Description
The purpose of this paper is to study whether Islamic investors lose portfolio efficiency
due to a limited asset universe.
Accounting Research Journal
Non-parametric performance measurement of international and Islamic mutual funds
J ose Francisco Rubio M. Kabir Hassan, Hesham J amil Merdad
Article information:
To cite this document:
J ose Francisco Rubio M. Kabir Hassan, Hesham J amil Merdad, (2012),"Non-parametric performance
measurement of international and Islamic mutual funds", Accounting Research J ournal, Vol. 25 Iss 3 pp.
208 - 226
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Ismail Cebeci, (2012),"Integrating the social maslaha into Islamic finance", Accounting Research J ournal,
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Lucia Dalla Pellegrina, (2012),"Does capitalization enhance efficient risk undertaking?: A comparison
between Islamic and conventional banks", Accounting Research J ournal, Vol. 25 Iss 3 pp. 185-207 http://
dx.doi.org/10.1108/10309611211290167
Rihab Grassa, (2012),"Islamic banks' income structure and risk: evidence from GCC countries", Accounting
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Non-parametric performance
measurement of international and
Islamic mutual funds
Jose Francisco Rubio and M. Kabir Hassan
Department of Economics and Finance, University of New Orleans,
New Orleans, Louisiana, USA, and
Hesham Jamil Merdad
Department of Finance & Economics,
King Fahd University of Petroleum and Minerals (KFUPM),
Dhahran, Saudi Arabia
Abstract
Purpose – The purpose of this paper is to study whether Islamic investors lose portfolio ef?ciency
due to a limited asset universe.
Design/methodology/approach – The paper contributes to prior literature by using
non-parametrical measurements of ef?ciency instead of regular (parametrical) methods. Data
envelopment analysis (DEA) was used in order to better characterize the risk and return relationship,
as well as estimating a single performance index to rank different funds and compare them to one
another.
Findings – Overall, the results are congruent with prior ?ndings. That is, there is strong evidence
suggesting that Islamic funds are highly ef?cient and that they outperform their international
counterparts. Also, results are robust to different estimation of DEA, the speci?cation of the asset
universe, and the inclusion of ?nancial crisis period in analysis.
Research limitations/implications – Though the paper’s ?ndings are robust to
different speci?cations of the DEA model and time periods, the authors caution readers due to the
limited sample.
Practical implications – Having de?ned a performance index, one can therefore isolate the funds
which are the most ef?cient and thus drive trading activities towards said funds.
Social implications – Since the paper’s ?ndings suggest that Islamic investors do not lose
ef?ciency, investing into a limited asset universe which follows social and ethical constraints (given by
Shariah law) is recommended.
Originality/value – The paper is able to con?rm prior literature, even by using a non-parametrical
measurement of ef?ciency. In this way, the authors have accounted for an extra penalty on the
risk-return relationship: skewness.
Keywords Islam, Fund management, Unit trusts, Portfolio investment, Islamic mutual funds,
Data envelopment analysis, Investment ef?ciency
Paper type Research paper
1. Introduction
As of April 2010, Muslims represented almost 21 percent of the world’s population with
an estimated of more than USD 800 billion to invest, which is growing at 15 percent
annually (Girard and Hassan, 2008). Because of this, many ?nancial institutions have
expanded their services to accommodate for Muslims’ religious preferences, resulting in
an increasing universe of Shariah compliant assets.
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1030-9616.htm
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Accounting Research Journal
Vol. 25 No. 3, 2012
pp. 208-226
qEmerald Group Publishing Limited
1030-9616
DOI 10.1108/10309611211290176
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Shariah, which is the moral code and religious law of Islam, rules out the
consumption of alcohol and pork and activities related to gambling. As a result, Muslims
should not invest in ?nancial assets that derive their income fromsuch activities[1]. This
results in the omission of stocks from ?rms such as hotels, casinos, clubs, bars,
restaurants, food producers, alcohol producers, etc. Moreover, Shariah compliant assets
are types of ethical investment which drive investors towards ?rms which have a sound
social responsibility. Thus, it can be expected that mutual fund managers who follow
Shariah law, and thus ethical codes, will tend to avoid extreme risk taking behavior.
While one could argue that Islamic funds bear less risk than traditional assets
thereby producing smaller average returns, one could also argue that Islamic funds are
less diversi?ed than traditional investment, making such investment riskier, thus
making investors require higher compensation to hold Islamic funds. In this paper, we
characterize a risk-return relationship for Islamic funds, International funds, and
American funds in order to explain which set of assets has the best performance.
Though the literature has analyzed the performance of Islamic mutual funds, ours,
to our knowledge, is the ?rst study that compares them to traditional unconstraint
investment on the bases of ef?ciency: which types of mutual funds provide the highest
level of outputs (returns) conditional on inputs (risk).
One of the major advantages of using data envelopment analysis (DEA) is that it
allows for multiple inputs and outputs to be included into a production framework while
still offering a single performance index. This in turn, allows easy comparison between
funds and thereby groups. Furthermore, the speci?cation of the models under DEA
allows for endogenous derived inputs and outputs weights which make this type of
models appealing (Glawischnig and Sommersguter-Reichmann, 2010). We apply two
types of DEA methods to our sample: a radially driven input-oriented measure, or the
BCC’s model, as well as a non-radially driven input-oriented measure, or the Russell’s
model.
Overall, our results are consistent with prior literature. Islamic funds do not seem to
lose ef?ciency despite their smaller asset universe. Furthermore, results are also robust
to different speci?cations of:
.
the asset universe; and
.
DEA model.
In lieu of the 2007-2008 US ?nancial crisis, we revise if the higher performance of
Islamic mutual funds is due their exposure to lower levels of risk; we ?nd that Islamic
investment is remarkably ef?cient regardless of the time period.
The remaining of this paper is structured as follows. Section 2 discusses the
previous literature. Section 3 brie?y explains further rationales to use DEA as well as
stating the relevant models[2]. Section 4 discusses the data. Section 5 shows the
empirical results of two DEA models. Section 6 checks the robustness of results to
different subsamples that accommodate the latest ?nancial crisis. Finally, Section 7
shows the summary and conclusions.
2. Previous literature
There are several studies whichfocus onIslamic ?nance especiallyafter the introductionof
several Islamic indices such as: the Dow Jones Islamic market index (DJIMI) which was
launched in 1999; FTSE Global Islamic Index Series (GIIS) which was launched at the end
Performance
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of 1998; MSCI global Islamic indices; and the Global Gulf Cooperation Council (GCC)
Islamic indexwhichwas launchedin2006. The maintheme of these studies is toinvestigate
whether there is a cost in adhering to the Shariah law. Some studies ?nd Islamic investing
affects performance, while others ?nd otherwise.
Elfakhani et al. (2007) ?ndings suggest that there is no statistical evidence of any
performance differences between Islamic funds and the employed market benchmarks.
However, their ?ndings suggest that Islamic mutual funds do offer a good hedging
opportunity against market downturns. Abdullah et al. (2007) apply Sharpe index and
adjusted Sharpe index, Jensen Alpha, timing and selectivity ability to Malaysian mutual
funds and ?nd that Islamic funds performed better than conventional funds during
bearish economic trends while, conventional funds showed better performance than
Islamic funds during bullish economic conditions.
Mansor and Bhatti (2011) study the monthly performances of 128 Islamic mutual funds
(IMFs) in Malaysia for the period of January 1990 to April 2009. They employ Sharpe,
Treynor and Jensen ratios to the risk-adjusted return performance based on extended
version of CAPM model. They ?nd on average IMFs in Malaysia outperform its
conventional peers and the market portfolio proxy by the KLCI returns. Shah et al. (2012)
showthat Pakistani Islamic funds, when compared to Pakistani non-Islamic funds, present
a lower average risk rate with higher compensations. Surprisingly, the authors also ?nd
Islamic funds are even better diversi?ed than conventional mutual funds.
Hoepner et al. (2009) ?nd mixed evidence on the performance of Islamic mutual funds.
They ?nd that Islamic funds from eight nations (mostly from the Western regions)
signi?cantly underperform their respective equity market benchmarks and Islamic funds
from only three nations outperform their respective market benchmarks. Furthermore,
they ?nd that Islamic funds fromthe GCCand Malaysia do not signi?cantly underperform
their respective market benchmarks. Finally, theyargue that Islamic equityfunds can offer
hedging opportunities because their investment universe is limited to low debt-to-equity
ratio stocks.
Donia and Marzban (2010) conclude that Shariah-compliant investments outperform
conventional investments using the mean-variance frontier because the former bene?ts
from the lower leverage feature. Also, Majid and Maulana (2010) apply a non-parametric
performance measure to assess performance and ?ndsigni?cant ef?ciencyof Islamic funds,
but they limit their study only to Indonesia.
Hassan et al. (2010) provide a case study on Malaysian Islamic unit trust funds. Their
?ndings show that there are no convincing performance differences between Islamic and
non-Islamic Malaysian unit trust funds.
Girard and Hassan (2008, 2012) study the performance of several Islamic indexes and
compare them with non-Islamic equivalents. They use parametrical methods such as
Sharpe ratio, Jensen and Fama’s selectivity, net selectivity, diversi?cation, and Carhart’s
(1997) four factor pricing model and ?nd that there is no signi?cant difference between the
Islamic and non-Islamic indexes.
BinMahfouz and Hassan (2012) conclude that the assumption that Shariah investment
constrains lead to inferior performance and riskier investment portfolios because of limited
investment universe seems to be rejected. This implies that Muslim investors can choose
Islamic investments that are consistent with their beliefs without being forced to either
sacri?ce performance or become exposed to higher risk.
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3. Non-parametric estimations
Since alternative investments or ?nancial assets have different statistical properties,
estimating a good performance index is a dif?cult task due to the different characteristics
of assets returns, such as skewed return distributions with fat tails. Because of this, it is
expected that parametrical performance measurements fail when accounting distributions
that present non-normal characteristics. We expect that use of non-parametric econometric
method, such as DEA, will add value to prior literature.
We expected that DEA will contribute a sound estimation of performance indexes
as well as a better explanation of the risk-return relationship. In this context, DEA
offers a good perspective as it accounts for multiple inputs and outputs simultaneously
while still offering a single real number as a performance index. DEA assumes a
production framework on which one uses inputs to produce outputs where inputs are
de?ned as bearers of risk while outputs are bearers of wealth.
Prior literature reveals that input candidates should re?ect investment risk, which is
proxied by the return momentums. Under normality, only the mean return and its
standard deviation will suf?ce. However, if distributions are non-normal, then higher
momentums should be required. Thus, the next section focuses on testing normality of
returns.
3.1 Normality testing
In order to measure normality, this paper employs the Jarque Bera ( JB) test statistic,
de?ned in equation (1). Normality is rejected when JB
j
is larger than 5.99 for the
5 percent signi?cance level and 9.21 for the 1 percent signi?cance level:
JB
j
¼
T
6
S
2
j
þ
K
2
j
4
" #
ð1Þ
where:
S
j
¼
E
j
ðr
t
2r
d
Þ
2
s
2
j
; the skewness of monthly returns of fund j
K
j
¼
E
j
ðr
t
2r
d
Þ
4
s
4
j
23; the excess kurtosis of monthly returns of fund j
r
t
, monthly return.
r
d
, average returns.
s
j
, standard deviation.
3.2 Inputs and outputs description
The speci?cation of the input-output model is given by the risk-return relationship.
In this case, all risk measures are considered as inputs while all return measurements
will be considered outputs. The input candidates are given by the fund’s standard
deviation, the lower partial momentums (LPM), and maximum drawdown period. The
output candidates are expected returns, the upper partial momentums (UPM ), and the
maximum period of consecutive gain.
Performance
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The partial momentums, both upper and lower, are estimated as the m
th
root of the
LPMs and UPMs given by equation (2), in percentages. The paper uses r
min
as the
mean return to differentiate between the downside and the upside of the investment
strategy. While the LPMs capture the downside or risk of holding a speci?c investment
asset, the UPMs will capture the upside or bene?t of the investment. Finally, UPM0 is
disregarded while LPM0 is further used; LPM0 is the percentage return of funds below
the target rate[3]:
LPM
j;m
¼
1
T
X
~
T
t¼1
ðr
min
2r
t;j
Þ
m
; m ¼ 0; . . . ; 4
UPM
j;m
¼
1
T
X
T
_
t¼1
ð r
t;j
2r
min
Þ
m
; m ¼ 0; . . . ; 4
ð2Þ
where:
r
min
, target rate.
r
t;j
, monthly return of fund j below target rate.
~
T, number of returns of fund j below target rate.
r
t;j
, monthly return of fund j above target rate.
T
_
, number of returns of fund j above target rate.
The maximum drawdown period (MDP) is estimated as the maximum number of
months that fund j has been below historically high net asset value (NAV). On the other
hand, the remainder outputs are the funds expected return, E(r
j
), and the maximum
number of months fund j has been above the minimum target rate, or MCG.
