Financing Cost and Risk Sharing in Islamic Finance
A New Endogenous Approach1
Fayçal Amrani2
Abstract
This paper suggests a new explanation to the low presence of Profit and Loss Sharing (PLS)
contracts in Islamic banks balance sheets. At the opposite of the mainstream literature that
explains this trend exclusively by supplies factors as moral hazard and adverse selection, we
demonstrate that the banishment of the PLS contracts is due to demands factors, and more
specifically, the way used to price the margin profit of the other main contract category: the
mark-up contracts. The current pricing practices of Islamic finance institutions lead to double
price in the market. We called this situation “artificial adverse selection” and we suggest a
new way of calculation to unify the financing cost of those two main categories of contracts.
This allows us to restore the condition of their coexistence in the market. The endogenous
profit margin we model is a function of the optimal share ratio of the PLS contract and its
default probability but also a function of the risk aversion of the entrepreneur. Furthermore,
our endogenous modeling allows us to distinguish between the Islamic mark-up contracts and
the conventional loans according to criteria as legal structuring and economic factors taking
into account for theirs remunerations.
Keywords: Risk Sharing, Pricing, Artificial Adverse Selection, Mark-up, PLS
1
This paper has already been presented at the 29th International Symposium on Money, Banking and Finance
(June 28-29, 2012 Nantes-France) of the GdRE (European Research Group).
2
PhD Candidate, LEDa- SDFi Department, Paris-Dauphine University.
E-mail: faycal.amrani@dauphine.fr
Telephone number: 00 336 68 70 43 30
1
Introduction
According to Islamic finance literature and industry, the main feature of Islamic Finance
practices is their strong commitment to the Profit and Loss Share (PLS) contracts. Indeed, at
the beginning of the modern Islamic banking industry, mark-up contracts were considered as
an exception since PLS contracts were the rule. For instance, the Murabaha contract, currently
the archetype of the mark-up contract, was designed and launched as a subsidiary contract.
Several authors have supported, for a long time, the superiority of the PLS contracts against
conventional financing, means using interest rate, but also against the other forms of Islamic
contracts. Besides, a large section of the literature is dedicated to prove this supremacy.
For example, Presley and Sessions (1994) demonstrate that sharing contracts, such as the
Mudharaba, under certain conditions, improve the information quality spread by the manager
to the investors.
Nonetheless, Islamic Finance Institutions (IFI) moved away gradually from this original
paradigm: PLS contracts step aside in favor of mark-up contracts. This situation has also been
described by several authors and confirmed by different IFI balance sheets analysis.
Dar and Presley (2001), in a paper entitled "Lack of Profit Lost Sharing in Islamic Banking",
note that the ongoing IFI practices are far from the theoretical model based on Mudharaba or
Musharaka contracts. Almost the entire financing projects of Islamic banks, companies and
funds are structured with commissions, mark-up or leasing contracts.
Aggarwal and Youcef (2000) made a summary of the PLS contracts used by banks since the
emergence of the contemporary Islamic Finance. This study includes countries where Islamic
finance coexists with conventional banking, like Egypt, but also countries where the financial
system as a whole is exclusively regulated by Islamic law, like Iran for example. The main
result of this study is the low proportion of PLS contracts in bank’s balance sheets.
2
Based on the data of the central bank, Yasseri (2002) presents an overview of the Iranian
banking system from 1995 to 1998. In 1995, the Mudharaba and Musharaka represent 26% of
the total financing contracts against 45% of forward sell contracts including Murabaha. This
trend is confirmed in 1998 with only 16% for both Mudharaba and Musharaka of the total
financial contracts, while the proportion of the mark-up rose to 56%.
In Malaysia, the biggest Islamic finance market in the world, PLS contracts are used at a very
low level by the finance industry.
For the current period, on 31st December 2010, the balance sheets of the three biggest IFI
show the following assets breakdown3:
1. Dubai Islamic Bank: PLS (22%), Murabaha (29%), others (none PLS contracts)
(49%).
2. Qatar Islamic Bank: PLS (3.1%), Murabaha + Mussawama (69.75%), others (nonPLS contracts) (27.15%).
3. Emirates Islamic Bank: there is no allusion to any kind of PLS financing, all of them
are none PLS Contracts.
By setting up a theoretical framework compliant with the Islamic law, under which the IFI are
supposed to deal with, this paper suggests a new explanation to the banishment of the PLS
financing from the IFI and we also set the conditions necessary to the coexistence of those
two categories of contracts.
