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Review of Islamic Economics, Vol. 1, No. 1 (1991),pp . 49-66
RISK AVER SION, MORAL HAZARDAND FINAN CIAL ISLAMIZATION
POLICY
Seif I . TA G EL-DINRiyadh , Saudi Arabia
1. IntroductionAmong the major challenges facing the advocates
of Islamic economicreforms, is the issue of Islamizing the
financial systems of modern Muslimsocieties. The fundamental
Islamic norm that any form of promised returnto financial capital
is usury and hence prohibited, presents the Islamic systemas being
purely equity-based. However, the historical experience and
familiar-ity with state-supported debt instruments, which are
securely embedded inbanking and financial systems, have created
some misgivings in Muslim
societies about the economic feasibility of the recent
Islamization initiatives.Such misgivings lead to the apprehension
that elimination of interest-baseddebt and complete reliance on
risk-bearing equities, could adversely affectthe supply of
investible funds leading to loss of efficiency in the
financialsystem and retardation of economic growth prospects.
Although that is oneof the most popular arguments raised against
the replacement of debt institu-tion by an interest-free system, it
has no firm theoretical basis in the literature.The issue was never
a serious concern to the Western pioneers of economictheory.In the
absence of a standard analytical formulation of such a view, we
shallconsider an indirect implication of the mean variance
portfolio choice theory,which establishes a Pareto optimal status
for the Capital Market Line (CML)through utility analysis of
risk-aversion. The CML stands for the institutionof lending and
borrowing among the risk-averse investors, at an assumedrisk-free
interest rate. It has been shown that the removal of the CML
depre-sses the welfare positions of all participants, who would
move towards lowerequilibria positions with purely risk-bearing
securities. This indirect implica-tion is perhaps the most solid
analytical exposition to be encountered in theliterature, in
support of the view that elimination of debt finance could
bringforth efficiency 1osses.l It is worth mentioning here that the
approach adoptedby Naqvi (1986) in support of the same view relies
on a rather ad-hoc mean-var-iance analysis of risk-aversion, as it
makes no reference to the standard ap-proach. Similarly, Masud
(1989) took no notice of the above-mentionedtheoretical implication
of the mean-variance portfolio choice theory.
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Review of Islamic Economics, Vol. 1, N o. 1He rather, proposed a
counter theorem to demonstrate that risk-aversion onthe supply side
does not matter if there is sufficient scope for
risk-diversifica-tion in the market. Alternatively, he offered a
thesis of 'moral hazards' toexplain the dominance of debt finance
in real life. Despite the interestingchange in emphasis from the
commonly held views about the influence ofrisk-aversion, the moral
hazard thesis indirectly contributes to the belief thatthere are
powerful behavioural norms which lead to the prevalence of
debtinstitution in actual practice. It implies that the policy of
Islamization is 'costly'in the sense that if a society chooses to
Islamize its financial system, it wouldhave to bear a 'deadweight
loss' in terms of necessary information costs toguard against the
'moral hazard' problem.
The main objective of this paper is to critically examine the
analytical basisof the proposition that removal of interest-based
finance is harmful to theprocess of supplying investible funds. The
possible harmful effects are eitherdue to the risk-averse nature of
fund suppliers, as indirectly implied by themean-variance portfolio
choice theory, or due to the 'moral hazard' problemhighlighted by
Masud. We will examine both of these approaches in this paper.
In the next section, we start with a discussion of the Pareto
optimal positionfor the Capital Market Line (CML) as implied by the
mean-variance theoryof portfolio choice. The discussion relates
mainly to the utility analysis ofrisk-aversion with particular
reference to the assumed convex curvature ofthe mean-variance
indifference curves which provides support to the existenceof the
CML in the Pareto optimal position. We question the
theoreticalassertion due to Tobin (1958, 1965, 1974) that these
indifference curves arenecessarily convex when investment returns
are assumed to be normallydistributed. This discussion involves
reference to Feldstein's (1969) criticismof Tobin, to show that he
overlooked a crucial point in Tobin's proof ofconvexity - namely,
the proof implied perfectly correlated investment returns.We
highlight that the assumed convex curvature is only an
analyticalconvenience and not a theoretical necessity. Hence, the
associated indirectnegative implication for the Islamic system
should not be taken too far. Insection three, we discuss the 'moral
hazard thesis' and show its irrelevanceto the modern corporate
sector and the financial choice in securities markets.The
discussion also includes a critical mathematical note about
Masud'sTheorem. The final section contains the summary and
conclusions.
