a theoretical analysis of profit and loss sharing …...1 mahmoud sami nabi senior researcher...

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Mahmoud Sami NABI Senior Researcher Economist, IRTI

A Theoretical Analysis of Profit and

Loss Sharing and Debt Contracts in

the Presence of Moral Hazard

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Outline

Motivation

Moral hazard and the optimality of debt Contract

Previous work on profit sharing and moral hazard

Research objective

The model

Principal results

Conclusion

3 Source: IRTI Knowledge Review, Islamic Banking and Finance Information System (IBFIS)

Motivation:

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Deviation of the Islamic Banks (IBs) from their theoretical

business model

o One of the explanations of the low use by Islamic banks of the “Profit and Loss Sharing” modes of finance relatively to “mark-up” modes is the difficulty to deal with the agency problems (moral hazard and adverse selection) (Siddiqui, 2006).

o According to Ul Haque and Mirakhor (1987, p161) “bankers ascribe the problem of moral hazard or asymmetric information to be an important explanation for individual preference for short-term liquidity.”

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Moral Hazard and the optimality of Debt Contract

Arises when the action (effort) that has efficiency consequence is not freely observable and so the agent (entrepreneur) taking it may choose to pursue his private interest at the expense of the principal (bank)’s interest.

Asymmetric information

Moral Hazard Problems Adverse Selection Problems

Pre-contractual Post-contractual

An ex-ante event which occurs when it

is not possible to separate good from

bad risks before the execution of the

contract. Lower risk will be overvalued,

and bad risk will be undervalued, so the

market will attract the bad risk

firms/clients/goods…

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Previous work on Profit Sharing and Moral Hazard

o Under asymmetric information about the level of effort, and in the case of equity contracts, the entrepreneur will provide lower effort relatively to the level that maximizes the project’s payoff since he does not get full benefit of the additional payoffs due to higher effort.

o This is not the case of the debt contract.

o There is a large literature showing that debt dominates profit sharing (equity contracts) in presence of information problems and costly monitoring. For example, in Townsend (1979) and Gale and Hellwig (1985) debt is optimal because it minimizes monitoring costs.

( )e

( )dR e

( )e

( )e

ˆ( )e *( )e

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o Stiglitz (1974), Jensen and Mackling (1976), Grossman and Hart (1982) argued that in presence of moral hazard there is a trade-off between the benefits of risk-smoothing under equity contracts and the incentive effects of debt contracts.

o Khan (1987) considers the two types of contracts in a one-period model and analyzes their Pareto optimality by comparing the expected payoff that they generate for the financier and the entrepreneur.

o Under symmetric information, it is shown that the equity contract dominates the debt contract because it generates smoother income for the entrepreneur while the financier is indifferent between the two types of contract for a given sharing rule.

o In presence of moral hazard the debt contract dominates the equity contract for sufficiently low level of risk aversion from the side of the financier because it minimizes the cost of monitoring.

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o Ul Haque and Mirakhor (1987) consider a two-period model where

the loanable funds correspond to the saving of a representative

consumer facing an a two-periods maximization problem and

trading-off between consumption and saving.

o In the case of symmetric information the level of investment is

higher in case of profit sharing contract and Pareto sub-optimality

does not necessarily occur.

o In presence of moral hazard with unobservable effort the level of

investment increases and the return to capital may be lower under

sharing contacts than in the previous cases.

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o Al-Suwailem (2005) develops a one-period model where the

effort undertaken by the entrepreneur (Mudharib) affects the

return of its project which also depends on a stochastic status of

the demand.

o The asymmetric information regarding the realized output of the

project is revealed by the financier (Rab-ul-Mal) through a

random auditing strategy which precludes the optimality of debt

over equity contracts from one of its essential ingredient which is

the deterministic auditing.

o The Mudharabah contract Pareto-dominates debt contract for a

determined range of the lender’s opportunity cost. The range of

the latter increases with the project’s probability of success and

bankruptcy cost.

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Research objective

o Explore the optimality of the Profit and Loss Sharing contract over the debt contract in the context of a two-period relationship between a risk-neutral financier and a risk-neutral entrepreneur in the presence of moral hazard which manifests as the hidden effort undertaken by the entrepreneur.

o We assume that the output is observable by the principal (financier) (Innes,1990)

o The optimality of profit sharing contract in our model will not rest on the existence of random auditing strategy and bankruptcy costs.

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The Model

o A two-date model. A risk-neutral entrepreneur operates a firm

which generates a stochastic payoff:

o The probability of realization of the high payoff at the end of the

production cycle depends on the effort level chosen by the

entrepreneur with

o The effort is private information of the entrepreneur and cannot be

observed by the financier who provides the external funds.

However, the latter can observe perfectly the payoff of the firm.

,e h l

1 0h l

with a probability of

with a probability of 1-

e

e

12

o The disutility of the effort is captured through the costs et and

verifying which means that the higher the effort the higher is its

cost.

o The investment funds needed to operate the firm are represented by .

The entrepreneur is initially endowed with an amount . The

complementary external funds equals with

o A risk-neutral financier requires an expected rate of return equal to

which is the available return on risk-free financial operation. Therefore,

the expected payoff of the financier should be equal to

hclc

h lc c

F

0(1 )x F

0x F 0 0.1%,100%x

0 1

0(1 )x F

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o Assumptions:

1. The expected payoff of the firm is superior to the investment F only in

the case of higher effort:

2. If the entrepreneur could self-finance the firm then he would chose the

higher level of effort:

3. The expected return from the investment in the firm is higher than the

risk-free return if and only if the higher level of effort is undertaken, i.e.:

h l

h lE E c c

1l hE F E

+(1 ) +(1 )h l

h h l lE F E

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o The PLS contract in a one-period relationship

At the beginning of the first period the entrepreneur and the financier

agree on a partnership contract whereby the entrepreneur

commits to undertake the high level of effort and participates with an amount

of capital of whereas the financier finances the firm by providing

an amount .

