Islamic banks, 26 takaful and 3 re-takaful (re-insurance)companies, which operate at both domestic and international levels.Bahrain is also a hot spot for international trading in sukuks, Islamic equityfunds, mutual funds and other instruments, with most of the Islamicinstitutions, such as Accounting and Auditing Organization for IslamicFinancial Institutions (AAOIFI), International Islamic Financial Market(IIFM), Islamic International Rating Agency (IIRA), located in Bahrain.

Iran earmarked nationwide IBF practices after the Islamic revolutionof 1979. In the first two decades, Iranian IBF practice remained highlycentralized and isolated from the Islamic and conventional markets. Sincethe mid-1990s, however, the Iranian government has been graduallyderegulating and privatizing its economy and financial sector. A numberof IFIs, including Bank Karafarin, Bank Eqtesdae-e Novin, Bank ParsianBank Saderat and Bank Rfah-e Kargaran, are now working in the privatesector to offer more innovative and competitive IBF products and servicesto their customers. The Iranian government is also keen on increasing itsinteraction with Islamic and conventional financial markets globally.

The Jordan Islamic Bank has been a pioneer of IBF in Jordan since1978, holding 10:1% of the total investments of the Jordanian bankingindustry in 2006. IBF has been a great success in the Jordanian financialsector over the years. According to the 2015/2016 State of the GlobalIslamic Economy Report issued by Thomson Reuters, Jordan rankedninth among the top ten countries in IBF. Currently, there are fouroperating Islamic banks (JIB, The Islamic International Arab Bank,DubaiIslamic Bank and Al Rajhi Bank), six Islamic finance and investment

12 1 Introduction

companies and two takaful—Islamic insurance companies. Islamic banksinside Jordan have around 140 branches in 2015. These banks presentinnovative banking tools and attract more than 18% of total deposits,11% of total equities, 16% of total assets and 23% of total liabilities ofthe banking system in 2015. Takaful services and sukuks both have goodfuture prospects in the business and finance spheres of Jordan.

Kuwait hosts the largest number of IFIs and is ranked as fifth, as perIslamic Finance Country Index (IFCI) composite report and there are allthe signs that by 2020, its financial sector will be predominantly Islamic.The country hosts the oldest and biggest Islamic bank—the KuwaitFinance House—that was established in 1977. In early 2006, the KuwaitiParliament approved the establishment of new IFIs, namely Jaber IslamicBank, Jaber Funds and Boubyan Bank. Currently, there are 5 IslamicBanks in Kuwait; Kuwait Finance House, Boubyan Bank, InternationalBank of Kuwait, Al Ahli United Bank, Warba Bank, Al-Rajhi Bank withtotal fund under there management is more than $120 billion. Currentlyfive takaful and one re-takaful companies hold 14% of shares of theKuwaiti insurancemarket. There is an increasing demand for sukuks in thecorporate and real estate sectors, with the Kuwaiti government workingon developing proper regulatory frameworks for sukuk issues and trading.

IBF is passing through an embryonic stage in Lebanon. The CentralBank of Lebanon first authorized Islamic banking in 2004. Currently,there are four main Islamic banks operating in Lebanon; Blom Develop-ment Bank, the Lebanese Islamic Bank, Al Baraka Bank; and the ArabFinance House, which is 37%-owned by Qatar Islamic Bank. Besidethese, there are other banks with Islamic Banking services includeArabBanking Corporation, Gulf International Bank, Byblos Bank Africa Ltd,Gulf International Bank B.S.C and the National Bank of Kuwait. How-ever, Islamic banks’ share is about 25% of the market share. The Sukukand Takaful sector is still under developed in Lebanon.

Qatar is another hot spot of IBF affairs in the Middle East. There arefour major Islamic banks in the country, namely the Qatar Islamic Bank(established in 1983), the Qatar International Islamic Bank (established in1991), Doha Islamic Bank (established in 2006) and Al Rayan Bank (estab-lished in 2006). Other IFIs in Qatar include First Finance Company,Investment House, Al Jazeera Islamic Company and Islamic FinancialSecurities, who mainly offer Islamic retail products and brokerage services

1.3 The Rationale of Islamic Finance 13

to Muslim clientele. The Qatar Islamic Bank decided to establish theIslamic Investment Bank of Qatar with US$1 billion of capitalizationat the Qatar Financial Centre. In recent years Qatar’s IBF sector hasexpanded rapidly with the support of the Qatari government and isgrowing faster than any other countries in theMiddle East. Recent reportsby the Qatar Central Bank (QCB) suggest IBF industry in Qatar isposting overall asset growth of 17.5% between January 2015 and January2016, compared with 14.4% growth in the conventional banking segmentduring the same period.

Just recently, the QCB announced signing of memorandum of under-standing between China and Qatar government that Chinese financialentities are considering to develop sharia-compliant financing opportuni-ties to invest in shipping and high speed rail link projects based on sukukstructure which may result raising $4.7 billion, which may be the largestever Islamic bonds issued in the world. The Qatar Islamic InsuranceCompany has emerged as one of the leading insurance service providers inthe country. In 2003, Qatar first issued sukuks which presently constitute20–35% of the total project financing in the country. IFIs have beenplaying a key role in the economic growth and development of Qatar.

Moreover, two state-owned Chinese banks—the Industrial and Com-mercial bank of China (ICBC) and the Agricultural Bank of China—listed conventional bonds on the Dubai Financial Market’s internationalexchange, NASDAQ Dubai, in 2015. Finally, the QIIB-Southwest Secu-rities deal, under which the former will assist the latter firm in settingup sharia-compliant investment opportunities in China, signals increasedcooperation between Qatar and China at the IBF corporate level.

In April 2015 QCB and the Kenyan government agreed to developthe African nation’s nascent sharia-compliant finance segment points toconsiderable potential for similar deals around the world in the comingyears. The deal was made public during the launch of a new Islamic unitby Kenya Commercial Bank. This followed the appointment of threeIslamic scholars to a newly formed sharia advisory committee in late 2014.More broadly, the Qatar partnership is expected to play a major role inthe development of IBF products under the soon-to-be launched NairobiFinancial Centre Authority, which was initiated by Kenya’s governmentin 2014 in an effort to turn the capital city into a major financial centrein Africa.

14 1 Introduction

“We want to establish an enabling environment that supports thedevelopment of sharia-compliant products and services,” Henry Rotich,Kenya’s Cabinet secretary for the national Treasury, told local mediain 2015. “This will be achieved through cooperation among industrystakeholders in order to address the identified challenges in Islamicfinancing.”

IBF activities have rapidly grown in Saudi Arabia over recent yearsas well, with two major players: Al Rajhi Banking and InvestmentCorporation, and Bank Al Jazira. Conventional banks are also servingIBF clientele by establishing their own Islamic window or subsidiary inthe country. Islamic banking operations now capture 64% of operationsat the Saudi Arabian financial market (Harrison 2006). Saudi Arabia isthe second largest IBF market followed by Iran. Its total market IBFshare is 31.7%. According to Ernst and Young (EY)’s World IslamicBanking Competitiveness Report 2015, the Kingdom’s Islamic bankingassets account for 48.9% of the total domestic banking segment in 2013.This figure is projected to reach 70% by 2019, expanding Saudi Arabia’sglobal market share to over one-third at US$683 billion. Over 2009–13,the Shariah banking industry doubled in size andmore than half (54%) ofall financing transactions in the country in 2013 were Shariah compliant.As of 2016, there are four fully fledge IB’s in the Kingdom; Bank Al-Jazeera, Al Baraka Investment&Development Co., National CommercialBank and the Al Rajhi Banking & Investment Corporation. Other IBFentities include Al Bilad, Amlak Finance and Dallah Al Baraka SaudiArabian British Bank (SABB) Takaful Company. In July 2006, SABIC:Saudi Arabia Basic Industry signed the underwriting agreement for itsdebut sukuk issuance for a total of SAR3 billion (US$799.98 million),which was the first public issuance in the Saudi market under the newCapital Market Law (Al-Humaidi 2006). According to Aljazira Capital, atotal of US$15.2 billion-worth of Sukuk was issued out of Saudi Arabia in2013, marking a 36.4% increase on a yearly basis. Data from Gulf Bondand Sukuk Association show that in 2014, total Saudi Sukuk issuancereached approximately US$10.43 billion.

Moreover, country host the world’s largest Takaful market, with 37licensed insurance and reinsurance companies, and 76 brokers as wellas 76 insurance agencies. At US$8.1 billion in premiums in 2014, the

1.3 The Rationale of Islamic Finance 15

Kingdom is not only the largest insurance player in the GCC but alsothe region’s second-fastest growing market with an eight-year compoundannual growth rate of 20.3%, according to Moody’s Investors Service.Saudi Arabia hosts Islamic Development Bank (IDB) which is performinga very crucial role in promoting IBF in the Muslim world. So far in 2015,the IDB is the only Saudi entity which sold Sukuk worth of US$1 billionUS dollar facility.

The entry of Syria into the IBF club was one of the most recentdevelopments in the Middle East, with the Syrian Parliament approvingIBF laws in 2005. By the end of 2006, the government permitted threeIslamic banks, namely Al-Sham Bank, Saudi Dalat Al-Baraka’s Al-BarakaBank and Syrian International Islamic Bank, to launch their operationsin the country. Moreover, three takaful companies, Aqeelah InsuranceCompany, Al-Nour Insurance Company and Syrian-Qatari Company,were ready to operate in the Syrian market after receiving their licensesfrom the Syrian Insurance Supervision Committee. IFIs may help inintegrating the Syrian financial market into the mainstream IBFs in theMiddle Eastern region. Currently, Syrian banking system can be describedas closed with total of 21 banks operating in the country, 2 of themare Islamic Banks, namely, Syria International Islamic Bank and theCham Bank. In recent years, Central Bank of Syria (CBS), imposes aminimum capitalization of Syrian Ponds 10 billion on conventional banksand 15 billion on Islamic banks. The US treasury restrict the Syriangovernment’s access to international capital by adding CBS, the SyriaInternational Islamic Bank and the Syrian Lebanese Commercial bank.These restrictions and international sanctions are also imposed by thegovernments of the Arab League, Canada, Turkey, European Union andthe UK. Therefore no latest figures are available.

Worldwide IBF practice originated in the United Arab Emirates (UAE)when the first and biggest Islamic bank—Dubai Islamic Bank (DIB)—came into being in 1975. There are now four other fully dedicated Islamicbanks in the UAE, namely, Sharjah Islamic Bank, Emirates Islamic Bank,Abu Dhabi Islamic Bank and Dubai Bank. Conventional banks also offerIslamic products either through an Islamic window or subsidiary.

The UAE Islamic banking sector was US$127 in the beginning of 2014and it is expected to double in next 5 years. According to Ernst & young

16 1 Introduction

report 2015, the sector is on the way to touch US$265 billion by the endof 2019, making it the fourth largest Islamic banking market by valuefollowed by Iran, Saudi Arabia and Malaysia. At the moment IBF sectorin UAE stands at 21.4% which represents a 14.6% share of the global IBmarket. Currently, there are following 9 Islamic Banks operating in thecountry; 1) Dubai Islamic Bank; 2) Abu Dhabi Islamic Bank; 3) EmiratesIslamic Bank; 4) Noor Islamic Bank; 5) Al Hilal Bank; 6) HSBC Amanah;7) Sharja Islamic bank; 8) Badr Al-Islami (Islamic Banking Division ofMashreq Bank); 9) Attijari Al Islami (Islamic Banking arm of CommercialBank of Dubai). Some of these banks operates overseas for catering theneed of halal finance for Muslims around the globe. Dubai Islamic Bankand Abu Dhabi Islamic bank are the two top banks with in UAE andranked 3rd and 4th respectively in the GCC region in terms of Assetsand net profits earners in IBF markets around the world. Moreover, thereimpact on the neighbouring countries are growing faster than expected.For example, in Oman the two top Islamic Banks, Al Noor and DubaiIslamic Bank are from UAE. Omani IBF industry is new compared to therest of the GCC countries, there are now six banks serving IBF products,among these are Al Noor, Al Izz Islamic Bank and Dubai Islamic Bank.However, IBF windows and other services are provided by Bank Nizwa,BankMuscat and theNational Bank of Oman. Yet, faithful Omanis preferto do their sharia compliance banking across the border in UAE.Major takaful companies in the UAE include Abu Dhabi National

Takaful, Dubai Islamic Insurance and Re-insurance Company (AMAN),Islamic Arabic Insurance and Re-insurance Company, and InsuranceIslam TAIB. Most of the funding needs for the UAE’s real estate sectorare met by Islamic mortgages and sukuk issues. DIB is the biggest dealerof the global sukuks market. There has been an increasing demand forIslamic retail finance and private equity funds in the UAE over time. BothDubai International Financial Exchange (DIFX) and Dubai InternationalFinancial Centre (DIFC) are encouraging trade in Islamic securities,equities, derivatives, funds, depositary receipts and other instruments.

Middle Eastern IFIs are greatly involved in real estate financing,which is worth trillions of dollars. The financial planning or the wealthmanagement sector has also emerged as the most lucrative and growingarea of Islamic financial markets. Private assets were estimated to be over

1.3 The Rationale of Islamic Finance 17

US$750 billion in the Middle East in 2006. More than 300,000 wealthyindividuals in the Middle East hold over US$1.4 trillion of capital (Salim2006). According to a 2005 survey of McKinsey & Company, more than75% of the top 30 global asset managers are now active in Dubai (Varley2006). In 10 years time these numbers doubled as per S & P report2015. Takaful services and the sukuks industry have received a very warmresponse from the Middle Eastern business sector and society, with theIslamic equity funds investments also rapidly growing in the region.

The Middle East region is the second-fastest-growing private-bankingmarket in the world which may bring an estimate of near 70 percentincrease in wealth growth through 2015 as personal financial assets in thebiggest GCC countries rise to around USD 2.7 trillion. Regional markets(beyond the GCC and including Turkey, Egypt, and the Middle East andNorth Africa more broadly) have seen even more strong nominal GDPgrowth, particularly in oil-rich states, with the S&P GCC CompositeIndex up over 24 percent in 2013. This has boosted investor confidenceand encouraged. As of 2016, there are 350 projects running in the MiddleEast worth US$92 billion beside crsh in oil prices which show a greateconomic growth and wealth accumulation potential in wider MiddleEastern region in the years to come. For example, as per McKinsey andCo report 2015, only, the property valuations in Dubai (perceived as arelative “safe haven” by Middle East and North African investors). Theseinvestors are now using UAE banks as a safe haven to hide their moneyrather than in customary Swiz banks.

More than 100 GCC companies were set to issue IPOs in the year2006. However, total IPO’s as of 2015 stood at USD 1.4 billion from6 deals compared to which is 50% below than the average annual US$3billion between the year 2010 to 2014. There were total of 65 IPO dealsduring this period which is lower than its peak in 2006. It is estimated thatIFIs can target more than US$1.3 trillion of Islamic investor funds in theMiddle Eastern markets (Alvi 2006). Current status of this fund is nowthree time than what it was 10 years ago. The region hosts an increasingnumber of regulatory and supporting bodies of the IBF world.

The majority of well-reputed and best performing IFIs are located inthe Middle East. An increasing number of conventional banks in theregion are converting their operations to be partially or completely in line

18 1 Introduction

with Islamic banking in order to serve a wider client base and sustain theirexisting market share. It seems more than likely that banking and financeinstitutions in the Middle East may experience a shift from the conven-tional paradigm to Islamic conventions, with these IBF developmentsin the region possibly having a far-reaching impact on global financialmarkets.

It is interesting to discuss these findings in the light of a recent paperby Basov and Bhatti (2014), which will be discussed in detail later. In thatpaper the authors argued that Islamic banks’ financial performance oftenlags behind that of their non-shariah-compliant competitors, since theirslight disadvantage due to the necessity to comply with shariah law isexacerbated by the practice of assorted matching in the hiring process,which tends to place less competent employees in shariah-compliantfinancial institutions. Notice, however, that if in a region there existmany wealthy investors with preferences to carry their investment projectsthrough Islamic banks, the initial disadvantage may disappear and eventurn into advantage if there are economies of scale. This may explain whywell-reputed and best performing IFIs are located in the Middle East.

1.3.3 IBF in South Asia

The South Asia region contains three mainMuslim countries that includePakistan, Bangladesh and Afghanistan, with the largest minority of 125millionMuslims being in India. A number of IBF institutions and wealthyindividuals from the Middle East are interested in pouring funds into theinfrastructure, real estate sectors and equity markets of India and Pakistan.IBF has been recently revived in Pakistan under a dual banking system.In 2006 there were six fully dedicated Islamic banks that jointly hold ashare of 2:2% of the total banking industry in Pakistan, with assets worthUSD$1:3 billion (Al-Refai 2006). After 10 years, there are 14 IB’s andadditional 15 conventional banks offering IF services with a total marketshare of IB increased to 10% in 2016. At present these banks attract 9.7%of total bank deposits, offering Islamic Financial Services with value of 9%of banking assets in the country.

The first Islamic bank in the region—Islami Bank Bangladesh—wasestablished in 1983 in Bangladesh, where the IBF system has made steady

1.3 The Rationale of Islamic Finance 19

progress over the decades since. Currently, there are eight IB’s in thecountry; ICB Islamic Bank, Islami Bank Bangladesh Ltd, Shahjalal IslamiBank, Sonali Bank Limited, First Security Islami Bank Limited, EximBank Limited, Al-Arafah Islami Bank Limited, and Social Islami BankLimited. In 2005, Islamic banking deposits accounted for 13% of thetotal banking deposits, with investments representing 5% of total invest-ments in the banking sector of Bangladesh (Rana 2006). As per state bankof Bangladesh 2015 report, the IB’s deposits increased to 22% whereasIB’s investment reached above 15%. Some Bangladeshi Islamic banksare interested in promoting shariah-compliant securitization financingin the corporate sector. The government needs to share the experienceand resources of the international IBF industry to promote further trulyinnovative, competitive and shariah-compliant banking operations in thecountry.

There is a significant chance of IBF taking roots in India andAfghanistan in the future. Currently, there are more than 180 millionMuslims live in India with 25% population of Muslims are concentratedin Kochi and Kerala. The Muslims from these states work in theArabian Gulf countries and like to keep their finances in Islamicway. To cater their demand following five financial firms are servingtheir Muslim clients; Atharvved Finance Corporation, TAMEEMIMPEX, Associated Industrial Credit Society Al-Siraat Investment &Banking, The Bank of Tokyo-Mitsubishi UFJ, Ltd., Baitun Nasr UrbanCooperative Society. The feasibility report on launching a full fledgedIslamic bank in India is, however, under the consideration of Indianhigher authorities. The entry of IBF institutions in India would enableMuslims in the country to do faithful banking. This would also createmore diversified business and finance opportunities for Indian marketplayers. The government of Afghanistan could also tap into Islamicbusiness investments by promoting IBF in the region. The top officialsof Afghanistan International Bank (AIB) have plans to add profit-loss sharing (PLS) instruments into the existing range of conventionalproducts. The recent 2015 report of the Da Afghanistan Bank (the centralBank of Afghanistan), observe that 11% of Afghans have deposited morethan 280 billion AFN ($4 billion) in IB’s. Currently there are total 8banks offering IB services. Among these Bank e Millie and the First

20 1 Introduction

Dawood Islamic Bank are the two full fledge IB’s. Meanwhile, in theneighbouring country, Azerbaijan’s governor central bank announced thecountry could see the launch of its first Islamic bank soon in conjunctionwith Saudi Arabia based IDB. Viability of Islamic banks in these countrieswill crucially depend on their ability to compete with conventional banks,which in turn will depend on their ability to attract skilled entrepreneurs,as emphasized by Basov and Bhatti (2014).

1.3.4 IBF in the Southeast Asia

In the Southeast Asia, Indonesia, Malaysia and Singapore are the majorcontributors to IBF. The region hosts the fastest growing economies thatare very liberal, competitive and globally integrated. These three countriesuse IBF as a powerful tool to attract business and investments from theMiddle East and Muslim countries, and can perform an increasinglycrucial role in promoting IBF in the global financial markets.

Malaysia is the second biggest hub of IBF. In 1983, the Malaysiangovernment established the first Islamic bank—Bank Islam MalaysiaBerhad—and then introduced IBF in the country under dual systemby 1993. Presently there are twelve fully-dedicated Islamic banks, thirtyfive commercial banks, ten merchant banks and five development banksin Malaysia, which offer IBF products and services. According to Chan(2015), it is fast becoming an international centre for Islamic financethanks to its religious heritage, strategic location and progressive regula-tory structure, despite the competition it faces from financial capitals suchas London and Dubai. IF is the fastest growing sector in the financialservices industry in Malaysia, with much of the growth caused by theincreasing demand for Shariah-compliant financial products and services.Over past five years IF grew at Malaysia at an annual rate of 17:3%.

Malaysia pioneeredmany Shariah-compliant products and services. Forexample, it was the first country to set up a Shariah-compliant depositinsurance scheme, commodity trading platform on the domestic stockexchange (Bursa Malaysia), a cross border Islamic investment platform,residential mortgage-backed securities, first Islamic exchangeable bond,first Islamic real estate investment trust, first hybrid sukuk, and the firstAsian Islamic exchange traded fund.

1.3 The Rationale of Islamic Finance 21

The existing IBF assets worth is RM117; 393 million (US$32:06million), which represents 11:8%of total assets in theMalaysian bankingsector, with a growth rate over 27% in the last ten years. The Malaysiangovernment has devised a road map targeting a 20% share of the totalbanking industry for Islamic banking by 2010. A large number of keyplayers from the domestic and international Islamic finance have com-menced their operations in Malaysia. Bank Negara issued licenses to tenfully committed Islamic banks in 2006. Malaysia is the major contributorto recent developments and innovations in IBF products, systems andregulations, with the Malaysian government establishing separate legal,tax and regulatory frameworks for IFIs.

Takaful industry took birth in Malaysia in 1989 and presently holdsassets worth RM 6:5 billion (US$1:77 billion). The country is the pioneerof Islamic capital market and hosts the first international Sukuk centre.The Islamic money instruments, mutual funds, unit trust funds, managedfunds are experiencing rapid growth in the Malaysian financial market.There are 886 Shariah-compliant Islamic securities representing 85% ofthe total Malaysian Stock market. The Malaysian Islamic wealth man-agement industry has also rapidly grown over the years. The Malaysiangovernment is a staunch believer that an efficient financial system isthe key to stimulate savings, investments and economic growth in thecountry.Indonesia, the biggest Muslim populous country in the world,

embarked upon the IBF venture by establishing Bank MuamalatIndonesia in 1992. The bank achieved steady progress and is at thepresent time one of the pioneering institutions of IBF worldwide. Twoother fully dedicated Islamic banks, namely Syariah Mandiri and BankSyariah Mega Indonesia, as well as the conventional banks, are offeringIBF services in Indonesia. Presently IBF assets represent 1:8% the totalIndonesian banking assets. Bank Indonesia has formulated a 10-yearroad map for growth and development of IBF operations of up to 6%of the total Indonesian banking industry by 2011 (Harisman 2006).Takaful industry has experienced an inflated growth over the recent yearsin the Indonesian insurance market. The Indonesia Stock Exchangecurrently offers 242 Shariah-compliant stocks and Jakarta Islamic Indexof 30 Islamic securities to Muslims and other investors. Jakarata Stock

22 1 Introduction

Exchange has experienced high growth in Sukuks trading over the recentyears, as Indonesia works on improving IBF regulatory framework,Shariah faculties and staff qualifications. This would ensure worldwidecompetitiveness and exposure of the Indonesian IBF industry.

Singapore has been actively involved in promoting IBF operationsin Southeast Asia since 2001. The country aims to become an inter-national trading centre in Islamic property funds, hedge funds, Sukuksand wealth management. Maybank Singapore and OCBC Bank currentlyoffer IBF products to the Singaporean Muslims. The Kuwait FinanceHouse (KFH) and DBS Bank, CIMB’s Singapore are also interested tooffering IBF products to the Singaporean Muslims as well. The Takafulindustry in Singapore holds assets worth more than US$500 million.HSBC Insurance and NTUC Income provide Islamic insurance servicesin Singapore, whilst DBS Bank was first to introduce Singaporean IjarahSukuk of worth US$38 million in 2001, and has now been workingon developing Sukuks for wakaf6 assets and property management. TheSingapore Stock Exchange has listed Shariah-compliant indices, namelyLion 30 and FTSE-SGX Asia Shariah 100 Index, whilst the MonetaryAuthority of Singapore is committed to introduce changes to its tax andregulatory systems to facilitate proper growth and development of IBF inthe country (Venardos 2006).

Singapore has about US$500 million Islamic insurance funds andabout US$1.32 billion of Shariah-compliant property funds in September2006. Recently, the Monetary Authority of Singapore reported that morethan US$1.6 billion of Shariah-compliant property and insurance fundswere now operating in Singapore. The Singapore strategy for Islamicfinance is to play a value-added role in the global growth of Islamicfinance, and to become an integral component of the internationalfinancial system. Therefore, for these reasons Singapore has taken spe-cific initiatives, which includes regulatory framework; taxation; IFSBmembership; wealth management industry; capital markets; hedge funds;REITs; Islamic insurance; and Islamic Equity Index (Saw and Wang

6In Shariah, wakaf is a voluntary charitable endowment, from ones’ personal belongings or wealthin the form of cash / property for Shariah compliant causes.

1.3 The Rationale of Islamic Finance 23

2008). Moreover, Singapore is also considered as a well-placed countryto contribute to capacity-building and understanding of Islamic financialproducts, leveraging on the expertise and the talent base in conventionalfinancial products and services. It attempts to be acknowledged as aninternational financial center, that does not only offers open markets,efficient infrastructure and transparent regulations but also acts as a fullservice centre with broad range of intermediaries and products for bothIslamic and conventional finance that can meet the interests and demandsof market players and investors in the Middle East and across the globe(Saw and Wang 2008).