While the mainstream literature explains the failure of PLS contracts in Islamic banks by the
insufficient supply of those contracts in the market, we will in this paper present an opposite
explanation, in which we demonstrate that the main reason of this situation is due to the
demand factors: the current calculating system of PLS contracts margin profit dissuade PLS
contracts demand from the managers. Actually, the current exogenous profit margin of the
3
It should be noted that these proportions are calculated in relation to total assets of investment and financing
(deposits at the central bank are not taken into account).
3
mark-up contracts used by the IFI lead to a dual pricing, generally prejudicial to PLS
contracts that can coexist with mark-up contracts only if their financing costs are equalized.
This result allows us to define the conditions that IFI should take into account to set the
appropriate endogenous mark-up: the new calculated mark-up integrates not only the
structural characteristics of the contracts but also the perception of risks involved by those
contracts from the managers.
The paper is organized as follow: at first, we present and define the two main categories of
Islamic Finance contracts in Section I. Then, in Section II we look over the prevalent
conclusions in the literature concerning the disappearance of PLS contracts in IFI. After that,
we propose in Section III an alternative explanation to this banishment, and then, a margin
profit model is put forward in Section IV. We conclude in Section V.
I- Mudharaba and Murabaha
The PLS category contains a certain number of contracts based either upon profit and lost
sharing as the Musharaka, with its different varieties, or only on the sharing of profit as the
Mudharaba. The only profit sharing profit sub-category, along with the Murabaha, will be
studied in the current paper. The results that came out are not substantially different from the
other PLS contracts.
Firstly, the Mudharaba is a contract that links two parties: the IFI (fund contributors or Rabel-mel) and the entrepreneur/contractor (Mudharib). The aim is to provide the required funds
to a party that has the capacity to achieve such a project. If the entrepreneur makes profit, it
will be shared between the two parties according to a prefixed ratio. However, if there is a
loss the funds provider (the IFI) will absorb it fully. As for the entrepreneur, his efforts would
be his only loss, which represents an “opportunity cost”.
Secondly, the other largest Sharia-compliant funding category is based upon profit margins
(mark-up). The main contract of this category is the Murabaha: it is the combination of three
4
different contracts linking the IFI to his client and his supplier. Firstly, the client submits a
purchase order to the IFI to buy a specific commodity. This purchase order comes with a firm
commitment from the organizer to buy the commodity once the IFI has purchased it. The
second contract binds the IFI as the buyer to the provider of the commodity. Thirdly, the IFI’s
client honors his commitment by purchasing the ordered commodity. Thus, its ownership is
transferred to the client when the purchase/ sale contract is signed. On the other hand, the
organizer owes the IFI a debt: he will pay at a given date or on a number of installments a
fixed amount that includes the price of the commodity and a profit margin set by the IFI, or
the Ribh, this is why it is called Murabaha. The set purchase/sale price of a Murabaha
transaction can never vary, neither due to an economic situation, nor to the non-compliance of
due dates. If the client is in good faith and he is unable to honor his commitments because of
extraordinary events, the IFI cannot impose extra charges and has to bear this kind of risk.
II- PLS Contracts in the Literature: the Reasons of a Banishment
Even if the first generation of Islamic finance literature praised the PLS contracts, the practice
of IFI has led researchers to try to determine the reasons of the banishment of these contracts.
The main argument developed in the second generation of the works focused on identifying
the defects inherent to these contracts. Mark-up dominance is explained almost exclusively by
the IFI’s will to limit the offer of PLS. Moral hazard problem and more generally agency
issues are in the heart of this argumentation.
Khalil, Rickwood and Murinde (2002) distinguish two types of agency problems regarding
the Mudharaba. The first one is the adverse selection problem arising from ex-ante
asymmetric information between the bank and his partner (talents, experience, ingenuity of
the entrepreneur and project viability). The second cover ex post asymmetric information.
Namely, moral hazard problems associated with the non-disclosure of the actual results and
5
the difficulty of observing the actions of the entrepreneur, which limits the control of his
discretionary power regarding decision of production and investment. Their conclusion is
unambiguous: in this type of contract, the problems of adverse selection and moral hazard are
so important that the PLS principles become inapplicable.
Aggarwal and Yousef (2000) defend the same point of view: considering that the IFI limit
their use of PLS because of the high level of moral hazard. The authors think that the Islamic
mark-up contracts, close to conventional debt, are more profitable for banks. The PLS or the
combinations of PLS and mark-up contracts could be optimal only if the level of moral hazard
is sufficiently low.
Jouaber and Mehri (2011) raise also the informational problem: despite their efforts to model
an optimal Mudharaba sharing profits ratio to face the problem of adverse selection, they also
explain the non-use of PLS by serious agency problems such as moral hazard and adverse
selection.
