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ARJ
25,3 Non-parametric performance
measurement of international and
Islamic mutual funds
208
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 efficiency
due to a limited asset universe.
Design/methodology/approach – The paper contributes to prior literature by using
non-parametrical measurements of efficiency 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 findings. That is, there is strong evidence
suggesting that Islamic funds are highly efficient and that they outperform their international
counterparts. Also, results are robust to different estimation of DEA, the specification of the asset
universe, and the inclusion of financial crisis period in analysis.
Research limitations/implications – Though the paper’s findings are robust to
different specifications of the DEA model and time periods, the authors caution readers due to the
limited sample.
Practical implications – Having defined a performance index, one can therefore isolate the funds
which are the most efficient and thus drive trading activities towards said funds.
Social implications – Since the paper’s findings suggest that Islamic investors do not lose
efficiency, 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 confirm prior literature, even by using a non-parametrical
measurement of efficiency. 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 efficiency
Paper type Research paper

1. Introduction
As of April 2010, Muslims represented almost 21 percent of the world’s population with
Accounting Research Journal an estimated of more than USD 800 billion to invest, which is growing at 15 percent
Vol. 25 No. 3, 2012
pp. 208-226 annually (Girard and Hassan, 2008). Because of this, many financial institutions have
q Emerald Group Publishing Limited expanded their services to accommodate for Muslims’ religious preferences, resulting in
1030-9616
DOI 10.1108/10309611211290176 an increasing universe of Shariah compliant assets.
 Shariah, which is the moral code and religious law of Islam, rules out the Performance
consumption of alcohol and pork and activities related to gambling. As a result, Muslims measurement
should not invest in financial assets that derive their income from such activities[1]. This
results in the omission of stocks from firms such as hotels, casinos, clubs, bars, of mutual funds
restaurants, food producers, alcohol producers, etc. Moreover, Shariah compliant assets
are types of ethical investment which drive investors towards firms which have a sound
social responsibility. Thus, it can be expected that mutual fund managers who follow 209
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 diversified 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 first study that compares them to traditional unconstraint
investment on the bases of efficiency: 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 specification 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 efficiency despite their smaller asset universe. Furthermore, results are also robust
to different specifications of:
.
the asset universe; and
.
DEA model.

In lieu of the 2007-2008 US financial crisis, we revise if the higher performance of

Islamic mutual funds is due their exposure to lower levels of risk; we find that Islamic
investment is remarkably efficient regardless of the time period.
The remaining of this paper is structured as follows. Section 2 discusses the
previous literature. Section 3 briefly 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 financial crisis. Finally, Section 7
shows the summary and conclusions.

2. Previous literature
There are several studies which focus on Islamic finance especially after the introduction of
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
ARJ of 1998; MSCI global Islamic indices; and the Global Gulf Cooperation Council (GCC)
25,3 Islamic index which was launched in 2006. The main theme of these studies is to investigate
whether there is a cost in adhering to the Shariah law. Some studies find Islamic investing
affects performance, while others find otherwise.
Elfakhani et al. (2007) findings suggest that there is no statistical evidence of any
performance differences between Islamic funds and the employed market benchmarks.
210 However, their findings 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 find 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 find on average IMFs in Malaysia outperform its
conventional peers and the market portfolio proxy by the KLCI returns. Shah et al. (2012)
show that Pakistani Islamic funds, when compared to Pakistani non-Islamic funds, present
a lower average risk rate with higher compensations. Surprisingly, the authors also find
Islamic funds are even better diversified than conventional mutual funds.
Hoepner et al. (2009) find mixed evidence on the performance of Islamic mutual funds.
They find that Islamic funds from eight nations (mostly from the Western regions)
significantly underperform their respective equity market benchmarks and Islamic funds
from only three nations outperform their respective market benchmarks. Furthermore,
they find that Islamic funds from the GCC and Malaysia do not significantly underperform
their respective market benchmarks. Finally, they argue that Islamic equity funds 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 benefits
from the lower leverage feature. Also, Majid and Maulana (2010) apply a non-parametric
performance measure to assess performance and find significant efficiency of 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
findings 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, diversification, and Carhart’s
(1997) four factor pricing model and find that there is no significant 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
sacrifice performance or become exposed to higher risk.
3. Non-parametric estimations Performance
Since alternative investments or financial assets have different statistical properties, measurement
estimating a good performance index is a difficult task due to the different characteristics
of assets returns, such as skewed return distributions with fat tails. Because of this, it is of mutual funds
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. 211
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
defined as bearers of risk while outputs are bearers of wealth.
Prior literature reveals that input candidates should reflect investment risk, which is
proxied by the return momentums. Under normality, only the mean return and its
standard deviation will suffice. 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,
defined in equation (1). Normality is rejected when JBj is larger than 5.99 for the
5 percent significance level and 9.21 for the 1 percent significance level:
" 2
#
T 2 Kj
JBj ¼ S þ ð1Þ
6 j 4