2. The Risk Aversion Thesis2.1 Necessary Background
The underlying theoretical framework of the standard
mean-variance theoryof portfolio choice relates to an
informationally efficient, frictionless financialmarket, with a
community of risk-averse investors who maximize the expectedutility
of their end of period wealth. The marketable securities are
assumedfixed in quantity and perfectly divisible. Investors are
price-takers with
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S.Z. Tag El-Din: Risk Aversion. Moral Hazard and Financial
Islamization Policyhomogeneous expectations, since information is
assumed to be costless andavailable simultaneously to all
investors. Finally, returns on securities havea multivariate normal
distribution, and a risk-free security exists such thatinvestors
may borrow or lend unlimited amounts at the risk-free rate.
Anelaborate exposition of the theory is available in any text book
on portfolioanalysis and is summarized in Figure 1below. Fama and
Miller (1972) providea more formal verification of the equilibrium
position, shown in Figure 1.
Figure (1 )Equilibrium in Financial
Capital Market
The risk-free rate
0 risk (a )
The basic model consists of three main building blocks: (1)An
investmentopportunity set constructed from knowledge of expected
returns, and variance1covariance parameters of the marketable
securities; (2 ) A set of mean-varianceindifference curves, to
characterize the community of risk-averse investors;and (3) A
Capital Market Line (CML), which defines all possible
portfoliosconsisting of the risk-free security and the market
portfolio of risky securities(p). Equilibrium is defined as the
point of tangency between CML and theefficiency frontier (EF) of
the investment opportunity set. As clearly shownin Figure 1, every
investor maximizes expected utility by getting involved inlending
and borrowing at the risk-free rate. Particularly, the portfolio
holdingsof the more risk-averse (i.e. those with relatively steep
indifference curves)are allocated proportionately, between the
risk-free security and the riskyportfolio (p).
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Review of Islamic Economics, Vol. I , No. IConsequently, if the
debt institution is abolished, the welfare positions ofinvestors
worsen. This is shown in Figure 2. Each investor is now
maximizing
expected utility at a lower tangential point with the efficiency
frontier (EF),involving only risky securities.
Figure 12)Welfare losses due to Removall o f CML
return
0 risk o
This brief description reveals how Pareto optimality in the
financial marketis lost by the abolition of debt institution (i.e.
the CML). In the current debateabout the feasibility of the
financial Islamization policy, this theoreticalimplication has led
some people to argue that the abolition of debt institutionbrings
forth efficiency losses in the financial market. As it appears, the
modeldescribes the act of lending and borrowing at interest as a
utility enhancingeconomic activity by exploiting convex
indifference curves. The convexityproperty implies increasing
risk-aversion for all participants in the financialmarket, but this
is a questionable property as we shall shortly explain.2.2 A
Critical Analysis
Despite its broad range of critics in the current literature,
the mean-variancetheory of portfolio choice gained popularity in
the applied field of security
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S.I. Tag El-Din: Risk Aversion, Moral Hazard and Financial
Islamization Policyanalysis, mainly due to the computational
convenience of this model.Faulhaber and Baumol (1988) consider the
portfolio selection model amongthe major innovations in economics.
On the other hand, various critics (e.g.Samuelson (1967); Borch
(1974); Feldstein (1969); Agnew (1971); and Roll(1977)) have
criticized several aspects of the theory. The criticisms of
Feldsteinare particularly relevant for our analysis as they relate
to the curvature ofmean-variance indifference curves. Feldstein
questioned the convex curvespecification utilized by Tobin's theory
of liquidity preference as behaviourtowards uncertainty (Tobin:
1958, 1965). In his critical discussion of Tobin'stheory, Feldstein
attained two significant results:First, it is not true that the
mean variance indifference curves are necessarilyconvex whenever
investment returns are assumed to follow any
two-parameterprobability distribution. Second, the portfolios
formed by combining morethan one security cannot in general be
ranked in terms of mean-varianceindifference curves. In other
words, an analysis through m and a is not strictlypossible 'unless
utility functions are assumed quadratic or probability
distribu-tions are severely restricted' (Feldstein: 1969, p. 11).
The first finding emergedfrom a critical analysis of Tobin's
assertion (Tobin: 1958, 1965) that wheneverinvestment returns
follow a two-parameter probability model, m-a indiffer-ence curves
are always convex from below.While rejecting the convexity
proposition in general, Feldstein acceptedTobin's assertion in case
of normally distributed returns, thus remarking,'Although Tobin's
proof is correct for normal distribution, for a number
ofeconomically interesting distributions the indifference curves
are not convex'(Feldstein: 1969, p.5). Tobin (1974), while
commenting on the criticisms ofFeldstein and Borch, re-asserted the
downward convexity property in case ofnormally distributed returns,
and emphasized the analytical convenience ofthe normal distribution
in the theory of portfolio analysis.