In a study based on a qualitative survey of a sample of Islamic banks managers, Habib and
Khan (2002) consider that the IFIs prefer mark-up models because of the high risky nature of
PLS contracts. The results of this survey highlight the fact that the bank managers have a high
aversion to the risks inherent to this type of contracts. This survey, which covers seventeen
Islamic banks, shows that they give an excessive importance to the risks related to PLS
contracts. According to these results, the Murabaha is the less risky contract from the banks’
point of view and the diminishing Musharaka, which is a PLS contract, the more risky one. In
other words, due to the high level of risks observed by the managers in the PLS contracts, the
IFIs avoid their use, and it would be the case as long as they could find out an alternative way
to finance their clients.
Other factors are sometimes mentioned in the literature to explain the Islamic banks distrust
of PLS contracts. Some authors suggest the weak regulation of property rights; the tax
6
treatment which is biased in favor of the conventional financing…etc. (Dar and Presley
2001). However, these arguments could be easily overcame and depend more on conjectural
factors than inherent characteristics of PLS.
Khan (1995) is one of the few authors who attempted to explain the lack of PLS by demand
factors, that is to say by taking into account the willingness of entrepreneurs to use these
contracts. He rejects the mainstream explanation that Islamic banking is in a position to
impose a particular form of contract to its clients. He suggests, therefore, to analyze
simultaneously the supply factors (sources of IFIs reluctance for PLS contracts) and demand
factors (customer preferences for PLS or mark-up contracts). However, if Khan does not limit
his analysis to supply sides factors, he does not offer a strong explanation based on demand
factors: the main idea of his article is the evolution of the entrepreneurs risk aversion during
the life of the company. Indeed, he considers that entrepreneurs have a high risk aversion
when they create and launch their business and this risk aversion decreases gradually during
the life of the company. Thus, new entrepreneurs are expected to prefer the use of PLS
contracts, while experienced entrepreneurs prefer mark-up contracts. In other words, Khan
encourages the IFIs to provide PLS contracts to the new entrepreneurs that have a high
aversion risk level.
Interested in the liabilities side of the IFIs, Chong and Liu (2009) underline another aspect of
the problem. So far, the issue is only around "PLS contracts vs. mark-up contracts" in the
assets of financial institutions, since the liability of an IFI cannot take, by definition, another
form than PLS. Indeed, the liability of an IFI contains four categories of funds: nonremunerated deposits, investment accounts, savings accounts and equity. Except the nonremunerated deposits of which the face value is guaranteed, the remuneration of the three
other classes of liabilities is based on the sharing of profits and losses.
7
The authors observe that the dominance of the mark-up contracts in the asset side transforms
the nature of liabilities to which the performance is linked. In addition to that, they note that
Islamic banks determine their profit margin for mark-up contracts by referring to interest rates
such as LIBOR. Thus, for the authors, these two facts explain that Islamic finance industry
has lost its original participatory nature. Indeed, being given that the performance of the
liabilities is backed to the performance of the asset class, which is evaluated by the reference
to the interest rate since the mark-ups contract are dominant in this side, the liability class
(legally Mudharaba) have not the characteristics of PLSs anymore. Its performance is
correlated with the rate of interest such as conventional bank.
This situation reveals how the determination of the mark-up, based on interbank interest rates,
disrupts the functioning of Islamic financial industry and underlines the necessity and the
importance of an endogenous profit margin theory for those contracts.
III- An Alternative Explanation: the Significance of the Demand’s Factors.
The proofs put forward by the mainstream literature are not sufficient to explain the current
use of PLS contracts by Islamic banks, because they are essentially based on an asymmetric
information approach.
Khan (1995) is the only author who attempted to take into account demand factors in his
argumentation. Despite the importance of his contribution, through the temporal
differentiation of entrepreneurs risk profiles, his theory is unable to explain the banishment of
the PLS contracts but, it explains well their non-exclusive use in a Sharia-compliant
financing.
In fact, the use of PLS financing methods depends on both the structural calculation of the
mark-up contracts profit margin and the underlying risks for each one of these two contracts.
At this stage of the reasoning, we must postulate that taking into account the risks related to a
contract cannot stop the borrower from holding it. It only depends on the remuneration of the
8
contract, which must include the risks born by the lender. This postulate is inconsistent with
the survey results of Habib and Khan (2002), who found that the risk allocation provided
within the PLS contracts, leads to their marginalization, instead of generating earnings
changes. In other words, the substitution of PLS financing in favor of mark-up contract is,
first and foremost, a question of prices and market adjustment; the current methods used by
the Islamic financial industry to determine the profit margins are detrimental to the PLS
contracts.