1.3.5 IBF in Africa: Sudan

The first Islamic bank in Africa—Faisal Islamic Bank Sudan—was estab-lished in Sudan in 1977 under the patronage of Saudi Prince MuhammadBin Faisal Al Saud. In 1983, Tadamon Islamic Bank Sudan, SudaneseIslamic Bank and Islamic Cooperative Bank also came into being. Thegovernment of Sudan passed the Islamic Shariah Act of Banking 1984which required the whole banking and finance sector of Sudan to betransformed on Islamic lines by the first of July 1984. The prolongedpolitical and economic turmoil in the country however did not allowIBF to grow and prosper. Since January 2005, the IBF practice hasbeen revived in Sudan under a dual banking system. There are 4 Islamicbanks in Northern Sudan, which are Omdurman National Bank, FaisalIslamic Bank, Bank of Khartoum and an agricultural bank (Mudawi2005). Sudan is known as a pioneer of Takaful products and servicesin the Islamic business and finance world, and is host to six Takafulcompanies.

1.3.6 IBF in European and Western Countries

IBF activities have been gradually gaining grounds in Europe, NorthAmerica and other Western countries. The United Kingdom’s FinancialServices Authority (UKFSA) currently aims to develop London as a centreof Islamic finance and investment from theMiddle East and otherMuslim

24 1 Introduction

countries. The FSA removed double stamp duty provision on Islamicmortgage contracts from November 2006, with necessary changes to theUK tax laws were introduced through the Finance Act of 2003, 2005and 2006, which removed hurdles in practising Murabahah and Ijarahmortgages, and diminished hurdles for entering Musharakah contracts.The UK’s Treasury and the FSA hold some more regulatory and taxchanges in the pipeline which would allow the issuance of Sukuks inthe UK’s domestic market (Amin 2007; Croft 2007). Presently IslamicBank of Britain (established in 2004), European Islamic Investment Bank(established in 2006) Friends Provident International, HSBC Amanah,Lloyds TSB,Mortgage Insurance UK andUnitedNational Bank are offer-ing a wide-range of Islamic finance and insurance products and servicesuch as fund management, retail and commercial property investment,consumer finance, saving products, credit cards and Takaful services toMuslims in the UK. Moreover, the UK is home to a number of dedicatedlocal and overseas Islamic Banks, as well as Islamic window operationsoffered through conventional banks. Some of the listed banks provideonly Investment or Wholesale banking, whilst others are more retailfocused. As per Global banking and finance review report 2016; there arecurrently, sixteen IBF service providers in the country. Among these are;Islamic Bank of Britain, Qatar Islamic Bank, EIIB (European IslamicInvestment Bank), HSBC Bank, Habib Bank, National Bank of Pakistan,Riyad Bank, Saudi American Bank (UK) Ltd., Arab Bankers Association,Habibsons Bank Ltd., Arab Banking Corp, Qatar National Bank, ArabAfrican International Bank, Bahrain Middle East Bank, Halal Mortgagesand Dallah Al Baraka. Just recently, the outgoing UK Chancellor ofthe Exchequer, George Osborne stated London will continue as a majorcentre for Islamic finance, stating “In recent years the City of Londonhas established itself as a global hub for renminbi, rupee, Islamic financeand green finance, as well as leading in new markets such as FinTech.”There are over 3 million Muslims in the UK, with the UK possibly actingas a gateway to promote IBF in other European countries where Muslimpopulation is more than 55 million.

IFIs took root in Europe in the early 1980s, with first joint Arab-Britishbanking ventures, Murabahah based arrangements, aimed at facilitatingGulf Islamic banks’ liquidity management operations and Arab investors’

1.3 The Rationale of Islamic Finance 25

property transactions. The development of Islamic finance, that followedits inception, has been beneficial for multiple stakeholders, both withinand outside of the region. It made it possible for the Muslim populationof Europe to bank in a Shariah-compliant manner. Growth of IFIs inthe region is facilitated by new regulatory policies and the Europeanexpertise in asset management. The Deloitte’s 2014 report on IF inEurope state that the share of the Muslim population in Europe isexpected to increase by 8% at the end of 2030, and hence EuropeanIB market conditions are favorable to sustain a steady growth of theIslamic finance products throughout Europe. While the UK hosts severalIslamic banks, Luxembourg is recognized as a leading hub for Islamicfunds.

The United Kingdom became the first non-Muslim country in theworld to issue sukuk, closely followed by Luxembourg. It drew attentionto sukuk as a viable alternative capital raising mechanism among sovereignand corporate issuers in Europe. Today, a range of Shariah-compliantbanking products and services are offered through window operations inFrance andGermany as well. Around 40 banking institutions have Islamicbanking operations across Europe. In the UK alone, six out of twentyinternational banks that engage in Islamic banking, are fully Shariah-compliant institutions. In France, a number of banks such as Paribas,Chaabi Bank and Société Générale started offerings Islamic financialproducts.

The first Islamic bank was open in Europe (Kuwait Finance House2014) currently, it is also operating in partnership with Kuveyt Turkbank which is the largest IB in Turkey. The process was launched by aconsortium of Gulf businessmen announcing an agreement to set up anew lender headquartered in Luxembourg. This bank, called Eurisbank,which have a start-up capital of 60 million Euros and have branches inParis, Brussels, Amsterdam and Frankfurt. The new entity is in the processof being licensed by the Luxemburg’s Supervisory Authority.

IBF is gaining momentum in North America, where the Muslimpopulation is estimated to be ten million by Islamic Horizons magazine.Presently IBF activities amount to US$1.5 billion and US$86.1 millionin the USA and Canada respectively (Ranzini 2007). However, Thomsonand Reuters 2016 report estimate that only in Canada the size of IBF

26 1 Introduction

is about US$8 billion which is required in near future. It further statethat Canada’s Islamic finance aspirations are strong in several areas:across asset management, Islamic investment fund, Shariah Mortgages,sukuk, retail and wholesale banking and as a source of foreign capital tobenefit the country’s companies and its governments which have largeinfrastructure investment needs to carry on future projects. The increasingnumber of Islamic and conventional institutions, that include Ameri-can Finance House LARIBA, University Bank of Michigan—UniversityIslamic Financial, Devon Bank, Guidance Financial Group, Saturan Cap-ital’s Aamaa Mutual Fund Group, Shariah Capital and Anchor FinanceGroup, have been offering Shariah-compliant products and services suchas deposits, home finance and mutual funds project financing, realestate financing, venture capital Islamic equity, hedge funds, Sukuks, andsyndication to Muslims in the USA. Furthermore, IBF activities haverecently emerged in Canada, with the United Muslims Financial Ontarionow offers Islamic mortgage services to CanadianMuslims. This may leadto an offering other Islamic instruments in the coming years.

1.3.7 IBF in Australia

The Muslim Community Cooperative Australia (MCCA) has been offer-ing Islamic saving and investment opportunities in Australia since 1989.In 2006, MCCA managed assets worth AUS$28.536 million (US$23.09million) with 8000 members, and is actively involved in Islamic financeactivities in the property and real estate sector. On average, MCCAannually transacts home mortgage contracts worth AUS$100 million(Sharif 2006). Currently, MCCA is a national organisation that hasfacilitated over $1 Billion in Islamic home finance and manages over $50million in investment funds for its more than 12000 members. Anotherconventional based financial institution—APV Sydney Finance—alsoprovides Islamic finance services to Australian Muslims. The NationalAustralia Bank is currently developing its own systems to introduce IBFproducts in Australia, and moreover the Oasis Group Holdings andAmInvestment Group are interested to offer IBF services in Australia aswell.

References 27

1.4 Conclusions

In this chapter we described the main tenets of Islamic finance and itsemergence and spread over the globe.We argued that while the constraintscan be useful in restricting trading in hot air, preventing boundedlyrational agents in taking unjustified risks, for example, via short sellingthe assets and curbing excessive interest, especially in the environmentswith weakly developed markets and legal institutions, they also imposesignificant costs on the economic agents bound by these constraints.For example, they may prevent efficient risk-sharing by banning trade incontingent commodities, short-sales or restricting the types of incentivecontracts that can be offered. We also argued that these restrictions, evenwhen they are not too burdensome by themselves, can handicap Islamicbanks in their competition for managerial talent. Therefore, viability ofIslamic banking at different geographic locations will crucially depend onthe presence of wealthy investors committed to using Islamic financialservices. In the next chapter we are going to discuss the main instrumentsused by Islamic banks.

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Ahmad, S.M. 1952. Economics of Islam. Lahore: Institute of Islamic Culture.Al-Humaidi, O. 2006. SABIC offers debut SAR 3 billion sukuk with signing of key

documents and underwriting agreement, mediarelease. Riyadh: SABIC. http://www.sabic.com/corporate/en/newsandmediarelations/news/24072006.aspx.

Amin, M. 2007. Facilitating Sukuk in UK. Islamic Finance News 4: 10–11.Al-Refai, M.A. 2006. Unicorn Investment Bank enters Pakistan, media release,

http://www.unicorninvestmentbank.com/default.asp?action=article&ID=195.

Alvi, I. 2006. The state of the Islamic capital market’. In Proceeding ofIIFM Workshop Sukuk, http://www.iifm.net/download/Presentations/The%20State%20of%20Islamic%20Capital%20Markets%20and%20Future%20Prospects%20may06.pdf .

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Basov, S., and M.I. Bhatti. 2014. On Sharia’a compliance, positive assortativematching, and return to investment banking. Journal of International Finan-cial Markets, Institutions and Money 30: 191–195.

Chan, C. 2015. Malaysia: the Islamic financial capital of the world. Global Bank-ing and Finance Review. http://www.globalbankingandfinance.com/malaysia-the-islamic-financial-capital-of-the-world/.

Croft, J. 2007. UK banks are catching up. Gulf News. http://www.gulf-news.com/Business/Business_Feature/10099406.html.

Graham, R. 2006. Shariah compliance is a riddle – but true riddles alwayscontains the answer. Islamic Finance News 4(33):12.

Harisman, R. 2006. Indonesia Islamic banking share seen up. Centralbank medi-arelease. Bank Indonesia. http://www.jogjacitycom/2006/10/10/indonesia-islamic-banking-share-seen-up-central-bank.

Harrison, R. 2006. SAIB launches Islamic banking program. Arab News. http://www.arabnews.com/?page=6&section=0&article=87203&d=26&m=9&y=2006.

Huda, M.A. 1964. Economics accepting Islam. Singapore: World Muslim League.Kettell, B. 2010. Islamic finance in a nutshell. West Sussex: Wiley.Khan, M.M., and M.I. Bhatti. 2008. Development in Islamic banking: a

financial risk-allocation approach. The Journal of Risk Finance 9: 40–51.Khojah, I. 2006. Kuwait leads global Islamic finance. Islamic Finance News 3: 3.Kuwait Finance House. 2014.Global Islamic finance: propositions to Europe. Kuala

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of Islamic Banking. London: The Islamic Foundation, pp. 26–37.Parker, M. 2006. Islamic banking gains momentum in Lebanon. Arab News.

4 April, viewed 22 August 2007.Qureshi, A.I. 1946. Islam and the theory of interest. Lahore: Sh. Md. Ashraf.Rana, F.H. 2006. Growing business prospect of Islamic banking. The Daily Star.

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2Islamic Financial Instruments

In this chapter we are going to describe the major Islamic financial instru-ments and compare them with the conventional ones. Islamic financialinstruments can be divided into equity-based and debt-based instruments.The first group includes musharakah, a contract governing the pooling oflabor and capital, and mudarabah, an agency contract. The second groupconsists of murabahah, a generic sale contract, salam, which allows theseller not to be in possession of the good at the time of sale; however, thegood must be fungible and readily available on the market, istisna’, whichis similar to salam, but dispenses with the fungibility requirement, andijarah, which refers to renting someone’s goods or services.

2.1 Overview

Islamic financial instruments are based on Islamic law and so to discussthem fully would require a comprehensive analysis of their sources.However, as the primary objective of this book is to highlight applicationsof modern economic theory to Islamic finance, rather than a discussionof the underpinning legal issues, we shall limit our discussion to the

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_2

31

32 2 Islamic Financial Instruments

main instruments, which we will use later to provide the foundations forformal modeling. Our main sources are Iqbal and Mirakhor (2011) andObaidullah (2005), who define each instrument from a banking perspec-tive, as well as Usmani (2007), who explains the key legal matters andeconomic significance of each instrument. Anyone interested in a morecomprehensive jurisprudential treatment of Islamic financial instrumentsis encouraged to begin with Mahmoud El-Gamal and Muhammad Eissa(2003), before going through more complicated texts.

One should remember that both conventional and Islamic financialinstruments are basically contracts stipulating an arrangement with finan-cial consequences for the parties involved. This is important becausesome instruments only have legal significance while others have financialsignificance. One example of this is how a musharakah (partnership)contract necessarily requires pro rata risk sharing, whereas a wakalah(agency) contract only governs the granting of powers to the agent butnot the nature of the compensation. A less obvious reason why thisis important is that the act of contracting itself imposes constraintsprescribed by Islamic law, such as the prohibition of making contracts thatare conditional upon each other unless it is a necessity such as a deliverycontract attached to a procurement contract. This is significant because,as discussed briefly in the previous chapter, it fundamentally affects theway financial institutions design their products, including the updatingof contracts in response to changes in economic conditions.In terms of risk-sharing, Islamic financial instruments can be classified

into equity-based and debt-based instruments. It is also possible toconstruct hybrid securities subject to the guidelines set out in Islamic lawwhich will be discussed in the next chapter.

2.2 Equity-Based Instruments

In this section we are going to describe the equity based instrumentsof musharakah and mudarabah. These contracts govern Principal–agentrelationships and partnerships. It is important to understand them todiscuss risk versus incentive provision trade-off in both principal–agentrelationships and teams as shaped by Islamic law.

2.2 Equity-Based Instruments 33

2.2.1 Musharakah

The musharakah contract governs the pooling of either labour or capitaland the distribution of the resulting profits and losses. It is usually whatcomes to mind when people think of equity-based instruments as it is verysimilar to the conventional concept of shares issued by a company.

Musharakah contract

2.2.1.1 Profit and Loss Sharing

Profit can only be shared as a percentage of the profit earned by themusharakah entity as opposed to being a lump-sum payment or a per-centage of the capital invested. There is a difference in opinion amongjurists on whether or not the profit-sharing ratios can differ from eachinvestor’s proportion of the investment, though they are unanimous insaying that losses should be borne according to each investor’s proportion.We will present a formal model along these lines and study its propertieslater in the book. We will show that an Islamic contract significantlyunderperforms in comparison with a standard one if the environment ischaracterized by a significant chance of loss.

34 2 Islamic Financial Instruments

2.2.1.2 The Nature of Capital

Another point to be considered is the form of capital that may becontributed; the issue is that if the initial capital for a given musharakahis comprised of a variety of assets, there would be trouble in valuingeach of them and determining how much each investor contributed; oneshould also take into account that assets can depreciate and appreciateover time. Usmani (2007) concludes that the form of capital contributedshould not matter if there are techniques which can provide an accu-rate market valuation for a given asset. The latter, however, is not aforegone conclusion since numerous asset pricing models exist and it isnot always obvious which one is the most appropriate in the circum-stances.

2.2.1.3 Management

In terms of running a business based on musharakah, any investor isallowed to utilize the pooled capital for the business and in doing so willbe legally held accountable as an agent working for the other investors.However, it is also possible for the investors to agree as to which of themwill be working and who will be the sleeping partners. For the latter,Islamic law indicates that they cannot have a profit-sharing ratio higherthan their investment ratio.

2.2.1.4 Termination

The last point to consider is the manner in which a musharakah-basedventure is terminated, which is usually through liquidation, when itsdistribution is proportionate to each investor’s contribution. Should apartner prefer to keep their share in its non-liquidated form, then thattakes priority if it is possible; for example gemstones in comparison toheavy machinery. However, Usmani (2007) identifies that prematuretermination is a possibility whether it occurs voluntarily, usually if apartner needs to realize their gains in the short term, or involuntarily,

2.2 Equity-Based Instruments 35

such as through death or loss of capacity. In the latter case, if an investordies then the matter falls to any heirs who can either take the placeof the deceased as an investor or just liquidate their share. However, ifthe investor becomes unfit for conducting commercial transactions themusharakah must be “reset”, that is terminated and restarted, should theremaining investors wish to continue with the venture. If an investorwishes to terminate their involvement while the others still want tocontinue, then it is simply a matter of purchasing the shares of thatinvestor at a price agreed by both sides.

2.2.2 Mudarabah

The mudarabah contract is a kind of agency contract, entailing themanagement of one party’s capital entirely by another party. The mostwidely used agency contract in Islamic finance is known as wakalah.Its applications range from brokerage services in permissible activities,such as trade in certain stocks, to covering agency relationships under aMurabaha transaction, where the client, who wants to be financed, actsas an agent of the bank to acquire the asset, which is then sold to him oncredit installments.Mudarabah is a more specific contract and it has somefeatures that distinguish it from the more genericwakalah contract, whichmight be confusing at first, but can be understood given the context it wasimplemented under (Fig. 2.1).

2.2.2.1 Profit and Loss Sharing

The profits of the venture are shared between the two parties according toa pre-agreed ratio. As in a musharakah agreement, one’s share of the profitcannot be a lump-sum or a percentage of the contributed capital; it mustbe a percentage of the resulting profit. However, something very differentfrom themusharakah agreement is that the losses are entirely borne by theinvesting party as the agent will necessarily expend resources in order togenerate returns on the assets they were entrusted with. This is of courseunless they are found guilty of negligence.

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Fig. 2.1 Mudarabah contract

2.2.2.2 The Nature of Capital

As mentioned previously, capital contribution is usually entirely by oneparty to be managed by another party. The managing party is also allowedto contribute to the pool of capital and might even be encouraged to doso in order to align their incentives with the investing party. However, themanaging party is generally not allowed to use this initial pool of capitalfor their personal expenses: they can only do so out of their share in theresulting profits of the investment.

2.2.2.3 Management

Management of the capital is the sole right of the managing party, withthe investing party only limited to a monitoring role. The investing partyis, however, allowed to define the parameters of the investment activity,for example requesting that it only be in certain industries or geographicallocations. Building on this, it is permissible to set the profit sharing ratiosas being conditional upon these parameters such as agreeing on a 40–60 split if the manager invests the capital in relatively easier projects but a70–30 split for relatively more difficult projects. This flexibility is valuable

2.3 Debt-Based Instruments 37

as it allows the managing party the freedom to adjust dynamically theirinvestment portfolios, yet at the same time protects them from liabilitysubject to both parties practicing due diligence.

2.2.2.4 Termination

Termination of a mudarabah contract can be done by either party simplyby giving notice to the other party. If the assets are completely liquidon termination, the initial capital is first returned to the investing partysubject to debt and other investment related expenses and any profit isdistributed as agreed beforehand. If any of the assets are illiquid, themanaging party is allowed to try and liquidate them first to realize thefinal profit. Again, similar to the musharakah agreement, the issue ofpremature termination still exists. In this case Usmani (2007) does notfind a clear, unanimous view in Islamic law permitting the stipulation ofa specified duration for the mudarabah agreement unless there is a risk ofsevere damage to either party.

2.3 Debt-Based Instruments

In this section we are going to describe the debt-based instruments:murabahah, salam, istisna’ and ijarah. These contracts govern the salesand rental of goods and services.

2.3.1 Murabahah

Murabahah is very close to a generic sale contract, the conditions of whichwere outlined in the previous chapter. The only difference is that the sellermust let the buyer know what the original cost of the underlying assetis and how much is being charged on top of that. Because this looksvery similar to principal and interest, it is very attractive for use as areplacement for the standard fixed interest bearing loan even though itis actually a sale contract. In fact, in terms of its financial consequences

38 2 Islamic Financial Instruments

Fig. 2.2 Murabahah contract

it is equivalent to the fixed interest rate contract, but does not allow fora variable interest rate, as is typical in conventional mortgage contracts(Fig. 2.2).

2.3.1.1 The Nature of Cash Flows

Due to its nature as a cost plus sale, cash flows in amurabahah occur in twostages. The first is between the seller and a third party vendor, while thesecond is between the seller and the actual buyer. Also, the buyer has theoption of paying everything at the start or deferring their payment. Thesale price itself must be fixed, consisting of the seller’s cost of procuringthe asset and a markup agreed upon by both parties.

2.3.1.2 The Nature of Underlying Asset

The constraints on the underlying asset again come from the fact that itis a sale contract—it therefore must satisfy what constitutes a valid objectsale according to Islamic law. The first of these conditions is that the assetmust exist and both be owned and in the possession of the seller before itcan be passed on to the buyer. Naturally, this constraint also applies to thevendor when the seller procures the asset at the start for sale to the buyer.

2.3 Debt-Based Instruments 39

Similarly, both parties must know exactly which asset is to be delivered.Furthermore, the object of sale must be something of innate value andit must not be something whose only utility is prohibited in Islamic law,such as wine.

2.3.1.3 Management

Many issues can arise from a murabahah when it is thought of purely as afinancial instrument instead of a sale contract. The first, and probablymore common one, is using murabahah to provide liquidity when itshould in fact be used to deliver assets. This practice is commonly donewhen utilizing a murabahah contract with a deferred payment wherethe seller then buys back on spot the asset sold to the buyer. Becausethis practice combines two contracts that are not critically related toeach other and subverts the true aim of the murabahah contract, it ishighly frowned upon and mostly prohibited by Islamic law scholars. Thesecond issue is that when the buyer properly approaches the seller forfinancing through murabahah, the seller might have first to procure theasset before the murabahah contract can be made. However, once theseller has the asset, at first glance there is nothing in Islamic law thatbinds the buyer to enter into the murabahah contract. If the cost ofprocurement for the seller is trivial then it might not be such an issue,but the fact is that murabahah contracts can facilitate the purchase ofthings like machinery and raw materials which can be very costly forthe seller. It is because of this potential harm, for the most part, thatIslamic scholars require the buyer to make a unilateral promise—whichin this case is legally binding—to buy the asset from the seller at theagreed price. Other reasons that expose the seller to the credit risk arethe taking of a security or requiring a guarantee. However, this bringsup another issue, which is the penalty rates the buyer should pay forfalling behind in his or her payment schedule. The solution agreed toby Islamic scholars is that penalty rates are permitted but not as incomefor the seller as this would be no different from taking interest. Rather,the proceeds from the penalty rates should be donated to charity. Thisway, the deterrent is still in place but not as a form of exploitation of

40 2 Islamic Financial Instruments

one party by another.1 The final issue to be discussed arises when thebuyer is in a better position to procure the desired asset. In this case,the seller usually appoints the buyer as an agent to purchase the asset onbehalf of the seller. However, at this point the role of both parties becomesunclear—because the buyer now has the control of the asset, therefore it istempting to just assume that all responsibility concerning the asset belongsto the buyer. In actual fact, it is still the responsibility of the seller untilthe actual murabahah occurs in which the seller formally sells the asset tothe buyer.

2.3.1.4 Termination

If payment of the murabahah is to be deferred, then the payment periodsmust be fixed and made unambiguous, for example it cannot dependon an uncertain future event. The other reason a murabahah can beterminated is usually in the case of a default or an arrangement mutuallyagreed upon.

2.3.2 Salam

Salam and istisna’ are special forms of the standard sale contract in whichit is not required for the goods to be sold to have existed, nor is the sellerrequired to be in ownership or possession of the goods for the sale to bevalid. The idea behind the two is to recognize the need for a mode offinancing that facilitates reasonably high-risk ventures which only pay offat a future date, such as agriculture and international trade. The maindifference between salam and istisna’ is that in the former the goods mustbe fungible and readily available in the market should they be ruinedbefore delivery.

1This provision made sense historically, when capital markets were not well developed. As a result,the opportunity cost of capital was low and the seller enjoyed sufficient market power. A similarprovision is less reasonable today.

2.3 Debt-Based Instruments 41

Salam contract

2.3.2.1 The Nature of Cash Flows

Scholars unanimously agree that the full price of the sale must be paid atthe start of the contract, although there is a recognized tendency to sellat a discount in order to compensate the buyer for the risk. The reasonfor the full advanced payment is because paying in installments by thebuyer would reduce the contract to one of trading debt for debt, which isstrictly prohibited in Islamic law. One must remember that the contractwas initially permitted as a solution to financing a venture with a specificcash flow schedule and a reasonably high level of risk—otherwise thereare alternative contracts that should suffice.

2.3.2.2 The Nature of the Underlying Asset

The goods that are eligible for this contract must satisfy two mainconditions. The first, as explained above, is that the goods must befungible and readily available such that should the supplier fail to producethe goods they can simply deliver goods purchased from the market. Thisimplicitly means that the buyer cannot require that the goods come from aspecific location. Second, the goods must be quantifiable and also genericenough that it is easy to specify their average quality. This suggests that livecattle would not be good candidates for a salam contract as each animalwould be unique, in contrast to fruits and nuts which are relatively moregeneric. This second condition facilitates the requirement that the goodsin a salam contract must be clearly specified in terms of both their quality

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and quantity to ensure that the buyer’s interests are preserved. Lastly, itis not permissible for the object of sale to be something that must bedelivered on spot, such as currency.

2.3.2.3 Management

As has been discussed, salam is like a normal deferred sale except that theprice is paid in full at the start and usually at a discount. The risks borneby the supplier would usually be related to operations and delivery, bothsomewhat mitigated by the contract itself, as it requires the object of saleto be fungible. Also, the buyer can ask the supplier for collateral in theevent that they cannot deliver the goods.