where:

E j ðr t 2 r d Þ2
Sj ¼ ; the skewness of monthly returns of fund j
s2j
E j ðr t 2 r d Þ4
Kj ¼ 2 3; the excess kurtosis of monthly returns of fund j
sj4
rt, monthly return.
r d, average returns.
sj , standard deviation.

3.2 Inputs and outputs description

The specification 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.
ARJ 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 rmin as the
25,3 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 specific investment
asset, the UPMs will capture the upside or benefit of the investment. Finally, UPM0 is
disregarded while LPM0 is further used; LPM0 is the percentage return of funds below
212 the target rate[3]:
~
1X T
LPM j;m ¼ ðr min 2 r t;j Þm ; m ¼ 0; . . . ; 4
T t¼1

_ ð2Þ
1X T
UPM j;m ¼ ð
rt;j 2 r min Þm ; m ¼ 0; . . . ; 4
T t¼1
where:
rmin, 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(rj), 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 dominating method to estimate fund performance. According to Glawischnig
and Sommersguter-Reichmann (2010), the use of the BCC model can be justified 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 justified 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 fixed cost digression; and
.
the use of the BCC model is advisable whenever ratios are used as inputs or outputs.

Having identified the input-output specifications, 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
of the best practices[6] followed by the industry given the multiple hyperplanes Performance
resulting from the use of multiple inputs and outputs; thereby making it is possible to
construct a performance index based upon the distance between specific funds and the
measurement
constructed frontier. of mutual funds
Formally, it is assumed that there are j ¼ 1, . . . , N funds where each uses xm ;m ¼
1; . . . ; M inputs to produce yr ;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): 213
p BCC ¼ minu s:t:
X
N
xmj lj # u · xmk ;m ¼ 1; . . . ; M
j¼1

X
N
yrj lj # yrk ;r ¼ 1; . . . ; R ð3Þ
j¼1

X
N
lj ¼ 1 with lj $ 0;j; m; r
j¼1

The LP given in equation (3) represents the percentage of efficiency 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, satisfies P BCC # 1 where P BCC ¼ 1
represents a fund which is 100 percent efficient. 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 efficient. Any deviation
from the PPF, given by P BCC , 1, will result in inefficiencies. Furthermore, the LP uses
exogenous weights, lj, to fit the best linear combination of all funds given a specific
input-output combination; lj – 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 mr and vm 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 efficient 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):
X
R
P BCC ¼ max0 mr yrk þ m 0 s:t:
vm ;mr ;m
r¼1

X
R X
M
mr yrj 2 vm xmj þ m 0 # 0 ;j ¼ 1; . . . ; N ð4Þ
r¼1 m¼1
ARJ X
M
vm xmk ¼ 1
25,3 m¼1

mr ; vm $ 0 and m 0 free
A limitation of the BCC model is that it assumes all inputs to be radial. But the possibility
214 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 sum of the
individual weights. Again, efficiency is achieved when P Russell ¼ 1. Formally:
PM
Russell um
P ¼ min m¼1 s:t:
M
X
N
xmj lj ¼ um · xmk ;m ¼ 1; . . . ; M
j¼1