According to the previous developments, we can now shape a feature of the Islamic banking
comparatively to the conventional banking system. While the conventional banks provide one
type of contract, with a predetermined and fixed remuneration (interest rate), Islamic banks
are bi-contractual, they offer to their customers the choice between two main categories of
financial contracts: PLS and mark-up. The question of the margin profit determination for the
last type of contracts remains without any theoretical answer in the literature.
This paper aims to find out a theoretical approach to the profit margin calculation method for
the markup category, in order to maintain the two categories of contracts available in the
market. The sine-qua-non condition of this achievement is to equalize the profit of the two
risks adjusted type of contracts.
Obviously, one of the two contracts is doomed to disappear, if one of them is more profitable
than the other. The reasoning of the IFI client is simple: he must choose between the contracts
available on the market, according to his share in the profits once the funds provider is paid.
For a given sharing profit ratio and a certain level of expected profit, PLS contracts become
more attractive for the borrower than the mark-up contracts.
By setting the Murabaha margin without taking into account the project’s expected returns,
the IFI divides its potential customers into two categories: the first category includes
9
entrepreneurs, who expect high returns for their projects and are interested in the mark-up
contracts because they do not want to share the high level of expected profit with the IFI.
The second category includes those expecting relatively low yield for their projects and then
preferring the PLS financing. This being said, when the Islamic banks refuse to provide PLS
contracts for reasons based on adverse selection and/or excessive risks, this affect only the
second category of customers, since the first clients category has been pushed aside by the
current way of calculating the margin profit in the mark-up contracts. Actually, Islamic banks
refuse to provide PLS contracts but only for some of its customers and not all of them. The
ones who want to subscribe to this type of contracts assess themselves as bad quality clients.
This fact explains the results of the survey conducted by Habib and Khan (2002). The IFI
managers perceive a lack of supply of PLS contracts for some of their customers as
concerning all of them. Finally, the predetermination of the mark-up creates what we call
“artificial adverse selection”: in the framework of the exogenous determination of the markup model, the demand of the PLS contract is a signal of poor quality.
Asymmetric information theories put forward by the mainstream literature hide an implicit
assumption about the contractual choice power: considering that the lack of PLS contracts
comes from the supply side in the market, the literature gives this contractual choice
exclusively to the bank. However, nothing can support this position under the assumption of a
reasonable banking competition, which is the case in most countries where Sharia-compliant
finance exists. Indeed, a sufficient number of IFIs, operating in a given economy, gives the
choice to the entrepreneurs to determine the appropriate contractual form to finance their
projects: the IFIs cannot, in principle, refuse any kind of financing contract, while the price
(the profit margin) of this contract takes into account the underlying risks.
However, the structures of the IFIs balance sheets show a mitigated use of PLS contracts.
Assuming that the level of bank competition is sufficient, this situation must have another
10
reason. In order to explain this lack of PLS contracts, a plausible research way is to look at the
demand side and assume that the customers are the ones who refuse the PLS contract, for a
given quality of their projects. The PLS contracts, including Mudharaba, becomes more
profitable to the client if the performance of the project reaches a given excepted profit level.
IV- The Murabaha Profit Margin
A Sharia compliant financial system, as mentioned above, provides to the economic agent the
choice between two categories of contracts: PLS contracts and Mark-up contracts. To
simulate this situation in a model, we must define first, the conditions under which we avoid
artificial adverse selection problems. To do this, we set up the following assumptions:
A1: To finance his project, an entrepreneur has only the choice between two types of
contracts: Murabaha (mark-up) and Mudharaba (PLS);
A2: An entrepreneur will always choose the contract maximizing the utility of his share in the
expected profits of the project;
A3: The repayments of the debt and profits distribution are always done at the end of the first
and unique period. At this date, the value of the financed asset is assumed to be null.
A4: In the financing operations, the stakeholders – entrepreneurs and funds providers - are
risk neutral. This is a temporary assumption that will be changed later on.
A5: The profit sharing ratio is an exogenous variable
A6: The Mudharaba contract is drawn up in such a way that it is more attractive for the
entrepreneur to reveal his real results than hide them.