2.3.2.4 Termination

There is a difference of opinion with regards to whether or not it ispermissible to stipulate a minimum delivery period. There is good reasonto have such a period, mainly because the contract of salam was onlyaccepted to benefit suppliers, such as farmers, who needed time to producetheir goods. On the other hand, the textual evidence governing salamdoes not mention a minimum period, just a fixed period. Also, thecontract is only valid through mutual consent and the supplier is onlyexpected to agree to a favorable contract. Usmani (2007) points out thatthere is a whole range of minimum periods prescribed by various Islamicscholars. The justification for this is that different circumstances requiredifferent minimum periods. Therefore, Usmani (2007) recommends thatno minimum period should be stipulated and that it should be left to beagreed upon by the buyer and seller.

2.3.3 Istisna’

As mentioned before, istisna’ is the other exception to a sale contractrequiring that the object of sale be in existence. It is literally a “requestto manufacture something”, which will then be purchased for an agreedprice. Istisna’ is the opposite of salam in the sense that it exists to facilitate

2.3 Debt-Based Instruments 43

the buyer’s need for a non-ubiquitous good as opposed to salam, whichfacilitates the seller’s need to produce a ubiquitous good that has highinherent risks. The diagram for istisna’ is the same as for salam.

2.3.3.1 The Nature of Cash Flows

Istisna’ is one of the very few contracts where it is permissible for bothparties to fulfill their obligations at a future date, in contrast even to salamwhich requires the full payment to be made at the start. This relates to thefact that it is permissible for each stage of manufacturing to be dealt withindividually, meaning that the buyer can pay for a given stage and proceedonly if progress is according to their specifications.

2.3.3.2 The Nature of the Underlying Asset

From its definition, one would use istisna’ for something that must bemanufactured. This usually concerns things that cannot be found inthe market, requiring a custom order, or things that, by nature, requiremanufacturing. A common example of the latter is the construction ofbuildings, which, because of their nature, cannot simply be bought fromthe market.

2.3.3.3 Management

It is permissible and well within the interest of both parties—especially thebuyer—for the manufacturing process and its payment to be divided intostages. This way the buyer can exercise due diligence at each productionstage to make sure that the final product is according to specification.

2.3.3.4 Termination

Istisna’ can be terminated unilaterally provided that manufacturing hasnot yet commenced.

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2.3.4 Ijarah

Ijarah can refer to employing someone’s services in exchange for payingthem a fixed wage or leasing an asset in exchange for rent payments. Inthe context of IBF, the latter meaning is usually taken. Specifically, whatis meant is for one party to transfer the usufruct2 of something they ownto another party for an agreed period of time and for an agreed form ofrent.

2.3.4.1 The Nature of Cash Flows

The cash flows from an ijarahmust be determined at the time of contractand they must be known throughout the leasing period. They can bevariable provided that the variation is agreed upon by both parties atthe time of contract. This means that neither party is allowed to changeunilaterally what has been agreed. One issue that is controversial in thisregard is whether or not the cash flows can be benchmarked accordingto interest movements such as LIBOR. Usmani (2007) opines that this ispermissible even though it is discouraged, as it makes the ijarah contractvery similar to an interest bearing loan. The dividing line is that the lesseein an ijarah contract is paying for an economic benefit which could verywell fluctuate in price and requires maintenance by the lessor, whereasa debtor is paying interest on cash that might not yield any economicbenefit at no real cost to the creditor. However, there is nothing to stopboth parties from choosing a more appropriate benchmark such as anindex for housing demand if the leased asset consists of real estate. Again,the view that debt bears no real cost to the creditor might have held truein the early days of Islam, when credit was in the form of gold coinstaken from a chest, but it is not true today, since lending money impliesforegoing other possible investments and therefore carries an opportunitycost.

2Usufruct is a limited real right that unites the two main characteristics of property rights: usus,the right to use or enjoy a thing possessed, directly and without altering it; and fructus, the right toderive profit from a thing possessed.

2.3 Debt-Based Instruments 45

Another point to be considered is that the lease is only in effect whenthe leased asset is made accessible to the lessee. This is regardless ofwhether or not the lessee uses the asset. On the other hand, it also meansthat any payments made before the asset could be accessed must be heldas prepayments for when the lease actually begins.

In terms of expenses, the leased property is still owned by the lessor,so any expenses related to ownership shall be borne by the lessor and anyexpenses related to use shall be borne by the lessee. This also applies toany maintenance required on the asset unless the damage was caused bythe lessee.

2.3.4.2 The Nature of the Underlying Asset

The definition of an ijarah implicitly imposes certain conditions on theunderlying asset. For example, the thing being leased must have a usufructand it must not be something that can only be used by consuming it. It isalso required that both parties specify which asset is to be leased and verifythat asset. For example, it is not enough for the lessor to agree to lease “ahouse” as requested by the lessee but for both parties to agree on a specifichouse, verify its availability and confirm that it is indeed the house to beleased.

2.3.4.3 Management

Management related issues in an ijarah concern several things which canbe divided into two categories: issues related to the usufruct and issues inregards to using it as a financing product. Concerning the former, an ijarahasset can only be used for what it is normally used for, which implies thatit is good if both parties first agree on what the limitations of the usufructare. Addressing the latter, it is tempting to view an ijarah contract asidentical to a regular financial lease, though there are differences that mustbe taken into account. These differences are mostly legal in nature, suchas making sure that the leasing phase and the ownership transfer phase arekept distinct, though some of them will have financial consequences. For

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example, if the potential lessor needs to acquire first the asset then they areliable for all the associated costs, even though these can be simply passedon to the potential lessee in the form of rent payments.

2.3.4.4 Termination

The period of the ijarah should be made clear and definite by bothparties—neither party is allowed to terminate unilaterally the contract.This is, of course, subject to a variety of stipulations, such as the suddenunavailability of the usufruct or another breach of the contract by thelessee.

2.4 Takaful

Takaful is a system of mutual insurance based on the system of aquila,which was practiced by the Muslims of Mecca and Medina in the earlydays of Islam. Under this system, individuals or companies make regularcontributions into a fund, which is used for reimbursement in the caseof loss. The fund is run by a takaful operator. We will consider devisingoptimal incentives for takaful operators later in this book.

The concept of takaful is grounded in Islamic banking and observesthe rules and regulations of Islamic law. Takaful is based on the followingsix principles:

1. Policyholders cooperate among themselves for their common good.2. Policyholders’ contributions are considered as donations to the fund

(pool).3. Every policyholder pays his or her subscription to help those who need

assistance.4. Losses are divided and liabilities are spread according to the community

pooling system.5. Uncertainty is eliminated concerning subscription and compensation.6. It does not derive advantage at the cost of others.

References 47

Takaful can be implemented using four different models. Under themudharabah model the managers (shareholders) are sharing the profitsand losses with the policyholders; under the wakala model the agencyfee is received up front from the contributions and transferred to ashareholders’ fund; a hybridmodel uses elements of bothmudharabah andwakala; finally, under the Al Waqf model part of the contributed capitalis irredeemable.

References

Iqbal, Z., and A. Mirakhor. 2011. An introduction to Islamic finance: theory andpractice. Hoboken: Wiley.

Mahmoud El-Gamal, A., and S. Muhammad Eissa. 2003. Financial transactionsin Islamic jurisprudence. Beirut, Lebanon: Dar al-Fikr.

Obaidullah, M. 2005. Islamic financial services. Jeddah: Scientific PublishingCentre, King Abdulaziz University.

Usmani, M.T. 2007. An itroduction to Islamic finance. Karachi: MaktabaM’aariful Qur’an.

3The Historical Roots and Evolution

of Islamic Financial Thought

Islamic banking is a modern phenomenon; however, its roots go deepinto history with its principles primarily derived from the Quran. Anearly market economy developed in the Islamic world between the eighthand twelfth centuries, which was based on an early form of mercantilism,sometimes called Islamic capitalism. A number of Islamic instrumentsand institutions, such as mudaraba and waqf, discussed above, as well asdifferent forms of capital (al-mal), capital accumulation (nama al-mal),checks, promissory notes,1 transactional accounts, loaning, ledgers andassignments date back to this time.Mudaraba contracts were particularlyimportant, since they governed the agency institution, which was alsointroduced during that time. Many of these early forms of capitalistorganizations were adopted and further advanced in medieval Europefrom the thirteenth century onwards.

Prohibition of usury, or riba in Arabic, is probably the best knownprovision of Islamic law. The word riba literally means excess or addition,and according to shariah law it implies any excess compensation without

1Muslim traders are known to have used the check or sakk system since the time of Harun al-Rashidof the Abbasid Caliphate in the ninth century.

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_3

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50 3 The Historical Roots and Evolution of Islamic Financial Thought

due consideration. In practice this meant the prohibition of interest,the principle, which was well-established and integrated into the Islamiceconomic system. During the “Islamic Golden Age” it was unlawful toapply interest to gold and silver currencies, but it was acceptable to fiatmoney—currencies made up of other materials such as paper or basemetals. One might speculate that the value of fiat money was morelikely to be subject to inflation, therefore interest may be necessary tocompensate for it.

The reasons for usury provision were not unique to Islam. The CatholicChurch shared a similar view. One may easily understand the origins ofthis prohibition from a historical perspective. Indeed, consider a villagethat consists of many poor peasants and one rich merchant. Suppose thecrops fail in a particular year and the peasants have to borrow some goldcoins from a merchant to buy food in the market. The merchant is likelyto have a supply of gold coins just lying in his chest, so the opportunitycost of lending will be zero. However, being the only lender available, hecan charge high interest. What is more, should the crops fail for a coupleof years in a row, the peasants might become permanently indebted andhave to sell themselves into slavery. It was to curb such excesses that usury(riba) prohibition was designed. It also encouraged small entrepreneurs toborrow to pursue risky, but valuable, projects.

Clearly, such reasoning hardly applies today, when lending moneycarries opportunity cost and capital markets are competitive, so theinterest rate reflects the marginal value of funds, rather than being aninstrument for undue exploitation. This kind of reasoning encouraged anineteenth-century school of Islamic thought, led by Syed Ahmad Khan,to argue for a differentiation between sinful usury, which they saw asrestricted to lending for consumption, and legitimate interest, for lendingfor commercial investment. However, the contemporary movement ofIslamic finance is based on the belief that all forms of interest are ribaand hence prohibited. Such a view may be too restrictive. However,comprehensive discussion of it will require us to compare costs andbenefits of debt and equity financing. We will return to this question afterpresenting Modigliani and Miller’s theorem in the next part.

In addition, Islamic law prohibits investing in businesses that areconsidered unlawful, or haram (such as businesses that sell alcohol or pork,

3 The Historical Roots and Evolution of Islamic Financial Thought 51

or businesses that produce media such as gossip columns or pornography,which are contrary to Islamic values). Furthermore, shariah prohibits whatis calledmaysir and gharar.Maysir is involved in contracts where the own-ership of a good depends on the occurrence of a predetermined, uncertainevent in the future, whereas Gharar describes speculative transactions.Both concepts involve excessive risk and are supposed to foster uncertaintyand fraudulent behavior. Therefore, the use of all conventional derivativeinstruments is impossible in Islamic banking. We will discuss the directand indirect costs of such restrictions in the last part of the book.

Despite the limitations imposed by Islamic law, in the twentiethcentury many Islamic scholars recognized the need for services providedby commercial banks. They proposed a banking system based on theconcept of Mudarabah, defined as a relationship in which one partycontributes capital and the other expertise so as to earn a profit whichis shared at an agreed upon ratio. Starting from the middle of thecentury Islamic financial institutions mushroomed around the world. By1995, 144 Islamic financial institutions had been established worldwide,including 33 government-run banks, 40 private banks and 71 investmentcompanies. By 2008 Islamic banking was growing at a rate of 10–15%per year.

Interpretations of shariah may also vary slightly by country. TheIslamic Republic of Iran follows a more liberal interpretation of shariahthan Malaysia, whose interpretation is more liberal than Turkey or Arabcountries. Mohammed Ariff also found a less exacting interpretation ofshariah compliance in Iran where the government had decreed “thatgovernment borrowing on the basis of a fixed rate of return from thenationalized banking system would not amount to interest” and wouldhence be permissible.

Part IIThe Law of Unexpected Consequences

In this part we demonstrate the subtlety of the interaction between thelegal framework and the economic consequences. Often policies haveconsequences other than the ones they were introduced for, the so-calledunintended consequences. The concept of unintended consequences wasintroduced to the social sciences by Merton (1936), though the idea datesback at least to Smith (1776).Merton listed five possible causes of unantic-ipated consequences: ignorance; error; immediate interest, coupled withthe failure to take into account long-term interests; conflict between basicvalues and economic self-interest; and self-defeating prophecy. In the caseof Islamic finance, the main objective as stated by Islamic scholars wasto lead to a more fair distribution of wealth, to encourage investmentand to stabilize the value of money. We will see later in this book thatthe unintended consequences are: the inability to share risk properly,while providing sufficient incentives; the failure to finance innovativeventures; and the inability to attract the best managers to Islamic FinancialInstitutions (IFIs). But before discussing instances of the law in the area ofIslamic finance, we would like to take amore general look at it and to arguethat its consequences are not limited to this kind of finance. The insightsthat comes from the law is that an intervention in a complex systemtends to create unanticipated and often undesirable outcomes by creatingperverse incentives and failing to account for the response of economicagents to the policy, which may be rational or rooted in cognitive or

54 II The Law of Unexpected Consequences

emotional biases. However, sometimes actions provide unexpected ben-efits. For example, the medieval policy of reserving land for hunting ledto its preservation as parks throughout the UK and continental Europe.Legalized abortion in the United States (by reducing the numbers ofunwanted children), can account for much of the drop in crime rates thatoccurred in the 1990s. However, more often unexpected consequences arenegative. For example, in 1990, the Australian state of Victoria made safetyhelmets mandatory for all bicycle riders. While there was a reductionin the number of head injuries, there was also an unintended reductionin the number of juvenile cyclists, which was due to the fact that theyconsidered wearing a bicycle helmet unfashionable. Subsequent researchshowed that the net effect on health that balances the chance of headinjury versus the decrease in exercise was negative. Prohibition in theUnited States in the 1920s, originally enacted to suppress the alcohol trade,drove many small-time alcohol suppliers out of business and consolidatedthe hold of large-scale organized crime over the illegal alcohol industry.Since alcohol was still popular, criminal organizations producing it werewell funded and hence also increased their other activities. The war ondrugs, intended to suppress the illegal drug trade, instead consolidatesthe profitability of drug cartels. Moreover, Basov et al. (2001) showed thatthe policy did not even lead to the decrease of the price of illegal drugs.There are many more examples of both positive and negative unintendedconsequences of policies. Below we will give two examples of situationswhere the immediate intuitive response to the question as to what arethe consequences of a policy may be misleading, namely the incidence oftaxation and the design of corporate structure.

References

Basov, S., M. Jacobson, and J.Miron. 2001. Prohibition and themarket for illegaldrugs. World Economics 2: 133–158.

Merton, R.K. 1936. The unancticipate consequences of purposive social action.American Sociological Review 1: 894–904.

Smith, A. 1776. An inquiry into the nature and causes of the wealth of nations.Chicago: University of Chicago Press.

4The Incidence of Taxation

In this chapter we consider a situation where a government levies a taxon the producer or on the consumer of the good. We show that, contraryto what one might guess, the economic burden of taxation, known ineconomics as tax incidence, does not depend onwhere the tax is levied, buton the price elasticity of demand and supply. The concept was highlightedby the French physiocrats, who argued that the incidence of all taxationfalls ultimately on landowners and is at the expense of land rent. Theyused this conclusion to advocate the replacement of the multiplicity ofcontemporary taxes by a single tax. Though the physiocrats were correctto insist that the incidence of taxation does not depend on where thetax is levied, their conclusion that the whole tax burden is ultimatelycarried by land owners is flawed. The correct analysis had to wait forthe rise of modern economic theory. This example illustrates both thelaw of unintended consequences and the importance of formal analysis.Bringing the rigor of formal analysis to the area of Islamic finance is themain objective of this book.

The theory of tax incidence has a number of practical applications. Forexample, United States social security payroll taxes are half-paid by theemployee and half-paid by the employer. However, this does not imply

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_4

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56 4 The Incidence of Taxation

that the tax burden is shared equally. If one assumes, as seems reasonable,that the labor supply is much less elastic than the labor demand, employeeswill bear almost the entire burden of the tax, irrespective of where it islevied.

For concreteness, let us consider the following model. Suppose acompetitive firm produces a good and faces a market demand q(p); wherep is the price at which the firm offers the good and q(�) is a strictlydecreasing differentiable function. Assume also that the firm’s supply iscaptured by a strictly increasing, differentiable function s(�): Let us alsoassume that q(0) > s(0) and that there existsbp > 0 such that q(bp) < s(bp).Then in the absence of a tax there exists a unique equilibrium price, pe;

given by:

q(pe) D s(pe): (4.1)

The corresponding quantity is given by qe. The consumer and theproducer surpluses are given by:

CS D

C1Z

pe

q(p)dp;PS D

peZ

0

s(p)dp: (4.2)

Now suppose the government introduces a per unit tax and levies it onthe producer. The new equilibrium price, pt; is given by:

q(pt) D s(pt � t): (4.3)

Totally differentiating Eq. (4.3) one obtains:

q0(pt)dpt D s0(pt � t)(dpt � dt): (4.4)

Solving for the derivative of the equilibrium price with respect to tax, oneobtains

dpt

dtD

s0(pt � t)

s0(pt � t) � q0(pt): (4.5)

4 The Incidence of Taxation 57

Let us introduce demand and supply elasticities at a given price by:

"s(p) Ds0(p)p

s(p); "d(p) D �

q0(p)p

q(p): (4.6)

The minus sign in the definition of the demand elasticity is selected tomake both elasticities non-negative numbers. Noting that at equilibriumdemand equals supply, one can rewrite Eq. (4.5) as:

dpt

dtjtD0 D

"es

"es C "e

d

; (4.7)

where superscript e denotes the equilibrium value of the elasticity.Now (4.2) should be modified:

CS D

C1Z

pt

q(p)dp;PS D

pt�tZ

0

s(p)dp: (4.8)

Differentiating these equations with respect to t one obtains:

dCS

dtjtD0 D �

qe"es

"es C "e

d

;dPS

dtjtD0 D �

qe"ds

"es C "e

d

: (4.9)

First, notice that both derivatives are negative, so both the consumer andthe producer feel the burden of taxation. Also note that

dCS

dtjtD0 C

dPS

dtjtD0 D �qe (4.10)

dCS=dt

dPS=dtjtD0 D

"es

"ed

; (4.11)

that is the total burden of taxation is proportional to the equilibriumoutput, while the relative burden of taxation is in inverse proportion tothe respective elasticities. If the elasticity of demand is much greater thanthe elasticity of supply (in notation, "e

d >> "es) then the producer bears

58 4 The Incidence of Taxation

the total burden of taxation. If, on the other hand, "es >> "

ed the burden

is borne by the consumer. Note also that Eq. (4.10) implies that

d(CS C PS C T)

dtjtD0 D 0; (4.12)

where T D tq is the government’s revenue, which in turn, implies thatthe welfare losses due to taxation are of a second order of magnitude withrespect to t:, that is proportional to t2.Suppose that a government aims to finance an income support program

by levying a per unit sale tax on a firm producing the consumer good.If the good is a necessity that poor households will find difficult tosubstitute away, that is their demand is inelastic, then the burden oftaxation will be almost completely borne by them. Since taxation is alwaysdistortionary, the total tax burden will always exceed the tax revenue.Combined together these two results imply that such a policy will resultin hurting the very group it was designed to support. The role of formaleconomic analysis is to warn policymakers about such possible undesiredconsequences.

4.1 Exercises

1. Assume that the government levies a per unit tax on the consumer.Find the derivatives of the equilibrium price, the consumer surplusand the producer surplus evaluated at zero tax. How is the tax burdendistributed?

2. Assume that both the demand and the supply for the good are isoelastic,that is q(p) D p�"; s(p) D p�; for some positive constants " and �.

(a) Find the equilibrium price, the consumer surplus and the producersurplus in the absence of a tax.

(b) Find the equilibrium price, the consumer surplus and the producersurplus when a per-unit tax is levied on the producer.

(c) Find the equilibrium price, the consumer surplus and the producersurplus when a per-unit tax is levied on the consumer. Compareyou results with those obtained in (b).

Reference 59

4.2 Bibliographic Notes

The review of the incidence of taxation can be found in any goodundergraduate textbook on public finance. For a modern exposition see,for example, Gruber (2010).

Reference

Gruber, J. 2010. Public finance and public policy. New York: Worth Publishers.

5The Basics of Corporate Finance:The Miller–Modigliani Theorem

The previous chapter illustrated that our intuition is not a very reliableguide when it comes to designing complex policies and that formalanalysis is often needed. The issue of tax burden, though important, is ofno direct relevance to the theory and practice of Islamic finance (IF). Theexample we consider in this chapter, how the value of the firm is affectedby the way it is financed, is of direct relevance to IF. When you decideto start a business, one of your first questions is likely to be how to raisethe money to finance your operations. Broadly, there are two ways to raisefunds: taking debt or issuing equity. Debt financing, however, requires oneto pay interest to the lender, typically a bank. Islamic law prohibits charg-ing interest or entering into a contract that requires one to pay interest. Issuch a requirement a significant handicap for Islamic businesses?

On the most basic level the question boils down to whether the wayof financing matters for the value of the firm. A quick Google searchof the phrase “debt vs equity financing” produces more than one and ahalf million results. The top ten results are from business magazines. Intheir discussion of the relative advantages of different forms of financingthey mix together reasons rooted in economic fundamentals (e.g. a betterincentive structure is provided by debt contracts), accidental reasons due

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_5

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62 5 The Basics of Corporate Finance: The Miller–Modigliani Theorem

to current tax and bankruptcy regulation, and psychological reasons, likefeeling in control. Miller and Modigliani (1958) abstracted from all acci-dental considerations and asked whether, in an ideal world—where thecost of debt is the opportunity cost of capital, there are no taxes and youcan design contracts that perfectly motivate the managers—there is anydifference in how a firm is financed. The negative answer to this questionis the content of the celebrated Miller–Modigliani (MM) theorem.

This theorem is of paramount importance to IF. It implies that pro-hibition of interest (riba) by itself is not enough to explain the economicconsequences of Islamic law. It is interaction of this prohibition with otherstipulations of the law, molded by a particular economic environment,which drives the performance of Islamic economic institutions.

5.1 The Miller–Modigliani Theorem

Consider a firm whose investments generate a stream of profits fxtg1tD0;

that is at period t it produces financial stream xt.1 For simplicity we willassume that there is no uncertainty. Let r be the market interest rate, thenthe present value, x; of the stream of profits is given by:

x D

1X

tD0

xt

(1 C r)t: (5.1)

The fundamental question is: given the present value of cash streams is thevalue of the firm affected by the capital structure? Before the seminal workof Miller and Modigliani, the prevailing view among finance specialistswas that the earnings to price ratio is not affected by the capital structure,implying that a leveraged firm has a higher value than one financed purelyby stock. Miller and Modigliani (1958) showed that if “the investmentdecisions of the firm are unaffected by the way it is financed (in particular,this excludes the possibility of bankruptcy) and the investors can borrowand lend at the same interest rates as the firm then the financial structure

1At some periods xt may be negative, which we will interpret as investment.

5.1 The Miller–Modigliani Theorem 63

of the firm does not affect its value.” Themain idea behind the proof is thefollowing. Consider two identical firms with different financial structures,for example one is financed fully through equity, while the other issuedsome debt. An investor can generate the same stream of income from bothfirms by appropriately adjusting his or her portfolio.

To show this formally it suffices to demonstrate that a value of aleveraged firm equals the value of a firm financed purely by equity,irrespective of the amount of leverage. Consider two firms. Firm one isfinanced by both debt and equity and firm two is financed by equity only.Both firms generate the same financial streams. Let Vi denote the valueof firm i; that is the value of its stock, Si and outstanding debt, Di.2 Weassume that V1 D S1 and V2 D S2 C D2; which leads to share prices

p1 DS1

V1D 1; p2 D

S2 C D2

S2: (5.2)

Our aim is to establish that V1 D V2. Suppose that V2 > V1 and consideran investor holding fraction ˇ > 0 of outstanding stock S2 of companytwo. This holding entitles her to return

Y2 D ˇ(x � rD2): (5.3)

Consider the following strategy on behalf of the investor. She sells herstock in company two and uses the proceeds to buy shares in companyone. She will be able to buy

s1 DˇS2p2

p1D ˇ(S2 C D2) (5.4)

shares, which will constitute share � of the stock of firm one, where

� Ds1

S1Dˇ(S2 C D2)

S1: (5.5)

2Value Di should be interpreted as a present value of debt obligations, which will require thepayment rDi per period.

64 5 The Basics of Corporate Finance: The Miller–Modigliani Theorem

After paying her share of the debt to the lenders of firm two, the investorwill receive returns:

Y1 D �x � rˇD2 D ˇ

�

V2

V1x � rD2

�

> Y2; (5.6)

so owners of company two will sell their shares and acquire shares of firmone, depressing S2 and V2 and increasing S1 and V1 until V1 D V2.In other words, the leverage does not pay since an investor can borrowdirectly on personal account. The assumption that an individual investorcan borrow at the same rate as the firm is crucial for the result. Showingthat it is impossible to have V2 < V1 is similar and is left as an exercise tothe reader.

5.2 Hidden Information and the Breakdownof the Miller–Modigliani Theorem

Consider the following situation.3 Suppose firms differ in their possiblecash flows. High-cash-flow firms have their cash flows coming from auniform distribution on Œ0;H�; while the low-cash-flow firms have theircash flows coming from a uniform distribution on Œ0; L� with L < H.Managers know what kind of firm they have, but investors do not. Theycan, however, observe debt D of the firm. In period zero, a managerchoosesD. In period one, the cash flow is realized and becomes commonlyknown. If the cash flow is not enough to pay out the debt, the firm goesbankrupt and the manager incurs penalty, P. Assume also that the firm’sowners do not suffer the extra cost of bankruptcy. It is straightforwardto see that the expected value of the firm in period one is L=2 for a low-cash-flow firm and H=2 for a high-cash-flow firm. Now let us assume thatthe manager maximizes the weighted sum of the value of the firm in thecurrent period, V0(D); and its expected value, net of bankruptcy cost, inthe next period, that is

3This example is from Milgrom and Roberts (1992).