Mudharabah

Musharakah

The contract stipulates also that the financier receives a share of the

payoff in case of success (failure) whereas the share of the entrepreneur is

if the high level (low level) of the payoff is realized with

From the Shari’ah perspective: for Musharakah contract the sharing of the

losses should be proportional to the capital participation of each party but the

sharing of profits could be different according to an initial agreement.

0( , , , )e h x F

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In case of success the financier and the entrepreneur share the profit

according to the contract agreement

In case of failure the two contracting parties receive a share equal to their

initial participation to the capital, i.e. the financier and the

entrepreneur share the loss in case of bad performance of the firm

proportionally to their contribution

*

0x

Loss

F

*

0x F

*

0(1 ) (1 )x F

Profit

F

*

0x F

*

0(1 ) (1 )x F

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Symmetric information

* *

0E(W *) +(1- ) (1 )inv

h h x F

* *E(W *) 1 +(1- ) 1ent

h h hc

Asymmetric information

The entrepreneur deviates from its commitment and perform the low

level of effort . This deviation is not observable by the financier and

could not be inferred from the observation of the end of periods’

payoffs. Indeed, the low payoff could occur even in the case of high

level of effort. Undertaking the lower effort just increases the

probability of its realization.

* *

0 0 0

1( ) [1 ]

h

h

E Fx x x

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Illustration of result 1

* *ˆ

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The PLS contract in a two-period relationship

The partnership between the financier and the entrepreneur covers now

two periods.

At the initial date the two parties agree on two separate partnership

contracts. At the beginning of the first period the entrepreneur

and the financier agree on a partnership contract

The entrepreneur commits to reinvest his share of the payoff during the

second period so that the new contract becomes

where

1 2 2 1( , , , )e h x F x

0 1 1 0( , , , )e h x F x

1

1

1

1 with prob 1

1 with prob 1-

e

e

x F

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The expected wealth of the financier in each period is equal to wealth he

would obtain if he invests his money in a risk-free financing which

requires the following conditions:

The share is decreasing with the payoff that takes place during

the first period Possible incentive to the entrepreneur to undertake

the higher effort during the first period in order to maximize its second

period payoff.

1 1 1 0

2 2 2 1

E(W ) +(1 ) (1 )

E(W ) +(1- ) (1 )

inv

h h

inv

h h

x F

x F

*

1 0

*

2 1

( )

( )

x

x

21


The decision of the entrepreneur is analyzed by considering its

expected inter-temporal discounted wealth :

11 2 2 1 2( , ) ( , )ent ent

eEW e e c EW e e

Result 2

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Illustration of Result 2: PLS contract in a two-period relationship

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o The Debt contract in a one-period relationship

0 0( ,min[ , ])x F x FZ

0(1 )x F

0x F

0x FZ

0x

Debt Contract PLS Contract

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25


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The Debt contract in a two-period relationship

We endow the debt contract with a second incentive mechanism which

has been suggested by Dang, V. A. (2010, “Optimal Financial Contracts

with Hidden Effort, Unobservable Profits and Endogenous Costs of

Effort”. Quarterly Review of Economics and Finance, Vol. 50, pp. 75-89)

in the context of two-period model without any initial endowment of the

entrepreneur and without the possibility to reinvest his first-period

residual cash-flow.

Dang (2010) identifies a threshold for the marginal cost of higher effort

beyond which the optimal contract should terminate at the end of the

first period in case of failure of the project.

Result 4

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Result 5: The economic inefficiency of debt contracts

The debt contract is economically inefficient because even projects with

positive net present value will be liquidated in case of failure at the end

of the first period.

liquidation of projects that failed because of the realization of the bad

state of the nature although the entrepreneur undertook the high

level of effort in the first period and is willing to undertake similarly

the high level of effort in the second period.

Let’s consider that the economy comprises a continuum of identical

entrepreneurs of mass 1 situated uniformly along the interval [0,1]. Each

entrepreneur is initially endowed with an amount of capital

equals to .

Assume that “equals” the index of the entrepreneur which is

equivalent to say that the entrepreneurs are ordered on increasingly with

their needs of external financing.

0,1i

0(1 )ix F

0

ix i

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Result 5: The economic inefficiency of debt contracts

o In order to determine the economic inefficiency of debt relatively to

the sharing contracts we consider the region where the two types of

contracts are feasible:

o We showed that in the context of a two-period relationship the

entrepreneur undertakes the higher effort during the first period to

increase the probability of success of its project which equals .

o Since the risks of the projects are identical and independent,

according to the law of large numbers the proportion of successful

projects is and the failing projects represent a proportion of .

o Since the financier under a debt financial contract wills renewal the

financing of the successful projects exclusively, the total investment

during the second period are:

h

0 min0,ix x

h 1 h

2 min

2 min

d

h

sh

I x F

I x F

2 2

2

100 (1 ) 100d sh

hsh

I I

I

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Conclusion

o In the considered framework the Profit and Loss Sharing contract do not dominate the debt contract in terms of access to finance.

o The PLS contract is economically efficient relatively to the Debt contract since it prevents the liquidation of profitable projects.

o Further analysis: public policy intervention in order to enlarge the region of financial access under PLS financing through taxation.

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Thank you

a theoretical analysis of profit and loss sharing …...1 mahmoud sami nabi senior researcher...

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