The Model
According to A2, the entrepreneur chooses between the two contracts supplied by the Islamic
bank. His choice will depend on the expected profit utility for each one of them. Entrepreneur
utility for Mudharaba and Murabaha contracts could be written down as follows:
11
+
π
{
𝑀𝑢𝑑𝑎𝑟𝑎𝑏𝑎 = 𝑈 [(1−∝) ( − 1) ]
𝐼
(1)
𝜋
𝑀𝑢𝑟𝑎𝑏𝑎ℎ𝑎 = 𝑈 [( − 1) − 𝛿]
𝐼
Where: 𝑈(𝑊) Utility of an agent for a random Wealth (𝑊).
is the share of the profit due to the owners of capital in a Mudharaba contract;
∝
I
is the initial investment made (I = 0 at the end of the production cycle)
𝛿
is the Murabaha profit margin for the IFI, and is expressed in relative terms, that are to
say, it represents a share of the initial investment I ;
𝜋
+
𝜋
( − 1) = 𝑚𝑎𝑥 ( − 1, 0)
𝐼
𝐼
;
Furthermore, the assumption of risk neutral agents’ behavior allows us to write down the
following expected value of the profit utility: 𝑈(𝑊) = 𝐸(𝑊). The entrepreneur gains, for the
two contracts, as expressed by relation (1), can be rewritten as follows:
π
{
+
𝑀𝑢𝑑ℎ𝑎𝑟𝑎𝑏𝑎 = 𝐸 [(1−∝) ( − 1) ]
𝐼
𝜋
(2)
𝑀𝑢𝑟𝑎𝑏𝑎ℎ𝑎 = 𝐸 [( − 1) − 𝛿]
𝐼
Where E (π) is the expected value of the raw profit of the project (with E (π) ≥ 0);
In a Mudharaba contract, the entrepreneur shares the gain with the funds provider: (1−∝) is
the net share of the funds provider and (∝) the share of the project manager or entrepreneur. In
case of failure, the fund provider loses the total amount of money brought to the project and
the entrepreneur takes on the time and efforts devoted to the project. Moreover, in a Murabaha
contract, the entrepreneur commits himself to pay to the IFI, in return for the purchasing of
the investment machine, the purchase price of the machine plus a profit margin(𝛿). In the
contract, the profit margin (𝛿) can be worked out independently from E(π) but the choice that
the entrepreneur has to do between the Murabaha and the Mudharaba contracts, requires a
calculation where the two profit margin must be similar. This leads us to say that the
determination of the profit margin impacts significantly the market equilibrium.
12
For illustration purpose, let us assume that the Murabaha profit margin (𝛿) is exogenously
determined, which represents the Islamic finance industry in ongoing practice. Let us also
assume that 𝛿 = 12 and ∝= 0,6. We observe that the results of this simulation are not linked to
the chosen value for ∝ and ; it is shown in Appendix 1 that the value change of the two
parameters impacts the switching equilibrium point between the contracts but not the
fundamental result. The following chart shows the expected value of the entrepreneur profit
for each contract, as expressed in equation (2), in the framework of an exogenous profit
margin determination.
Profil des gains: Moudharaba vs. Mourabaha
3.5
3
2.5
2
Gains
1.5
1
Point Thêta
0.5
0
-0.5
Moudharaba
Mourabaha
-1
-1.5
0
0.5
1
1.5
2
2.5
Profit net
3
3.5
4
4.5
5
This illustration shows that the entrepreneur would have three different areas of gain. The first
area covers the cases where the project does not generate enough cash flow to cover the initial
investment cost I, while the second case corresponds to the case where the net profit of the
project is positive without reaching the level Ө. In these two areas the entrepreneur must use
the Mudharaba contract since it always provides a gain equal or greater than what he would
get by choosing a Murabaha contract. The third area corresponds to scenarios where the net
profit of the project is higher than the point Ө: in this area the choice of Murabaha seems
more profitable for the entrepreneur. This demonstration remains valid with a multitude of
entrepreneurs: the members of the first two areas seek PLS contracts while the best
entrepreneurs, members of the third area, seek mark-up contracts.
13
Proposition 1: There is an Artificial Adverse Selection involved by the exogenous
determination of the Murabaha profit margin. This factor explains, for the most part, the low
level of PLS contracts in Islamic finance industry.
This being given, the only situation where Mudharaba and Murabaha have the same
satisfaction level occurs when the net expected gain for both contracts is the same. This could
be written as follows:
(2)
⇔
𝜋
+
𝜋
(1−∝)𝐸 [( − 1) ] = 𝐸 ( − 1) − 𝛿
𝐼
𝐼
𝜋
𝜋
𝐼
𝐼
+
𝛿 = [𝐸 ( − 1) − (1−∝)𝐸 [( − 1) ]]
(3)
The calculation of δ with these parameters restores the equilibrium in the market, and also
ensures the existence of the two contracts by eradicating the sources of the artificial adverse
selection. Here, the profit margin of the Murabaha is endogenously determined, which is
basically different from the current exogenous pricing way of the Islamic banks. The margin
profit is an increasing function of the expected value of the profit E (π) and of the fund
provider profit share (α). This means that the determination of the Murabaha profit margin is
not a matter of setting a benchmark like the interbank interest rate of the conventional
financial system.