3.3 The input-output DEA model
Prior literature has shown that the input-oriented BCC (Banker et al., 1984) with radial[4]
inputs is the dominatingmethodto estimate fundperformance. Accordingto Glawischnig
and Sommersguter-Reichmann (2010), the use of the BCC model can be justi?ed because:
.
as the CCR (Charnes et al., 1978) model and the output-oriented BCC model are
not translation invariant[5] towards outputs, the input-oriented BCC model is
often the metric of choice;
.
the assumption of variable returns to scale (VRS) is justi?ed by the fact that
alternative investment funds might operate in regions of increasing or
decreasing return to scale due to, for example, minimum investment
requirements or ?xed cost digression; and
.
the use of the BCCmodel is advisable whenever ratios are usedas inputs or outputs.
Having identi?ed the input-output speci?cations, we estimate a frontier (the production
possibility frontier (PPF)) to the production possibility set (PPS) that envelops the PPS
as tightly as possible. When comparing the DEA frontier with standard portfolio
theory (the Markowitz portfolio theory) the DEA frontier is essentially the same but
with a different approach. The DEA frontier is resulting from the convex combination
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of the best practices[6] followed by the industry given the multiple hyperplanes
resulting from the use of multiple inputs and outputs; thereby making it is possible to
construct a performance index based upon the distance between speci?c funds and the
constructed frontier.
Formally, it is assumed that there are j ¼ 1, . . . , N funds where each uses x
m
;m ¼
1; . . . ; M inputs to produce y
r
;r ¼ 1; . . . ; R outputs. Then the performance for the k
th
fund, p
BCC
, is estimated by the linear program (LP) given by equation (3):
p
BCC
¼ minu s:t:
X
N
j¼1
x
mj
l
j
# u · x
mk
;m ¼ 1; . . . ; M
X
N
j¼1
y
rj
l
j
# y
rk
;r ¼ 1; . . . ; R ð3Þ
X
N
j¼1
l
j
¼ 1 with l
j
$ 0;j; m; r
The LP given in equation (3) represents the percentage of ef?ciency of each particular
fund k. equation (3) minimizes the equiproportionate (radial) contraction u of the inputs
produced by unit k. The performance index, P
BCC
, satis?es P
BCC
# 1 where P
BCC
¼ 1
represents a fund which is 100 percent ef?cient. That is, given the input-output
combination which characterizes the best practice frontier, P
BCC
¼ 1 represents
the k
th
fund which is on the actual frontier and thus the fund is ef?cient. Any deviation
from the PPF, given by P
BCC
, 1, will result in inef?ciencies. Furthermore, the LP uses
exogenous weights, l
j
, to ?t the best linear combination of all funds given a speci?c
input-output combination; l
j
– 0 represents the best practice units that delimit the
frontier.
As with every liner program, equation (4) shows a dual to the primal in equation (3).
The dual is helpful as it also estimates the number of inputs and outputs used in the
production framework. In this case, the weights m
r
and v
m
represent which particular
inputs/outputs are incorporated into the fund performance index estimation. The dual
P
BCC
is estimated using the endogenously derived weighs on the m ¼ 1, . . . , M inputs
and r ¼ 1, . . . , R outputs instead of applying the weights onto the funds as in
equation (3). From the economic stand point, the ef?cient funds should have all inputs
and outputs incorporated when estimating the fund performance index to include the
investor’s gain given the risk exposure. Finally, the variable m
0
in the dual LP (4) is free
and guaranties VRS (Glawischnig and Sommersguter-Reichmann, 2010, footnote 12):
P
BCC
¼
v
m
;m
r
;m
0
max
X
R
r¼1
m
r
y
rk
þm
0
s:t:
X
R
r¼1
m
r
y
rj
2
X
M
m¼1
v
m
x
mj
þm
0
# 0 ;j ¼ 1; . . . ; N ð4Þ
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X
M
m¼1
v
m
x
mk
¼ 1
m
r
; v
m
$ 0 and m
0
free
Alimitation of the BCCmodel is that it assumes all inputs to be radial. But the possibility
of non-radial inputs exists. Thus, the results are checked using an input-oriented
non-radial model, P
Russell
. This model incorporates non-proportional input reductions
using data driven lower bounds regarding input weights under VRS. In other words, the
model does not assume a constant u common for all inputs. Instead, it weights each input
independently and then estimates the overall performance of the index as the sumof the
individual weights. Again, ef?ciency is achieved when P
Russell
¼ 1. Formally:
P
Russell
¼ min
P
M
m¼1
u
m
M
s:t:
X
N
j¼1
x
mj
l
j
¼ u
m
· x
mk
;m ¼ 1; . . . ; M
X
N
j¼1
y
rj
l
j
# y
rk
;r ¼ 1; . . . ; R ð5Þ
X
N
j¼1
l
j
¼ 1 with l
j
$ 0;j; r and u
m
# 1
4. Data description
In this section, the DEA models described in Section 3 are estimated based on a
comprehensive data set of mutual funds. Two datasets are employed to form the fund
universe. The fund universe is de?ned as the merger between Saudi Arabia funds
(which proxy for Islamic investments), International funds, and American funds.
Initially, the fund universe consists of 45096, from which 42,340 are regarded as
American, 2,614 are International, and only 142 are Islamic.
For the Islamic funds, a sample data consisting of daily NAVs of 143 out of
234 mutual funds available in Saudi Arabia during the period from January 2003 to
December 2010 is selected. Information on these funds is obtained from three main
sources: the of?cial site of the Saudi Stock Exchange (Tadawul) (www.tadawul.com.
sa), the of?cial site of HSBC Saudi Arabia Limited (www.hsbcsaudi.com), and Zawya
database[7]. Because the data on Islamic funds is not continuous, a one month holding
period return estimated at the end of the month is computed.
Additionally, we take data from CRSP to account for the remaining funds.
International funds are de?ned as those funds listed in CRSP with objective code
“International Fund,” “International,” or “IF.” Finally, everything else is de?ned as
American funds. Only monthly returns as well as monthly NAV’s from CRSP for the
period of January 1999 to September 2011 are considered. For robustness check, CRSP
sample data is restricted to match Islamic funds data sample.
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Furthermore, funds employed in the sample are only those which have continuous
returns data with at least two years’ worth of observations. That is, those funds which
have complete years (no missing monthly returns or NAV), and no missing years in
between the series. After controlling for this, the sample reduces to 20,946 American
funds, 1,504 International funds, and only 95 Islamic ones.
The effective asset universe then results in 56 percent of the original Islamic funds,
51 percent of American funds, and 57 percent of International funds. Despite the high
reduction of the data universe, we still expect to get more robust results as most of
surviving funds will be accounted for.
5. Empirical results
5.1 Normality testing
Based on the information provided in Section 3.1, in this section, equation (1) is tested to
check whether or not the returns show normality. Two types of testing groups are
de?ned: the whole universe and independent individual subgroups. Table I summarizes
the results. When the whole fund universe is considered, only about 34 percent of returns
can be considered as normally distributed with a 95 percent con?dence level.
Moreover, when analyzing individual subgroups, each group is analyzed
independently; it is observable that Islamic returns show the highest normality
results, with around 50 percent of funds following normality. This is quite a puzzle,
since it is expected that American returns to be closer to normality, per the Central
Limit Theorem, as there are more observations for American funds than there are for
International and Islamic funds. However, these results pave the way for future
measurements of DEA based performance indexes that include higher momentums,
especially when the fund universe is considered.
5.2 Inputs and outputs speci?cations
Based on Section 3.2., the different input and output candidates are estimated. Following
the literature, the correlation of the different inputs and outputs to de?ne a suitable
production framework for the BCC model is investigated. This paper uses such
production framework on which risk and return are positively correlated, thus requiring
inputs and outputs to be positively correlated. Therefore, the inputs MCG and
LPM0-LPM4, as well as the outputs MDP and UPM1-UPM4 are initially considered.
Total number of funds 5% signi?cance 1% signi?cance
Fund universe 22,545 7,829 9,090
(34.72%) (40.31%)
American funds 20,946 7,127 8,302
(34.02%) (39.63%)
International funds 1,504 654 716
(43.45%) (47.57%)
Islamic funds 95 48 72
(50.52%) (75.78%)
Note: The table shows how many funds are normally distributed with the corresponding percentage
of the group
Table I.
The JB test statistic for
normality of time series
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The forth momentums, LPM4 and UPM4, are disregarded due to the extreme high
correlations; LPM3 and LPM4 as well as UPM3 and UPM4 show a correlation greater
than 0.999[8]. Still, using the third momentum is enough to apply an extra penalty
(bonus) to funds with extremely low (high) returns. Table II summarizes the
descriptive statistics of the input-output speci?cations considered for the production
framework used in further tests.
It is worthwhile mentioning that it is striking that there are funds among the fund
universe that achieve 100 percent on LPM0. That means that there are funds that have
had only returns below average (LPM0 ¼ 1) during the time window of the study.
Further analysis between the subgroups, when each group is analyzed independently,
shows that these funds come from the American and Islamic subsamples. In addition,
it comes as no surprise that the American subsample is quite similar to the fund
universe, as the American subsample accounts for almost 93 percent of the data.
Further analysis of Table II gives additional information about the performance of
each of the subsamples. It is observable that the International subgroup has the best
performance, followed by the Islamic funds and ?nally the American funds. As
International funds show the smallest average input values with the highest average
output values as well as the smallest maximum drawback period.
The only estimate on which the Islamic funds show superiority comes from the
maximum consecutive gain. Not only is the mean MCG remarkably higher for Islamic
funds (63 months compared to 1.5 months for American funds and one month for the
International subgroup), the minimum and maximum values are quite impressive as
well. That is, while the minimum MCG for the Islamic funds (24 months) is well above
the minimum MCG for both American and International funds (0 months for both,
respectively), the maximum MCG for the Islamic funds (84 months) is astonishing
MDP
(months)
LPM0
(%)
LPM1
(%)
LPM2
(%)
LPM3
(%)
MCG
(months)
UPM1
(%)
UPM2
(%)
UPM3
(%)
Panel A: the fund universe
Minimum 1 0.125 0.0012 0.0028 0.0035 0.0000 0.0000 0.0000 0.0000
Maximum 96 1 0.1166 0.1834 0.2386 10.0000 0.1274 0.1799 0.2160
Mean 33.1261 0.4718 0.0175 0.0347 0.0486 1.4912 0.0185 0.0306 0.0393
SD 25.0836 0.1095 0.0091 0.0169 0.0233 1.4573 0.0115 0.0175 0.0220
Panel B: American funds
Minimum 1 0.125 0.0012 0.0028 0.0034 0.0000 0.0000 0.0000 0.0000
Maximum 96 1 0.1165 0.1833 0.2385 10.0000 0.1275 0.1800 0.2160
Mean 33.4684 0.4697 0.0170 0.0338 0.0474 1.5342 0.0180 0.0298 0.0383
SD 25.5837 0.1094 0.0091 0.0169 0.0233 1.5026 0.0115 0.0175 0.0221
Panel C: International funds
Minimum 1 0.2917 0.0087 0.0145 0.0215 0.0000 0.0043 0.0140 0.0220
Maximum 64 0.8333 0.0645 0.1152 0.1542 4.0000 0.0507 0.0890 0.1171
Mean 29.0705 0.4721 0.0243 0.0468 0.0651 1.0007 0.0250 0.0416 0.0528
SD 16.2616 0.0470 0.0060 0.0090 0.0116 0.2861 0.0064 0.0091 0.0104
Panel D: Islamic funds
Minimum 4 0.3452 0.0020 0.0024 0.0026 24.0000 0.0000 0.0000 0.0000
Maximum 83 1 0.0595 0.1137 0.1534 84.0000 0.0506 0.0873 0.1244
Mean 33.6526 0.6781 0.0208 0.0412 0.0569 63.9474 0.0194 0.0343 0.0452
SD 17.1121 0.2498 0.0176 0.0351 0.0483 21.7556 0.0186 0.0319 0.0421
Table II.
The descriptive statistics
of the proposed
input-output speci?cation
used to estimate the DEA
performance index
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higher than the maximum MCG for both the American and International subgroups
(ten and four months, respectively).
5.3 The fund universe performance
In this section, the performance of the overall fund universe is estimated and then it is
comparedtoeachindividual subgroup. Inother words, the DEAef?ciencyfrontier basedon
the fund universe is estimated and then each subgroup is compared to the estimated
frontier. Table III summarizes the ?ndings. The overall ef?ciency of the fund universe is
estimate based on equation (3) (panel A) and equation (5) (panel B). That is, the fund
performance indexis estimatedbasedonradial inputs, P
BCC
, andnon-radial inputs, P
Russell
.