X
N
yrj lj # yrk ;r ¼ 1; . . . ; R ð5Þ
j¼1

X
N
lj ¼ 1 with lj $ 0;j; r and um # 1
j¼1

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 defined 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 official site of the Saudi Stock Exchange (Tadawul) (www.tadawul.com.
sa), the official 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 defined as those funds listed in CRSP with objective code
“International Fund,” “International,” or “IF.” Finally, everything else is defined 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.
 Furthermore, funds employed in the sample are only those which have continuous Performance
returns data with at least two years’ worth of observations. That is, those funds which measurement
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 of mutual funds
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 215
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
defined: 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 confidence 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 specifications

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 define 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% significance 1% significance

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%)
Table I.
Note: The table shows how many funds are normally distributed with the corresponding percentage The JB test statistic for
of the group normality of time series
ARJ The forth momentums, LPM4 and UPM4, are disregarded due to the extreme high
25,3 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 specifications considered for the production
framework used in further tests.
216 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 finally 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 LPM0 LPM1 LPM2 LPM3 MCG UPM1 UPM2 UPM3

(months) (%) (%) (%) (%) (months) (%) (%) (%)

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
Table II. SD 16.2616 0.0470 0.0060 0.0090 0.0116 0.2861 0.0064 0.0091 0.0104
The descriptive statistics Panel D: Islamic funds
of the proposed Minimum 4 0.3452 0.0020 0.0024 0.0026 24.0000 0.0000 0.0000 0.0000
input-output specification Maximum 83 1 0.0595 0.1137 0.1534 84.0000 0.0506 0.0873 0.1244
used to estimate the DEA Mean 33.6526 0.6781 0.0208 0.0412 0.0569 63.9474 0.0194 0.0343 0.0452
performance index SD 17.1121 0.2498 0.0176 0.0351 0.0483 21.7556 0.0186 0.0319 0.0421
higher than the maximum MCG for both the American and International subgroups Performance
(ten and four months, respectively). measurement
of mutual funds
5.3 The fund universe performance
In this section, the performance of the overall fund universe is estimated and then it is
compared to each individual subgroup. In other words, the DEA efficiency frontier based on
the fund universe is estimated and then each subgroup is compared to the estimated 217
frontier. Table III summarizes the findings. The overall efficiency of the fund universe is
estimate based on equation (3) (panel A) and equation (5) (panel B). That is, the fund
performance index is estimated based on radial inputs, P BCC, and non-radial inputs, P Russell.
At first glance, it is found that efficiency 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 specific subset is more efficient 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 efficient, 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 efficient 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 efficient with respect to the PPF which envelops the whole fund universe.
In fact, American funds seem to be the least efficient of all three subsamples.
International founds account for 320 efficient funds, or 21.28 percent of their
subgroup while Islamic funds account for 37 efficient funds, or 39 percent of all Islamic
funds. Thus, it is observable that there are more efficient 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 Efficient Average Funds above Efficient Average Funds above
funds funds (%) average funds (%) average