Our calculation method of (δ) shows the way to determine the share due to the fund provider,
in the value added creation process, and at the same time, it underlines the principle of sharing
profits and losses, which is supposed to be a strong feature of the Islamic finance for all types
of Sharia-compliant contracts. By using this calculation method, the IFI determines a specific
profit margin for each project, or at least, for each sector, which is most plausible. Moreover,
the IFI must assess the profit margin until his client derives the same satisfaction from the
Murabaha or Mudharaba contracts; this means that he becomes indifferent with regard to any
of these contracts. Lastly, the IFI must also take into account the specific risk underlying each
contract.
14
Economic Agents Risk Aversion
Previously, we assumed a risk neutral behavior of all stakeholders in order to be compliant
with A4. From now on, we assume that economic agents are risk averse; and we assume that
the entrepreneur choices are expressed with the following entropic utility function:
𝑈𝐸 (𝑊) = − γ𝐸 ln E [𝑒𝑥𝑝 (−
1
γ𝐸
𝑊)]
(4)
where 𝑊 is the random wealth of the entrepreneur.
Relation (1) allows us to express the market equilibrium as follow:
+
π
𝜋
𝑈𝐸 [(1−∝) ( − 1) ] = 𝑈𝐸 [( − 1) − 𝛿]
𝐼
𝐼
The entropic utility function is characterized, amongst others, by its cash-invariance, which
gives us the following formula:
𝜋
𝜋
𝑈𝐸 [( − 1) − 𝛿] = 𝑈𝐸 [( − 1)] − 𝛿
𝐼
𝐼
Then, the equilibrium condition can be rewritten as follows:
𝜋
π
𝐼
𝐼
+
𝛿 = 𝑈𝐸 [ − 1] − 𝑈𝐸 [(1−∝) ( − 1) ]
(5)
What the entrepreneur could pay for a Murabaha contract is equal to his disutility of what he
would pay for a Mudharaba contract, which is[𝛼 (𝜋𝐼 − 1) ⥣{𝜋−1≥0} + (𝜋𝐼 − 1) ⥣{𝜋−1<0}].
𝐼
Where ⥣{𝜋−1≥0} = { 1
𝐼
𝑂
𝑖𝑓
𝜋
𝐼
𝐼
−1≥0
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
It is interesting to highlight the subjective dimension of the profit margin: the entrepreneur
does not compare monetary amounts, but he compares a monetary amount (𝛿) with his own
disutility for the IFI share, in the Mudharaba contract: [𝑈𝐸 [𝜋𝐼 − 1] −
π
+
𝑈 [(1−∝) ( − 1) ]].
𝐼
This subjective dimension (Utility/disutility), expressed through the risk aversion/ appetite,
marks out the difference between the Murabaha profit margin and the interest rate of a
conventional loan: the Murabaha profit margin depends on the risk aversion of the
entrepreneur, beyond the expected profit. Thus, the calculation of the profit margin has a
15
double dimension: the first one is the economic activity sector, because of the expected
profitability depends on the sector growth, for the most part. The second one is personal and
depends on the entrepreneur risk aversion.
Being given that, entrepreneur preferences can be described by an entropic utility function;
the Murabaha profit margin in equation (5) can then be rewritten as follows:
𝛿 = [− γ𝐸 𝑙𝑛 𝐸 [𝑒𝑥𝑝 (−
1
γ𝐸
(𝑍 − 1))] + γ𝐸 𝑙𝑛 𝐸 [ 𝑒𝑥𝑝 (−
1−∝
γ𝐸
(𝑍 − 1)+ )]]
(6)
where: 𝑍 = 𝜋𝐼
𝜋
We also assume that the raw profit of the project 𝑍 = 𝐼 , follows a Gamma distribution with
two parameters 𝜃 and k (where 𝜃 and k are strictly positive real numbers). And we know that
the probability density function of a Gamma distribution is given by:
𝑥
𝑥 𝑘−1 𝑒 𝜃
𝑓𝑍 (𝑥) =
Γ(𝑘 )θ𝑘
Then, we can rewrite the Mudharaba margin profit as follows (see Appendix 2):
𝛿 = [−1 + 𝛾𝐸 𝑘 ln (1 +
θ
𝛾𝐸
) +𝛾𝐸 ln (1 −
1
Γ(𝑘 )
1
1
𝜃
(1−α)θ 𝑘
Γ(𝑘 )(1+
)
𝛾𝐸
Γ( ,𝑘 ) +
1
(1−α)
𝜃
𝛾𝐸
Γ( +
, 𝑘 ))]
(7)
This equation shows that the profit margin depends on:

The appetite/ aversion for the risk,

The Mudharaba profit sharing ratio

The two random variable parameters ( and𝑘), representing the project expected profit.