At ?rst glance, it is found that ef?ciency is highly penalized under the assumption of
non-radial inputs. This might be driven by the non-proportional input reduction
condition on the Russell’s model which applies higher penalties to different inputs. The
question of whether a radial or non-radial production framework should be assumed
remains unanswered because it is beyond the scope of this paper. The main focus of this
paper is to investigate which speci?c subset is more ef?cient than the other. Thus, the
difference amongst groups, rather than the difference amongst methods is analyzed.
Focusing on panel A, results indicate that 3,944 funds out of the whole fund
universe can be considered as ef?cient, which accounts for 17.49 percent of all funds.
Granted, the majority of them are American, 3,587 funds accounting for 90 percent of
all ef?cient funds. Yet when comparing them to their own subsample, they only
account for 17.12 percent. That is, about 17 percent of American funds can be
considered ef?cient with respect to the PPF which envelops the whole fund universe.
In fact, American funds seem to be the least ef?cient of all three subsamples.
International founds account for 320 ef?cient funds, or 21.28 percent of their
subgroup while Islamic funds account for 37 ef?cient funds, or 39 percent of all Islamic
funds. Thus, it is observable that there are more ef?cient funds within the Islamic
subsample than either the American or International subsamples. These results are
consistent even to different comparisons.
Because BCC provides an actual performance index, it is possible to estimate the
average performance of each subgroup and then compare each fund to the proposed
Panel A: P
BCC
Panel B: P
Russell
No of
funds
Ef?cient
funds
Average
(%)
Funds above
average
Ef?cient
funds
Average
(%)
Funds above
average
Fund
universe
22,545 3,944 52.00 8,574 6 27.52 8,431
(17.49%) (38.03%) (0.03%) (37.39%)
American
funds
20,946 3587 52.47 8,149 4 27.85 8,007
(17.12%) (38.90%) (0.02%) (38.23%)
International
funds
1,504 320 44.84 339 0 21.55 362
(21.28%) (22.54%) (0.00%) (24.07%)
Islamic
funds
95 37 60.89 38 2 47.16 38
(38.95%) (40.00%) (2.11%) (40.00%)
Notes: The American, International, and Islamic subsets are compared to the PPF based on the whole
fund universe; the percentages in parenthesis correspond to the fraction of ef?cient funds or funds
above average with respect to its subgroup
Table III.
The estimation of
equation (3), panel A, and
equation (5), panel B,
based on the whole fund
universe
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performance index. It is worthwhile mentioning that the Islamic subgroup shows the
highest average performance, 60.89 percent, followed by the Americanand International
funds with 52.47 and 44.84 percent average performance, respectively. Finally, Islamic
funds also show the highest ef?ciency levels when measuring the number of funds
above average. Islamic funds lead with 38 ef?cient funds above average, or 40.0 percent
of their subgroup, followed bythe American andInternational funds with 8,149 funds, or
38.9 percent of the subsample, and 339 funds, or 22.54 percent of the subsample,
respectively.
Likewise, the non-radial model on panel B con?rms observed results, despite a
penalty imposed on the estimation. Though the number of actual ef?cient funds drops
considerably, we ?nd the same dominance by Islamic funds. Around 2 percent of Islamic
funds are ef?cient, while only 0.02 percent of American funds are ef?cient and no
International funds are ef?cient. As for the average performance and number of funds
above average, the results are consistent with the estimation under the BCC model; the
average performance is quite smaller but the number of funds above average remains
similar to the results in panel A.
Despite the limitation on Islamic funds due to investing only in Shariah compliant
assets, the results suggest that such assets do not loose ef?ciency when comparing themto
more “free investment” opportunities. In fact, Shariah investments seem to be even better
than those traditional investment strategies. Overall, our results indicate that when
comparing individual subgroups to the whole envelop of the DEA performance index,
Islamic funds seemto dominate the ef?ciencymeasures. Taken together withthe results on
Table II, one can consider Islamic funds to be a solid investment alternative, if not the best.
Still, a question remains on whether Islamic mutual funds together with other
investment assets should be analyzed. This is because those who invest in Islamic
assets are not going to invest in non-Shariah compliant assets in any case. In other
words, when analyzing Islamic investments, the fund universe should be limited to
only Islamic assets, since Islamic investors will not even consider investing in assets
that are not Shariah compliant. The following section analyzes individual subgroups
independently of one another.
5.4 Independent subgroups
Because Islamic investors are constraint for non-Shariah investment, it is logical to
study Islamic mutual funds independently. In this section, the ef?ciency of the
individual subgroups is investigated. However, results for the American subgroup are
not included due to their similarities with those for the fund universe. Both DEA
methods are applied, the radial and non-radial inputs, to the individual subgroups:
International funds and Islamic funds. Moreover, results of equation (4) are included to
analyze the input-output composition of the radial input BCC.
Table IV summarizes the results of the BCC model for the fund universe and both
International and Islamic subgroups. The results suggest that when limiting the
universe to their own subgroup thus reshaping the PPF, the International and American
funds gain little ef?ciency while the Islamic subgroup remains the same; the number
of ef?cient International and American funds increases from 320 to 338 and 3,587 to
3,590, respectively, but the number of ef?cient Islamic funds stays on 37.
However, the most signi?cant result comes fromthe increase onthe average performance
of Islamic funds when their PPS is limited to account only for their own subgroup:
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while American funds decreased from 52.47 to 51.74 percent and International funds
increased from 44.84 to 80.01 percent, Islamic funds increased from 60.89 to 92.60 percent
which is magni?cently high. Moreover, even the number of funds above average increases
for the Islamic subgroup from 40 to 61 percent. Overall, it can be concluded that despite
the limitations of the asset universe faced by Islamic funds, they are most ef?cient than
their counterparts.
As a comparison benchmark for ef?ciency, Table V shows similar results under the
non-radial production framework. The trend is quite similar to those of the
input-oriented BCC model. Results show a higher number of ef?cient Islamic funds
(8 or 8.42 percent of their subgroup), compared to the number of ef?cient International
funds (9 or 0.6 percent of their subgroup), and ef?cient American funds (11 or
0.05 percent of their subgroup). The average performance is also consistent with the
prior results giving the highest average performance to the Islamic funds with an
average ef?ciency of 68.05 percent followed by the International and American
counterparts with an average of 50.93 and 27.74 percent, respectively.
It is noteworthy to mention that the use of individual subgroups shows a
remarkable increase on ef?ciency under equation (5), the non-radial production
framework. While the results of the radial model under either the full universe PPF or
Total number
of funds
Number of ef?cient
funds P
BCC
¼ 1
Expected
ef?ciency (%)
Number of funds
above average
Fund
universe
22,545 3,944 52.00 8,574
(17.49%) (38.03%)
American
funds
20,946 3,590 51.74 7,658
(17.14%) (36.56%)
International
funds
1,504 338 80.01 664
(22.47%) (44.15%)
Islamic funds 95 37 92.60 58
(38.95%) (61.05%)
Note: The percentages in parenthesis correspond to the fraction of ef?cient funds or funds above
average with respect to its subgroup
Table IV.
The results from
equation (3), the radially
driven input-oriented
model, based on the fund
universe and the
independent subgroups
(each subgroup has its
own PPF)
Total number
of funds
Number of ef?cient
funds P
Russell
¼ 1
Expected
ef?ciency (%)
Number of funds
above average
Fund
universe
22,545 6 27.52 8,431
(0.03%) (37.40%)
American
funds
20,946 11 27.74 8,028
(0.05%) (38.33%)
International
funds
1,504 9 50.93 504
(0.6%) (33.51%)
Islamic funds 95 8 68.05 47
(8.42%) (49.47%)
Note: The percentages in parenthesis correspond to the fraction of ef?cient funds or funds above
average with respect to its subgroup
Table V.
The results from
equation (5), the
non-radially driven
input-oriented model,
based on the fund
universe and the
independent subgroups
(each subgroup has its
own PPF)
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the self-group-limited-universe PPF are quite close. For instance both show 37 ef?cient
Islamic funds, assuming the latter changes the results considerably when assessing a
non-radial production framework. All the studying parameters (number of ef?cient
funds, average performance, and number of funds above average performance) seem
considerably higher when limiting the universe to the speci?c subgroups. Still, despite
the increase in all subgroups, Islamic funds are still the most ef?cient.
5.5 Speci?cs of the inputs and outputs
By using a dual programming to equation (3), it is possible to compare the number of
inputs and outputs being used to analyze the production framework. This subsection
focuses on the BCC model since it is the model of choice in prior literature[9]. It is
expected that ef?cient funds would incorporate as few inputs as possible in order to
produce as much outputs as possible. Yet, it is found that a signi?cant number of
ef?cient funds are unable to generate any output whatsoever. Table VI summarizes the
results.
Panel Ashows the input-output mix for the fund universe. Results indicate that there
are 3,886 ef?cient funds, which accounts for 17 percent of all funds. Further analysis
shows that neither ef?cient nor inef?cient funds could incorporate all inputs together. In
fact, the majority of funds could only use a maximum of three inputs at the same time
(of a maximum of ?ve), and only a few could even achieve four inputs simultaneously.
Examining the outputs, on the other hand, showthat ef?cient funds can achieve more
outputs than inef?cient funds. For instance, almost 5 percent of ef?cient funds, that is
194 funds, can achieve three outputs (of a maximum of four) simultaneously compared
to only one fund achieving the same number of outputs for the inef?cient funds. In
addition, only ef?cient funds can achieve the maximum number of outputs, although
they account for less than 0.1 percent of ef?cient funds. Despite the highest performance
of ef?cient funds, there is still some inef?ciency within them. That is, 37.3 percent of
ef?cient funds cannot achieve any output at all. What is more puzzling, however, is that
there are less funds with zero outputs, 31.5 percent, coming from the inef?cient
subsample.
Inputs Outputs
Number of funds 1 2 3 4 5 0 1 2 3 4
Panel A: fund universe
Inef?cient 18,659 817 15,062 2,756 24 – 5,886 9,410 3,362 1 –
Ef?cient 3,886 1,486 725 1,649 26 – 1,450 828 1,411 194 3
Panel B: American funds
Inef?cient 17,417 3,133 12,121 2,153 10 – 10,476 4,901 2,040 – –
Ef?cient 3,529 1,096 964 1,465 4 – 1,058 1,883 473 104 11
Panel C: International funds
Inef?cient 1,177 249 927 1 – – 43 1,076 58 – –
Ef?cient 327 107 9 188 23 – 54 94 178 1 –
Panel D: Islamic funds
Inef?cient 66 1 22 39 4 – 12 39 12 3 –
Ef?cient 29 5 11 12 1 3 10 10 6 –
Notes: Table VI shows the input-output combination used in the production process; it also shows
production inef?ciencies given by the number of funds with zero outputs
Table VI.
The results from
equation (4), the dual to
the radially driven
input-oriented model,
based on the fund
universe and the
independent subgroups
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Though panel A shows important results, other panels show further means to
comparing ef?ciency between Islamic, International, and American funds. At ?rst
inspection, there seems no signi?cant difference in the input mix between the subgroups,
but results do indicate that only American ef?cient funds can achieve the maximum
number of outputs. Note that the same pattern presented in panel A is con?rmed:
.
most funds, regardless if they are ef?cient or inef?cient, use a maximum of three
inputs; and
.
even ef?cient funds present some level of inef?ciency due to the presence of
funds that produce zero outputs.
Deeper examination of Table VI shows that Islamic funds can still be considered better
performing than their counterparts. Results show that 30.5 percent of Islamic funds can
be regarded as ef?cient with inef?ciencies accounting for only 10.3 percent, whereas
21.7 percent of International funds are ef?cient with inef?ciencies of 16.5 percent, and
only 5.2 percent of American funds are ef?cient with inef?ciencies accounting for
almost 30 percent. In this context, inef?ciencies are regarded as the percentage of
ef?cient funds which produced zero-outputs.
Overall, results suggest that Islamic mutual funds do not lose ef?ciency even though
they are limited to a smaller universe of assets. Perhaps a possible explanation for such
ef?ciency gain is that despite limitations, Islamic investors are ethically driven and thus
theyprefer to avoidinvestingonto the most riskyassets. Therefore, these results might be
biases in favor of Islamic funds due to the fact that the latest 2007-2008 crisis was mainly
driven by excessive investment onto risky assets (Gorton, 2010). Such results are also
consistent with ?ndings of Merdad et al. (2010) who compared Islamic and conventional
mutual funds managed by HSBC, the fourth largest fund manager in Saudi Arabia, from
January 2003 to 2010. They show that Islamic funds underperform conventional funds
during both the full sample period and the bullish period, but outperform conventional
funds during bearish and ?nancial crisis periods. The next section covers this issue by
splitting the dataset in order to account for the 2007-2008 ?nancial crises.
6. Robustness check
The 2007-2008 ?nancial crisis swept through globally, and thus it is expected to have
affected worldwide assets. However, due to the constraints on Shariah law, it is
believed that Islamic funds have been somehow immunized to the effects of the crisis,
which would explain their higher ef?ciency compared to their counterparts. Therefore,
in this section, equation (3) is estimated based on the re-estimation of the inputs and
outputs to account for the ?nancial crisis.