Fund 22,545 3,944 52.00 8,574 6 27.52 8,431

universe (17.49%) (38.03%) (0.03%) (37.39%)
American 20,946 3587 52.47 8,149 4 27.85 8,007
funds (17.12%) (38.90%) (0.02%) (38.23%)
International 1,504 320 44.84 339 0 21.55 362
funds (21.28%) (22.54%) (0.00%) (24.07%)
Islamic 95 37 60.89 38 2 47.16 38 Table III.
funds (38.95%) (40.00%) (2.11%) (40.00%) The estimation of
equation (3), panel A, and
Notes: The American, International, and Islamic subsets are compared to the PPF based on the whole equation (5), panel B,
fund universe; the percentages in parenthesis correspond to the fraction of efficient funds or funds based on the whole fund
above average with respect to its subgroup universe
ARJ performance index. It is worthwhile mentioning that the Islamic subgroup shows the
25,3 highest average performance, 60.89 percent, followed by the American and International
funds with 52.47 and 44.84 percent average performance, respectively. Finally, Islamic
funds also show the highest efficiency levels when measuring the number of funds
above average. Islamic funds lead with 38 efficient funds above average, or 40.0 percent
of their subgroup, followed by the American and International funds with 8,149 funds, or
218 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 confirms observed results, despite a
penalty imposed on the estimation. Though the number of actual efficient funds drops
considerably, we find the same dominance by Islamic funds. Around 2 percent of Islamic
funds are efficient, while only 0.02 percent of American funds are efficient and no
International funds are efficient. 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 efficiency when comparing them to
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 seem to dominate the efficiency measures. Taken together with the 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 efficiency 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 efficiency while the Islamic subgroup remains the same; the number
of efficient International and American funds increases from 320 to 338 and 3,587 to
3,590, respectively, but the number of efficient Islamic funds stays on 37.
However, the most significant result comes from the increase on the average performance
of Islamic funds when their PPS is limited to account only for their own subgroup:
while American funds decreased from 52.47 to 51.74 percent and International funds Performance
increased from 44.84 to 80.01 percent, Islamic funds increased from 60.89 to 92.60 percent measurement
which is magnificently 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 of mutual funds
the limitations of the asset universe faced by Islamic funds, they are most efficient than
their counterparts.
As a comparison benchmark for efficiency, Table V shows similar results under the 219
non-radial production framework. The trend is quite similar to those of the
input-oriented BCC model. Results show a higher number of efficient Islamic funds
(8 or 8.42 percent of their subgroup), compared to the number of efficient International
funds (9 or 0.6 percent of their subgroup), and efficient 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 efficiency 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 efficiency under equation (5), the non-radial production
framework. While the results of the radial model under either the full universe PPF or

Total number Number of efficient Expected Number of funds

of funds funds P BCC ¼ 1 efficiency (%) above average

Fund 22,545 3,944 52.00 8,574

universe (17.49%) (38.03%)
American 20,946 3,590 51.74 7,658 Table IV.
funds (17.14%) (36.56%) The results from
International 1,504 338 80.01 664 equation (3), the radially
funds (22.47%) (44.15%) driven input-oriented
Islamic funds 95 37 92.60 58 model, based on the fund
(38.95%) (61.05%) universe and the
independent subgroups
Note: The percentages in parenthesis correspond to the fraction of efficient funds or funds above (each subgroup has its
average with respect to its subgroup own PPF)

Total number Number of efficient Expected Number of funds

of funds funds P Russell ¼ 1 efficiency (%) above average

Fund 22,545 6 27.52 8,431

universe (0.03%) (37.40%) Table V.
American 20,946 11 27.74 8,028 The results from
funds (0.05%) (38.33%) equation (5), the
International 1,504 9 50.93 504 non-radially driven
funds (0.6%) (33.51%) input-oriented model,
Islamic funds 95 8 68.05 47 based on the fund
(8.42%) (49.47%) universe and the
independent subgroups
Note: The percentages in parenthesis correspond to the fraction of efficient funds or funds above (each subgroup has its
average with respect to its subgroup own PPF)
ARJ the self-group-limited-universe PPF are quite close. For instance both show 37 efficient
25,3 Islamic funds, assuming the latter changes the results considerably when assessing a
non-radial production framework. All the studying parameters (number of efficient
funds, average performance, and number of funds above average performance) seem
considerably higher when limiting the universe to the specific subgroups. Still, despite
the increase in all subgroups, Islamic funds are still the most efficient.
220
5.5 Specifics 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 efficient funds would incorporate as few inputs as possible in order to
produce as much outputs as possible. Yet, it is found that a significant number of
efficient funds are unable to generate any output whatsoever. Table VI summarizes the
results.
Panel A shows the input-output mix for the fund universe. Results indicate that there
are 3,886 efficient funds, which accounts for 17 percent of all funds. Further analysis
shows that neither efficient nor inefficient 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 five), and only a few could even achieve four inputs simultaneously.
Examining the outputs, on the other hand, show that efficient funds can achieve more
outputs than inefficient funds. For instance, almost 5 percent of efficient 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 inefficient funds. In
addition, only efficient funds can achieve the maximum number of outputs, although
they account for less than 0.1 percent of efficient funds. Despite the highest performance
of efficient funds, there is still some inefficiency within them. That is, 37.3 percent of
efficient 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 inefficient
subsample.