5.2 Hidden Information and the Breakdown of the Miller–Modigliani… 65

(1 � � )V0(D) C �

�

T

2�

PD

T

�

; (5.7)

where � 2 (0; 1) and T 2 fL;Hg. We would like to show that managerscan use the level of debt to signal the type of the firm. Indeed, assumethat the manager of a low-cash-flow firm chooses a level of debt DL andthe manager of a high-cash-flow firm chooses a level of debt DH: Theprobability of bankruptcy is given by the probability that the cash flow isbelow debt, that is

pB D Pr(c < D) DD

T: (5.8)

Therefore, the expected cost of bankruptcy for a firm of type T is pBP DPD=T .

Note that V0(DH) D H=2 and V0(DL) D L=2: Indeed, under theassumption that the debt levelDH is chosen by and only by high-cash-flowfirms and the debt level DL is chosen by and only by low-cash-flow firms,then investors will infer the firm’s type from the manager’s choices. So, theresult follows from the values of the firm in period one, as given above.Next, let us write the incentive compatibility constraints for the managersof both types, that is inequalities that ensure that the manager of a low-cash-flow firm prefers to choose level DL to level DH and the manager ofa high-cash-flow firm prefers to choose level DH to level DL, and let usshow that DH > DL: The condition that the manager of the high-cash-flow firm prefers DH to DL is:

(1 � �)H

2C �

�

H

2�

PDH

H

�

� (1 � � )L

2C �

�

H

2�

PDL

H

�

: (5.9)

Indeed, suppose the true type of the firm is H: If he or she chooses thelevel of debt DH the investors will (correctly) perceive the value of thefirm to be H=2; which will determine its stock price and, presumably,the manager’s compensation in period zero. In period one the true cashflow is realized, which has an expected value H=2 and the expected costof bankruptcy is PDH=H. This explains the left-hand side. If, on the

66 5 The Basics of Corporate Finance: The Miller–Modigliani Theorem

other hand, the manager chooses the level of debt DL the investors will(incorrectly) perceive the value of the firm to be L=2;which will determineits stock price and, presumably, the manager’s compensation in periodzero. In period one the true cash flow is realized, which has an expectedvalue H=2; irrespective of the level of debt chosen, and the expected costof bankruptcy is PDL=H. Simplifying, (5.9) becomes:

(1 � � )(H � L) � 2�P

H(DH � DL): (5.10)

Similarly, the condition that the manager of the low cost firm prefers DL

to DH is:

(1 � � )L

2C �

�

L

2�

PDL

L

�

� (1 � � )H

2C �

�

L

2�

PDH

L

�

: (5.11)

Simplifying, (5.9) becomes:

2�P

L(DH � DL) � (1 � � )(H � L) (5.12)

or, combining (5.10) and (5.12):

DL C(1 � � )(H � L)L

2�P� DH � DL C

(1 � � )(H � L)H

2�P: (5.13)

In particular, DH > DL, since H > L.It is easy to see that

DL D 0; DH D(1 � � )(H � L)L

2�P: (5.14)

satisfy both constraints. Note that for this choice of DH constraint (5.10)is slack, that is it holds as a strict inequality. Therefore, the managers oflow-cash-flow firms are indifferent between choosing levels of debtDL andDH; while the managers of the high-cash-flow firms strictly prefer DH toDL. Note also that DH decreases as the cost of bankruptcy increases.

5.3 Prohibition of Riba in the Light of the Miller–Modigliani Theorem 67

5.3 Prohibition of Riba in the Lightof the Miller–Modigliani Theorem

Onemight argue that prohibition of riba comes at no economic cost, sincedebt financing can also be replaced by equity financing without any eco-nomic cost. This statement is based on theMM theorem. However, as theabove analysis demonstrates, the theorem breaks down in the presence ofprivate information. So, in general, the prohibition of interest will imposeeconomic costs. The example in the previous section demonstrates thatthe existence of the hidden information breaks down the MM theorem.

Let us consider another example, the provision of mortgages by Islamicbanks to see how the MM theorem is broken down by the presence ofhidden action.

First, let us consider a conventional mortgage contract. Assume thatan individual with wealth W is interested in buying a house at price P0.Assume that P0 is substantially higher than W; so the individual either hasto borrow to buy the house or to rent the house, and for simplicity assumeshe borrows the entire amount P0.4 The individual lives in the house forone period, and at the end she sells it at price P1;

5 repays the loan to thebank with interest r; bequests W C P1 � (1 C r)P0 to her offspring anddies. So, payoffs to the bank are�P0 at period zero and (1Cr)P0 at periodone, while the payoffs to the individual are zero at period zero and P1 �(1 C r)P0 at period one. Now let us consider the contract offered by theIslamic bank, which cannot charge interest and therefore buys the houseand rents it to the individual.6 You may recognize this as an ijara contract.At time one the bank collects rent payment R; the individual bequests toher offspring W � R and the bank sells the house for P1. Note that periodzero payoffs are the same under both the conventional and the Islamicmortgage, while the period one payoffs and the Islamic contract are W �Rfor the individual and P1 C R for the bank. To compare these with the

4Allowing her to borrow only a fraction of P0 and use her own funds to pay the rest will not changethe argument.5We assume that there is no uncertainty concerning the value of P1.6Again, the bank can buy a share of the house, while the individual buys the rest. The rent will beadjusted accordingly. These complications do not concern us here.

68 5 The Basics of Corporate Finance: The Miller–Modigliani Theorem

payoffs of the conventional bank, assume that the rent the Islamic bankcharges is the market rent for similar houses, which is determined on theconventional market. The rent is determined by no arbitrage condition:one cannot make money by buying a house and renting it to someone, orby selling her house and living as renter. Therefore,

R D (1 C r)P0 � P1 (5.15)

and the payoffs for the Islamic bank are exactly the same as the payoffs forthe conventional bank. This is a particular case of the MM theorem, sincean Islamic mortgage can be considered to be an equity based contract,while the conventional one is a debt based one.

Note, however, that the crucial assumption for this equivalence wasthat P1 is fixed and does not depend on the ownership of the house. Inpractice, P1 will be affected by the care the tenant takes of the house, whois muchmore likely to take good care of it if she is the residual claimant onthe profits from sale, as she is under the conventional debt contract ratherthan the equity contract. This consideration implies that P1 is likely tobe lower under the Islamic contract and that the Islamic bank will make asmaller profit than a conventional one. Even if this loss of profit is not verysevere, it can impair Islamic banks’ competitiveness in the labor market,which will lead to a further deterioration of their performance, as we willsee in the last part of the book.

5.4 Exercises

1. Consider a project that generates payments of US$50 in even periodsand US$100 in odd periods, with time running from zero to infinity.Find its present value as a function of the market interest rate, r:

2. Consider two firms. Firm one is financed by both debt and Equity,and firm two is financed by equity only. Both firms generate the samefinancial streams. Let Vi denote the value of firm i; that is the value ofits stock, Si and outstanding debt, Di. Let V1 D S1 and V2 D S2 CD2:

Assume V2 < V1 and that the investor holds fraction ˛ > 0 of theoutstanding stock of company one. Following the logic presented inthe text, formulate an arbitrage strategy for the investor.

5.6 Unexpected Consequences of the Provisions of Islamic Law 69

5.5 Bibliographic Notes

The main part of this chapter is based on Miller and Modigliani (1958).The example of the breakdown of the MM theorem as due to the useof debt as a signal of the firm’s perception can be found in Milgromand Roberts (1992). This book also discusses other instances of imperfectinformation and its relevance for the theory of organizations and corpo-rate finance.

5.6 Unexpected Consequencesof the Provisions of Islamic Law

In Chap. 1 we listed the rationale for Islamic banking as professed byIslamic banking practitioners. To remind the reader briefly, this included:increases in the efficiency in the investment sector, which was supposedto result from the flow of investment towards ventures which provide agreater return and chances of success due to the PLS principle; more equaldistribution of wealth and the provision of help and assistance to thosewho are less fortunate; stimulation of the efficiency in asset allocationand offering stability to the value of money; and increases in the volumeof investments by encouraging risk-taking by entrepreneurs.

Are these claims backed by the actual performance of Islamic banks?Let us for a moment abstract from normative issues like wealth distri-bution and ask whether Islamic banking indeed increases the efficiency ofinvestment and encourages entrepreneurial daring. The evidence seems tocontradict this claim. Recently, Derigs and Marzban (2009) consideredthe effects of different strategies for constructing a shariah compatiblefinancial portfolio. They argued that shariah-compliant strategies resultin much lower portfolio performance than conventional strategies.

It is important to understand the reasons behind the lower performanceof Islamic financial institutions. Derigs andMarzban argue that it happensmainly because shariah compliance limits the set of admissible invest-ments. We believe that this is at best a partial story and that a factor of atleast equal importance is the adjustment of optimal contracts provided tothe entrepreneurs by Islamic banks compared with conventional ones.

70 5 The Basics of Corporate Finance: The Miller–Modigliani Theorem

Our insight on the issue is two-fold. First we argue that, though in aworld of perfect financial markets such a limitation will indeed alwayshinder performance, the situation is more ambiguous in the real world.Indeed, if a firm is financed primarily by debt, while it is run in theinterest of shareholders, who are protected by limited liability, it may haveincentives to take excessive risks. Shariah finance prohibits investmentin certain assets and industries, such as conventional bonds, derivatives,armaments, and the sex and gambling industries. If excessively riskyprojects are more likely to occur in these industries, the commitment ofIslamic banks not to invest in these projects, enforced by shariah boards,may result in an improvement of financial performance and attract moredebt financing. Debt financing may also prove to be more beneficial thanshare financing from the point of view of providing better incentivesto the management. This means that the effects of limiting the set ofadmissible investments by shariah law is ambiguous and invites us to seekan alternative explanation for the low performance of Islamic banks.

Second, the optimal contracts that Islamic banks offer to entrepreneursdiffer from the ones offered by conventional banks. In Part IV of this bookwe develop a framework for analyzing business loans that can be applied tostudying investment clubs, religious communities and other social groups.Within religious communities the problem is often complicated by thefact that the rules of a particular religion may provide further restrictionson the set of allowable contracts. For example, shariah law requires thatlosses are shared in proportion to the initial investment and that nointerest can be charged on the principal value of the initial loan. Weconsidered the effects of these restrictions in Basov and Bhatti (2011),where we concentrated on the trade-off between mitigating the moralhazard problem and attracting more skilled entrepreneurs. The problemcan be to some degree resolved by devising an optimal non-linear pricingscheme, but the contracts offered will still be important in determining thedistribution of types that a potential lender faces. This trade-off providesan alternative explanation for the low performance of Islamic banks.

This explanation is another example of the application of the lawof unintended consequences. The claim that Islamic loans encourageentrepreneurial risk-taking, for example, implicitly assumes that anentrepreneur will be compensated for success by the Islamic bank in

References 71

the same way as by a conventional one. However, if the bank is restrictedby shariah law such that it can share losses with the entrepreneur itwill optimally adjust the share of profits the entrepreneur gets, whichwill weaken the incentives for working hard. This is an unintendedconsequence of the PLS rule that losses should be shared in proportionto the investment. Though the result is rather intuitive, a formalinvestigation must wait until Part IV.

References

Basov, S., and M.I. Bhatti. 2011. Social norms and economic performance: Anexample of business loans by Islamic banks. SSRN Electronic Journal, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1968702.

Derigs, U., and S. Marzban. 2009. New strategies and a new paradigm forSharia’a-compliant portfolio optimization. Journal of Banking and Finance 33:1166–1176.

Miller, M., and F. Modigliani. 1958. The cost of capital, orporation finance andthe theory of investment. American Economic Review 48: 261–297.

Milgrom, P., and J. Roberts. 1992. Economics, organization and management.Englewood Cliffs: Prentice-Hall.

Part IIIGame Theory and Mechanism Design

In this part we will introduce the reader to the main theoretical toolsnecessary for the rigorous analysis of Islamic financial institutions. Thesetools are widely used in other areas of economics and are known as gametheory and mechanism design.

Following the seminal contributions of von Neumann and Morgen-stern (1944) and Nash (1951), game theory has found numerous appli-cations in different areas of economics, management and more recentlyevolutionary biology. The mechanism design approach has helped us toanswer important questions in the theory of optimal taxation (Mirrlees1971), managerial compensation and the theory of the firm (Milgromand Roberts 1992), and the theory of non-linear tariffs (Mussa and Rosen1978; Baron and Myerson 1982). More recently research has moved onto the theory of mechanism design with multidimensional characteristics(Wilson 1993; Armstrong 1996; Rochet and Chone 1998; Basov 2001),which has opened new areas of application and allowed us to obtain newinsights into old ones. For a review of the recent state of multidimensionalmechanism design theory and its applications, see Basov (2005). In thispart we will introduce the reader to the basic techniques of game theory,with a particular emphasis on its rapidly developing application: mecha-nism design theory. These techniques will be applied in Part IV to developsome formal models of performance in Islamic financial institutions.

74 III Game Theory and Mechanism Design

References

Armstrong, M. 1996. Multiproduct nonlinear pricing. Econometrica 64: 51–75.Baron, D., and R. Myerson. 1982. Regulating a monopolist with unknown cost.

Econometrica 50: 911–930.Basov, S. 2001. Hamiltonian approach to multidimensional screening. Jounal of

Mathematical Economics 36: 77–94.Basov, S. 2005. Multidimensional screening, series: Studies in economic theory,

volume 22. Berlin: Springer-Verlag.Milgrom, P., and J. Roberts. 1992. Economics, organization and management.

Englewood Cliffs: Prentice-Hall.Mirrlees, J. 1971. An exploration in the theory of optimum income taxation.

Review of Economic Studies 38: 175–208.Mussa, M., and S. Rosen. 1978. Monopoly and product quality. Journal of

Economic Theory 18: 301–317.Nash, J. 1951. Non-cooperative games. The Annals of Mathematics 54: 286–295.von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic

behavior. Princeton: Princeeton University Press.Rochet, J.C., and P. Chone. 1998. Ironing, sweeping and multidimensional

screening. Econometrica 66: 783–826.Wilson, R. 1993. Non-linear pricing. Oxford: Oxford University Press.

6Game Theory

In this chapter we will start by defining the concept of a game, beforedefining that of Nash equilibrium and evolutionary game theory.

To describe a game in general one has to specify: the players, that iswho is involved; the rules, that is who moves when, what they know whenthey move, what they can do; the outcomes, that is for each possible setof actions, what will happen and what the payoffs are.

6.1 The Normal Form and the Extensive Form

The extensive form of a game explicitly specifies the order of actions.Formally, a game in an extensive form consists of:

1. A set of nodes, X; a set of actions, A; and a set of players I D f1; : : : ; Ig.2. Function p W X ! X [ ¿; specifying the immediate prede-

cessor, p(x) ¤ ¿ for all nodes but one, called the initial node.

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_6

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76 6 Game Theory

Correspondence s W X ! X [ ¿ called the immediate successor anddefined by s(x) D p�1(x) (i.e. p(s(x)) D x). If s(x) D ¿ the node iscalled terminal. Iterating p(x) and s(x) we find all predecessors and allsuccessors of node x. No node is both a predecessor and a successor ofnode x.

3. The set of actions available at any non-terminal node.4. The partition of nodes into information sets. If a player is within an

information set, he or she cannot distinguish between the nodes thatbelong to this set. In particular, the set of actions available at any nodeof an information set should be the same.

5. Assignment to each information set of a player (or nature), who movesat it.

6. If nature controls an information set, one should assign the set ofprobabilities with which each possible choice is made.

7. In each terminal node payoffs to each player are specified in terms oftheir Bernoulli utilities.

An important notion is that of strategy. Intuitively, a strategy is a fullycontingent plan of actions. Suppose you would like to send your agentto play the game for you. For example, if you are a prime minister youmight want your ambassador to conduct the trade negotiations. In thatcase, you might want to provide him or her with a fully contingent planof how to behave in response to different proposals.

Formally, a pure strategy of player i is a rule that assigns to eachinformation set controlled by player i an action available to this set. Notethat actions should be specified even for information sets that will not bereached due to the previous actions of player i.

The normal form of a game specifies the set of players, theirstrategies and the payoffs that correspond to each strategy profile. Onecan always move from an extensive form to a normal form, but theimportant information about timing (or rather the information availableat the time of the move) will be lost. On the other hand, one canmove from the normal form to the extensive form if one is willingto make assumptions about the timing (e.g. all the moves are madesimultaneously).

6.3 Simultaneous-Move Games of Complete Information 77

6.2 Mixed Strategies and BehavioralStrategies

The notion just introduced was that of a pure strategy. Sometimes,however, a player might wish to randomize his or her choice. For example,the prisoner (in a prisoner’s dilemma) might decide to flip a coin andconfess iff it comes up heads. This is a mixed strategy and formally it isa probability distribution on the set of pure strategies. We will see laterthat sometimes the players will decide to randomize their choices to keepopponents from guessing.

If we have an extensive form game we can capture the idea of random-ization in two different ways:

1. write a corresponding normal form game and allow for the mixedstrategies;

2. consider randomized actions at each information set.

The latter procedure gives rise to behavioral strategies. It is clear that toeach behavioral strategy there corresponds a mixed one. Can any mixedstrategy be represented as a behavioral strategy? It turns out that the answeris yes, as long as the players have a perfect recall: that is the player doesnot forget what he or she knew.

6.3 Simultaneous-Move Games of CompleteInformation

In this section I assume that the players have complete information, thatis the normal form of the game is known to all players.

6.3.1 Dominant and Dominated Strategies

Consider a game � D fI; fSig; uig where I is the set of players, Si is a setof strategies of player i, and ui is his or her Bernoulli utility. Let s�i denotea strategy profile that all players expect for player i, and let S�i denote theset of all possible strategy profiles for the players other than i:

78 6 Game Theory

Definition 1. A strategy si 2 Si is called a strictly dominant strategy iffor all s0

i 2 Si, s0i ¤ si

ui(si; s�i) > ui(s0i; s�i)

for 8s � i 2 S � i.

In plain language, no matter what the others do there exists no otherstrategy that performs at least as good as si.

Definition 2. A strategy si 2 Si is called strictly dominated if 9s0i 2 Si,

s0i ¤ si

ui(s0i; s�i) > ui(si; s�i)

for 8s�i 2 S�i.

In plain language, there exists another strategy that performs betterthan si no matter what the others do. No rational player will ever playa strictly dominated strategy.

Definition 3. A strategy si 2 Si is called weakly dominated if 9s0i 2 Si,

s0i ¤ si

ui(s0i; s�i) � ui(si; s�i)

for 8s�i 2 S�i.

In plain language, there exists another strategy that performs at least asgood as si no matter what the others do. Thus it is quite reasonable toassume that players will not play strictly dominated strategies. However,that statement is not as innocent as it sounds.

6.3 Simultaneous-Move Games of Complete Information 79

6.3.1.1 Iterated Deletion of Strictly Dominated Strategies,Rationalizable Strategies and Common Knowledgeof Rationality

Consider the DA game.

DC C

DC 0;�2 �8;�1C �1;�8 �5;�5

Note that Strategy DC is a strictly dominated strategy for the columnplayer. After it is eliminated the row player faces a payoff matrix.

C

DC �8;�1C �5;�5

Now DC is strictly dominated and the result is (C;C). The processdescribed is known as an iterated deletion of strictly dominated strategies.Note that for the row player not to play DC he or she should not onlybe rational but also believe that the column player is rational and will notplayDC. Under the common knowledge of rationality (CKR) assumptionthis process can go on indefinitely (for games with more strategies). Onlythe strategies that survive it may be played by the players who haveCKR. Instead of eliminating strictly dominated strategies one might haveeliminated strategies that are never a best response to any mixed strategyof the rivals. This process is known as the elimination of the never bestresponses and the set of strategies that survives it is known as the set ofrationalizable strategies. If I D 2 there is no difference between the setof the rationalizable strategies and the set of strategies that survive theiterated deletion of the strictly dominant strategies.

80 6 Game Theory

6.4 The Nash Equilibrium

Definition 4. A strategy profile s D (s1; : : : sI) constitutes a Nashequilibrium (NE) if

ui(si; s�i) � ui(s0i; s�i)

for 8s0i 2 Si:

In plain language, a strategy profile is an NE if unilateral deviationis not optimal for any player. Of course, if all players have strictlydominating strategies (e.g. prisoner’s dilemmas) then the NE exists andis unique. The NE never contains a strictly dominated strategy though itmay contain a weakly dominated one.

6.5 Simultaneous-Move Games of IncompleteInformation

A game is called a game of perfect information if all information sets aresingletons. An example of such a games is chess: a player exactly knowsall the positions. Of course, all simultaneous-move games are games ofimperfect information. So are most card games.

A game is a game of complete information if each player knows the gametree (or the payoff matrix for the simultaneous-move game). All gameswe have considered so far are those of complete information. However,it is easy to come up with economically relevant examples when the lastassumption is violated. Consider, for example, the first price sealed bidauction. Two players bid for an object. Valuation of the first bidder is v1

and of the second bidder is v2. Each player submits a bid bi � 0. Theplayer with the highest bid wins the object and pays his or her bid. If heor she ties, the allocation is determined by the toss of a fair coin. Theexpected utility of player i who submits bid bi is

ui(bi) D (vi � bi)� (bi � bj);

6.5 Simultaneous-Move Games of Incomplete Information 81

where

� (bi � bj) D

8

ˆ

<

ˆ

:

1; if bi > bj

1=2; if bi D bj

0; if bi < bj

:

Since bi may in general take infinitely many values, the payoff matrix willbe infinitely dimensional. However, if we assume that bi is allowed to takeonly finitely many values, we can draw it. For example, if rules are suchthat bi 2 f1; 2g the matrix has a form

1 21 1=2(v1 � 1); 1=2(v2 � 1) 0; v2 � 22 v1 � 2; 0 1=2(v1 � 2); 1=2(v2 � 2)

:

If the valuations were public knowledge this would be a game of completeinformation. However, in reality this is rarely the case. Usually, vi is privateinformation. Therefore, neither player knows the payoff matrix and thegame is one of incomplete information.

6.5.1 Harsanyi’s Doctrine

Note that all solution concepts we developed in the Sects. 6.3–6.4 do notwork for games of incomplete information. To overcome this difficultyHarsanyi proposed looking at such games from a different perspective,which reduces them to games of imperfect information.

Consider the auction example above and assume that at time zero bothplayers do not know their own valuations or those of their opponents.Then the chance moves and assigns types to the players with someprobabilities (in the above example, it may select independently valuationsof the bidders from a set V D fv1; : : : :; vng with respective probabilitiesp1; : : : ; pn. Both, set V and the probabilities are common Knowledge(CK). At time t D 1 each player observes their valuation). In general, I willrefer to the private information a player has as her type. In the exampleabove, the type of the player is her valuation. At time zero each player

82 6 Game Theory

devises a fully contingent plan of how to behave for every realization ofher type. This trick reduces a game with incomplete information to thegame of imperfect information. The price you have to pay is that thenotion of a strategy becomes more complicated. Now the strategy is notsimply an action you were going to take after your type is realized but afunction from the type space into the action space. For example, a strategy inthe first price auction is a bidding function, which states how much youwill bid for any possible valuation, rather than just what you actually bid.A NE in the game so defined is called a Bayesian NE.

7The Revelation Principle

The main application of game theory to IF comes through a techniqueknown as mechanism design. In a mechanism design problem a designer,a principal, (a seller of a good, a government, a board of directors, etc.)tries to design an economic mechanism (a pricing schedule, a tax code,an employment contract, etc.) to achieve a certain social or economicobjective. The agent (a buyer, a tax payer, a manager, etc.) chooses his orher most preferred action, given the mechanism. The mechanism designproblem is complicated by the fact that the agents usually have privateinformation, which may concern their own costs and abilities, know-howor the objective state of the economy. Private information of the consumeris summarized by his or her type.

Let � be the set of all possible types and X the set of all possibleoutcomes (e.g. good qualities and prices, outstanding tax obligations). Ona very general level the mechanism design problem is formalized in thefollowing way:

1. The principal specifies the message space M and commits to sell aconsumer an outcome x(m) for every m 2 M.

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_7

83

84 7 The Revelation Principle

2. A consumer decides whether to participate and if yes sends a messagem(� ):

3. Payoffs are realized.

A strategy of a consumer is a function from � into M. We may thinkof it in the following way. At time zero, a consumer does not know hisor her type. The uncertainty is to be resolved by nature at date one. Theconsumer chooses a fully contingent plan at time zero. An NE in such agame is called a Bayesian NE.

Proposition 5 (The Revelation Principle). Let (t(m); x(m)I m(�)) be aBayesian NE in a message game. Then there exists another mechanism suchthat M D (0; 1); m(�) D � on the equilibrium path and the monopolistgets the same payoffs as in the initial mechanism.

Intuitively, in equilibrium the monopolist can deduce the type fromthe message sent, so why not ask for it directly? The revelation principlestates that without loss of generality one may restrict attention to thetruth telling mechanisms. Another important fact is given by the taxationprinciple.

7.1 Bibliographic Notes

Thematerial in the last two chapters can be found in anymodern graduatetextbook on microeconomics. The presentation here follows closely Mas-Colell et al. (1995).

Reference

Mas-Colell, A., M.D. Whinston, and J.R. Green. 1995. Microeconomic theory.Oxford: Oxford University Press.