As before, results are presented based on the full universe PPF and individual
groups PPF for the BCC model. The same input/output combinations proposed in the
prior section are still used, but they are now estimated based on two subsamples:
January 2003 to December 2006 and January 2007 to December 2010. This generates
two subsamples with different number of funds. The pre-crisis subsample accounts for
14,509 funds in the fund universe from which 13,589 are American, 843 are
International, and 77 are Islamic, while the post-crisis subsample, which is fairly
similar in number of funds in the whole sample, has 22,531 assets in the fund universe
from which 20,932 are American, 1,504 are International, and 95 are Islamic.
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6.1 The fund universe performance
As before, a PPF is de?ned as that which envelops all assets in the universe and then
each subgroup is compared to the proposed PPF. Table VII summarizes the results. As
expected, there is a decrease on ef?ciency as the crisis starts. Although all subgroups
are affected, American funds remain quite the same. In fact, only a decrease of
0.53 percent on the percentage of ef?cient American funds is observed, while
International and Islamic both have a decrease of 18.7 and 9.1 percent, respectively.
Furthermore, results show a signi?cant decrease on the average performance as well as
number of funds above average performance consistent for all funds.
Still, when comparing the funds with one another, the same results are found;
Islamic funds outperform their counterparts regardless of the subsample period. In
fact, sorted by ef?ciency, the order remains the same regardless of the time period:
Islamic funds followed by International funds and American funds at last. Although
the order changes when comparing average performance and the number of funds
above average, it can be safely concluded that Islamic funds are still more ef?cient
despite the ?nancial crisis.
It is worthwhile noting that though the number of ef?cient Islamic funds is the same
regardless of the time period (37 funds), they are not all the same funds. In fact, results
indicate that ?ve funds differ; that is, ?ve funds stopped being ef?cient and ?ve started
being ef?cient after the crisis.
6.2 Subgroups performance
We estimate PPF for each group and then compare their performances. This is done
with the rational that Islamic investment is self-constraint to a limited asset universe
and thus it makes sense to limit the PPF which will only envelop such assets. Table VIII
summarizes the results.
Once again, prior results are con?rmed at the ?rst glance; Islamic funds are always
the most ef?cient regardless of the time period followed by International and American
funds. However, focusing on panel A, it is noticeable that International and Islamic
funds have more ef?cient funds when the PPF is limited to their own subgroup. This
result shows that the post-crisis decrease is even more signi?cant.
Panel A: 2003-2006 Panel B: 2007-2010
No of
funds
Ef?cient
funds
Average
(%)
Funds
above
average
No of
funds
Ef?cient
funds
Average
(%)
Funds
above
average
Fund
universe
14,509 2,792 73.10 5,934 22,531 3,969 46.32 7,176
(19.24%) (40.90%) (17.62%) (31.85%)
American
funds
13,589 2,418 73.00 5,596 20,932 3,612 46.66 6,778
(17.79%) (41.18%) (17.26%) (32.38%)
International
funds
843 337 74.40 340 1,504 320 40.93 320
(39.98%) (40.33%) (21.28%) (21.28%)
Islamic
funds
77 37 76.93 42 95 37 58.07 38
(48.05%) (54.55%) (38.95%) (40.00%)
Notes: This estimation is based on the whole fund universe; the American, International, and Islamic
subsets are compared to the PPF based on the whole fund universe; the percentages in parenthesis
correspond to the fraction of ef?cient funds or funds above average with respect to its subgroup
Table VII.
The estimation of
equation (3) for the two
subsamples: 2003-2006 on
panel A and 2007-2010
on panel B
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Further analysis shows that Islamic funds lost average performance lead to International
funds after the crisis. While panel A shows an Average performance of 93.69 percent
for Islamic funds and 91.48 percent for International funds, panel B gives the lead to
International funds with 69.32 percent followed by Islamic funds with 62.88 percent.
Yet the number of above average performance funds is still higher for Islamic funds.
Deeper examination reveals that all Islamic ef?cient funds are the same regardless
of the PPF speci?cation for the post-crisis subsample. This is an extra robustness
check as this incorporates both speci?cation of the PPF or time period. This also
suggests that even if Islamic investors where to open themselves towards the whole
asset universe, they will not achieve any extra ef?ciency. In fact, Islamic funds appear
as ef?cient as if they were part of the whole asset universe.
7. Summary and conclusions
The main purpose of this paper is to investigate whether or not Islamic funds loose
ef?ciency due to investment limitations towards Shariah compliant assets. With this
purpose, an extensive dataset with three different types of investment assets is created:
Islamic mutual funds, International mutual funds, and American mutual funds. ADEA
performance index is employed to measure ef?ciency in order to account for the fact
that different investment alternatives present different data characteristics and DEA
can account for such characteristics as it can handle multiple inputs and outputs.
Initially, a PPS that accounted for all the assets in the obtained sample is considered.
Then a PPF that envelops the whole universe of assets is created. However, Islamic
investors would not even consider non-Shariah compliant assets as investment
opportunities and thus they should not be part of their fund universe. For this reason,
PPS is limited to include only individual subgroup’s assets thereby reshaping the
overall PPF. Regardless of the frontier de?nition, ef?ciency is always de?ned as the
percentage number of funds that are on the frontier. Finally, to extend comparison
between subgroups, identifying which subgroup had the highest percentage number of
funds closer to the PPF is considered, which is measured by the percentage number of
funds above average performance.
Panel A: 2003-2006 Panel B: 2007-2010
No of
funds
Ef?cient
funds
Average
(%)
Funds above
average
No of
funds
Ef?cient
funds
Average
(%)
Funds
above
average
Fund
universe
14,509 2,792 73.10 5,934 22,531 3,969 46.32 7,176
(19.24%) (40.90%) (17.62%) (31.85%)
American
funds
13,589 2,382 71.77 57,100 20,932 3,600 46.39 6,582
(17.53%) (42.02%) (17.20%) (31.44%)
International
funds
843 354 91.48 404 1,504 330 69.32 380
(41.99%) (47.92%) (21.94%) (25.27%)
Islamic
funds
77 41 93.69 52 95 37 62.88 37
(53.25%) (67.53%) (38.95%) (38.95%)
Notes: This estimation is based on independent universes; the American, International, and Islamic
subsets are compared to the PPF based on their own universe; the percentages in parenthesis
correspond to the fraction of ef?cient funds or funds above average with respect to its subgroup
Table VIII.
The estimation of
equation (3) for the two
subsamples: 2003-2006 on
panel A and 2007-2010 on
panel B
Performance
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In summary, obtained results suggest that though Islamic funds are limited to a
smaller asset universe, they do not lose ef?ciency regardless of the speci?cation of the
PPF. Islamic funds are the most ef?cient followed by International and then American
funds. Overall, these results are persistent for the percentage number of ef?cient funds,
the average performance index, and the percentage number of funds above average
performance. Also, these results are robust to different speci?cations of the DEA
model. In this regard, two different models are analyzed:
(1) an input-oriented DEA model with a proportional input framework; and
(2) a DEA model with a non-proportional input-oriented framework.
But we focus more on the BCC model, as it is the method of choice in prior literature.
Even though results indicate that there is some level of inef?ciencies remaining
within the ef?cient funds, it can be safely concluded that Islamic funds remain highly
ef?cient despite their investment limitations, and they show the smallest number of
inef?ciencies amongst the subgroups.
Finally, since Islamic investors are limited to Shariah and Ethical investment, thus
preferring less risky assets, it is believed that the obtained results would be biased in
favor of Islamic investment. That is, given that the 2007-2008 ?nancial crisis originated
due to high investment on toxic assets and Islamic investor would rather avoid them,
it is expected that Islamic funds be somehow immunized to the effects of the crisis.
Results show evidence suggesting that even though all assets lost ef?ciency and
average performance, Islamic funds remain the most ef?cient.
On a practical perspective, regardless of the investment preference, our results
indicate that Islamic funds are an effective investment opportunity. Non-Muslim
Investors who seek to maximize their risk-adjusted returns could highly pro?t
from diversifying towards Islamic mutual funds. While Muslin investors should
not be concerned about the opportunity cost of investing only in Shariah compliant
assets. That is, a typical investor could reduce their risk exposure by swapping
their portfolios to also include Islamic funds. In fact, since DEA allows for an
identi?cation of fullyef?cient funds, suchfunds shouldbe considered for every investor’s
portfolio. All in all, Islamic mutual funds create a highly pro?table new avenue of
investment.
Nonetheless, caution must be taken before generalizing the results due to the
limitations of the data. First, the dataset on Islamic mutual funds accounts for roughly
60 percent of all available Islamic mutual funds, thus putting an initial limitation onto
the Islamic universe sample. Second, the obtained Islamic fund universe is by far the
smallest; it only accounts for 0.4 percent of the overall fund universe, hence making it
almost irrelevant to the estimation of the fund universe’s PPF. However, the latter
concern is mitigated by studying each subgroup individually.
Notes
1. For a deep explanation on Shariah complaint assets refer to Derigs and Marzban (2009).
2. For a deeper lit review on the evolution of DEA models refer to Glawischnig and
Sommersguter-Reichmann (2010). Or for an in-depth analysis of DEA methods refer to
Cooper et al. (2000).
3. LPM0 ¼ 1-UPM0 which makes the use of both simultaneously redundant.
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4. Given the inputs (x
1
, x
2
, . . . , x
n
), they are consider radial if they increase proportionally given
an a . 0, such that the inputs increase as (ax
1
, ax
2
, . . . , ax
n
) (Cooper et al., 2000).
5. Translation invariance is meant by the fact that dealing with alternative investments is
likely that some of the outputs, such as average and minimum return, are negative.
Translation invariance of the respective DEA model towards outputs therefore becomes an
issue because DEA cannot handle negative data.
6. Best practices, in this context, refer to those funds with the highest level of outputs given the
prevailing level of inputs.
7. Zawya is one of leading Middle Eastern business information ?rms. Their main web site is:
www.zawya.com we would like to express my deep appreciation to Mr James Randall, the
International business manager, for providing me a trial excess to the database.
8. Just like Glawischnig and Sommersguter-Reichmann (2010), the results show high
correlation among LPM2 and LPM3 (UPM2 and UPM3), as well as LPM2 and LPM4
(UPM2 and UPM4). Despite that high correlation, they are still incorporated into the model
to apply an extra penalty/bene?t for higher momentums due to non-normality of returns.
9. See the introduction of Glawischnig and Sommersguter-Reichmann (2010).
References
Abdullah, F., Hassan, T. and Mohamed, S. (2007), “Investigation of the performance of Malaysian
Islamic unit trust funds: comparison with conventional unit trust funds”, Managerial
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scale inef?ciencies indata envelopment analysis”, Management Science, Vol. 30, pp. 1078-93.
BinMahfouz, S. and Hassan, M.K. (2012), “A comparative study between the investment
characteristics of Islamic and conventional equity mutual funds in Saudi Arabia”, Journal
of Investing (in press).
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Vol. 52 No. 1, pp. 57-82.
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units”, European Journal of Operational Research, Vol. 2, pp. 429-44.
Cooper, W.W., Seiford, L.M. and Tone, K. (2000), Data Envelopment Analysis – A Comprehensive
Text With Models, Applications, References and DEA-Solver Software, Springer, Berlin.
Derigs, U. and Marzban, S. (2009), “A new paradigm and new strategies for Shariah compliant
portfolio optimization – management and system-oriented approach”, Journal of Banking
& Finance, Vol. 33 No. 6, pp. 1166-76.
Donia, M. and Marzban, S. (2010), “Shariah-compliant equity investments frameworks, trends
and crisis”, working paper.
Elfakhani, S., Hassan, M.K. and Sidani, Y. (2007), “Islamic mutual funds”, in Hassan, M.K. and
Lewis, M. (Eds), Handbook of Islamic Banking, Chapter 16, Edward Elgar, Aldershot.
Girard, E. and Hassan, M.K. (2008), “Is there a cost to faith-based investing: evidence from FTSE
Islamic indices”, The Journal of Investing, No. 17, pp. 112-21.
Girard, E. and Hassan, M.K. (2012), “Faith-based ethical investing: the case of Dow Jones Islamic
indexes”, Islamic Economic Studies (in press).
Glawischnig, M. and Sommersguter-Reichmann, M. (2010), “Assessing the performance of
alternative investments using non-parametric ef?ciency measurement approaches: is it
convincing?”, Journal of Banking & Finance, Vol. 34 No. 2, pp. 295-303.
Performance
measurement
of mutual funds
225
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Gorton, G. (2010), “Questions and answers about the ?nancial crisis”, NBER Working Paper
15787, February.
Hassan, M.K., Khan, A.N.F. and Ngow, T. (2010), “Is faith-based investing rewarding? The case
for Malaysian Islamic unit trust funds”, Journal of Islamic Accounting & Business
Research, Vol. 1 No. 2, pp. 148-71.