A profit margin simulation, based on the first two parameters, shows the following curves.
We observe that the profit margin is an increasing function of the appetite for risk of the
entrepreneur γ𝐸 and the Mudharaba profits sharing ratio.
16
The Murabaha Default Risk
A fundamental component of the Murabaha contract has been deliberately omitted: as
mentioned above, the entrepreneur honors to the IFI an amount of (𝐼 + 𝛿) at the end of the
production cycle. Nonetheless, this can be done for sure only in certain framework. In a risky
environment, a default can occur and the provider funds profits must be rewritten as follows:
+
−
𝜋
𝜋
𝑀𝑢𝑑ℎ𝑎𝑟𝑎𝑏𝑎𝐼𝐹𝐼 = 𝑈𝐼𝐹𝐼 [𝛼 ( − 1) − ( − 1) ]
𝐼
𝐼
{
𝛿
𝜋
𝑀𝑢𝑟𝑎𝑏𝑎ℎ𝑎𝐼𝐹𝐼 = 𝑈𝐼𝐹𝐼 [ ⥣{𝜋≥(1+𝛿)𝐼} + ( − 1) ⥣{𝜋<(1+𝛿)𝐼} ]
𝐼
𝐼
𝜋
𝜋
−
Where (𝜋𝐼 − 1) = { 𝐼 − 1 𝑠𝑖 𝐼 − 1 < 0
𝑂
𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Thus, the equalization of the fund provider profits, for the two contracts, gives us the new
formula of IFI profit margin (𝛿). Even if the margin was previously obtained by
entrepreneur’s preferences, the uniqueness of δ can be deduced by equalizing the preference
of the fund providers. We can therefore write:
𝐸 𝑒𝑥𝑝 [−
+
1
𝜋
𝜋
1 𝛿
𝜋
(𝛼 ( − 1) + ( − 1) ⥣{𝜋−1≤0} )] = 𝐸 𝑒𝑥𝑝 [−
( ⥣𝜋
+ ( − 1) ⥣{𝜋−1<𝛿} )]
γ𝐼𝐹𝐼
𝐼
𝐼
γ𝐼𝐹𝐼 𝐼 { 𝐼 −1≥𝛿}
𝐼
𝐼
𝐼
This equation expresses the value of the margin δ that is function of itself. Indeed, the
introduction of the potential default of the borrower requires to take into account, ex-ante, in
the profit margin calculation method that, ex-post, the project could not generate enough cash
17
flow to cover the commitment at the end of the production cycle (I + δ). Mathematically, this
means that there can be no explicit solution for (δ): the margin of the Murabaha contract in
the presence of probability of default has to be done digitally. Nevertheless, we can make
some rearrangements of the above equation which is useful for the interpretation of the
determinants (δ) (see Appendix 3):
+
𝜋
𝜋
𝛿
𝜋
𝑈𝐼𝐹𝐼 (𝛼 ( − 1) + ( − 1) ⥣{𝜋−1≤0} ) ≤ 𝐸 [( ⥣{𝜋−1≥𝛿} + ( − 1) ⥣{𝜋−1<𝛿} )]
𝐼
𝐼
𝐼
𝐼
𝐼
𝐼
𝐼
𝛿
𝐼
≥
1
𝜋
𝐼
𝑃( −1≥𝛿)
𝜋
+
𝜋
𝜋
[𝑈𝐼𝐹𝐼 (𝛼 ( − 1) + ( − 1) ⥣{𝜋−1≤0} ) − 𝐸 (( − 1) ⥣{𝜋−1<𝛿} )]
𝐼
𝐼
𝐼
𝐼
(8)
𝐼
Moreover, the entrepreneur, under Murabaha contract, can provide guarantees to the Islamic
bank in case he could not honor its commitments. These guarantees cannot, in principle, be
used by the bank if the borrower is in good faith and if he did not have misconduct, even in
case of failure. Thus, when collaterals are engaged in the contracts, the risk for the bank
decreases and the Murabaha profit margin also goes down. This is due to the fact that the
calculation of the margin is done with the same method, with or without guarantees. Indeed,
providing a guarantee for the total loan amount is equivalent to consider that the borrower
will never fail. Thus, the profit margin, even with guarantees, is still written as equation (6)
shows:
𝛿 = I −1 + 𝛾𝐸 𝑘 ln (1 +
θ
1
1
) +𝛾𝐸 ln 1 −
Γ( ,𝑘 ) +
𝛾𝐸
Γ(𝑘 ) 𝜃
[
(
1
1 (1 − α)
Γ( +
,𝑘 )
(1 − α)θ
𝜃
𝛾𝐸
Γ(𝑘 ) (1 +
)
𝛾𝐸
)]
Proposition 2 : The coexistence of the two types of contracts in the market can occur only if 𝛿
is a function of the sharing profit ratio, the probability of default of the contract and the risk
aversion of the entrepreneur. These parameters are the determinants of the cost of money in a
Sharia compliant economy.