8Monopolistic Screening

In this chapter we look at the monopolistic screening model, which isa particular example of the non-linear pricing model. Non-linear tariffsinclude railroad and electricity schedules and rental rates for durable goodsand space. Another application of these models is to devise an optimalcompensation scheme for a firm’s manager. The major justification fornon-linear pricing is the existence of private information on the side ofconsumers. In the early papers on the subject, private information wascaptured either by assuming a finite number of types (e.g., Adams andYellen 1976) or by a unidimensional continuum of types (Mussa andRosen 1978). The economics of unidimensional problems is by now wellunderstood.

The unidimensional models, however, do not cover all the situations ofpractical interest. Indeed, often the non-linear tariffs specify the paymentas a function of a variety of characteristics. For example, railroad tariffsspecify charges based on weight, volume and distance of each shipment.Different customers may value each of these characteristics differently,hence the customer’s type will not in general be captured by a unidimen-sional characteristic, thus a problem of multidimensional screening arises.In such models the consumer’s private information (his or her type) is

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_8

85

86 8 Monopolistic Screening

captured by an m-dimensional vector, while the good produced by themonopolist has n quality dimensions. Multidimensional models will playsome role in Part IV, where private information of an entrepreneur willconsist of his or her ability and degree of opportunism, therefore we willbriefly introduce the reader to the necessary techniques. For a compre-hensive review, see Basov (2005). We will start this chapter by consideringthe simplest screening model in which the private information about theagent can take only two different values.

8.1 The Monopolistic Screening Modelwith Two Types

Assume a monopolist can produce a unit of good with quality x at acost c(x), where c(x) is a strictly convex, twice differentiable function.The monopolist is risk neutral. Preferences of a consumer over a unit ofgood with quality x are given by a twice continuously differentiable utilityfunction u(�; x). The preferences of consumers are quasi-linear in money:

v(�; x;m) D u(�; x) C m:

Each consumer wants to buy at most one unit of the monopolist’s goods.Type � is private information of a consumer. However, it is commonknowledge that the type is distributed according to a distribution f (�) foreach consumer. The distribution has compact support (for concreteness� 2 (0; 1)) and f (�) > 0. If the consumer does not purchase a good fromthe monopolist he or she receives utility u0(�). For simplicity, assume itdoes not depend on type and normalize it to be zero. Finally, assume

u1 > 0; u2 > 0; u12 > 0:

Here ui is the derivative of u with respect to the ith argument, u12 is thecross partial derivative with respect to � and x. The last of these conditionsis known as the Spence–Mirrlees condition or the single-crossing property. Themonopolist and the consumers play the following game:

8.1 The Monopolistic Screening Model with Two Types 87

Proposition 6 (Taxation Principle, Rochet 1985). Without loss of gen-erality the monopolist can restrict his or her choice of a mechanism to a choiceof a non-linear tariff t(x).

The taxation principle follows directly from the revelation principle.Indeed, assume two types �1 and �2 receive the same allocation atequilibrium, but t(�1) > t(�2). Then type �1 will always find itprofitable to pretend to be �2; which contradicts the revelation principle.Therefore, types which get the same allocation should pay the sametariff, that is the tariff depends on type only through the allocation.Therefore, the monopolist’s problem without loss of generality can berepresented by:

max

1Z

0

(t(x) � c(x))f (� )d�

s:t:x(� ) 2 arg max(u(�; x) � t(x))

max(u(�; x) � t(x)) � 0:

Let us concentrate on the case � 2 f�L; �Hg: Then the integral should bereplaced by the sum

max pH(tH � c(xH)) C (1 � pH)(tL � c(xL));

where pH D Pr(� D �H) and the constraints become

u(xL; �L) � tL � 0 (8.1)

u(xL; �L) � tL � u(xH; �L) � tH (8.2)

u(xH; �H) � tH � 0 (8.3)

u(xH; �H) � tH � u(xL; �H) � tL: (8.4)

Constraints (8.1) and (8.3) state that both types would like to participatein the contract and are known as the individual rationality constraints,

88 8 Monopolistic Screening

and the constraints (8.2) and (8.4), known as the incentive compatibilityconstraints, ensure that no one would like to choose the contract meantfor the other type. The basic results is Stole’s constraint reduction theoremthat states that for the optimal allocation only two of these constraintsbind: (8.1) and (8.4): that is the lowest type gets his or her reservationutility (in this case, zero) and the highest type gets the information rentthat is just enough to prevent him or her from pretending to be the lowtype. This implies that

tL D u(xL; �L)

tH D u(xH; �H) � u(xL; �H) C u(xL; �L):

Therefore, the monopolist solves

max pH(u(xH; �H)�u(xL; �H)Cu(xL; �L)�c(xH))C(1�pH)(u(xL; �L)�c(xL)):

The first order conditions are

u1(xH; �H) D c0(xH)

u1(xL; �L) � c0(xL) DpH

1 � pH(u1(xL; �H) C u1(xL; �L)) > 0:

Note that xH is at the efficient level (no distortions at the top) and xL isbelow the efficient level. Type �H earns the information rents

I21 D u(xH; �H) � tH D u(xL; �H) � tL D u(xL; �H) � u(xL; �L):

8.2 The Unidimensional Screening Model

In this section we are going to assume that the type of consumer cantake continuum values, which can be parametrized by a single number,� 2 Œ0; 1�. Assume a monopolist who faces a continuum of consumersproduces a good of quality x. The cost of production is assumed to begiven by a strictly increasing, convex, twice differentiable function, c(�).

8.3 The Spence–Mirrlees Condition and Implementability 89

Each consumer is interested in consuming at most one unit of the goodand has a utility

u(�; x) � t; (8.5)

where � is his or her unobservable type distributed on (0; 1) accordingto a strictly positive, continuous density function f (�); t is the amountof money transferred to the monopolist, and u(�; x) is a continuousfunction, strictly increasing in both arguments. Consumers have anoutside option u0(�). The monopolist is looking for a mechanism thatwould maximize his or her profits.The same logic as in the previous section implies that the taxation

principle holds and that the monopolist faces a problem in selecting acontinuous function t W R ! R to solve

maxt(�)

1Z

0

(t(x(� )) � c(x(�)))f (� )d�; (8.6)

where c(x) is the cost of producing a good with quality x and x(�) satisfies

x(� ) 2 arg max(u(�; x) � t(x)) (8.7)

max(u(�; x) � t(x)) � 0: (8.8)

Here we assume that the utility of the outside option is type independentand normalized to be zero. This model was first introduced by Mussa andRosen (1978). We will now start a detailed study of its properties.

8.3 The Spence–Mirrlees Condition andImplementability

Suppose you are given an allocation x(� ). Under what conditions doesthere exist a non-linear tariff such that (8.7) is satisfied? If such a tariffexists the allocation is called implementable. Formally, the followingdefinition holds.

90 8 Monopolistic Screening

Definition 7. An allocation x(�) is called implementable if it is measur-able and there exists a measurable function t(�) such that

x(� ) 2 arg maxx2RC

(u(�; x) � t(x)): (8.9)

Our first objective is to characterize the set of implementable alloca-tions. We will do this under an additional condition: function u(�; x) istwice continuously differentiable and

u�x > 0: (8.10)

Equation (8.10) is known as the Spence–Mirrlees condition of the single-crossing property. The latter reflects the fact that under (8.10) the indif-ference curves of the consumers of different types in (x; t) space cross onlyonce. A well-known result is given by the following theorem (Mussa andRosen 1978).

Theorem 8. Allocation x(�) is implementable if and only if it is increasing.

Note that if u(�; �) satisfies the single crossing property then functionU(�; �) defined by

U(�; x) D u(�; x) � t(x) (8.11)

is supermodular in its arguments for any t(�). Therefore, the necessity ofthis result follows from the monotone maximum theorem. (I, Theorem155). Let us prove its sufficiency.

Proof. Suppose x(�) is increasing. Then it is measurable and we can definethe tariff t(�) by

t(ˇ) D u(ˇ; x(ˇ)) �

ˇZ

0

u� (�; x(� ))d�: (8.12)

8.3 The Spence–Mirrlees Condition and Implementability 91

Note that the pair of functions x(�) and t(�) define a non-linear tariff t(x)in a parametric form. Consider the decision of a consumer of type � .From his or her perspective, choosing quality x is equivalent to choosingtype ˇ that he or she pretends to be (this statement is a particular caseof the revelation principle, see Mas-Colell et al. (1995) for a discussion),therefore she solves

maxˇ2Œ0;1�

(u(�; x(ˇ)) � u(ˇ; x(ˇ)) C

ˇZ

0

u� (�; x(� ))d� ): (8.13)

Let

V(�; ˇ) D u(�; x(ˇ)) � u(ˇ; x(ˇ)) C

ˇZ

0

u� (�; x(� ))d�: (8.14)

Our objective is to prove that

V(�; � ) � V(�; ˇ); (8.15)

which implies that

� 2 arg maxˇ2Œ0;1�

(u(�; x(ˇ)) � u(ˇ; x(ˇ)) C

ˇZ

0

u� (�; x(� ))d� ); (8.16)

and therefore tariff (8.12) implements allocation x(�):To prove (8.15) note that

V(�; � ) D

�Z

0

u� (�; x(� ))d� (8.17)

92 8 Monopolistic Screening

and one can transform (8.14) to take the following form

V(�; ˇ) D

�Z

ˇ

u� (�; x(ˇ))d� C

ˇZ

0

u� (�; x(� ))d�: (8.18)

Therefore,

V(�; ˇ) � V(�; � ) D

�Z

ˇ

(u� (�; x(ˇ)) � u� (�; x(� ))d�: (8.19)

Suppose that � � ˇ then � � ˇ over the integration range, since x(�) isincreasing x(ˇ) � x(�) and by the single crossing property u� (�; x(ˇ)) �u� (�; x(�)) for all � 2 Œˇ; ��; therefore V(�; ˇ) � V(�; �) � 0. Similarreasoning proves that V(�; ˇ) � V(�; �) � 0 in the case � � ˇ; whichcompletes the proof. �

This theorem allows us to reformulate the monopolist’s problem. Forthis purpose define the consumer’s surplus by:

s(� ) D maxx

(u(�; x) � t(x)): (8.20)

Note that this surplus is a Fenchel u-conjugate of the tariff (I, Definition56). According to the generalized envelope theorem (I, Theorem 167) s(�)is almost everywhere differentiable and

s0(� ) D u� (�; x): (8.21)

Using the definition of the consumer surplus to exclude the tariff fromthe monopolist’s objective, the problem can be restated as:

1Z

0

(u(�; x) � s(� ) � c(x))f (� )d� (8.22)

s:t:s0(� ) D u� (�; x); s(� ) � 0, x(�) is increasing

8.4 The Concept of the Information Rent 93

One might also ask whether a particular surplus function is imple-mentable. The answer is that it is if and only if the unique allocationthat solves (8.21) is increasing. This is left as an exercise for the reader toshow that if a surplus function is implementable the implementing tariffsolves

t(x) D max�

(u(�; x) � s(�)); (8.23)

that is the tariff is a Fenchel u-conjugate of the surplus.Let us for a moment ignore the implementability constraint in prob-

lem (8.22). The problemwewill end upwith is called the relaxed problem.There are three ways to solve it. Before discussing them, however, we willintroduce an important economic concept: the information rent.

8.4 The Concept of the Information Rent

Let us integrate Eq. (8.21) from �1 to �2. We obtain

s(�2) � s(�1) � I12 D

�2Z

�1

u� (�; x(�))d�: (8.24)

Given any incentive compatible allocation x(�); integral (8.24) determinesuniquely the information rent type that �2 earns over �1. Note that theinformation rent depends only on allocation and not on which incentivecompatible mechanism is used to implement it.

The concept of information rent is of central importance to thescreening literature and is the key to understanding the economic rootsof the difference between the unidimensional and the multidimensionalcase. Intuitively, since in the unidimensional case there exists only oneline connecting any two types, the possibility of defining the informationrents does not put any restrictions on the allocation. This makes theunidimensional model technically simple and amenable to a variety ofapproaches, which I will discuss in the next section.

94 8 Monopolistic Screening

In the multidimensional case, however, any two points can be con-nected by a continuum of paths. Each of them can be used to definethe information rent by a formula similar to (8.24). However, for theinformation rent to be a meaningful economic concept, this integralshould be path independent. This puts severe restrictions on the setof implementable allocations and makes the multidimensional problemmuch harder than the unidimensional one. In particular, this is the mainreason why the direct approach, which I describe in the next section, hasvery limited applicability in the multidimensional case.

8.5 Three Approaches to the UnidimensionalRelaxed Problem

In this section we closely follow Basov (2004). Consider problem (8.22)and drop for a moment the constraint that x(�) is increasing. The resultingproblem is called the relaxed screening problem. Three approaches to thesolution of this problem are possible.

8.5.1 The Direct Approach

This approach was used by Mussa and Rosen (1978) and uses theintegration by parts technique. Let us evaluate

�

1Z

0

s(�)f (�)d� D

1Z

0

s(� )d(1 � F(�)) D �s(0) C

1Z

0

s0(�)d(1 � F(�)):

Here F(�) is the cumulative distribution function corresponding to thedensity function f (�). Using the envelope condition, the monopolist’sobjective can be rewritten as

1Z

0

(u(�; x) � c(x) �1 � F(�)

f (� )u� (�; x))f (�)d� � s(0): (8.25)

8.5 Three Approaches to the Unidimensional Relaxed Problem 95

The profit maximization then implies that s(0) D 0 and x is a pointwisemaximizer of the integrand. The first-order condition is

(ux(�; x) � c0(x))f (� ) � u�x(�; x)(1 � F(�)) D 0: (8.26)

Note that for � D 1 Eq. (8.26) implies

ux(1; x) D c0(x) (8.27)

that is the highest type consumes the good of the efficient quality. Thisproperty is known as no distortion at the top. In the next chapter we aregoing to investigate to what extent this property generalizes to the multi-dimensional case.

8.5.2 The Dual Approach

In this approach we start by solving Eq. (8.21) for x in terms of �; s; ands0 and substitute the result into the monopolist’s objective (8.22) to get acalculus of variations problem. For expositional simplicity assume that

u(�; x) D �x: (8.28)

Then

s0(� ) D x (8.29)

and the monopolist solves

max

1Z

0

(�s0 � s(� ) � c(s0))f (�)d�: (8.30)

The Euler equation has a form

@

@�(Œ� � c0(s0)�f (� )) D �f (�): (8.31)

96 8 Monopolistic Screening

Note that the Euler equation contains only the derivative of the surplusbut not the surplus itself. This means that if s�(�) is a solution, so iss�(� ) C C. The constant should be adjusted to make profits as large aspossible, subject to the participation constraint. Hence, s(0) D 0. On theother hand (� D 1) is free, so the transversality condition holds at � D 1

c0(s0(1)) D 1.

The Euler equation and the transversality condition imply

Œ� � c0(x)�f (� )) D 1 � F(�); (8.32)

which is exactly Eq. (8.26) for u(�; x) D �x:

8.5.3 The Hamiltonian Approach

Suppose we cannot find an explicit formula for x in terms of �; s; ands0 from condition (8.21). Then we can consider the monopolist’s relaxedproblem is an optimal control problem.

max

1Z

0

(u(�; x) � s(�) � c(x))f (� )d�

s:t:s0(� ) D u� (�; x); s(0) D 0.

Here s is the state variable, x is the control, the left end is fixed (s(0) D 0)and the right end is free. Form a Hamiltonian:

H D (u(�; x) � s(� ) � c(x))f (� ) C �u� (�; x): (8.33)

Then the first-order conditions have a form

�0(�) D �@H

@sD f (� ) (8.34)

8.5 Three Approaches to the Unidimensional Relaxed Problem 97

�(1) D 0 (8.35)

Hx D (ux(�; x) � c0(x))f (� ) C �u�x(�; x) D 0: (8.36)

Here � is the costate variable whose evolution is governed by Eq. (8.34).Economically, �(�) is the marginal value for the monopolist of relaxingthe local downward incentive compatibility constraint for type � . Equa-tion (8.35) is the transversality condition that should hold at the free end.Finally, Eq. (8.36) is the Pontryagin’s maximum principle.Equations (8.34) and (8.35) imply that �(�) D F(�) � 1. Substituting

in into (8.36) results in

(ux(�; x) � c0(x))f (� ) � (1 � F(�))u�x(�; x) D 0: (8.37)

Note that Eq. (8.37) coincides with Eq. (8.26). Moreover, they coincidewith (8.32) for u D �x. Therefore, all three approaches lead to the samesolution of the relaxed problem. The Hamiltonian approach also allowsus to deal easily with type dependent participation constraints. All one hasto do is to put a Lagrange multiplier on the constraint and add this termto the Hamiltonian. We will discuss this problem later in this chapter.

If the solution to the relaxed problem is weakly increasing it coincideswith the solution of the complete problem. The sufficient conditions forthis to be the case are

u��x � 0 (8.38)

and

LR0(� ) � 0; (8.39)

where the likelihood ratio, LR(�); is defined by:

LR(� ) D1 � F(� )

f (� ): (8.40)

98 8 Monopolistic Screening

The last condition is known as the monotone likelihood ratio property(MLRP). Indeed, it is easy to see that (8.38) and (8.40) imply that themonopolist’s objective

(u(�; x) � c(x)) �1 � F(�)

f (�)u� (�; x) (8.41)

is supermodular in (�; x). Therefore, the monotone maximum theorem(I, Theorem 155) implies that its pointwise maximizer is increasing. If theutility has the form

u(�; x) D �x; (8.42)

the solution to the relaxed problem will satisfy

c0(x) D v(� ); (8.43)

where the virtual type, v(� ) is defined by

v(� ) D � �1 � F(�)

f (� ): (8.44)

The solution will be implementable if and only if the virtual type isincreasing in � . If the solution is not increasing in � it should be modified.We will discuss the necessary modifications in the next section.

8.6 The Hamiltonian Approach to theUnidimensional Complete Problem

Though all three approaches described in the previous section workequally well for the relaxed problem, the first two do not allow us to arriveat the solution of the complete problem in a regular way.Mussa and Rosen(1978) used some heuristic arguments to show that if the implementabilityconstraint is binding the solution will have at least one (and probablyseveral) bunches, that is, segments Œai; bi� on which x(�) is fixed on some

8.6 The Hamiltonian Approach to the Unidimensional Complete… 99

constant level, x. They also derived the conditions that should hold on thebunch. Here, we will show that the Hamiltonian approach can be usedto arrive at the solution of the complete problem in a regular way. Thisapproach was first taken by Fudenberg and Tirole (1992).

Let us consider the optimal control problem:

max

1Z

0

(u(�; x) � s(� ) � c(x))f (� )d� (8.45)

s:t: s0(� ) D u1(�; x); (8.46)

x0(� ) D �; (8.47)

� � 0; (8.48)

s(0) D 0: (8.49)

Here conditions (8.47) and (8.48) incorporate the monotonicity con-straint explicitly in the optimal control problem. The state variables forthis problem are s and x and the control is � . The constraint (8.48)is known as a phase constraint. (For a more thorough discussion of theoptimal control problemwith phase constraints, see Tikhomirov and Ioffe1979). Form a Hamiltonian

H(�; � I x; s; �1; �2) D (u(�; x) � s(�) � c(x))f (� ) C �1u1(�; x) C �2�:

Here s and x are state variables, �1; �2 are costate variables, � is the controlvariable. The evolution of the costate variables is governed by

�01(�) D f (�) (8.50)

�02(�) D �Œ(u2(�; x) � c0(x))f (� ) C �1u12(�; x)� (8.51)

�1(1) D 0; �2(1) D 0: (8.52)

Pontryagin’s maximum principle states that

� 2 arg max H(�; � I x; s; �1; �2) (8.53)

s:t:(8.48): (8.54)

100 8 Monopolistic Screening

Let be the Lagrange multiplier for (8.48). Then the Kunh–Tuckernecessary conditions imply:

�2 C D 0 (8.55)

� 0; � D 0: (8.56)

Note that we could have obtained the system ((8.50)–(8.52), (8.55), (8.56)immediately by adding term � term to the Hamiltonian. Equa-tions (8.50) and (8.52) imply that �1(�) D F(�) � 1. If constraint (8.48)does not bind then the complementary slackness condition (8.56) impliesthat D 0. Therefore, by (8.55) �2 D 0 and x is determined from

(u2(�; x) � c0(x))f (� ) C �1u12(�; x) D 0; (8.57)

which coincides with (8.37). Suppose (8.48) binds on some segmentŒa; b�. Then Eq. (8.47) implies that x D x on Œa; b� for some constantx. From the continuity of the optimal allocation at a and b (see Chap. 9for the proof of the continuity of the optimal allocation):

(u2(a; x) � c0(x))f (a) � (1 � F(a))u12(a; x) D 0; (8.58)

(u2(b; x) � c0(x))f (b) � (1 � F(b))u12(b; x) D 0: (8.59)

Moreover, since �1(a) D �1(b) D 0 we have

bZ

a

Œ(u2(�; x) � c0(x))f (� ) � (1 � F(�)u12(�; x)�d� D 0: (8.60)

System (8.58)–(8.60) fully characterizes a bunch. Multiple bunches cor-respond to the multiple solutions of the system.

References

Adams, W.J., and J.L. Yellen. 1976. Commodity bundling and the burden ofmonopoly. Quarterly Journal of Economics 90: 475–498.

References 101

Basov, S. 2004. Three approaches to multi-dimensional screening. In: Progressin economics research, ed. Albert Tavidze, volume 7, 159–178. New York, NY,USA: Nova Publishers.

Basov, S. 2005.Multidimensional screening, Series: Studies in Economic Theory,volume 22. Berlin: Springer-Verlag.

Fudenberg, D., and J. Tirole. 1992. Game theory. Cambridge: MIT Press.Mas-Colell, A., M.D. Whinston, and J.R. Green. 1995. Microeconomic theory.

Oxford: Oxford University Press.Mussa, M., and S. Rosen. 1978. Monopoly and product quality. Journal of

Economic Theory 18: 301–317.Rochet, J.C. 1985. The taxation principle and multitime Hamilton-Jacobi

equations. Journal of Mathematical Economics 14: 113–128.Tikhomirov, V.M., and A.D. Ioffe. 1979. Theory of extremal problems. Amster-

dam: North Holland Publishing Company.

9The Multidimensional Screening Model

In this chapter we will discuss the multidimensional screening problem,that is the problem that occurs when the private information of the con-sumer cannot be captured in one characteristic. The general formulationof this problem is provided by Armstrong (1996) and Wilson (1993), andgoes as follows. Consider a multiproduct monopoly producing n goods(or a good with n quality dimensions) with a convex cost function. Thepreferences of a consumer for these goods can be parameterized by an m-dimensional vector. The types of consumers are distributed according toa density function f (�) defined over a convex open bounded set� � Rm.Assume that f (�) is continuously differentiable on� and can be extendedby continuity on its closure. The monopolist is interested in maximizingprofits by choosing a tariff which is a function from the set of bundles ofgoods to the real line. The tariff determines how much a consumer willpay for a particular bundle of goods.

More formally, assume a monopolist who faces a continuum of con-sumers produces a good with n quality dimensions, which can be capturedby a vector x 2 Rn. For example, if the monopolist produces cars, thenx1 can be the maximal speed, x2� the power of the air conditioning, x3�the engine efficiency, etc. The cost of production is assumed to be given

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_9

103

104 9 The Multidimensional Screening Model

by a strictly increasing, convex, twice differentiable function, c(�). Eachpurchaser is interested in consuming at most one unit of the good andhas a utility

u(�; x) � t; (9.1)

where � 2 Rm is his or her unobservable type distributed on an open,bounded, convex set� � Rm according to a strictly positive, continuousdensity function f (�); t is the amount of money transferred to the monop-olist, and u(�; x) is a continuous function, strictly increasing in botharguments. Consumers have an outside option s0(�). The monopolistis looking for a mechanism that would maximize his or her profits.Reasoning in the same way as in the unidimensional case, one can withoutloss of generality assume that the monopolist simply announces a non-linear tariff t(x).The above considerations can be summarized by the following model.

The monopolist selects a continuous t W RnC ! R to solve

maxt(�)

Z

�

(t(x(� )) � c(x(� )))f (�)d�; (9.2)

where c(x) is the cost of producing a good with quality x and x(�) satisfies

x(� ) 2 arg maxx2Rn

C

(u(�; x) � t(x)); (9.3)

max(u(�; x) � t(x)) � s0(�): (9.4)

In this chapter we are going to explore some properties of this model.Our first step will be to reformulate the problem as a multidimensionaloptimal control problem and obtain the first-order characterization of asolution.

Our understanding of multidimensional screening models hasadvanced greatly over the last two decades. For a book level treatment,see (Basov 2005).

9.1 The Hamiltonian Approach and the First-Order Conditions 105

9.1 The Hamiltonian Approachand the First-Order Conditions

The use of partial differential equations in screening theory was pioneeredby Chone and Rochet (1998). They considered a rather simple utilityfunction, which is bilinear in types and goods. Their approach wasextended to a much broader class of utilities in (Basov 2001, 2005). Themain step in deriving the system of partial differential equations thatdescribe the optimal allocation is to convert the problem (9.2)–(9.4) intoan optimal control problem.

Let us start with defining a consumer’s surplus function

s(� ) D maxx2Rn

C

(u(�; x) � t(x)): (9.5)

The envelope theorem then implies

rs(�) D r�u(�; x). (9.6)

It is natural to interpret s as a state variable, and x as a vector of controls.The problem is that for m > n the number of controls is smaller than thenumber of equations in the system (9.6). Therefore, these equations can-not be independent and their dependency should be taken into accountexplicitly. The formal trick is to introduce new variables z by formulae

zi D@u

@� i(�; x); i D n C 1;m; (9.7)

zi D xi; i D 1; n (9.8)

(z D x if m � n). Then zi can be interpreted as new Controls, and thenumber of controls is now the same as the number of equations in the sys-tem (9.6). The controls, however, are dependent because of the Eq. (9.7).