Hoepner, A.G.F., Rammal, H.G. and Rezec, M. (2009), “Islamic mutual funds’ ?nancial
performance and international investment style: evidence from 20 Countries”, European
Journal of Finance (in press).
Majid, M. and Maulana, H. (2010), “Assessing performance of mutual funds in Indonesia”,
Journal of Economic Cooperation & Development, Vol. 31 No. 4.
Mansor, F. and Bhatti, M.I. (2011), “The Islamic mutual fund performance: new evidence on
market timing and stock selectivity”, paper presented at 2011 International Conference on
Economics and Finance Research, Vol. 4.
Merdad, H., Hassan, M.K. and Al-Henawi, Y. (2010), “Analysis of Islamic versus conventional
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Shah, I.U., Iqbal, J. and Malik, M.F. (2012), “Comparative valuation between Islamic and
conventional mutual fund”, International ResearchJournal of Finance andEconomics, No. 96.
Further reading
BinMahfouz, S. and Hassan, M.K. (2012), “Sustainable and socially responsible investing: does
Islamic investing make a difference?”, Managerial Finance, March 18 (in press).
Fa¨re, R. and Lovell, C.A.K. (1978), “Measuring the technical ef?ciency of production”, Journal of
Economic Theory, Vol. 19, pp. 150-62.
Jarque, C.M. and Bera, A.K. (1987), “Atest for normality of observations and regression residuals”,
International Statistical Review/Revue Internationale de Statistique, Vol. 55 No. 2, pp. 163-72.
Corresponding author
M. Kabir Hassan can be contacted at: [email protected]
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This article has been cited by:
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International Journal of Islamic and Middle Eastern Finance and Management 6:2, 105-121. [Abstract]
[Full Text] [PDF]
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doc_861705168.pdf
The purpose of this paper is to study whether Islamic investors lose portfolio efficiency
due to a limited asset universe.
Accounting Research Journal
Non-parametric performance measurement of international and Islamic mutual funds
J ose Francisco Rubio M. Kabir Hassan, Hesham J amil Merdad
Article information:
To cite this document:
J ose Francisco Rubio M. Kabir Hassan, Hesham J amil Merdad, (2012),"Non-parametric performance
measurement of international and Islamic mutual funds", Accounting Research J ournal, Vol. 25 Iss 3 pp.
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Non-parametric performance
measurement of international and
Islamic mutual funds
Jose Francisco Rubio and M. Kabir Hassan
Department of Economics and Finance, University of New Orleans,
New Orleans, Louisiana, USA, and
Hesham Jamil Merdad
Department of Finance & Economics,
King Fahd University of Petroleum and Minerals (KFUPM),
Dhahran, Saudi Arabia
Abstract
Purpose – The purpose of this paper is to study whether Islamic investors lose portfolio ef?ciency
due to a limited asset universe.
Design/methodology/approach – The paper contributes to prior literature by using
non-parametrical measurements of ef?ciency instead of regular (parametrical) methods. Data
envelopment analysis (DEA) was used in order to better characterize the risk and return relationship,
as well as estimating a single performance index to rank different funds and compare them to one
another.
Findings – Overall, the results are congruent with prior ?ndings. That is, there is strong evidence
suggesting that Islamic funds are highly ef?cient and that they outperform their international
counterparts. Also, results are robust to different estimation of DEA, the speci?cation of the asset
universe, and the inclusion of ?nancial crisis period in analysis.
Research limitations/implications – Though the paper’s ?ndings are robust to
different speci?cations of the DEA model and time periods, the authors caution readers due to the
limited sample.
Practical implications – Having de?ned a performance index, one can therefore isolate the funds
which are the most ef?cient and thus drive trading activities towards said funds.
Social implications – Since the paper’s ?ndings suggest that Islamic investors do not lose
ef?ciency, investing into a limited asset universe which follows social and ethical constraints (given by
Shariah law) is recommended.
Originality/value – The paper is able to con?rm prior literature, even by using a non-parametrical
measurement of ef?ciency. In this way, the authors have accounted for an extra penalty on the
risk-return relationship: skewness.
Keywords Islam, Fund management, Unit trusts, Portfolio investment, Islamic mutual funds,
Data envelopment analysis, Investment ef?ciency
Paper type Research paper
1. Introduction
As of April 2010, Muslims represented almost 21 percent of the world’s population with
an estimated of more than USD 800 billion to invest, which is growing at 15 percent
annually (Girard and Hassan, 2008). Because of this, many ?nancial institutions have
expanded their services to accommodate for Muslims’ religious preferences, resulting in
an increasing universe of Shariah compliant assets.
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1030-9616.htm
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Accounting Research Journal
Vol. 25 No. 3, 2012
pp. 208-226
qEmerald Group Publishing Limited
1030-9616
DOI 10.1108/10309611211290176
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Shariah, which is the moral code and religious law of Islam, rules out the
consumption of alcohol and pork and activities related to gambling. As a result, Muslims
should not invest in ?nancial assets that derive their income fromsuch activities[1]. This
results in the omission of stocks from ?rms such as hotels, casinos, clubs, bars,
restaurants, food producers, alcohol producers, etc. Moreover, Shariah compliant assets
are types of ethical investment which drive investors towards ?rms which have a sound
social responsibility. Thus, it can be expected that mutual fund managers who follow
Shariah law, and thus ethical codes, will tend to avoid extreme risk taking behavior.
While one could argue that Islamic funds bear less risk than traditional assets
thereby producing smaller average returns, one could also argue that Islamic funds are
less diversi?ed than traditional investment, making such investment riskier, thus
making investors require higher compensation to hold Islamic funds. In this paper, we
characterize a risk-return relationship for Islamic funds, International funds, and
American funds in order to explain which set of assets has the best performance.
Though the literature has analyzed the performance of Islamic mutual funds, ours,
to our knowledge, is the ?rst study that compares them to traditional unconstraint
investment on the bases of ef?ciency: which types of mutual funds provide the highest
level of outputs (returns) conditional on inputs (risk).
One of the major advantages of using data envelopment analysis (DEA) is that it
allows for multiple inputs and outputs to be included into a production framework while
still offering a single performance index. This in turn, allows easy comparison between
funds and thereby groups. Furthermore, the speci?cation of the models under DEA
allows for endogenous derived inputs and outputs weights which make this type of
models appealing (Glawischnig and Sommersguter-Reichmann, 2010). We apply two
types of DEA methods to our sample: a radially driven input-oriented measure, or the
BCC’s model, as well as a non-radially driven input-oriented measure, or the Russell’s
model.
Overall, our results are consistent with prior literature. Islamic funds do not seem to
lose ef?ciency despite their smaller asset universe. Furthermore, results are also robust
to different speci?cations of:
.
the asset universe; and
.
DEA model.
In lieu of the 2007-2008 US ?nancial crisis, we revise if the higher performance of
Islamic mutual funds is due their exposure to lower levels of risk; we ?nd that Islamic
investment is remarkably ef?cient regardless of the time period.
The remaining of this paper is structured as follows. Section 2 discusses the
previous literature. Section 3 brie?y explains further rationales to use DEA as well as
stating the relevant models[2]. Section 4 discusses the data. Section 5 shows the
empirical results of two DEA models. Section 6 checks the robustness of results to
different subsamples that accommodate the latest ?nancial crisis. Finally, Section 7
shows the summary and conclusions.
2. Previous literature
There are several studies whichfocus onIslamic ?nance especiallyafter the introductionof
several Islamic indices such as: the Dow Jones Islamic market index (DJIMI) which was
launched in 1999; FTSE Global Islamic Index Series (GIIS) which was launched at the end
Performance
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of 1998; MSCI global Islamic indices; and the Global Gulf Cooperation Council (GCC)
Islamic indexwhichwas launchedin2006. The maintheme of these studies is toinvestigate
whether there is a cost in adhering to the Shariah law. Some studies ?nd Islamic investing
affects performance, while others ?nd otherwise.
Elfakhani et al. (2007) ?ndings suggest that there is no statistical evidence of any
performance differences between Islamic funds and the employed market benchmarks.
However, their ?ndings suggest that Islamic mutual funds do offer a good hedging
opportunity against market downturns. Abdullah et al. (2007) apply Sharpe index and
adjusted Sharpe index, Jensen Alpha, timing and selectivity ability to Malaysian mutual
funds and ?nd that Islamic funds performed better than conventional funds during
bearish economic trends while, conventional funds showed better performance than
Islamic funds during bullish economic conditions.
Mansor and Bhatti (2011) study the monthly performances of 128 Islamic mutual funds
(IMFs) in Malaysia for the period of January 1990 to April 2009. They employ Sharpe,
Treynor and Jensen ratios to the risk-adjusted return performance based on extended
version of CAPM model. They ?nd on average IMFs in Malaysia outperform its
conventional peers and the market portfolio proxy by the KLCI returns. Shah et al. (2012)
showthat Pakistani Islamic funds, when compared to Pakistani non-Islamic funds, present
a lower average risk rate with higher compensations. Surprisingly, the authors also ?nd
Islamic funds are even better diversi?ed than conventional mutual funds.
Hoepner et al. (2009) ?nd mixed evidence on the performance of Islamic mutual funds.
They ?nd that Islamic funds from eight nations (mostly from the Western regions)
signi?cantly underperform their respective equity market benchmarks and Islamic funds
from only three nations outperform their respective market benchmarks. Furthermore,
they ?nd that Islamic funds fromthe GCCand Malaysia do not signi?cantly underperform
their respective market benchmarks. Finally, theyargue that Islamic equityfunds can offer
hedging opportunities because their investment universe is limited to low debt-to-equity
ratio stocks.
Donia and Marzban (2010) conclude that Shariah-compliant investments outperform
conventional investments using the mean-variance frontier because the former bene?ts
from the lower leverage feature. Also, Majid and Maulana (2010) apply a non-parametric
performance measure to assess performance and ?ndsigni?cant ef?ciencyof Islamic funds,
but they limit their study only to Indonesia.
Hassan et al. (2010) provide a case study on Malaysian Islamic unit trust funds. Their
?ndings show that there are no convincing performance differences between Islamic and
non-Islamic Malaysian unit trust funds.
Girard and Hassan (2008, 2012) study the performance of several Islamic indexes and
compare them with non-Islamic equivalents. They use parametrical methods such as
Sharpe ratio, Jensen and Fama’s selectivity, net selectivity, diversi?cation, and Carhart’s
(1997) four factor pricing model and ?nd that there is no signi?cant difference between the
Islamic and non-Islamic indexes.
BinMahfouz and Hassan (2012) conclude that the assumption that Shariah investment
constrains lead to inferior performance and riskier investment portfolios because of limited
investment universe seems to be rejected. This implies that Muslim investors can choose
Islamic investments that are consistent with their beliefs without being forced to either
sacri?ce performance or become exposed to higher risk.
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3. Non-parametric estimations
Since alternative investments or ?nancial assets have different statistical properties,
estimating a good performance index is a dif?cult task due to the different characteristics
of assets returns, such as skewed return distributions with fat tails. Because of this, it is
expected that parametrical performance measurements fail when accounting distributions
that present non-normal characteristics. We expect that use of non-parametric econometric
method, such as DEA, will add value to prior literature.
We expected that DEA will contribute a sound estimation of performance indexes
as well as a better explanation of the risk-return relationship. In this context, DEA
offers a good perspective as it accounts for multiple inputs and outputs simultaneously
while still offering a single real number as a performance index. DEA assumes a
production framework on which one uses inputs to produce outputs where inputs are
de?ned as bearers of risk while outputs are bearers of wealth.
Prior literature reveals that input candidates should re?ect investment risk, which is
proxied by the return momentums. Under normality, only the mean return and its
standard deviation will suf?ce. However, if distributions are non-normal, then higher
momentums should be required. Thus, the next section focuses on testing normality of
returns.
3.1 Normality testing
In order to measure normality, this paper employs the Jarque Bera ( JB) test statistic,
de?ned in equation (1). Normality is rejected when JB
j
is larger than 5.99 for the
5 percent signi?cance level and 9.21 for the 1 percent signi?cance level:
JB
j
¼
T
6
S
2
j
þ
K
2
j
4
" #
ð1Þ
where:
S
j
¼
E
j
ðr
t
2r
d
Þ
2
s
2
j
; the skewness of monthly returns of fund j
K
j
¼
E
j
ðr
t
2r
d
Þ
4
s
4
j
23; the excess kurtosis of monthly returns of fund j
r
t
, monthly return.
r
d
, average returns.
s
j
, standard deviation.
3.2 Inputs and outputs description
The speci?cation of the input-output model is given by the risk-return relationship.
In this case, all risk measures are considered as inputs while all return measurements
will be considered outputs. The input candidates are given by the fund’s standard
deviation, the lower partial momentums (LPM), and maximum drawdown period. The
output candidates are expected returns, the upper partial momentums (UPM ), and the
maximum period of consecutive gain.