18
V- Conclusion
This paper suggests a new explanation to the low presence of Profit and loss share (PLS)
contracts in Islamic banks balance Sheets. According to the model we have developed, this
issue is due to the calculation method of the profit margin used by Islamic financial
institutions for mark-up contracts. Then, we propose an alternative method based on the
equalization of the financing cost for the two major categories of contracts in Islamic Finance
Industry. Using this approach, we avoid artificial adverse selection that results from the
exogenous determination of the margin in the mark-up contracts. Indeed, in the case of an
endogenous determination of the Murabaha profit, the function of this margin depends on the
sharing profit ratio, the default probability of the contract and the risk aversion of the
entrepreneur.
Moreover, while the pricing of a conventional loan is based on an only interest rate, common
to the whole economy, the profit margin of a Murabaha contract integrates the specificities of
the economic sector of the project with the entrepreneur risk profile.
19
Bibliography
Abalkhail Mohammad and Presley John : How informal risk capital investors manage
asymmetric information in profit/loss sharing In Islamic Banking and Finance: New
perspectives on profit-sharing and risk (2002).
Aggarwal Rajash and Youcef Tarik : Islamic Banks and Investment Financing. Journal of
Money, Credit and Banking. Vol 32, n 1. (2000).
Ahmed Habib: Incentive compatible profit-sharing contracts : a theoretical treatment. In
Islamic Banking and Finance: New perspectives on profit-sharing and risk (2002).
Al-Suwailem Sami: Optimal Sharing Contracts. Presented at the Fifth International
Conference on Islamic Economics and Finance (2003).
Chong Beng Soon and Liu Ming Hua: Islamic banking: Interest-free or interest-based ?
Pcific-Basin Finance Journal 17 (2009).
Dar Humayon et Presley John : Lack of Profit Loss Sharing in Islamic Banking management
and Control Imbalances. Economic Research Paper No 00/24. Loughborough University
(2001).
Haque Nadeem and Mirakhor Abbas: Optimal Profit-Sharing Contracts and Investment in an
Interest-Free Islamic Economy. International Monetary Fund, Working Paper (1986).
Jouaber Kaouther and Mehri Meryem : A Theory of Sharing Ratio under Adverse Selection:
The Case of Islamic Venture Capital. Presented at the workshop: International Sustainable
Finance Paris-Dauphine University (September 2011).
Khalil Abdel-Fattah, Rickwood Colin and Murinde Victor: Evidence on agency-contractual
problems in mudarabah financing operations by Islamic banks. In Islamic Banking and
Finance New perspectives on profit-sharing and risk (2002).
Khan Tariqullah: Demande for and supply of mark-up and PLS funds in Islamic banking.
Islamic Development Bank: IRTI (1995).
20
Khan Tariqullah et Habib Ahmed: Gestion des risques analyse de certains aspects liés à
l’industrie de la finance islamique. Banque Islamique de Développement : IRTI (2002).
Nienhaus Volker: Prifitability of Islamic PLS Banks Competing with Interest Banks:
Problems and Prospects. Journal of Research in Islamic Economics. Vol 1, (1983).
Presley John and Sessions John: Islamic Economics The Emergence of a New Paradigm. The
Economic Journal, Vol 104, No 424 (1994).
Tag-El-Din Seif: Income Ratio, Risk-Sharing and the Optimality of Mudarabah. Journal of
King Abdulaziz University: Islamic Economics. Vol 21-2 (2008).
Yasseri Ali Islmic banking contracts as enforced in Iran. In Islamic Banking and Finance New
perspectives on profit-sharing and risk (2002).
21