One can give the following economic interpretation of this procedure.Interpret z as a vector of artificial goods, utils. If m > n there are mdifferent types of utils; however, the set of combinable feasible utils is an

106 9 The Multidimensional Screening Model

n-dimensional manifold in RmC. Hence, the problem with m > n can

be interpreted as a problem with m D n subject to some productionconstraints. Geometrically it means that the set of combinable feasibleutils is an n-dimensional manifold in Rm.Define the relaxed problem by

maxz�0

Z

�

(u(˛; z) � s(˛) � c(z))f (˛)d˛;

s:t: s 2 H1(�);

rs(˛) D r˛u(˛; z); i D 1;m;

zi D @u=@˛i(˛; z); i D n C 1;m;

s(˛) � s0(˛);

(9.9)

Z

�

((u(�; z) � c(z))f (� ) C �r�u(�; z))d�: (9.10)

The following theorem was proved in Basov (2005):

Theorem 9. Suppose the surplus function s�(�) solves the problem (9.9).Then there exist almost everywhere continuously differentiable vector functions� W � ! Rm, and distributions � W � ! Rm�n, � W � ! RC

(�; � 2 H1(�)) such that and the following first-order conditions hold:8

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

<

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

:

div� D �@H

@sa.e. on �;

h�; ni D 0 a.e. @�,

� � 0; s � s0(˛);

�(s(˛) � s0(˛)) D 0;

z 2 arg max H(s; z; ˛I�;);

(9.11)

9.2 An Example 107

where the Hamiltonian H(s; z; � I�;) is defined by

H D (u � s � c)f C � � r�u C

mX

iDnC1

i

�

zi �@u

@� i

�

C �(s � s0): (9.12)

The above theorem allows us to reduce the analysis of the relaxedproblem to the analysis of the system of partial differential equations. Notethat an appropriate solution concept here is the generalized solution, sincethe solution might be a distribution rather than a function. It is a separatequestion whether the solution to the relaxed problem solves the completeproblem (see, Basov 2005 for the most general answer to this question).It suffices to say that if the consumer’s utility is linear in his or her typethe solution for the relaxed problem also solves the complete problem ifand only if it is convex (Rochet 1987). In the next section I give a concreteexample of the problem that is solved using the above technique.

9.2 An Example

In this section we are going to consider an example of applying theHamiltonian approach. Assume the utility is given by

u(�; x; t) D �1x1 C �2x2 � t (9.13)

and the cost of production is

c(x) D1

2

nX

iD1

x2i : (9.14)

Let the type space be the unit circle

�n D f� 2 RnC W k�k � 1g;

where k�k denotes the Euclidean norm

kˇk D

v

u

u

t

nX

iD1

ˇ2i : (9.15)

108 9 The Multidimensional Screening Model

and let the distribution of types be uniform. The solution to the relaxedproblem is given by

nX

iD1

@2s

@�2i

D 3; (9.16)

nX

iD1

� i@s

@� iD 1 for k�k D 1: (9.17)

The allocation is related to the surplus by the envelope condition:

xi D@s

@� i: (9.18)

Let us look for the solution of (9.16)–(9.17) in the form

s D s(k�k): (9.19)

Then (9.18) implies

xi D s0(k�k)� i

k�k� (k�k)� i (9.20)

and (9.16)–(9.17) reduce to

(k�k2 )0 D 3 k�k ; (9.21)

(1) D 1: (9.22)

Solving the last system one obtains that in the participation region:

xi D

�

3

2�

1

2 k�k2

�

� i: (9.23)

The exclusion region is given by

�0 D

�

� 2 � W k�k �1

p3

D R

�

: (9.24)

References 109

Therefore, finally

xi D

8

<

:

32 (1 � ( R

k�k)2)� i; for k�k � R;

0; for k�k < R.(9.25)

Since matrix A is defined by

aij D@xi

@� jD

@2s

@� i@� j(9.26)

and is symmetric and positively definite in �n�0; the surplus is convexin the participation region. Therefore, allocation (9.25) is implementable.Note that an increase in n has two effects on the allocation.

9.3 Exercises

1. Solve the model of the last section for n D 3. What happens to theradius of the exclusion region? What happens to its measure? Providean intuitive explanation of these changes.

References

Armstrong, M. 1996. Multiproduct nonlinear pricing. Econometrica 64: 51–75.Basov, S. 2001. Hamiltonian approach to multidimensional screening. Journal of

Mathematical Economics 36: 77–94.Basov, S. 2005.Multidimensional screening, Series: Studies in Economic Theory,

vol. 22. Berlin: Springer-Verlag.Rochet, J.C. 1987. A necessary and sufficient condition for rationalizability in a

quasi-linear context. Journal of Mathematical Economics 16: 191–200.Wilson, R. 1993. Non-linear pricing. Oxford: Oxford University Press.

Part IVMechanism Design Applications

to Islamic Finance

Here we apply the results of the previous part to the theory of Islamicfinance. Our objective is to analyze whether Islamic financial institutionsdo indeed achieve the aims they strive for. For example, do they succeed inincreasing the efficiency of the investment sector, which was supposed toresult from the flow of investment towards ventures which provide greaterreturn and chances of success due to the profit–loss sharing principle? InPart II we have already provided a negative answer to this question andprovided some new intuitive proposals, which we will return to here bydeveloping formal models. Though our models do not directly addressquestions of equity of distribution, a decrease in the overall output dueto decreased efficiency of investments will produce adverse effects on anyredistributional or social programme, which will be felt more acutely.

The commitment of Islamic banks not to invest in certain industriesmay also have a positive effect on efficiency in the world of imperfectfinancial markets. However, overall adherence to the principles of Islamiclaw imposes economic costs and Islamic financial institutions shoulddevelop sophisticated strategies to minimize them.

10Business Loans, Trust, and ContractRestriction Faced by Islamic Banks

In this chapter we consider the effect of social norms on economicperformance, using an example of an Islamic bank providing a businessloan to an entrepreneur. We show that the ability to rely on a social normmitigates the moral hazard problem, but introduces rigidities that preventan optimal response to adverse economic consequences, thereby improv-ing performance during booms, but handicapping it during recessions.In the case of an Islamic bank, another consequence of this rigidity isa greater reluctance to invest in daring new ideas, which are profitablein expectation, but may also result in significant losses. Though we useIslamic banks as our main example, the conclusions have broader validityand are not limited to religious social norms.

10.1 Model

Suppose the project requires upfront cost K to finance it. The profits fromthe project are x; and are distributed for a given effort e; according to

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_10

113

114 10 Business Loans, Trust, and Contract Restriction Faced…

distribution function F(x; e). Exerting effort is costly; we assume that thecost is quadratic, that is

c(e) De2

2: (10.1)

The bank cannot observe the effort, but it can still suggest effort level e�.The entrepreneur, who promises to exert effort e� but exerts effort levele, suffers psychological cost

cP(e; e�) D1

2�(e � e�)2: (10.2)

Parameter � is the private information of the agent and can be Thought ofas a degree of religious opportunism. An agent with � D 0 is completelyfaithful and will exert the promised level of effort, while the agent with aninfinite value of � is completely opportunistic. The bank offers a menuof contracts, where each item on the menu is a triple fı;w(�); e�g; whereı is the share of the upfront cost the entrepreneur should bear, w(�) is theentrepreneur’s wage as a function of profit, and e� is the suggested effort.1If the entrepreneur is constrained by liquidity then the contracts on themenu should satisfy

ıK � L; (10.3)

where L is the amount of liquidity the entrepreneur possesses.After observing her value of � the entrepreneur decides whether to

accept any contract and if yes what level of effort to exert. Assume thatthe entrepreneur’s utility is linked to her income, w; and the effort shechooses to exert by:

u(w; eI �; e�) D v(w(x)) � c(e) � cP(e; e�); (10.4)

1Since all profit realizations in our model are non-negative, Islamic law does not impose anyconnection between ˛ and ı.

10.1 Model 115

where v(�) is a concave, twice differentiable, increasing function, satisfying

v(0) D 0; v0(0) > 0: (10.5)

If an entrepreneur accepts contract fı; ˛; e�g and the physical and psy-chological costs of effort are given by (12.13) and (12.14) she will choosean effort to solve:

e 2 arg max

�

U(eI ı;w(�); e�) �

Z

v(w(x))dF(x; e) �e2

2�

1

2�(e � e�)2

�

:

(10.6)Let

s(� I w(�); ı; e�) D maxe

U(eI ı;w(�); e�) � 0; (10.7)

then the entrepreneur of type � will select

(w� (x); ı(� ); e�(� )) 2 arg max s(� I w(�); ı; e�) (10.8)

and will choose to take a loan as long as

max s(� I w(�); ı; e�) � 0 (10.9)

and (10.3) holds.Finally, the wage schedule should satisfy:

w0(x) D ı for x < 0; (10.10)

that is the losses should be shared in proportion to the investment,while there are no constraints on w(�) for the positive values of profits.Therefore, if there is no possibility of losses then the Islamic bank facesthe same constraints as a conventional bank and may even outperform itif more faithful individuals (those with low values of � ) prefer to deal withit. However, if there is a considerable possibility of a loss of performance,an Islamic bank will be hindered by constraint (10.10). The consequencesof this are twofold. First, an Islamic bank is expected to perform relatively

116 10 Business Loans, Trust, and Contract Restriction Faced…

worse during a recession. Second, it may decide not to invest in highlyinnovative projects which have a high expected value but also a highprobability of a loss.

The bank is assumed to be risk neutral and will select menufı;w(x); e�g to maximize

Z Z

Œ(x � w(x) � (1 � ı)K�dF(x; e)dG(� ); (10.11)

subject to (10.3), (10.6), (10.7), (10.10), where G(�) is the distributionfunction of � .

10.1.1 The Optimal Contract for a Linear-ExponentialModel

Let us assume that L D 0; that is the entrepreneur has no funds; but nowwe are going to assume that the profit can take a continuum of values. Weassume that

x D e C "; (10.12)

where " is a normally distributed random variable with zero mean andvariance �2. In this subsection we will assume a particular form for theentrepreneur’s utility function, namely

u(w(�);wI �; e�) D Ew �

2Var(w) � c(e) � cP(e; e�); (10.13)

where functions c(�) and cP(�; �) are given by (10.1) and (10.2) respectively.Assume that the bank offers a piece-wise, linear wage contract, that is

w D ˛max(x; 0) C ˇ: (10.14)

Here ˇ can be interpreted as the fixed wage earned by the entrepreneur,˛ is the share of the enterprise’s profits he or she is entitled to. Note thatin accordance with shariah law, the entrepreneur does not share in the

10.1 Model 117

losses, which is implied by (10.10) with ı D 0. Note that for positiveˇ constraint (10.10) is stronger than the limited liability constraint for aconventional bank, which stipulates that w � 0. It is straight forward toshow that

Ew D ˇ C ˛

2

4e C� exp

�

� e2

2�2

p2�ˆ( e

�)

3

5 ; (10.15)

Var(w) D ˛2�2

2

41 �e

p2��

exp�

� e2

2�2

ˆ( e�

)�

exp�

� e2

�2

2�ˆ2( e�

)

3

5 (10.16)

where ˆ(�) is the standard cumulative normal distribution function. Letus define function H(�I˛) by:

Ew �

2Var(w) D ˛e C ˇ �

˛2�2

2C H(eI˛); (10.17)

where

H(eI˛) D˛� exp

�

� e2

2�2

p2�ˆ( e

�)

C˛2�2

2

2

4

ep

2��

exp�

� e2

2�2

ˆ( e�

)C

exp�

� e2

�2

2�ˆ2( e�

)

3

5 :

(10.18)Given contract (10.14) the entrepreneur of type � selects the effortaccording to:

e De�

1 C �C

�

1 C �(˛ C He); (10.19)

where the subscript denotes the derivative. Assuming the value of theoutside option independent of type and normalizing it to be zero, ˇ mustsatisfy:

ˇ � c(e) C cP(e; e�) C˛2�2

2� H(eI˛) � ˛e (10.20)

118 10 Business Loans, Trust, and Contract Restriction Faced…

for all � . The first term on the right-hand side of Eq. (10.19) is the partof effort, which is not responsive to the incentive pressure. This decreasesin �; the degree of opportunism of the agent and helps to mitigate themoral hazard problem.

Let us first consider the case when � is observable. Then Eq. (10.20)should be satisfied as equality for all � and it is easy to show that the bankwill select e and ˛ to maximize the total certainty equivalent:

TCE D e �˛2�2

2

2

41 �e

p2��

exp�

� e2

2�2

ˆ( e�

)�

exp�

� e2

�2

2�ˆ2( e�

)

3

5

�e2

2�� (e � ˛ � He)2

2: (10.21)

In obtaining Eq. (10.21) we used (10.19) to exclude e� from the psycho-logical cost.

Let us first consider the case when � ! 0; ! 1; but in sucha way that �2 ! 0 > 0; that is we consider infinitely risk averseagents operating in a low risk environment. In that case truncation ofthe distribution of profits at zero becomes irrelevant, and one can setH D 0. The optimal effort can be found bymaximizing the total certaintyequivalent

TCE D e �0˛

2

2�� (e � ˛)2

2�

e2

2: (10.22)

subject to:

e De�

1 C �C

�˛

1 C �; (10.23)

Solving the maximization problem one obtains:

˛ D�

(1 C � )0 C �(10.24)

e D1 C �˛

1 C �D

�2 C (1 C � )0 C �

(1 C � )((1 C � )0 C � ); e� D 1: (10.25)

10.1 Model 119

It is straightforward to establish that

d˛

d�D

0

((1 C � )0 C �)2> 0 (10.26)

de

d�D �

�

0(� C 1)

(1 C � )((1 C � )0 C �)

�2

< 0; (10.27)

that is the more faithful the agent, the lower is the power of incentivesand the higher the actual exerted effort. Note that the promised effort isalways equal to the efficient effort, irrespective of the religious attitude ofthe agent. Also, observe that ˛(0) D 0; that is a fully faithful agent willface flat incentives.

Let us define

˛c D1

1 C 0(10.28)

to be the power of incentives provided by a conventional bank, whichdoes not rely on any social norms, that is operates under assumption� D 1.2 Note that ˛ < ˛c; that is the Islamic bank provides lowerpowered incentives. The reason for this is that it partially relies on thesocial norm to motivate the entrepreneur. Since the possibility of a lossis neglected in this approximation, an Islamic bank, which has an extrainstrument, obtains higher profits than a conventional bank, while anentrepreneur in both cases obtains utility equal to the value of his or heroutside option. Constant term ˇ can be found from the entrepreneur’sparticipation constraint.

Let us consider the opposite case, when � ! 1; ! 0; but in sucha way that �2 ! 0 > 0; that is we consider almost risk neutral agentsoperating in the environment of extreme uncertainty. In that case

TCE D e �0˛

2

2

�

1 �2

�

�

�� (e � ˛)2

2: (10.29)

2One can justify this assumption by assuming that religious borrowers have finite �; when dealingwith an Islamic bank, but that everyone is opportunistic, i.e. has infinite � , when dealing with aconventional bank.

120 10 Business Loans, Trust, and Contract Restriction Faced…

Let us introduce parameter

D 0

�

1 �2

�

�

< 0: (10.30)

Parameter is the effective degree of risk aversion, which is smaller than0 because the entrepreneur is fully protected against the possibility ofloss. So far the model looks isomorphic to the previous case, with 0replaced by . The first difference arises from the fact that since < 0the relation between ˛ and ˛c is ambiguous. On the one hand, sincethe Islamic bank exploits the finite value of �; it tends to provide lowerpowered incentives than the conventional bank (see, formula (10.26)). Onthe other hand, since it insures the entrepreneur from negative payoffsit can provide higher power incentives ( < 0). An Islamic bank willprovide incentives that are weaker than a conventional bank provided

� <�

2� 1 � 0:571: (10.31)

A more important difference is, however, that the constant payment, ˇ;in this case diverges to �1 according to

ˇ D ���

p2�Œ(1 C � ) C ��

C O(1) (10.32)

to compensate for high positive payoffs. This does not formally contradictliquidity constraints, since in the case of low profit realization, it can berecorded as the entrepreneur’s debt to be repaid out of future projects.Such an arrangement has the flavor of a murabaha contract, discussedin Chap. 1, that is the bank sells the entrepreneur a good (in this casethe business loan) for a future repayment. The promise of repayment,however, will only be credible if the general economic environment isfavorable. Otherwise, the bank will be unable to recover its losses.

Now let us allow for � to be the private information of the entrepreneur,which is distributed on Œ0;1) according to a strictly positive densityfunction g(�). Without loss of generality one can assume that the bankoffers a menu of contracts, where each contract consists of a stipulated

10.1 Model 121

fraction of the profits, accruing to the entrepreneur, ˛; recommendedeffort, e�; and fixed payment (bond), ˇ; depending on ˛ and e�. Themodel below can apply to both extreme situations described above,provided the general economic environment is favorable. If we are in anenvironment of extreme uncertainty, that is � ! 1; ! 0; definefunction t(˛; e�) by:

ˇ(˛; e�) D �˛�

p2�

C t(˛; e�); (10.33)

otherwise

ˇ(˛; e�) D t(˛; e�): (10.34)

Then the bank’s profits are given by:

�b D (1 � ˛)e � t(e�; ˛): (10.35)

The entrepreneur solves a two stage problem. At stage one he or she selectsa contract, that is chooses e� and ˛. At the second stage he or she selectseffort, that is solves:

maxe

�

˛e C t(e�; ˛) ��˛2

2�

e2

2�

1

2�(e � e�)2

�

; (10.36)

where � D if we are working in conditions of extreme uncertainty and0 if we are working under conditions of certainty. The solution to thesecond stage is given by:

e De�

1 C �C

�˛

1 C �(10.37)

and therefore the first-stage utility function is given by:

U(e�; ˛I � ) D2˛e� C ˛2� � e�2

2(1 C �)C t(e�; ˛) �

�˛2

2: (10.38)

122 10 Business Loans, Trust, and Contract Restriction Faced…

Let us define the entrepreneur’s surplus by:

s(� ) D maxe�;˛

U(e�; ˛I � ): (10.39)

The envelope theorem implies

s0(� ) D(˛ � e�)2

2(1 C �)2: (10.40)

The relaxed problem for the bank is

max

1Z

0

�

(1 � ˛)(e� C �˛)

1 C �� s(� ) (10.41)

C2˛e� C ˛2� � e�2

2(1 C � )��˛2

2

�

g(� )d�

s:t:s0(� ) D(˛ � e�)2

2(1 C � )2; s(� ) � 0: (10.42)

Standard integration by part technique (Mussa and Rosen 1978) impliess(0) D 0; that is completely faithful agents earn no information rents,and (e�; ˛) solve:

maxe�;˛

�

(1 � ˛)(e� C �˛)

1 C �C

2˛e�C˛2� � e�2

2(1 C � )��˛2

2�

1 � G(� )

2g(� )

(˛ � e�)2

(1 C �)2

�

:

(10.43)Let us assume that types are distributed exponentially, that is

G(� ) D 1 � exp(��): (10.44)

Then

1 � G(� )

g(� )D 1 (10.45)

10.2 Comparing the Performance of a Conventional and an Islamic Bank 123

and the bank solves:

maxe�;˛

�

(1 � ˛)(e� C �˛)

1 C �C

2˛e� C ˛2� � e�2

2(1 C �)��˛2

2�

1

2

(˛ � e�)2

(1 C � )2

�

:

(10.46)

The solution is:

e� D(� C 1)(� C 1)

� C 2� C �� C 1; ˛ D

� C 1

� C 2� C �� C 1: (10.47)

The effort exerted by type � is

e D1 C � C �

� (� C 1) C 2� C 1: (10.48)

The corresponding surplus is:

s(� ) D�2

2(� C 1)

�

1

2� C 1�

1

� (� C 1) C 2� C 1

�

: (10.49)

Note that both e� and ˛ are increasing in �; therefore the solution to therelaxed problem is implementable. On the other hand, e decreases in �;that is more opportunistic agents face stronger incentives, but exert lesseffort.

Our results imply that if possibility of loss is not an issue, Islamic bankscan perform relatively well compared to conventional ones. But if thereis a significant chance of loss, due either to a recession or to the nature ofthe project, Islamic banks will fail to provide profitable business loans.

10.2 Comparing the Performance of aConventional and an Islamic Bank

In comparing the performance of a conventional and an Islamic bank letus start with the case of low uncertainty. Let as also assume that each agentis characterized by a disutility, a; of dealing with a conventional bank. It

124 10 Business Loans, Trust, and Contract Restriction Faced…

is natural to assume that a is negatively correlated with �; that is morereligious people will experience higher psychological costs of lying. Underthose circumstances the Islamic banks will attract individuals with low �;who will work harder for lower compensation, that is they will performbetter than the conventional banks. Their relative performance can bestrengthened if the entrepreneurs have a different value of �; when facingan Islamic and a conventional bank. In an extreme scenario, all agentsare opportunistic toward a conventional bank, that is they have � D 1.This may explain why conventional business loans do not recommendany level of effort. The situation may change if potential entrepreneursdiffer on some other dimension, for example, education. If more educatedentrepreneurs are less religious, but more productive, then conventionalbanks can outperform Islamic banks even in this environment. Fora discussion of the effects of demographics and education on clients’perception of Islamic banks in the UAE, see Al-Tamimi et al. (2009).

In a situation of increased uncertainty, the performance of Islamicbanks will strongly depend on the overall economic performance. If theeconomy is in the boom stage and the entrepreneur is expected to havehigh income from her overall set of undertaken projects, the Islamic bankmay issue debt (10.32) against her future earnings and offer a contract,which is otherwise similar to the one in a low uncertainty case. Such acontract has the flavor of aMurabaha contract, discussed in Chap. 1, sincethe bank sells the entrepreneur a good (contract) for a future repayment.If, however, the economic environment is not favorable, for example theeconomy is in a recession, the total debt the bank can credibly issue againstthe entrepreneur is bounded by some B, which is likely to be less than thevalue of the contract. In that case the bank may choose not to finance theenterprise at all.

10.3 Bibliographic Notes

Most literature concerning the topics developed in this chapter has beenpurely descriptive. For a discussion of the effects of demographics andeducation on clients’ perceptions of Islamic banks in the UAE, see Al-Tamimi et al. (2009). The theoretical model developed in this chaptercan be found in Basov and Bhatti (2011).

References 125

References

Al-Tamimi, H.A.H., A.S Lafi, and M.H. Uddin. 2009. Bank image in the UAE:Comparing Islamic and conventional banks. Journal of Financial ServicesMarketing 14: 232–244.

Basov, S., and M.I. Bhatti. 2011. Social norms and economic performance: Anexample of business loans by Islamic banks. SSRN Electronic Journal, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1968702.

Mussa, M., and S. Rosen. 1978. Monopoly and product quality. Journal ofEconomic Theory 18: 301–317.

11Loans Provision and Adverse SelectionWithin Orthodox Religious Communities

In this chapter we investigate the wisdom of restricting business loans tothe members of a club, which can be interpreted as a community unitedalong social, cultural or religious principles. Members of the club can bemore trustworthy, which will help to mitigate moral hazard problems,but may also possess lower levels of human capital. If human capital isimperfectly observable, this will create an adverse selection problem. Wediscuss this trade-off, developing a multidimensional screening modelof loan provision. As a particular application of the general model weconsider business loans provision by Islamic banks.

11.1 The Model

Suppose an entrepreneur with no funds seeks financing for a projectwith an up-front cost K > 0. The profits from the project are x; andare distributed for a given effort e; according to distribution functionF(xI e; �1); where ��

1 > ���1 implies F(xI e; ��

1 ), which first-orderstochastically dominates F(xI e; ���

1 ). Exerting effort is costly, so weassume that the cost is quadratic, that is

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_11

127

128 11 Loans Provision and Adverse Selection Within Orthodox…

c(e) De2

2: (11.1)

The bank cannot observe the effort, but can still suggest effort level e�.The entrepreneur, who promises to exert effort e� but who exerts effortlevel e, suffers psychological cost

cP(e; e�) D1

2�2(e � e�)2: (11.2)

Vector � D (�1; �2) is the private information of the entrepreneur.Component �1 can be thought of as the agent’s human capital and �2can be thought of as the degree of religious opportunism. We will assumethat random variables �1 and �2 are affiliated. An agent with �2 D 0 iscompletely faithful and will exert the promised level of effort, while theagent with an infinite value of �2 is completely opportunistic. However,due to affiliation assumption, a fully faithful agent is likely to have low �1.The timing is the following. First, the bank offers a contract that

consists of a wage schedule w(x) and the recommended level of effort.After observing her value of vector � the entrepreneur decides whether toaccept any contract and if yes what level of effort to exert.