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The partial momentums, both upper and lower, are estimated as the m
th
root of the
LPMs and UPMs given by equation (2), in percentages. The paper uses r
min
as the
mean return to differentiate between the downside and the upside of the investment
strategy. While the LPMs capture the downside or risk of holding a speci?c investment
asset, the UPMs will capture the upside or bene?t of the investment. Finally, UPM0 is
disregarded while LPM0 is further used; LPM0 is the percentage return of funds below
the target rate[3]:
LPM
j;m
¼
1
T
X
~
T
t¼1
ðr
min
2r
t;j
Þ
m
; m ¼ 0; . . . ; 4
UPM
j;m
¼
1
T
X
T
_
t¼1
ð r
t;j
2r
min
Þ
m
; m ¼ 0; . . . ; 4
ð2Þ
where:
r
min
, target rate.
r
t;j
, monthly return of fund j below target rate.
~
T, number of returns of fund j below target rate.
r
t;j
, monthly return of fund j above target rate.
T
_
, number of returns of fund j above target rate.
The maximum drawdown period (MDP) is estimated as the maximum number of
months that fund j has been below historically high net asset value (NAV). On the other
hand, the remainder outputs are the funds expected return, E(r
j
), and the maximum
number of months fund j has been above the minimum target rate, or MCG.
3.3 The input-output DEA model
Prior literature has shown that the input-oriented BCC (Banker et al., 1984) with radial[4]
inputs is the dominatingmethodto estimate fundperformance. Accordingto Glawischnig
and Sommersguter-Reichmann (2010), the use of the BCC model can be justi?ed because:
.
as the CCR (Charnes et al., 1978) model and the output-oriented BCC model are
not translation invariant[5] towards outputs, the input-oriented BCC model is
often the metric of choice;
.
the assumption of variable returns to scale (VRS) is justi?ed by the fact that
alternative investment funds might operate in regions of increasing or
decreasing return to scale due to, for example, minimum investment
requirements or ?xed cost digression; and
.
the use of the BCCmodel is advisable whenever ratios are usedas inputs or outputs.
Having identi?ed the input-output speci?cations, we estimate a frontier (the production
possibility frontier (PPF)) to the production possibility set (PPS) that envelops the PPS
as tightly as possible. When comparing the DEA frontier with standard portfolio
theory (the Markowitz portfolio theory) the DEA frontier is essentially the same but
with a different approach. The DEA frontier is resulting from the convex combination
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of the best practices[6] followed by the industry given the multiple hyperplanes
resulting from the use of multiple inputs and outputs; thereby making it is possible to
construct a performance index based upon the distance between speci?c funds and the
constructed frontier.
Formally, it is assumed that there are j ¼ 1, . . . , N funds where each uses x
m
;m ¼
1; . . . ; M inputs to produce y
r
;r ¼ 1; . . . ; R outputs. Then the performance for the k
th
fund, p
BCC
, is estimated by the linear program (LP) given by equation (3):
p
BCC
¼ minu s:t:
X
N
j¼1
x
mj
l
j
# u · x
mk
;m ¼ 1; . . . ; M
X
N
j¼1
y
rj
l
j
# y
rk
;r ¼ 1; . . . ; R ð3Þ
X
N
j¼1
l
j
¼ 1 with l
j
$ 0;j; m; r
The LP given in equation (3) represents the percentage of ef?ciency of each particular
fund k. equation (3) minimizes the equiproportionate (radial) contraction u of the inputs
produced by unit k. The performance index, P
BCC
, satis?es P
BCC
# 1 where P
BCC
¼ 1
represents a fund which is 100 percent ef?cient. That is, given the input-output
combination which characterizes the best practice frontier, P
BCC
¼ 1 represents
the k
th
fund which is on the actual frontier and thus the fund is ef?cient. Any deviation
from the PPF, given by P
BCC
, 1, will result in inef?ciencies. Furthermore, the LP uses
exogenous weights, l
j
, to ?t the best linear combination of all funds given a speci?c
input-output combination; l
j
– 0 represents the best practice units that delimit the
frontier.
As with every liner program, equation (4) shows a dual to the primal in equation (3).
The dual is helpful as it also estimates the number of inputs and outputs used in the
production framework. In this case, the weights m
r
and v
m
represent which particular
inputs/outputs are incorporated into the fund performance index estimation. The dual
P
BCC
is estimated using the endogenously derived weighs on the m ¼ 1, . . . , M inputs
and r ¼ 1, . . . , R outputs instead of applying the weights onto the funds as in
equation (3). From the economic stand point, the ef?cient funds should have all inputs
and outputs incorporated when estimating the fund performance index to include the
investor’s gain given the risk exposure. Finally, the variable m
0
in the dual LP (4) is free
and guaranties VRS (Glawischnig and Sommersguter-Reichmann, 2010, footnote 12):
P
BCC
¼
v
m
;m
r
;m
0
max
X
R
r¼1
m
r
y
rk
þm
0
s:t:
X
R
r¼1
m
r
y
rj
2
X
M
m¼1
v
m
x
mj
þm
0
# 0 ;j ¼ 1; . . . ; N ð4Þ
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X
M
m¼1
v
m
x
mk
¼ 1
m
r
; v
m
$ 0 and m
0
free
Alimitation of the BCCmodel is that it assumes all inputs to be radial. But the possibility
of non-radial inputs exists. Thus, the results are checked using an input-oriented
non-radial model, P
Russell
. This model incorporates non-proportional input reductions
using data driven lower bounds regarding input weights under VRS. In other words, the
model does not assume a constant u common for all inputs. Instead, it weights each input
independently and then estimates the overall performance of the index as the sumof the
individual weights. Again, ef?ciency is achieved when P
Russell
¼ 1. Formally:
P
Russell
¼ min
P
M
m¼1
u
m
M
s:t:
X
N
j¼1
x
mj
l
j
¼ u
m
· x
mk
;m ¼ 1; . . . ; M
X
N
j¼1
y
rj
l
j
# y
rk
;r ¼ 1; . . . ; R ð5Þ
X
N
j¼1
l
j
¼ 1 with l
j
$ 0;j; r and u
m
# 1
4. Data description
In this section, the DEA models described in Section 3 are estimated based on a
comprehensive data set of mutual funds. Two datasets are employed to form the fund
universe. The fund universe is de?ned as the merger between Saudi Arabia funds
(which proxy for Islamic investments), International funds, and American funds.
Initially, the fund universe consists of 45096, from which 42,340 are regarded as
American, 2,614 are International, and only 142 are Islamic.
For the Islamic funds, a sample data consisting of daily NAVs of 143 out of
234 mutual funds available in Saudi Arabia during the period from January 2003 to
December 2010 is selected. Information on these funds is obtained from three main
sources: the of?cial site of the Saudi Stock Exchange (Tadawul) (www.tadawul.com.
sa), the of?cial site of HSBC Saudi Arabia Limited (www.hsbcsaudi.com), and Zawya
database[7]. Because the data on Islamic funds is not continuous, a one month holding
period return estimated at the end of the month is computed.
Additionally, we take data from CRSP to account for the remaining funds.
International funds are de?ned as those funds listed in CRSP with objective code
“International Fund,” “International,” or “IF.” Finally, everything else is de?ned as
American funds. Only monthly returns as well as monthly NAV’s from CRSP for the
period of January 1999 to September 2011 are considered. For robustness check, CRSP
sample data is restricted to match Islamic funds data sample.
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Furthermore, funds employed in the sample are only those which have continuous
returns data with at least two years’ worth of observations. That is, those funds which
have complete years (no missing monthly returns or NAV), and no missing years in
between the series. After controlling for this, the sample reduces to 20,946 American
funds, 1,504 International funds, and only 95 Islamic ones.
The effective asset universe then results in 56 percent of the original Islamic funds,
51 percent of American funds, and 57 percent of International funds. Despite the high
reduction of the data universe, we still expect to get more robust results as most of
surviving funds will be accounted for.
5. Empirical results
5.1 Normality testing
Based on the information provided in Section 3.1, in this section, equation (1) is tested to
check whether or not the returns show normality. Two types of testing groups are
de?ned: the whole universe and independent individual subgroups. Table I summarizes
the results. When the whole fund universe is considered, only about 34 percent of returns
can be considered as normally distributed with a 95 percent con?dence level.
Moreover, when analyzing individual subgroups, each group is analyzed
independently; it is observable that Islamic returns show the highest normality
results, with around 50 percent of funds following normality. This is quite a puzzle,
since it is expected that American returns to be closer to normality, per the Central
Limit Theorem, as there are more observations for American funds than there are for
International and Islamic funds. However, these results pave the way for future
measurements of DEA based performance indexes that include higher momentums,
especially when the fund universe is considered.
5.2 Inputs and outputs speci?cations
Based on Section 3.2., the different input and output candidates are estimated. Following
the literature, the correlation of the different inputs and outputs to de?ne a suitable
production framework for the BCC model is investigated. This paper uses such
production framework on which risk and return are positively correlated, thus requiring
inputs and outputs to be positively correlated. Therefore, the inputs MCG and
LPM0-LPM4, as well as the outputs MDP and UPM1-UPM4 are initially considered.
Total number of funds 5% signi?cance 1% signi?cance
Fund universe 22,545 7,829 9,090
(34.72%) (40.31%)
American funds 20,946 7,127 8,302
(34.02%) (39.63%)
International funds 1,504 654 716
(43.45%) (47.57%)
Islamic funds 95 48 72
(50.52%) (75.78%)
Note: The table shows how many funds are normally distributed with the corresponding percentage
of the group
Table I.
The JB test statistic for
normality of time series
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The forth momentums, LPM4 and UPM4, are disregarded due to the extreme high
correlations; LPM3 and LPM4 as well as UPM3 and UPM4 show a correlation greater
than 0.999[8]. Still, using the third momentum is enough to apply an extra penalty
(bonus) to funds with extremely low (high) returns. Table II summarizes the
descriptive statistics of the input-output speci?cations considered for the production
framework used in further tests.
It is worthwhile mentioning that it is striking that there are funds among the fund
universe that achieve 100 percent on LPM0. That means that there are funds that have
had only returns below average (LPM0 ¼ 1) during the time window of the study.
Further analysis between the subgroups, when each group is analyzed independently,
shows that these funds come from the American and Islamic subsamples. In addition,
it comes as no surprise that the American subsample is quite similar to the fund
universe, as the American subsample accounts for almost 93 percent of the data.
Further analysis of Table II gives additional information about the performance of
each of the subsamples. It is observable that the International subgroup has the best
performance, followed by the Islamic funds and ?nally the American funds. As
International funds show the smallest average input values with the highest average
output values as well as the smallest maximum drawback period.
The only estimate on which the Islamic funds show superiority comes from the
maximum consecutive gain. Not only is the mean MCG remarkably higher for Islamic
funds (63 months compared to 1.5 months for American funds and one month for the
International subgroup), the minimum and maximum values are quite impressive as
well. That is, while the minimum MCG for the Islamic funds (24 months) is well above
the minimum MCG for both American and International funds (0 months for both,
respectively), the maximum MCG for the Islamic funds (84 months) is astonishing
MDP
(months)
LPM0
(%)
LPM1
(%)
LPM2
(%)
LPM3
(%)
MCG
(months)
UPM1
(%)
UPM2
(%)
UPM3
(%)
Panel A: the fund universe
Minimum 1 0.125 0.0012 0.0028 0.0035 0.0000 0.0000 0.0000 0.0000
Maximum 96 1 0.1166 0.1834 0.2386 10.0000 0.1274 0.1799 0.2160
Mean 33.1261 0.4718 0.0175 0.0347 0.0486 1.4912 0.0185 0.0306 0.0393
SD 25.0836 0.1095 0.0091 0.0169 0.0233 1.4573 0.0115 0.0175 0.0220
Panel B: American funds
Minimum 1 0.125 0.0012 0.0028 0.0034 0.0000 0.0000 0.0000 0.0000
Maximum 96 1 0.1165 0.1833 0.2385 10.0000 0.1275 0.1800 0.2160
Mean 33.4684 0.4697 0.0170 0.0338 0.0474 1.5342 0.0180 0.0298 0.0383
SD 25.5837 0.1094 0.0091 0.0169 0.0233 1.5026 0.0115 0.0175 0.0221
Panel C: International funds
Minimum 1 0.2917 0.0087 0.0145 0.0215 0.0000 0.0043 0.0140 0.0220
Maximum 64 0.8333 0.0645 0.1152 0.1542 4.0000 0.0507 0.0890 0.1171
Mean 29.0705 0.4721 0.0243 0.0468 0.0651 1.0007 0.0250 0.0416 0.0528
SD 16.2616 0.0470 0.0060 0.0090 0.0116 0.2861 0.0064 0.0091 0.0104
Panel D: Islamic funds
Minimum 4 0.3452 0.0020 0.0024 0.0026 24.0000 0.0000 0.0000 0.0000
Maximum 83 1 0.0595 0.1137 0.1534 84.0000 0.0506 0.0873 0.1244
Mean 33.6526 0.6781 0.0208 0.0412 0.0569 63.9474 0.0194 0.0343 0.0452
SD 17.1121 0.2498 0.0176 0.0351 0.0483 21.7556 0.0186 0.0319 0.0421
Table II.