The downward convexity property of the m-a indifference curves
has beenderived by Tobin as a consequence of expected utility
maximization wheninvestment returns are normally distributed. This
theoretical assertion is bynow, often reported as an accepted text
book result.2 In this paper we questionthe validity of this
assertion. The issue seems to have been by-passed due tothe more
recent developments and theoretical refinements of portfolio
theory.Because of many implications of this assertion, the issue
deserves anothercritical review. We will attempt to show that even
when investment returnsare assumed to be normally distributed, the
m-a indifference curves may takea number of possible shapes and not
necessarily the convex one. The convexspecification is commonly
accepted only as an analytical convenience. It isshown that Tobin's
proof of convexity implies pairwise perfectly correlatedinvestment
returns in the mean-variance space. Surprisingly this
obviousmathematical point went unnoticed by earlier critics.
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Review of Islamic Economics, Vol. I , N o. 12.3 Indifference
Curves and Correlated Returns
T he main po int n oted by Feldstein in his critical discussion
of Tobin 's the oryof liquidity preference was that: Not every
two-parameter probability modelcan be cast into the standard normal
form (i.e. z = (x-m)/o), as implied byTobin's proof for the
convexity assertion about m -o indifference curves. T hisclearly
explains Feldstein's acceptance of the proof in case of
normallydistributed investment returns. H owev er, th e crucial
point to no te is that evenin the normal distribution case, the
validity of the proof is restricted to thecase where investment
return s ar e pairwise perfectly correlated. Th is can beseen from
a careful examination of Tobin's proof showing that risk
avertors(i.e. th ose with declining marginal utility of m oney
incom e) have convex m -oindifference curves (T obin : 1958, pp .
75-6 ). T he proof involves the followingsteps, as explained by
Feldstein (1969, p.6).
(i) Expe cted utility is defined in terms of norm al distribu
tion, an d the utilityfunction U(x), asroo
= U ( m + o z) 0 (z) dzS,where 0(z) is the standard normal
density, and the cardinal utility functionfor money income U(x) is
assumed to obey the Nueman-Morgensternconsistency axioms of
rational choice under uncertainty.
(ii) Declining marginal utility (i.e. U,, = < o) implies that
for every 2 .
Th us, representing risk aversion.( ii i) Let the two points (m
,o) an d ( m 1 ,a ' ) ie on th e same indifference curvefor an
investor, i.e.
(iv) T h en , from (i),(ii) and (iii), it follows tha
t:u{(m+-mf) /2, (o + o' ) /2 ) Z ) > u(m , o )= u ( m l , o l
)
which implies that the indifference curve is convex from below
since themidpoint {(m+ m1 )/2, (o + a f )/ 2 ) of th e straight
line connecting the two points{ ( m , ~ ) ,m ',o ) lies above the
indifference curve which connects these th reepoints. See Figure 3
.
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S.Z. Tag El- Di n: Risk Aversion , Moral Hazard and Financial
Islamization P olicy
Figure (3 )olm'.o") > ulm.o) = u(m' ,o ' )
return I
2.3.1 Indeterminacy of the Convexity AssertionIt is immediately
noticeable from step (ii) above that the three points{ ( m , ~ )
;m' + o t ) ; ((m+m1)/2, (o+o1)/2)), correspond to three pair-wise
perfectly correlated return variables, (X,Xr and Xu), defined in
termsof the same standard normal variable Z, as:
That is a(X, X') = o(X, X") = o(X1,X ) = 1 (9)from the
definition of correlation coefficient, e.g.o(Xt, X) = cov (XI, X)
/o to , where cov (X1,X)= o'oOtherwise, if the three points in the
(m,o) space stand for independent ornon-perfectly correlated return
variables, it will not be possible to maintainstep (ii) which is
crucial for the proof. In this case the three return variablesturn
out to be:
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Review of Islamic Economics, Vo l. I , N o. 1Where mu= (m+mf)/2;
orL(o+a')/2; and the standard normal variates Z,Z1,Z" are pairwise
independent or non-perfectly correlated. The determinaterelation of
step (ii), which still holds if Z" = (Z+Z1)/2will now be
replacedwith the indeterminate relation of the form:
>U(mlr, a" Z") -(1/2) U(m +a Z)