Assume that the entrepreneur’s utility is linked to her income, w; andthe effort she chooses to exert by:

u(w; eI �; e�) D v(w) � c(e) � cP(e; e�); (11.3)

where v(�) is a concave, twice differentiable, increasing function, satisfying

v(0) D 0; v0(0) > 0: (11.4)

If an entrepreneur accepts contract fw(�); e�g and physical and psycho-logical costs of effort are given by (12.13) and (12.14) she will choose aneffort to solve:

e 2 arg max

�

U(eI ı;w(�); e�) �

Z

v(w(x))dF(x; e) �e2

2�

1

2�(e � e�)2

�

:

(11.5)

11.1 The Model 129

For simplicity we will specialize to the case when

x D �1e C "; (11.6)

where " is a normally distributed random variable with zero mean andvariance �2 and the bank is constrained to offer linear contracts

w D ˛x C ˇ. (11.7)

Shariah law does not impose any constraints on ˛ if the profit realizationis positive, but requires ˛ D 0 if x < 0.1 In this book we will neglectthis constraint2 as well as the limited liability constraint. Both of theseassumptions can be justified if the minimal equilibrium effort is muchbigger than � . We also assume that

v(w) D1 � exp(�R(w � c(e) � cP(e; e�))

R; (11.8)

that is it has a Constant Absolute Risk Aversion (CARA) form. It isstraightforward to show that under these assumptions the entrepreneur’scertainty equivalent is given by:

CE D R

�

˛�1e C ˇ � c(e) �1

2�2(e � e�)2 �

1

2˛2R2�2

�

:3 (11.9)

Omitting positive factor R in (11.9), one can see that the entrepreneurmaximizes her expected utility if and only if she maximizes:

U(˛; e�; eI �1; �2) C ˇ(˛; e�); (11.10)

where

U(˛; e�; eI �1; �2) D ˛�1e �e2

2�

1

2�2(e � e�)2 �

1

2˛2R2�2: (11.11)

1More generally, the requirement is that the losses should be shared proportionally to the investment.Assuming the entrepreneur has no own funds implies ˛ D 0.2For a discussion of how this constraint can be incorporated in the problem, see Basov and Bhatti(2011).3For an arbitrary utility function v(�) the certainty equivalent is defined as a solution to v(CE) DEv(x):

130 11 Loans Provision and Adverse Selection Within Orthodox…

Conditional on participation, the entrepreneur will choose effort tomaximize (11.11), which implies that

e D˛�1�2 C e�

1 C �2: (11.12)

Substituting this expression into (11.11) one obtains

U(˛; e�I �1; �2) D1

2(1 C �2)2(�2

1�2Œ�2 C 3�˛2 C 2�1Œ1 � �2�˛e�

� (1 � �2)e�2) �1

2˛2R2�2: (11.13)

The bank selects power of incentives, ˛; recommended effort, e�; andfixed payment schedule, ˇ(˛; e�) to solve:

maxZ �

(1 � ˛)�1˛�1�2 C e�

1 C �2� ˇ

�

dG(� ) (11.14)

s:t:(˛; e�) 2 arg maxŒU(˛; e�I �1; �2) C ˇ(˛; e�)�

max˛;e�

ŒU(˛; e�I �1; �2) C ˇ(˛; e�)� � 0 ; (11.15)

where G is the joint cumulative distribution function of � .Before discussing the general case, let us note that in the case R D 0

(i.e. the case of a risk-neutral entrepreneur) moral hazard does not leadto any additional welfare losses compared to the pure adverse selectioncase, since the bank has a sufficient number of instruments to screenfor private information of the entrepreneurs. The logic of this result issimilar to the unidimensional case considered in Picard (1987). If this isthe case, the policy of restricting loans to the members of the club willbe unambiguously dominated by making the loans available to everyone.However, if the dimensionality of private information is bigger than thenumber of instruments, then moral hazard is relevant even under riskneutrality (see, Basov and Danilkina 2010). Such a situation may arise if,in addition to productivity and the degree of opportunism, the physicalcost of the effort is the private information of the entrepreneur.

11.1 The Model 131

Let us define the entrepreneur’s surplus by:

s(� ) D max max˛;e�

ŒU(˛; e�I �1; �2) C ˇ(˛; e�)�: (11.16)

The envelope theorem implies that

rs(� ) D r�U(˛; e�I �1; �2): (11.17)

Excluding ˇ from Eq. (11.16) one can write the bank’s relaxed problem as:

maxZ �

(1 � ˛)�1˛�1�2 C e�

1 C �2C U � s

�

dG(� ) (11.18)

s:t:rs(� ) D r�U(˛; e�I �1; �2)

s(� ) � 0: (11.19)

The bank’s complete problem has an additional constraint in that s(�) isGeneralized as U-convex in � (see, Basov 2005).In general we will assume that random variables �1 and �2 are affiliated.

If the joint density function, g(�); exists and is strictly positive, this bydefinition means that ln(g) is supermodular. In particular, it implies that�1 and �2 are positively correlated and

E(h(� j)j� i) (11.20)

is increasing in � i for any increasing function h(�). The last property canbe taken to be the definition of the affiliated random variables in the casewhen joint density does not exist. If the distribution of � is joint normalthen �1 and �2 are affiliated if and only if they are positively correlated,since

@2 ln(g)

@�1@�2D

�

(1 � �2)�1�2; (11.21)

where � is the correlation coefficient of �1 and �2 and �1 and �2 are therespective standard deviations. Therefore, ln(g) is supermodular if andonly if � > 0.

132 11 Loans Provision and Adverse Selection Within Orthodox…

The problem cannot be solved analytically for an arbitrary distributionof Types; however, the nature of the arising trade-offs can be understoodby analyzing formula (11.12). Assume that banks restrict loans only tomembers of a club and to enter the club individuals will be asked toproduce a signal at cost c;where c is affiliated with �2, that is more oppor-tunistic types have a higher cost of signal. Then the club will tend to attractmembers with low �2; who are more trustworthy; however, by affiliationof �1 and �2 the club will also attract members with sufficiently low �1.

Note that this model implies that if an Islamic bank, which attemptsto screen on two dimensions, faces the same pool of entrepreneurs as aconventional bank it will in fact do better than the latter, which screensonly on one dimension: ability. The problem for the Islamic bank is thatopportunistic managers will prefer to take jobs at conventional banks and,if ability is affiliated with the degree of opportunism, will leave the Islamicbanks with a weaker pool of potential clients. This is yet another exampleof the law of unintended consequences: by trying to select trustworthyemployees and using a social hazard to overcome a moral hazard, anIslamic bank restricts the available pool of human capital for its clients.This problem is relevant to a much wider context than Islamic finance.

References

Basov, S. 2005.Multidimensional screening, Series: Studies in Economic Theory,vol. 22. Berlin: Springer-Verlag.

Basov, S., and S. Danilkina. 2010.Multitasking, multidimensional screening, andmoral hazard with risk neutral agents. The Economic Record 86(s1): 80–86.

Basov, S., and M.I. Bhatti. 2011. Social norms and economic performance: Anexample of business loans by Islamic banks. SSRN Electronic Journal, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1968702.

Picard, P. 1987. On the design of incentive contracts under moral hazard andadverse selection. Journal of Public Economics 33: 305–332.

12Shariah Compliance and Risk-Incentive

Trade-Offs

In this chapter we are going to consider the principal–agent relationship.We will start by reminding the reader of the results of the conventionalprincipal–agent problem, then consider it under a mudarabah contract,before finally discussing how social norms can be used to mitigate therisk-incentive trade-offs.

12.1 A Simple Principal–Agent Model

Let us start by recalling a simple conventional principal–agent model. Letthe gross profit of the principal be given by

… D z C "; (12.1)

where z is the effort undertaken by the agent, and " is the normallydistributed random noise with zero mean and variance �2. Only … isobservable by the principal and verifiable by both parties. The utility ofthe agent is given by:

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_12

133

134 12 Shariah Compliance and Risk-Incentive Trade-Offs

U D 1 � exp

�

�(w �z2

2)

�

: (12.2)

where w is the agent’s payment (wage) conditioned on z through …. Ifone restricts attention to affine payment schemes:

w D ˛…C ˇ; (12.3)

then the certainty equivalent for the agent will have the form:

CE D E(w) �

2Var(w) �

z2

2; (12.4)

The principal wants to maximize expected profits net of the wage,subject to the incentive compatibility constraint:

z 2 arg max

�

E(w) �

2Var(w) �

z2

2

�

(12.5)

and the individual rationality (participation) constraint:

E(w) �

2Var(w) �

z2

2� 0: (12.6)

In the absence of any limitations on the set of the allowable contracts, itis straightforward to show that the optimal affine contract has:

˛ D1

1 C �2; ˇ D

�2 � 1

2(1 C �2)2: (12.7)

To see this, note that ˛ is chosen to maximize a total surplus W defined as

W D E(CE C… � w); (12.8)

subject to (12.5), and ˇ is chosen to ensure that (12.6) holds. Since in thiscase the objective function of the agent is strictly concave, the incentive

12.2 The Principal–Agent Model Under a Mudarabah Contract 135

constraint can be replaced by the first-order condition z D ˛. Pluggingthis into (12.8), solving the maximization program, and using (12.6) toobtain ˇ, yields (12.7).

The net profit of the principal and the utility of the agent under theoptimal affine compensation scheme are given by:

E(… � w) D1

2(1 C �2); U D 0: (12.9)

One can see that the slope ˛ of the optimal compensation scheme andthe profit of the principal decrease in � , while the utility of the agentis determined by the reservation utility, which is normalized at zerohere. Hence, noise damps incentives and dissipates social surplus. Note,however, that no matter how noisy the environment is and how risk aversethe agent is, the project will be undertaken and a positive effort will beexerted.

12.2 The Principal–Agent Model Undera Mudarabah Contract

Now let us consider a similar situation, but let us assume that theparticipants are bound by Islamic law. In fact, we will assume that theywrite a mudarabah contract. Recall that a mudarabah contract cannotinvolve lump-sum payments to either party or payments determinedas a proportion of the capital given by the investor (rabb-ul-mal orthe principal). It is agreed upon by all schools of Islamic jurisprudencethat the asset manager (mudarib or the agent) cannot take any periodicsalary, fee or remuneration from the capital he or she is entrusted with,although some Islamic scholars have inferred that there are exceptionalcircumstances. This means that the asset manager can only take from hisor her portion of the profit as negotiated with the investor. The relevancethis has for the model is that it restricts the intercept of the wage schedule,ˇ; to be equal to zero. A further restriction imposed by Islamic law is thatlosses must be shared in proportion to the investment, that is ˛ mustbe zero for negative profit realizations, assuming the agent has no funds.

136 12 Shariah Compliance and Risk-Incentive Trade-Offs

This restriction, however, can be neglected assuming effort is sufficientlyproductive, which in this case translates into condition � << 1.Let us assume that the principal is forced to set ˇ D 0; then the agent’s

incentive constraint becomes

z D ˛ (12.10)

and the principal solves

maxŒ˛(1 � ˛)�s:t:˛2(1 � �2) � 0:

(12.11)

The solution is

z D ˛ D 1=2 (12.12)

as long as �2 < 1 and z D ˛ D 0 for �2 � 1:We will interpret thelatter as non-participation. Note that, conditional on the participation,the optimal contract will have the same slope ˛ D 1=2 irrespective of therisk attitudes of the agent or the riskiness of the environment. Comparingthis with the optimal slope under no restrictions on the intercept, we seethat conditional on participation amudarib faces weaker incentives than aconventional agent. However, if the environment is too risky or the agentis too risk averse then the project will not be undertaken. The reasonfor this is that now the principal has only one degree of freedom, ˛; tosatisfy two constraints: incentive constraint and participation constraint,which in general cannot be done. Therefore, some projects, possibly themost innovative ones, will not be undertaken under the system of Islamicfinancing.

One way out of this situation is to rely on social norms to mitigatethe moral hazard problem. Another possibility is to consider non-linearwage schedules. Such schedules will have additional degrees of freedomand therefore will be able to take into account both participation andincentive constraints. However, such schemes will be more complex.

12.3 Social Norms and Risk-Incentive Trade-Offs 137

12.3 Social Norms and Risk-IncentiveTrade-Offs

The material of this section is based on Basov and Bhatti (2013). Here wepresent the skeleton of the argument, and direct the reader for the detailsto the published paper.

Suppose a principal hires an agent to perform a task. The profitsgenerated by the agent, x; are distributed for a given effort, e; according todistribution function F(x; e). Exerting effort is costly; we assume that thecost is given by a convex function, c(�): For example, it can be quadratic

c(e) De2

2: (12.13)

The principal cannot observe the effort exerted, but she can decidewhether to rely on a conventional financial contract or to invoke a socialnorm. If a social norm is invoked then the principal can make the agentpromise to exert effort level e�. The social norm requires the agent tobe honest and keep his promise, but it also restricts the principal in theamount of risk she cannot provide too powerful incentives. The idea isthat too powerful incentives are seen as a sign of mistrust. We will modelthis by assuming that the social norm imposes a limit on the slope of theoptimal incentive scheme. An agent who promises to exert effort e� butexerts e suffers a psychological cost, given by:

cP(e; e�) D1

2�c1(e � e�); (12.14)

where c1(�) is a differentiable, increasing, convex function and � is thedegree of opportunism of the agent. An agent with � D 0 always keepshis promise, while agent with � D C1 experiences no psychologicalcosts from cheating. The cost is born, however, only if the principal livesup to her part of the norm and does not provide too powerful incentives.The principal offers a differentiable wage schedule, w(�) and assumes thatthe agent’s utility is linked to her realized income, w(x); and the effort shechooses to exert by:

138 12 Shariah Compliance and Risk-Incentive Trade-Offs

u(w; e; e�) D v(w(x) � c(e) � �cP(e; e�)); (12.15)

where v(�) is a concave, twice differentiable, increasing function, satisfying

v(0) D 0; v0(0) > 0 (12.16)

and � D 1; if sup(w0(x)) � ˛c and � D 0 otherwise. Here, ˛c is themaximal power of incentives allowable by the social norm. If the agentaccepts contract fw(�); e�g, she will choose the effort to solve:

e 2 arg maxŒU(eI w(�); e�) �

Z

u(w(x); e; e�)dF(x; e): (12.17)

Let us assume the profits are linked to the agent’s effort by:

x D e C "; (12.18)

where " is a normally distributed random variable with zero mean andvariance �2.

If one assumes that the agent’s utility function is of a CARA form, thatis

v(y) D1 � exp(�y)

(12.19)

then the psychological cost c1(�) is captured by the same function as thephysical cost c(�) and both of them have the form (12.13) and restrict theset of allowable contracts to be affine in income, that is

w(x) D ˛x C ˇ; (12.20)

for some constants ˛ and ˇ. Then, for any effort the wage is distributednormally and the agent’s certainty equivalent is given by:

u(w(�); eI �; e�) D Ew �

2Var(w) � c(e) � �cP(e; e�): (12.21)

12.3 Social Norms and Risk-Incentive Trade-Offs 139

It is straightforward to see that

Ew D ˇ C ˛e; (12.22)

Var(w) D ˛2�2 (12.23)

Given contract (12.20) the agent of type � selects the effort according to:

e De�

1 C �C

�˛

1 C �: (12.24)

Let us introduce a notation

�2 D 0 > 0: (12.25)

In (12.25) above, parameter 0 measures the importance of the risk-sharing motive and captures both the degree of the agent’s risk aversionand the noisiness of the environment. Under these assumptions theproblem can be solved to obtain:

˛ D�

(1 C � )0 C �(12.26)

e D1 C �˛

1 C �D

�2 C (1 C � )0 C �

(1 C � )((1 C �)0 C � ); e� D 1: (12.27)

A participation constraint can be used to solve for ˇ. The result is:

ˇ D(1 C � )0 C �20 � �2

2Œ(1 C � )0 C ��2: (12.28)

Equations (12.26), (12.27) provide us with a solution as long as the risk-sharing motive is strong enough:

0 >(1 � ˛c)�

1 C �: (12.29)

140 12 Shariah Compliance and Risk-Incentive Trade-Offs

Note that if this condition holds the social norm mitigates the moralhazard problem, that is the effort is higher than it would have been inthe absence of the social norm. In particular, effort remains positive inthe limit where the risk-sharing motive becomes infinitely important andthe power of optimal incentives converges to zero. Note also that the socialnorm is always invoked if ˛c > 1 or � D 0.If condition (12.29) does not hold, the principal has two choices. She

can either not invoke the social norm at all and offer the optimal financialcontract, which will have ˛ > ˛c; or she can invoke the social norm andoffer a contract with ˛ D ˛c: If she chooses not to invoke the social normthen the optimal solution will be:

˛ D e D1

1 C 0; ˇ D

0 � 1

2(1 C 0)2; (12.30)

resulting in the profits

� D1

2(1 C 0): (12.31)

If, on the other hand, the principal decides to rely on a social norm, shewill set ˛ D ac; e� D 1 and obtain profits1

� D1 C 2˛c � (1 C 0(1 C �)˛c)2

2(1 C � ): (12.32)

A routine calculation establishes that at the neighborhood of c0 deter-

mined by

c0 D

(1 � ˛c)�

1 C �(12.33)

the principal is still better off relying on the social norm, that is there exists" > 0 such that for 0 2 Œc

0 � "; c0� the optimal contract will provide

1These results require some simple calculations that are standard and so are omitted.

12.3 Social Norms and Risk-Incentive Trade-Offs 141

incentives ˛c and invoke the social norm. The intuition for this resultis quite simple. Assume that 0 is only slightly smaller than c

0. If theagent continued to feel disutility from breaking his promise, irrespectiveof ˛, the optimal contract would have specified ˛ only slightly below˛c. Therefore, specifying ˛ D ˛c and still relying on the social normresults in a loss in profits of the order O(c

0 �0). On the other hand, notinvoking the social norm and not denying oneself the use of instrumente�; will result in the loss of profit of O(1). Therefore, for 0 sufficientlyclose to c

0 it is optimal to rely still on the social norm. On the otherhand, for 0 D 0 the profits under a contract that relies on the socialnorm are:

� sn D1 C 2˛c � ˛2

c

2(1 C � ); (12.34)

while the profits under the optimal financial contract are

� fc D1

2: (12.35)

Therefore, if

� < 2˛c � ˛2c (12.36)

it is always optimal to invoke the social norm. Otherwise, asrisk sharing becomes less important, the social norm will ceaseto be invoked. In particular, if � > 1, irrespective of ˛c in asufficiently safe environment, the social norm is not invoked. Inthat case the structure of the solution is the following. There exist�

0 such that for 0 2 Œ0; �0 � the social norm is not invoked

and

˛ D e D1

1 C 0; ˇ D

0 � 1

2(1 C 0)2; (12.37)

142 12 Shariah Compliance and Risk-Incentive Trade-Offs

for 0 2 Œ�0 ;

c0� the social norm is invoked and

˛ D ˛c (12.38)

e D1 C �˛c

1 C �; e� D 1: (12.39)

and finally, for 0 > c0 the social norm is invoked and

˛ D�

(1 C � )0 C �(12.40)

e D1 C �˛

1 C �D

�2 C (1 C � )0 C �

(1 C � )((1 C � )0 C � ); e� D 1: (12.41)

Note that one observes either high power incentives with

˛ 2

�

1

1 C �0

; 1

�

(12.42)

or low power incentives with

˛ 2

�

0;�

(1 C � )c0 C �

�

: (12.43)

Medium power incentives are in the range

˛ 2

�

�

(1 C � )c0 C �

;1

1 C �0

�

; (12.44)

that is the model predicts a gap in the power of the incentive schemes.

12.4 Bibliographic Notes

This chapter is based on articles by Arbi et al. (2014) and Basov and Bhatti(2013).

References 143

References

Arbi, L., S. Basov, and M.I. Bhatti. 2014. On Sharia’a-compliance and return toinvestment. Journal of Stock and Forex Trading 3: 116.

Basov, S., and M.I. Bhatti. 2013. Optimal contracting model in a social envi-ronment and trust-related psychological costs. The BE Journal in TheoreticalEconomics (Contributions) 13: 1–14.

13Shariah Compliance, Positive AssortativeMatching and the Performance of IFI’s

Recently, Derigs and Marzban (2009) considered the effects of differentstrategies for constructing a shariah-compatible financial portfolio. Theyargued that shariah-compliant strategies result in a much lower portfolioperformance than conventional strategies, because such compliance limitsthe set of admissible investments. Shariah finance does indeed prohibitinvestment in certain assets and industries, such as conventional bonds,derivatives, armaments, sex, tobacco and the gambling industries. How-ever, the effects of these prohibitions are not exclusively negative. Forexample, a firm that is run in the interest of shareholders, protectedby limited liability, is prone to excessive risk taking. If excessively riskyprojects are more likely to occur in these industries, the commitmentof Islamic banks not to invest, enforced by shariah advisory boards, mayresult in an improvement of financial performance and attract more debtfinancing. Debt financing may also prove to be more beneficial thanequity financing from the point of view of providing better incentives tomanagement. This means that the effects of limiting the set of admissibleinvestments by shariah law is ambiguous and invites us to seek for analternative explanation of the low performance of Islamic banks. Let usbriefly consider the costs and benefits of asset restriction.

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_13

145

146 13 Shariah Compliance, Positive Assortative Matching…

13.1 Costs and Benefits of Asset Restrictions

So far we have analyzed how contractual restrictions of Islamic lawaffect optimal contracts offered to entrepreneurs and restrict the poolof potential clients of such banks. Apart from restrictions on the set ofavailable contracts, Islamic law prohibits investment in particular kinds ofassets, so it is obvious that under the assumption of perfect capital marketsrestricting the set of available investment decreases returns.

However, in the world of imperfect capital markets the commitmentnot to invest in certain projects may enhance efficiency if it prevents banksfrom taking excessive risks. Consider the following example. Let’s assume afirm is interested in undertaking a project that requires initial investment,c;which is collected through debt. Assume that the project is equally likelyto generate profit � or to fail and generate no profit. The expected netpresent value (in millions) is

NPV D�

1 C r� c; (13.1)

where r is the interest rate. Therefore, the project should be undertakenonly if

� > (1 C r)c: (13.2)

However, if the firm is run by shareholders, who pay the debt in the caseof success and declare bankruptcy otherwise, then they will undertake theproject as long as

NPVS D1

2(1 C r)(� � c � b) � 0; (13.3)

where b is the cost of bankruptcy, that is, they will undertake the project if

� > b C c: (13.4)

Therefore, as long as the cost of bankruptcy is not too big

b C c < � < (1 C r)c; (13.5)

13.2 Positive Assortative Matching as a Magnification Mechanism 147

which implies (b < rc); that the project will be undertaken. In thisexample the value of the firm will depend on the way it is financed, thusviolating Modigliani and Miller (1958) theorem.

13.2 Positive Assortative Matchingas a Magnification Mechanism

Islamic law restricts the set of contracts that can be offered to theemployees of an Islamic bank and imposes certain norms of behavioron both employees and employers. We have seen some examples of thisin previous chapters. As argued by Derigs and Marzban (2009), suchrestrictions can put an Islamic bank at a disadvantage. However, as weargued above, this disadvantage is likely to be small. In this sectionwe review a recent paper by Basov and Bhatti (2014), who argued thateven a slight disadvantage can be magnified by the self-selection ofemployees with different levels of human capital. They assumed thatthere are two types of banks, conventional and Islamic, and two typesof potential employees, a low type and a high type. Producing output(e.g. undertaking an investment project) requires a bank to be matchedwith an employee; the value of the match depends on both the employee’sskill and the bank type. We assume that, controlling for the employee’sskill, the value produced in a match with an Islamic bank is slightlysmaller than the one produced in a match with a conventional bank,for the reasons identified by Derigs and Marzban (2009) and/or Arbiet al. (2014). They further assumed that the output depends on both thebanks inherent productivity parameter and the employee’s human capital.Under reasonable assumptions on the matching process, there exists anequilibrium with positive assortative matching, i.e., with more productivemanagers matched with more productive banks. Therefore, even if assetlimitations convey very small advantage to the conventional bank overthe Islamic one, the matching will result in employees with high humancapital to be matched to the conventional bank, while the employees withthe low human capital matched with the Islamic bank, exacerbating thesmall initial disadvantage on the side of the Islamic banks. The differences

148 13 Shariah Compliance, Positive Assortative Matching…

in performance will persist in the limit of the original asymmetry causedby the asset’s limitations converging to zero. Before arguing the generalpoint, let us start by providing an example.

Example. Let us assume that there are two banks, an Islamic one and aconventional one, and two managers, a more productive type, H, and aless productive type, L. Type H managers produce a revenue of US$1; 000when matched with a conventional bank and US$900, when matchedwith the Islamic bank, while type L managers produce a revenue ofUS$500 when matched with the conventional bank, and US$450 whenmatched with the Islamic bank. Note that, by controlling for the typeof manager, the Islamic bank has an assets productivity of 90 % of theconventional one. We can say that the matching of banks and managersis unstable if a bank can replace its manager with one from the otherbank in such a way that both the bank and the manager are better off.Otherwise, the match is called stable. Let us argue that the match of theH manager to the Islamic bank and of the L manager to the conventionalbank is unstable. Let wH be the wage the Islamic bank pays to the typeH manager and let wL be the wage the conventional bank pays to thetype L manager. In order to attract the H type manager the conventionalbank has to offer him or her at least wH . For the match to be stable, thisshould not be worthwhile for the conventional bank, that is, the followinginequality must hold:

500 � wL � 1000 � wH , wH � wL � 500: (13.6)

Similarly, the condition that the Islamic bank is unwilling to attract the Ltype manager implies

900 � wH � 450 � wL , wH � wL � 450: (13.7)

Clearly, conditions (13.6) and (13.7) are incompatible. Therefore, theonly stable match occurs when the Islamic bank is matched with the Ltype manager and the conventional bank with the H type manager. Theresulting revenues are US$1000 for the conventional bank and US$450for the Islamic bank, that is the Islamic bank receives only 45 % of

13.2 Positive Assortative Matching as a Magnification Mechanism 149

the revenues of the conventional one, despite its assets being 90 % asproductive. The wages that support such a match satisfy

8

ˆ

<

ˆ

:

0 � wL � 4500 � wH � 900

450 � wH � wL � 500

: (13.8)

With a non-negative pair of wages satisfying (13.8), such a match can besupported. The exact wages will depend onmarket conditions. The profitsearned by the Islamic and the conventional bank will depend on wages.At one extreme, wL D 0; wH D US$500; that is the Islamic bank hasall the bargaining power when negotiating with the L type manager, andthe H type manager has all the bargaining power when negotiating withthe conventional bank. In that case the profits of the conventional bankare US$500 and the profits of the Islamic bank are US$450, that is theIslamic bank makes 90 % of the profit of the conventional bank. In theopposite case, wL D US$450; wH D US$900; the conventional bankmakes US$100 in profits, while the Islamic bank makes no profits at all.Therefore, a priori, one may expect that the Islamic bank will make 45 %of the profits of the conventional one.