The descriptive statistics
of the proposed
input-output speci?cation
used to estimate the DEA
performance index
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higher than the maximum MCG for both the American and International subgroups
(ten and four months, respectively).
5.3 The fund universe performance
In this section, the performance of the overall fund universe is estimated and then it is
comparedtoeachindividual subgroup. Inother words, the DEAef?ciencyfrontier basedon
the fund universe is estimated and then each subgroup is compared to the estimated
frontier. Table III summarizes the ?ndings. The overall ef?ciency of the fund universe is
estimate based on equation (3) (panel A) and equation (5) (panel B). That is, the fund
performance indexis estimatedbasedonradial inputs, P
BCC
, andnon-radial inputs, P
Russell
.
At ?rst glance, it is found that ef?ciency is highly penalized under the assumption of
non-radial inputs. This might be driven by the non-proportional input reduction
condition on the Russell’s model which applies higher penalties to different inputs. The
question of whether a radial or non-radial production framework should be assumed
remains unanswered because it is beyond the scope of this paper. The main focus of this
paper is to investigate which speci?c subset is more ef?cient than the other. Thus, the
difference amongst groups, rather than the difference amongst methods is analyzed.
Focusing on panel A, results indicate that 3,944 funds out of the whole fund
universe can be considered as ef?cient, which accounts for 17.49 percent of all funds.
Granted, the majority of them are American, 3,587 funds accounting for 90 percent of
all ef?cient funds. Yet when comparing them to their own subsample, they only
account for 17.12 percent. That is, about 17 percent of American funds can be
considered ef?cient with respect to the PPF which envelops the whole fund universe.
In fact, American funds seem to be the least ef?cient of all three subsamples.
International founds account for 320 ef?cient funds, or 21.28 percent of their
subgroup while Islamic funds account for 37 ef?cient funds, or 39 percent of all Islamic
funds. Thus, it is observable that there are more ef?cient funds within the Islamic
subsample than either the American or International subsamples. These results are
consistent even to different comparisons.
Because BCC provides an actual performance index, it is possible to estimate the
average performance of each subgroup and then compare each fund to the proposed
Panel A: P
BCC
Panel B: P
Russell
No of
funds
Ef?cient
funds
Average
(%)
Funds above
average
Ef?cient
funds
Average
(%)
Funds above
average
Fund
universe
22,545 3,944 52.00 8,574 6 27.52 8,431
(17.49%) (38.03%) (0.03%) (37.39%)
American
funds
20,946 3587 52.47 8,149 4 27.85 8,007
(17.12%) (38.90%) (0.02%) (38.23%)
International
funds
1,504 320 44.84 339 0 21.55 362
(21.28%) (22.54%) (0.00%) (24.07%)
Islamic
funds
95 37 60.89 38 2 47.16 38
(38.95%) (40.00%) (2.11%) (40.00%)
Notes: The American, International, and Islamic subsets are compared to the PPF based on the whole
fund universe; the percentages in parenthesis correspond to the fraction of ef?cient funds or funds
above average with respect to its subgroup
Table III.
The estimation of
equation (3), panel A, and
equation (5), panel B,
based on the whole fund
universe
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performance index. It is worthwhile mentioning that the Islamic subgroup shows the
highest average performance, 60.89 percent, followed by the Americanand International
funds with 52.47 and 44.84 percent average performance, respectively. Finally, Islamic
funds also show the highest ef?ciency levels when measuring the number of funds
above average. Islamic funds lead with 38 ef?cient funds above average, or 40.0 percent
of their subgroup, followed bythe American andInternational funds with 8,149 funds, or
38.9 percent of the subsample, and 339 funds, or 22.54 percent of the subsample,
respectively.
Likewise, the non-radial model on panel B con?rms observed results, despite a
penalty imposed on the estimation. Though the number of actual ef?cient funds drops
considerably, we ?nd the same dominance by Islamic funds. Around 2 percent of Islamic
funds are ef?cient, while only 0.02 percent of American funds are ef?cient and no
International funds are ef?cient. As for the average performance and number of funds
above average, the results are consistent with the estimation under the BCC model; the
average performance is quite smaller but the number of funds above average remains
similar to the results in panel A.
Despite the limitation on Islamic funds due to investing only in Shariah compliant
assets, the results suggest that such assets do not loose ef?ciency when comparing themto
more “free investment” opportunities. In fact, Shariah investments seem to be even better
than those traditional investment strategies. Overall, our results indicate that when
comparing individual subgroups to the whole envelop of the DEA performance index,
Islamic funds seemto dominate the ef?ciencymeasures. Taken together withthe results on
Table II, one can consider Islamic funds to be a solid investment alternative, if not the best.
Still, a question remains on whether Islamic mutual funds together with other
investment assets should be analyzed. This is because those who invest in Islamic
assets are not going to invest in non-Shariah compliant assets in any case. In other
words, when analyzing Islamic investments, the fund universe should be limited to
only Islamic assets, since Islamic investors will not even consider investing in assets
that are not Shariah compliant. The following section analyzes individual subgroups
independently of one another.
5.4 Independent subgroups
Because Islamic investors are constraint for non-Shariah investment, it is logical to
study Islamic mutual funds independently. In this section, the ef?ciency of the
individual subgroups is investigated. However, results for the American subgroup are
not included due to their similarities with those for the fund universe. Both DEA
methods are applied, the radial and non-radial inputs, to the individual subgroups:
International funds and Islamic funds. Moreover, results of equation (4) are included to
analyze the input-output composition of the radial input BCC.
Table IV summarizes the results of the BCC model for the fund universe and both
International and Islamic subgroups. The results suggest that when limiting the
universe to their own subgroup thus reshaping the PPF, the International and American
funds gain little ef?ciency while the Islamic subgroup remains the same; the number
of ef?cient International and American funds increases from 320 to 338 and 3,587 to
3,590, respectively, but the number of ef?cient Islamic funds stays on 37.
However, the most signi?cant result comes fromthe increase onthe average performance
of Islamic funds when their PPS is limited to account only for their own subgroup:
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while American funds decreased from 52.47 to 51.74 percent and International funds
increased from 44.84 to 80.01 percent, Islamic funds increased from 60.89 to 92.60 percent
which is magni?cently high. Moreover, even the number of funds above average increases
for the Islamic subgroup from 40 to 61 percent. Overall, it can be concluded that despite
the limitations of the asset universe faced by Islamic funds, they are most ef?cient than
their counterparts.
As a comparison benchmark for ef?ciency, Table V shows similar results under the
non-radial production framework. The trend is quite similar to those of the
input-oriented BCC model. Results show a higher number of ef?cient Islamic funds
(8 or 8.42 percent of their subgroup), compared to the number of ef?cient International
funds (9 or 0.6 percent of their subgroup), and ef?cient American funds (11 or
0.05 percent of their subgroup). The average performance is also consistent with the
prior results giving the highest average performance to the Islamic funds with an
average ef?ciency of 68.05 percent followed by the International and American
counterparts with an average of 50.93 and 27.74 percent, respectively.
It is noteworthy to mention that the use of individual subgroups shows a
remarkable increase on ef?ciency under equation (5), the non-radial production
framework. While the results of the radial model under either the full universe PPF or
Total number
of funds
Number of ef?cient
funds P
BCC
¼ 1
Expected
ef?ciency (%)
Number of funds
above average
Fund
universe
22,545 3,944 52.00 8,574
(17.49%) (38.03%)
American
funds
20,946 3,590 51.74 7,658
(17.14%) (36.56%)
International
funds
1,504 338 80.01 664
(22.47%) (44.15%)
Islamic funds 95 37 92.60 58
(38.95%) (61.05%)
Note: The percentages in parenthesis correspond to the fraction of ef?cient funds or funds above
average with respect to its subgroup
Table IV.
The results from
equation (3), the radially
driven input-oriented
model, based on the fund
universe and the
independent subgroups
(each subgroup has its
own PPF)
Total number
of funds
Number of ef?cient
funds P
Russell
¼ 1
Expected
ef?ciency (%)
Number of funds
above average
Fund
universe
22,545 6 27.52 8,431
(0.03%) (37.40%)
American
funds
20,946 11 27.74 8,028
(0.05%) (38.33%)
International
funds
1,504 9 50.93 504
(0.6%) (33.51%)
Islamic funds 95 8 68.05 47
(8.42%) (49.47%)
Note: The percentages in parenthesis correspond to the fraction of ef?cient funds or funds above
average with respect to its subgroup
Table V.
The results from
equation (5), the
non-radially driven
input-oriented model,
based on the fund
universe and the
independent subgroups
(each subgroup has its
own PPF)
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the self-group-limited-universe PPF are quite close. For instance both show 37 ef?cient
Islamic funds, assuming the latter changes the results considerably when assessing a
non-radial production framework. All the studying parameters (number of ef?cient
funds, average performance, and number of funds above average performance) seem
considerably higher when limiting the universe to the speci?c subgroups. Still, despite
the increase in all subgroups, Islamic funds are still the most ef?cient.
5.5 Speci?cs of the inputs and outputs
By using a dual programming to equation (3), it is possible to compare the number of
inputs and outputs being used to analyze the production framework. This subsection
focuses on the BCC model since it is the model of choice in prior literature[9]. It is
expected that ef?cient funds would incorporate as few inputs as possible in order to
produce as much outputs as possible. Yet, it is found that a signi?cant number of
ef?cient funds are unable to generate any output whatsoever. Table VI summarizes the
results.
Panel Ashows the input-output mix for the fund universe. Results indicate that there
are 3,886 ef?cient funds, which accounts for 17 percent of all funds. Further analysis
shows that neither ef?cient nor inef?cient funds could incorporate all inputs together. In
fact, the majority of funds could only use a maximum of three inputs at the same time
(of a maximum of ?ve), and only a few could even achieve four inputs simultaneously.
Examining the outputs, on the other hand, showthat ef?cient funds can achieve more
outputs than inef?cient funds. For instance, almost 5 percent of ef?cient funds, that is
194 funds, can achieve three outputs (of a maximum of four) simultaneously compared
to only one fund achieving the same number of outputs for the inef?cient funds. In
addition, only ef?cient funds can achieve the maximum number of outputs, although
they account for less than 0.1 percent of ef?cient funds. Despite the highest performance
of ef?cient funds, there is still some inef?ciency within them. That is, 37.3 percent of
ef?cient funds cannot achieve any output at all. What is more puzzling, however, is that
there are less funds with zero outputs, 31.5 percent, coming from the inef?cient
subsample.
Inputs Outputs
Number of funds 1 2 3 4 5 0 1 2 3 4
Panel A: fund universe
Inef?cient 18,659 817 15,062 2,756 24 – 5,886 9,410 3,362 1 –
Ef?cient 3,886 1,486 725 1,649 26 – 1,450 828 1,411 194 3
Panel B: American funds
Inef?cient 17,417 3,133 12,121 2,153 10 – 10,476 4,901 2,040 – –
Ef?cient 3,529 1,096 964 1,465 4 – 1,058 1,883 473 104 11
Panel C: International funds
Inef?cient 1,177 249 927 1 – – 43 1,076 58 – –
Ef?cient 327 107 9 188 23 – 54 94 178 1 –
Panel D: Islamic funds
Inef?cient 66 1 22 39 4 – 12 39 12 3 –
Ef?cient 29 5 11 12 1 3 10 10 6 –
Notes: Table VI shows the input-output combination used in the production process; it also shows
production inef?ciencies given by the number of funds with zero outputs
Table VI.
The results from
equation (4), the dual to
the radially driven
input-oriented model,
based on the fund
universe and the
independent subgroups
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Though panel A shows important results, other panels show further means to
comparing ef?ciency between Islamic, International, and American funds. At ?rst
inspection, there seems no signi?cant difference in the input mix between the subgroups,
but results do indicate that only American ef?cient funds can achieve the maximum
number of outputs. Note that the same pattern presented in panel A is con?rmed:
.
most funds, regardless if they are ef?cient or inef?cient, use a maximum of three
inputs; and
.
even ef?cient funds present some level of inef?ciency due to the presence of
funds that produce zero outputs.
Deeper examination of Table VI shows that Islamic funds can still be considered better
performing than their counterparts. Results show that 30.5 percent of Islamic funds can
be regarded as ef?cient with inef?ciencies accounting for only 10.3 percent, whereas
21.7 percent of International funds are ef?cient with inef?ciencies of 16.5 percent, and
only 5.2 percent of American funds are ef?cient with inef?ciencies accounting for
almost 30 percent. In this context, inef?ciencies are regarded as the percentage of
ef?cient funds which produced zero-outputs.