This example shows how a small inefficiency caused by fundamentalscan be magnified via positive assortative matching. One can generalizethis result beyond the simple numerical example given above. For thispurpose, let us assume the output produced from a match of a bank andan employee depends on both the bank’s type and the employee’s humancapital. The effect on the productivity parameter by the bank’s type, b; isgiven by:

b D ı �(I D 1) C 1 (1 � �(I D 1)); (13.9)

where ı 2 (0; 1) and �(I D 1) is the indicator function, which equalsone if the bank is Islamic and zero if it is conventional. The bank’sproductivity parameter is determined by the investment possibilities opento the bank. Equation (13.9) summarizes Derigs and Marzban’s findingthat the limitation on the set of assets puts Islamic banks at a disadvantage.

150 13 Shariah Compliance, Positive Assortative Matching…

To produce output (e.g. undertake an investment) a bank also needsto hire an employee. Employees differ in their level of human capital, y.If a bank with productivity parameter b hires an employee with humancapital level y; the output will be given by:

x D f (b; y): (13.10)

We will refer to f as the production function associated with the bank’sproductive capability.Our next objective is to demonstrate that if the bank’s productivity

parameter and the skill of the employee are complements in the pro-duction of the output expressed by (13.10), then in any stable matchconventional banks are matched with highly productive employees andIslamic banks are matched with low productive employees.

Definition. Production function f W fyL; yHgfı; 1g ! R is called strictlysupermodular if

f (yH; ı) C f (yL; 1) < f (yH; 1) C f (yL; ı). (13.11)

Supermodularity is the mathematical expression of the idea of comple-mentarity; for a detailed discussion, see Topkis (1998).

The main result established in the assortative matching literature(Becker 1973) is that, assuming f (�) is supermodular, the only matchesthat produce core allocations result from positive assortative matching.In this particular context, this will mean that if one finds a low abilityemployee hired by a conventional bank then all Islamic banks shouldhave low quality employees and all high quality employees must be hired.Alternatively, if a high quality employee is hired by an Islamic bank, itwill mean that all conventional banks have high quality employees. Inother words, any conventional bank will always have at least as many highquality employees as any Islamic bank. For another worked out examplethat assumes a particular functional form of the production function, seeBasov and Bhatti (2014).

References 151

13.3 Bibliographic Notes

The theory of positive assortative matching was first developed by Becker(1973). An application of the theory to Islamic finance is based on Basovand Bhatti (2014).

References

Arbi, L., S. Basov, and M.I. Bhatti. 2014. On Sharia’a-compliance and return toinvestment.Journal of Stock and Forex Trading 3: 116.

Basov, S., and M.I. Bhatti. 2014. On Sharia’a compliance, positive assortativematching, and return to investment banking. Journal of International Finan-cial Markets, Institutions and Money 30: 191–195.

Becker, G.S. 1973. A theory of marriage: Part I. Journal of Political Economy 81:813–846.

Derigs, U., and S. Marzban. 2009. New strategies and a new paradigm forSharia’a-compliant portfolio optimization. Journal of Banking and Finance 33:1166–1176.

Modigliani, F., and Miller, M.H. 1958. The cost of capital, corporation financeand the theory of investment. American Economic Review 48: 261–297.

Topkis, D.M. 1998. Supermodularity and complementarity. Princeton: PrincetonUniversity Press.

14Optimal Incentives for Takaful Operators

In this chapter we are going to discuss the structure of the optimalincentives for takaful (Islamic insurance) operators (TOs). This is basedon a recently published paper by Khan (2015). As emphasized by Khan,the main difference between conventional and Islamic insurance, relevantto the structure of optimal incentives, is that, while the conventionalinsurance contract is a contract of risk transfer, the Islamic insurancecontract is one of risk-sharing.

Khan (2015) argues that to be compliant with Islamic Law, financialincentives offered to TOs must be based on: (i) an agency (wakalah)contract where a TO manages takaful operations against an upfrontagency fee; (ii) a mudarabah (profit-sharing) contract where the TOreceives a share in the investment income from technical reserves; and (iii)a modifiedmudarabah (surplus-sharing) contract where the TO receives ashare in the insurance surplus. A general linear contract along these lineswill have the form

W D ˛P C mIT C s((1 � ˛)P C (1 � m)II � OE); (14.1)

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_14

153

154 14 Optimal Incentives for Takaful Operators

where P is the net earned premium, II is the investment income fromtechnical reserves, OE are the operating expenses, and the constants ˛;m; and s capture the relative power of incentives related to (i)–(iii).Policyholders are assumed to be risk neutral and strive to maximize theexpected value of the insurance surplus, net of compensation of theoperator, that is

E(P C II � OE � W): (14.2)

A TO can exert eu to screen potential customers and invest in a fixedendogenously determined proportion k; of expected technical reserves.Assume further that

8

ˆ

<

ˆ

:

OE D n(c � ueu) C "c

II D rI C "i

I D kn((1 � ˛)p � (c � ueu)

; (14.3)

where n is the total pool of potential customers, c is an average claimthat will arise if eu D 0; that is the operator does not screen customers,p D P=n; and r is the rate of return on the investment. Shocks "c and "r

are assumed to be normally distributed and independent with zero mean.The operator is assumed to be risk-averse, with a CARA utility functionand a quadratic cost of effort

C Dcpn2

2C

(neu)2

2C

I2

2: (14.4)

Therefore, the setting is similar to that described in Basov and Bhatti(2013), which we discussed earlier. Going through the standard calcu-lations, which we will not repeat here,1 Khan concludes that optimalincentives should always include the positive weight on surplus-sharing(s > 0); while wakalah and mudarabah contracts should be offered onlyunder special circumstances.

1The interested reader is referred to Khan (2015) for details.

References 155

This analysis abstracts from any role social norms may play in selectingthe optimal contract. If the willingness of the operator to comply withsocial norms depends on the power of incentives, and in particular on hisbeing exposed to risk via providing strong incentives over dimensions hehas little control of, some of the conclusions may change. The reader iswelcome to undertake research in this direction. A good starting pointwould be to combine the models of Basov and Bhatti (2013) and Khan(2015).

14.1 Exercises

1. Rework Khan’s (2015) model, when the principal, in addition toproviding financial incentives, asks the agent (the TO) to promise toexert effort levels e�

u ; I� and in addition to the physical costs of effortthe agent experiences psychological costs,

cP D�1(eu � e�

u )2

2�1C�2(I � I�)2

2�2; (14.5)

with � i D 1 if the total derivative of the expected wage of the agent withrespect to eu or I respectively exceeds some critical level, and � i D 0otherwise.

14.2 Bibliographic Notes

Khan (2015) is the pioneering work in this area. For an introduction tothe standard theory of insurance, see Mas-Colell et al. (1995).

References

Basov, S., and M.I. Bhatti. 2013. Optimal contracting model in a social envi-ronment and trust-related psychological costs. The BE Journal in TheoreticalEconomics (Contributions) 13: 1–14.

156 14 Optimal Incentives for Takaful Operators

Khan, H. 2015. Optimal incentives for takaful (Islamic insurance) operators.Journal of Economic Behavior and Organization 109: 135–144.

Mas-Colell, A., M.D. Whinston, and J.R. Green. 1995. Microeconomic theory.Oxford: Oxford University Press.

15Can Short-Selling Prohibition Be Optimal?

In the first chapter of this book we listed ten conditions a sale contractshould satisfy to be legitimate under Islamic law. In particular, we arguedthat these conditions prevent short-selling. The reason for this is mainlyhistorical. If legal institutions are not properly developed, short-sellingcan invite cheating by collecting the fee and not delivering the good orthe asset. In modern financial markets the ability to short-sell assets isbelieved to undermine efficient risk-sharing. Most asset pricing models,for example the Fama-Frenchmodel, CAPM (capital asset pricingmodel),APT (arbitrage pricing theory) and their variations, assume that thetraders are able to short sell their assets.

However, the bulk of empirical work, starting with the early papers byFama (1963) and Mandelbrot (1963), points to the existence of fat tails inthe distribution of asset returns. In this chapter we build on this empiricalinsight and assume that asset returns possess a stable maximally skeweddistribution. We argue that under this assumption a rational uniformlyrisk-averse agent will never choose to sell an asset short. In such anenvironment the prohibition of short sales will be harmless, and can evenbe beneficial if some traders are boundedly rational. Note, however, thatthis environment is rather special, and in most environments forbidding

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_15

157

158 15 Can Short-Selling Prohibition Be Optimal?

short sales is costly. Ultimately, which environment is best in describingactual financial markets is an empirical question.

Assume there are N assets, the random return of asset i is denoted by�i and its expectation is assumed to be ri.

Definition. A portfolio of assets is a vector x 2 RN such that

nX

iD1

xi D 1: (15.1)

The expected return of the portfolio is

rP D

nX

iD1

rixi: (15.2)

Assume an individual’s preferences over lotteries are governed by a CARAutility function

u(w) D � exp(�w): (15.3)

To proceed further we will need to introduce the concept of stabledistribution, which we will do briefly in the next section; for details, seeSamorodnitsky and Taqqu (1994).

15.1 Stable Distributions

A random variable is said to be stable (or to have a stable distribution) if ithas the property that a linear combination of two independent copies ofthe variable has the same distribution, up to location and scale parameters.More precisely, let us give the following definition.

Definition. Random variable X is said to have a stable distribution if forany two independent copies of X denoted X1 and X2; and any constantsA and B there exist constants C and D such that

15.1 Stable Distributions 159

AX1 C BX2dD CX C D:1 (15.4)

For example, if X is normal with mean and variance �2 condition (15.4)is satisfied for

C Dp

A2 C B2; D D (A C B �p

A2 C B2): (15.5)

The following characterization of stable distribution holds (see, e.g.,(Samorodnitsky and Taqqu 1994)). Recall that for random variable X itscharacteristic function is defined as:

X(t) D E(exp(itX)); (15.6)

where i Dp

�1: If the random variable possesses density, it can berecovered from its characteristic function as:

f (x) D1

2�

C1Z

�1

X(t) exp(�itx)dt: (15.7)

Lemma 1. A random variable X has a stable distribution if there existparameters ˛ 2 (0; 2�; ˇ 2 Œ�1; 1�; � � 0; and 2 R such that itscharacteristic function is given by:

X(t) D expfit � �˛ jtj˛ (1 � iˇ�(t)W(˛; t))g (15.8)

where

W(˛; t) D

(

tan �˛2 if ˛ ¤ 1

� 2�

ln jtj if ˛ D 1; � (t) D

8

ˆ

<

ˆ

:

1; if t > 00; if t D 0�1 if t < 0

: (15.9)

1SigndD reads “equals in distribution.”

160 15 Can Short-Selling Prohibition Be Optimal?

The characteristic exponent, ˛; describes the degree to which the distri-bution is heavy tailed, index ˇ captures the skewness, while � is the scaleparameter, which determines the spread of distribution. Parameters A; B;and C from definition (15.4) satisfy:

C˛ D A˛ C B˛: (15.10)

If ˛ D 2 then the distribution is normal with mean and standarddeviation � D �: If 1 < ˛ < 2; then the distribution has an infinitevariance, but finite mean : If ˛ < 1 then all the moments are infinite. IfX is stable with parameters ˛; ˇ; �; and;we will writeX � S˛(�; ˇ; ):For example, if X � S1(�; 0; 0) then the distribution is Cauchy, that is ithas density

f (x) D�

�(�2 C x2): (15.11)

Note that for Cauchy distribution � is infinite. However, if one truncatesthe Cauchy distribution from the left, � will be finite while all themoments remain infinite. If ˛ � 1 the distribution has infinite support,while for ˛ < 1 the support is Œ;C1):

One can generalize the concept of a stable distribution for a vector ofrandom variables. If asset returns are distributed according to a multivari-ate stable distribution then a portfolio formed from this asset will follow aunivariate stable law with parameters defined by those of the multivariatestable distribution. In this case the scale and skewness parameters are bothreplaced by finite measure �(ds) defined on the unit sphere. This measureis known as the spectral measure. More precisely, the following theoremholds (for a proof, see Samorodnitsky and Taqqu 1994):

Lemma 2. Let ˛ 2 (0; 2�; then X is an ˛�stable vector in Rd if and only ifthere exists a finite measure � on unit sphere Sd and a vector �0 2 Rd suchthat its characteristic function, X(�); is given by:

X(�) D exp

8

<

:

�

Z

Sd

j�; sj˛ (1 � i� ((�; s))W(˛;�))�(ds)Ci(�;�0)

9

=

;

(15.12)

15.1 Stable Distributions 161

where

W(˛;�) D

(

tan �˛2 if ˛ ¤ 1

� 2�

ln j�; sj if ˛ D 1; � (t) D

8

ˆ

<

ˆ

:

1; if t > 00; if t D 0�1 if t < 0

: (15.13)

Pair (�;�0) is unique.

An attractive property of stable distributions for financial modeling isthat a linear combination of stable random variables with the same stabil-ity parameter ˛ will be a stable random variable with the same stabilityparameter, that is a portfolio of assets will have the same distribution asthe individual assets. More precisely, if X1 and X2 are two independentstable variables distributed according to S˛(� i; ˇi; i) then X D X1 C X2

is distributed according to S˛(�; ˇ; ); where

� D �1 C �2; ˇ Dˇ1�1 C ˇ2�2

�1 C �2; D 1 C 2:

2 (15.14)

Moreover, if X � S˛(�; ˇ; ) and a 2 R then

X C a � S˛(�; ˇ; C a); aX � S˛(jaj˛ �; � (a)ˇ; a) (15.15)

For the derivation, see Samorodnitsky and Taqqu (1994).

Definition. We say that random variable X is stable and maximallyskewed if X � S˛(�; ˇ; ) with ˇ 2 f�1; 1g:

Below we will assume that the asset returns have maximally skeweddistribution with ˇ D 1. This implies that the support of the distributionof returns is bounded from the left. The assumption is in good agreementwith the empirical finding of Constantinides and Savel’ev (2013), who

2Parameter ; being the mean of the distribution for the case ˛ 2 (1; 2�; is additive even if thevariables are not independent.

162 15 Can Short-Selling Prohibition Be Optimal?

report an empirical value of ˇ D 0:9 and sufficiently compact distribu-tion of returns for S&P 500.

Theorem. Let us assume that the returns to individual assets are distributedaccording to S˛(� i; 1; i) with ˛ 2 (1; 2) and the investor’s utility is givenby (15.3). Then the investor will always choose xi � 0; i.e. he or she will neverchoose to sell an asset short.

Proof. According to (15.15) if the investor chooses some weight xi < 0;then the returns on this asset will have a stable distribution with ˇ D �1;and the entire portfolio will have a stable distribution with ˇ 2 (�1; 1).Since we assume ˛ < 2; this means that the expected utility divergesto minus infinity. On the other hand, if all weights are non-negative,then according to (15.15) any portfolio of such assets will be distributedaccording to S˛(�P; 1; P) and

Eu(w) D � exp(�P C�P˛

cos( (2�˛)�2 )

) > �1: (15.16)

Therefore, short sales will never be optimal. �

Though we obtained our result by assuming a particular functionalform for the Bernoulli utility function, one can show that the result stillremains true if the investors are uniformly risk averse, that is if theirArrow–Pratt coefficient of risk aversion is positive and bounded awayfrom zero.3 Note, however, that for an investor to invest in risky assets,but abstain from short sales, one must have ˇ D 1. For any ˇ < 1 auniformly risk averse investor will choose to invest exclusively in the risk-free asset. Therefore, conditions under which short-selling restrictions areoptimal are very special.

3In order words, they are uniformly more risk averse, in the sense of Basov and Danilkina (2010),than risk-neutral agents.

References 163

References

Basov, S., and S.Danilkina. 2010.Multitasking, multidimensional screening, andmoral hazard with risk neutral agents. The Economic Record 86(s1): 80–86.

Constantinides, A., and S.E. Savel’ev. 2013. Modelling price dynamics: A hybridtruncated Lévy Flight–GARCH approach. Physica A 392: 2072–2078.

Fama, E.F. 1963. Mandelbrot and the stable Paretian hypothesis. The Journal ofBusiness 36: 420–429.

Mandelbrot, B. 1963. The variation of certain speculative prices. The Journal ofBusiness 36: 393–413.

Samorodnitsky, G., andM.S. Taqqu. 1994. Stable non-Gaussian random processes.London: Chapman and Hall.

16Conclusions

In this book we have described the historical roots of Islamic financialInstitutions (IFIs), the objectives they try to achieve and the formalframework developed, which allowed us to analyze whether they do infact achieve their stated goals. We found that often the good intentionsof Islamic banks and other institutions are frustrated by the law ofunintended consequences. Usually the law comes into play when bankers,policymakers, religious authorities or other decision-makers fail to takeinto account the fact that economic actors will adjust their behavior inthe light of new policies. In all these examples action of an economicactor goes against the intentinons of the policy maker. The governmentimposed a tax on a firm to get resources to help consumers, but anunintended result that goes against the government’s intention is theraise of the price of the good, produced by the firm. The bank may beprohibited from sharing losses with enterpreneurs in order to attract moreenterpreneurs to business activities, but the banks response, descreaseof the premium for success can have exactly the opposite effect. Sinceinability to share losses is a characteristic feature of Islamic banks, theenterpreneurs who are more likely to succeed may choose not to approachthem at all, and approach conventional banks instead.

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8_16

165

166 16 Conclusions

Many provisions of Islamic law were dictated by historical realitiesunder which this law was formed. Under those circumstances the pro-hibition of interest and short-selling, for example, indeed had the abilityto stimulate risk-taking and the controlling of the concentration of wealthand power, as stated by Siddiqi (1983). In modern times such restrictionsimpose costs on IFIs, which can be exacerbated by different magnificationmechanisms, such as positive assortative matching. Does this mean thatone has to give up Islamic finance and banking? We believe such aconclusion to be wrong. Indeed, as we documented in Chap. 1, there is astrong demand for the services of IFIs from the world’s wealthy Muslims,who otherwise may choose not to invest their funds and keep their savingstucked under the mattresses. In this way, Islamic banking and financefunctions in a way similar to a Keynesian demand stimulus (Keynes1936), bringing into circulation funds which where otherwise sitting inhouseholds’ piggy-banks. Note that both Keynesian demand stimulus andIslamic banking are costly if judged against perfect capital markets, whereall savings are invested; however, they can be crucial in addressing anyunbalance between investments and savings that arise from capital marketimperfections, weaknesses in the legal system, religious beliefs, or othercauses. Therefore, IFIs do serve a useful function in the world of finance,and the material presented in this book will allow practitioners to runthemmore efficiently and to be more aware of the competitive challengerspresented by conventional banks. Moreover, unlike Keynesian demandstimulus, which must be financed via distortionary taxation imposed onall economic agents, IFIs do not create distortions for the agents whochoose not to participate in them.

Though the Islamic financial model mostly imposes costs on its opera-tors, under certain circumstances they can turn out to be beneficial froma purely economic point of view. For example, suppose you would liketo open a financial institution or run a business in an overwhelminglyMuslim country. There is a growing realization among economists thatexploiting local social norms to tap into the well of good will can helpalleviate the moral hazard problem. However, as Basov and Bhatti (2013)

16 Conclusions 167

emphasized,1 to use social norms effectively to elicit cooperation of theagents the principal should live up to his or her part of the bargain. In aMuslim country this may well mean running one’s business in accordancewith Islamic law.

Another claim often made in the literature is that IF can bring morefinancial stability.Wewill briefly discuss this possibility below in the widercontext of limited purpose banking. However, as noted by Belouafi et al.(2015), who provide an extensive review of the theoretical and empiricalliterature, any conclusive evidence about the direct economic advantagesof the IF model is yet to emerge. They also argue that partially this may bedue to an uneven playing filed, which provides tax advantages to debt overequity, and conclude that an enabling environment, as advocated by thetheoretical literature, for financing arrangements based on these principleshas to be seriously taken into consideration.

Both Islamic and conventional banks can benefit from the implemen-tation of limited purpose banking, a new banking paradigm developedby Kotlikoff (2010). This involves an extremely simple set of reforms ofthe US financial, tax, health care and retirement income systems. Bank-ing transforms all financial companies with limited liability, includingincorporated banks, insurance companies, financial exchanges and hedgefunds into pass-through mutual funds, which do not borrow to invest inrisky assets, but, instead, allow the public to choose directly what risks itwishes to bear by purchasingmore or less riskymutual funds. Limited pur-pose banking keeps banks, insurance companies, hedge funds and otherfinancial corporations from borrowing short and lending long and leavingthe public to pick up the pieces when things go south. Instead, it forcesfinancial intermediaries to limit their activities to their sole legitimatepurpose: financial intermediation. Limited purpose banking substitutesthe vast array of extant federal and state financial regulatory bodies witha single financial regulator called the Federal Financial Authority (FFA).The FFA would have a narrow purpose, namely to verify, disclose andoversee the independent rating and custody of all securities purchased andsold by mutual funds.

1See Chap. 12 for a summary of the results of that paper.

168 16 Conclusions

In Kotlikoff ’s scenario, banks would be shorn of their risk-takingfunctions. A deposit would be pooled with other deposits in a new kindof mutual fund, equivalent to a stock mutual fund but with all the moneyheld in plain old cash so there’s no chance of not getting it back (though itcould still lose value to inflation). That eliminates any reason for a panickybank run. Mutual funds would supply loans, too. Already, companiesraise money by issuing bonds, which are bought by fixed-income mutualfunds on behalf of investors. Kotlikoff says loans could work in the sameway: mutual funds would pool investors’ money and use it to make loansto vetted borrowers. That would cut banks out of the picture, exceptas go-betweens. The advantage is that if certain borrowers didn’t repay,there would be no systemic, global-economy-threatening crisis, like theones that can occur when one bank goes down and drags others withit. Instead, the worst that could happen is that investors who funded aparticular loan would lose part or all of their investment. Insurers couldn’tgo bust, either, because they would no longer be on the hook for payingclaims. People who wanted insurance would simply pool their money fora certain period, and those with verified claims would divvy up whateverwas in the pot at the period’s end. Therefore, compliance or otherwisewith shariah law or other ethical principles will be the responsibility ofindividual borrowers and lenders.

References

Basov, S., and M.I. Bhatti. 2013. Optimal contracting model in a social envi-ronment and trust-related psychological costs. The BE Journal in TheoreticalEconomics (Contributions) 13: 1–14.

Belouafi, A., C. Bourakba, and K. Saci. 2015. Islamic finance and financialstability: A review of the literature. JKAU: Islamic Economics 28: 3–44.

Keynes, J.M. 1936. The general theory of employment, interest and money. London:McMillan.

Kotlikoff, L. 2010. Jimmy Stewart is dead: Ending the world’s ongoing financialplague with limited purpose banking. Hobokon: John Wiley & Sons.

Siddiqi, M.N. 1983. Banking without interest. Leicester: The Islamic Foundation.

Bibliography

Constantinides, A., and S.E. Savel’ev. 2013. Modelling price dynamics: A hybridtruncated Lévy Flight–GARCH approach. Physica A 392: 2072–2078.

Kettell, B. 2010. Islamic finance in a nutshell: A guide for non-specialists. Hoboken:Wiley.

Kremer, M. 1993. The O-Ring theory of economic development. QuarterlyJournal of Economics 108: 551–575.

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8

169

Index

AAdverse selection, 127–32Assortative matching

negative, 145positive, 145–50

BBayes-Nash equilibrium, 75, 80, 82,

84

CClub, 12, 70, 127, 130, 132Coefficient of

absolute risk aversion, 162Complete problem, 97, 98–100, 107Cost of effort

physical, 115, 128, 130, 138, 155psychological, 114, 128, 137, 138,

155

DDirect approach, 94–5Distribution

normal, 5, 117stable, 5, 158–62of types, 70, 108

Dual Approach, 95–6

EEffort, 7, 11, 113–15, 117–19, 121, 123,

124, 127–30, 133, 135–40, 154,155

Extensive form game, 77

GGharar, 6, 51

© The Editor(s) (if applicable) and The Author(s) 2016S. Basov, M.I. Bhatti, Islamic Finance in the Light of ModernEconomic Theory, DOI 10.1057/978-1-137-28662-8

171

172 Index

HHamiltonian approach, 96–9, 105–7Harsanyi doctrine, 81–2

IIjarah, 22, 24, 31, 37, 44–6Implentability, 89–93, 98Information rent(s), 88, 93–4, 122Islamic Banking and Finance (IBF),

7–26, 44, 66

LLinear-exponential model, 116–22

MMechanism design, 3, 4, 73, 83, 112Menu of contracts, 120Miller-Modigliani Theorem, 61–71Monopolistic screening models

multidimensional, 85, 86, 93, 94,103–9

with two types, 86–8unidimensional, 85, 88–9, 93,

94–5, 98–100Mudarabah, 35, 36, 135, 136, 153, 154Murabahah, 37, 38, 120, 124Musharakah, 24, 31–7

NNash equilibrium, 75, 80Normal form game, 77

OOrthodox religious communities,

127–32

PPLS. See Profit-loss sharingPresent value, 62, 63, 68, 146Principal-agent model, 133–6Profit-loss sharing (PLS), 7, 19, 69,

71, 112

RRandom variables

affiliated, 128, 131independent, 158, 161

Relaxed problem, 93, 94–8, 106, 107,122, 123, 131

Revelation principle, 83–4, 87, 91Riba, 49, 50, 62, 67, 68Risk-incentive trade-off, 133–42

SSalam, 31, 37, 40–3Short-selling, 5, 157–62, 165Social norms, 113, 119, 133, 136,

137–8, 155, 166Spence-Mirrlees condition, 86, 89–93Strategy

behavioral, 77dominant, 77–9dominated, 77–80mixed, 77, 79

Index 173

TTakaful, 9, 11, 12, 14–17, 21–4, 46,

47, 153–62Taxation principle, 87

UUtility function

Bernoulli, 162CARA, 138, 154, 158

VValue of the firm, 61, 62, 64, 66, 147

WWage schedule, 115, 128, 135–37