Overall, results suggest that Islamic mutual funds do not lose ef?ciency even though
they are limited to a smaller universe of assets. Perhaps a possible explanation for such
ef?ciency gain is that despite limitations, Islamic investors are ethically driven and thus
theyprefer to avoidinvestingonto the most riskyassets. Therefore, these results might be
biases in favor of Islamic funds due to the fact that the latest 2007-2008 crisis was mainly
driven by excessive investment onto risky assets (Gorton, 2010). Such results are also
consistent with ?ndings of Merdad et al. (2010) who compared Islamic and conventional
mutual funds managed by HSBC, the fourth largest fund manager in Saudi Arabia, from
January 2003 to 2010. They show that Islamic funds underperform conventional funds
during both the full sample period and the bullish period, but outperform conventional
funds during bearish and ?nancial crisis periods. The next section covers this issue by
splitting the dataset in order to account for the 2007-2008 ?nancial crises.
6. Robustness check
The 2007-2008 ?nancial crisis swept through globally, and thus it is expected to have
affected worldwide assets. However, due to the constraints on Shariah law, it is
believed that Islamic funds have been somehow immunized to the effects of the crisis,
which would explain their higher ef?ciency compared to their counterparts. Therefore,
in this section, equation (3) is estimated based on the re-estimation of the inputs and
outputs to account for the ?nancial crisis.
As before, results are presented based on the full universe PPF and individual
groups PPF for the BCC model. The same input/output combinations proposed in the
prior section are still used, but they are now estimated based on two subsamples:
January 2003 to December 2006 and January 2007 to December 2010. This generates
two subsamples with different number of funds. The pre-crisis subsample accounts for
14,509 funds in the fund universe from which 13,589 are American, 843 are
International, and 77 are Islamic, while the post-crisis subsample, which is fairly
similar in number of funds in the whole sample, has 22,531 assets in the fund universe
from which 20,932 are American, 1,504 are International, and 95 are Islamic.
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6.1 The fund universe performance
As before, a PPF is de?ned as that which envelops all assets in the universe and then
each subgroup is compared to the proposed PPF. Table VII summarizes the results. As
expected, there is a decrease on ef?ciency as the crisis starts. Although all subgroups
are affected, American funds remain quite the same. In fact, only a decrease of
0.53 percent on the percentage of ef?cient American funds is observed, while
International and Islamic both have a decrease of 18.7 and 9.1 percent, respectively.
Furthermore, results show a signi?cant decrease on the average performance as well as
number of funds above average performance consistent for all funds.
Still, when comparing the funds with one another, the same results are found;
Islamic funds outperform their counterparts regardless of the subsample period. In
fact, sorted by ef?ciency, the order remains the same regardless of the time period:
Islamic funds followed by International funds and American funds at last. Although
the order changes when comparing average performance and the number of funds
above average, it can be safely concluded that Islamic funds are still more ef?cient
despite the ?nancial crisis.
It is worthwhile noting that though the number of ef?cient Islamic funds is the same
regardless of the time period (37 funds), they are not all the same funds. In fact, results
indicate that ?ve funds differ; that is, ?ve funds stopped being ef?cient and ?ve started
being ef?cient after the crisis.
6.2 Subgroups performance
We estimate PPF for each group and then compare their performances. This is done
with the rational that Islamic investment is self-constraint to a limited asset universe
and thus it makes sense to limit the PPF which will only envelop such assets. Table VIII
summarizes the results.
Once again, prior results are con?rmed at the ?rst glance; Islamic funds are always
the most ef?cient regardless of the time period followed by International and American
funds. However, focusing on panel A, it is noticeable that International and Islamic
funds have more ef?cient funds when the PPF is limited to their own subgroup. This
result shows that the post-crisis decrease is even more signi?cant.
Panel A: 2003-2006 Panel B: 2007-2010
No of
funds
Ef?cient
funds
Average
(%)
Funds
above
average
No of
funds
Ef?cient
funds
Average
(%)
Funds
above
average
Fund
universe
14,509 2,792 73.10 5,934 22,531 3,969 46.32 7,176
(19.24%) (40.90%) (17.62%) (31.85%)
American
funds
13,589 2,418 73.00 5,596 20,932 3,612 46.66 6,778
(17.79%) (41.18%) (17.26%) (32.38%)
International
funds
843 337 74.40 340 1,504 320 40.93 320
(39.98%) (40.33%) (21.28%) (21.28%)
Islamic
funds
77 37 76.93 42 95 37 58.07 38
(48.05%) (54.55%) (38.95%) (40.00%)
Notes: This estimation is based on the whole fund universe; the American, International, and Islamic
subsets are compared to the PPF based on the whole fund universe; the percentages in parenthesis
correspond to the fraction of ef?cient funds or funds above average with respect to its subgroup
Table VII.
The estimation of
equation (3) for the two
subsamples: 2003-2006 on
panel A and 2007-2010
on panel B
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Further analysis shows that Islamic funds lost average performance lead to International
funds after the crisis. While panel A shows an Average performance of 93.69 percent
for Islamic funds and 91.48 percent for International funds, panel B gives the lead to
International funds with 69.32 percent followed by Islamic funds with 62.88 percent.
Yet the number of above average performance funds is still higher for Islamic funds.
Deeper examination reveals that all Islamic ef?cient funds are the same regardless
of the PPF speci?cation for the post-crisis subsample. This is an extra robustness
check as this incorporates both speci?cation of the PPF or time period. This also
suggests that even if Islamic investors where to open themselves towards the whole
asset universe, they will not achieve any extra ef?ciency. In fact, Islamic funds appear
as ef?cient as if they were part of the whole asset universe.
7. Summary and conclusions
The main purpose of this paper is to investigate whether or not Islamic funds loose
ef?ciency due to investment limitations towards Shariah compliant assets. With this
purpose, an extensive dataset with three different types of investment assets is created:
Islamic mutual funds, International mutual funds, and American mutual funds. ADEA
performance index is employed to measure ef?ciency in order to account for the fact
that different investment alternatives present different data characteristics and DEA
can account for such characteristics as it can handle multiple inputs and outputs.
Initially, a PPS that accounted for all the assets in the obtained sample is considered.
Then a PPF that envelops the whole universe of assets is created. However, Islamic
investors would not even consider non-Shariah compliant assets as investment
opportunities and thus they should not be part of their fund universe. For this reason,
PPS is limited to include only individual subgroup’s assets thereby reshaping the
overall PPF. Regardless of the frontier de?nition, ef?ciency is always de?ned as the
percentage number of funds that are on the frontier. Finally, to extend comparison
between subgroups, identifying which subgroup had the highest percentage number of
funds closer to the PPF is considered, which is measured by the percentage number of
funds above average performance.
Panel A: 2003-2006 Panel B: 2007-2010
No of
funds
Ef?cient
funds
Average
(%)
Funds above
average
No of
funds
Ef?cient
funds
Average
(%)
Funds
above
average
Fund
universe
14,509 2,792 73.10 5,934 22,531 3,969 46.32 7,176
(19.24%) (40.90%) (17.62%) (31.85%)
American
funds
13,589 2,382 71.77 57,100 20,932 3,600 46.39 6,582
(17.53%) (42.02%) (17.20%) (31.44%)
International
funds
843 354 91.48 404 1,504 330 69.32 380
(41.99%) (47.92%) (21.94%) (25.27%)
Islamic
funds
77 41 93.69 52 95 37 62.88 37
(53.25%) (67.53%) (38.95%) (38.95%)
Notes: This estimation is based on independent universes; the American, International, and Islamic
subsets are compared to the PPF based on their own universe; the percentages in parenthesis
correspond to the fraction of ef?cient funds or funds above average with respect to its subgroup
Table VIII.
The estimation of
equation (3) for the two
subsamples: 2003-2006 on
panel A and 2007-2010 on
panel B
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In summary, obtained results suggest that though Islamic funds are limited to a
smaller asset universe, they do not lose ef?ciency regardless of the speci?cation of the
PPF. Islamic funds are the most ef?cient followed by International and then American
funds. Overall, these results are persistent for the percentage number of ef?cient funds,
the average performance index, and the percentage number of funds above average
performance. Also, these results are robust to different speci?cations of the DEA
model. In this regard, two different models are analyzed:
(1) an input-oriented DEA model with a proportional input framework; and
(2) a DEA model with a non-proportional input-oriented framework.
But we focus more on the BCC model, as it is the method of choice in prior literature.
Even though results indicate that there is some level of inef?ciencies remaining
within the ef?cient funds, it can be safely concluded that Islamic funds remain highly
ef?cient despite their investment limitations, and they show the smallest number of
inef?ciencies amongst the subgroups.
Finally, since Islamic investors are limited to Shariah and Ethical investment, thus
preferring less risky assets, it is believed that the obtained results would be biased in
favor of Islamic investment. That is, given that the 2007-2008 ?nancial crisis originated
due to high investment on toxic assets and Islamic investor would rather avoid them,
it is expected that Islamic funds be somehow immunized to the effects of the crisis.
Results show evidence suggesting that even though all assets lost ef?ciency and
average performance, Islamic funds remain the most ef?cient.
On a practical perspective, regardless of the investment preference, our results
indicate that Islamic funds are an effective investment opportunity. Non-Muslim
Investors who seek to maximize their risk-adjusted returns could highly pro?t
from diversifying towards Islamic mutual funds. While Muslin investors should
not be concerned about the opportunity cost of investing only in Shariah compliant
assets. That is, a typical investor could reduce their risk exposure by swapping
their portfolios to also include Islamic funds. In fact, since DEA allows for an
identi?cation of fullyef?cient funds, suchfunds shouldbe considered for every investor’s
portfolio. All in all, Islamic mutual funds create a highly pro?table new avenue of
investment.
Nonetheless, caution must be taken before generalizing the results due to the
limitations of the data. First, the dataset on Islamic mutual funds accounts for roughly
60 percent of all available Islamic mutual funds, thus putting an initial limitation onto
the Islamic universe sample. Second, the obtained Islamic fund universe is by far the
smallest; it only accounts for 0.4 percent of the overall fund universe, hence making it
almost irrelevant to the estimation of the fund universe’s PPF. However, the latter
concern is mitigated by studying each subgroup individually.
Notes
1. For a deep explanation on Shariah complaint assets refer to Derigs and Marzban (2009).
2. For a deeper lit review on the evolution of DEA models refer to Glawischnig and
Sommersguter-Reichmann (2010). Or for an in-depth analysis of DEA methods refer to
Cooper et al. (2000).
3. LPM0 ¼ 1-UPM0 which makes the use of both simultaneously redundant.
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4. Given the inputs (x
1
, x
2
, . . . , x
n
), they are consider radial if they increase proportionally given
an a . 0, such that the inputs increase as (ax
1
, ax
2
, . . . , ax
n
) (Cooper et al., 2000).
5. Translation invariance is meant by the fact that dealing with alternative investments is
likely that some of the outputs, such as average and minimum return, are negative.
Translation invariance of the respective DEA model towards outputs therefore becomes an
issue because DEA cannot handle negative data.
6. Best practices, in this context, refer to those funds with the highest level of outputs given the
prevailing level of inputs.
7. Zawya is one of leading Middle Eastern business information ?rms. Their main web site is:
www.zawya.com we would like to express my deep appreciation to Mr James Randall, the
International business manager, for providing me a trial excess to the database.
8. Just like Glawischnig and Sommersguter-Reichmann (2010), the results show high
correlation among LPM2 and LPM3 (UPM2 and UPM3), as well as LPM2 and LPM4
(UPM2 and UPM4). Despite that high correlation, they are still incorporated into the model
to apply an extra penalty/bene?t for higher momentums due to non-normality of returns.
9. See the introduction of Glawischnig and Sommersguter-Reichmann (2010).
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Merdad, H., Hassan, M.K. and Al-Henawi, Y. (2010), “Analysis of Islamic versus conventional
mutual funds in Saudi Arabia”, Journal of King Abdul Aziz University: Islamic Economics,
Vol. 23 No. 2, pp. 161-98.
Shah, I.U., Iqbal, J. and Malik, M.F. (2012), “Comparative valuation between Islamic and
conventional mutual fund”, International ResearchJournal of Finance andEconomics, No. 96.
Further reading
BinMahfouz, S. and Hassan, M.K. (2012), “Sustainable and socially responsible investing: does
Islamic investing make a difference?”, Managerial Finance, March 18 (in press).
Fa¨re, R. and Lovell, C.A.K. (1978), “Measuring the technical ef?ciency of production”, Journal of
Economic Theory, Vol. 19, pp. 150-62.
Jarque, C.M. and Bera, A.K. (1987), “Atest for normality of observations and regression residuals”,
International Statistical Review/Revue Internationale de Statistique, Vol. 55 No. 2, pp. 163-72.
Corresponding author
M. Kabir Hassan can be contacted at: [email protected]
ARJ
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