Inputs Outputs
Number of funds 1 2 3 4 5 0 1 2 3 4

Panel A: fund universe

Inefficient 18,659 817 15,062 2,756 24 – 5,886 9,410 3,362 1 –
Efficient 3,886 1,486 725 1,649 26 – 1,450 828 1,411 194 3
Panel B: American funds
Inefficient 17,417 3,133 12,121 2,153 10 – 10,476 4,901 2,040 – –
Efficient 3,529 1,096 964 1,465 4 – 1,058 1,883 473 104 11
Panel C: International funds
Table VI. Inefficient 1,177 249 927 1 – – 43 1,076 58 – –
The results from Efficient 327 107 9 188 23 – 54 94 178 1 –
equation (4), the dual to Panel D: Islamic funds
the radially driven Inefficient 66 1 22 39 4 – 12 39 12 3 –
input-oriented model, Efficient 29 5 11 12 1 3 10 10 6 –
based on the fund
universe and the Notes: Table VI shows the input-output combination used in the production process; it also shows
independent subgroups production inefficiencies given by the number of funds with zero outputs
Though panel A shows important results, other panels show further means to Performance
comparing efficiency between Islamic, International, and American funds. At first measurement
inspection, there seems no significant difference in the input mix between the subgroups,
but results do indicate that only American efficient funds can achieve the maximum of mutual funds
number of outputs. Note that the same pattern presented in panel A is confirmed:
.
most funds, regardless if they are efficient or inefficient, use a maximum of three
inputs; and 221
. even efficient funds present some level of inefficiency 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 efficient with inefficiencies accounting for only 10.3 percent, whereas
21.7 percent of International funds are efficient with inefficiencies of 16.5 percent, and
only 5.2 percent of American funds are efficient with inefficiencies accounting for
almost 30 percent. In this context, inefficiencies are regarded as the percentage of
efficient funds which produced zero-outputs.
Overall, results suggest that Islamic mutual funds do not lose efficiency even though
they are limited to a smaller universe of assets. Perhaps a possible explanation for such
efficiency gain is that despite limitations, Islamic investors are ethically driven and thus
they prefer to avoid investing onto the most risky assets. 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 findings 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 financial crisis periods. The next section covers this issue by
splitting the dataset in order to account for the 2007-2008 financial crises.

6. Robustness check
The 2007-2008 financial 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 efficiency 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 financial 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.
ARJ 6.1 The fund universe performance
25,3 As before, a PPF is defined 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 efficiency 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 efficient American funds is observed, while
222 International and Islamic both have a decrease of 18.7 and 9.1 percent, respectively.
Furthermore, results show a significant 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 efficiency, 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 efficient
despite the financial crisis.
It is worthwhile noting that though the number of efficient Islamic funds is the same
regardless of the time period (37 funds), they are not all the same funds. In fact, results
indicate that five funds differ; that is, five funds stopped being efficient and five started
being efficient 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 confirmed at the first glance; Islamic funds are always
the most efficient 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 efficient funds when the PPF is limited to their own subgroup. This
result shows that the post-crisis decrease is even more significant.

Panel A: 2003-2006 Panel B: 2007-2010

Funds Funds
No of Efficient Average above No of Efficient Average above
funds funds (%) average funds funds (%) average

Fund 14,509 2,792 73.10 5,934 22,531 3,969 46.32 7,176

universe (19.24%) (40.90%) (17.62%) (31.85%)
American 13,589 2,418 73.00 5,596 20,932 3,612 46.66 6,778
funds (17.79%) (41.18%) (17.26%) (32.38%)
International 843 337 74.40 340 1,504 320 40.93 320
funds (39.98%) (40.33%) (21.28%) (21.28%)
Table VII. Islamic 77 37 76.93 42 95 37 58.07 38
The estimation of funds (48.05%) (54.55%) (38.95%) (40.00%)
equation (3) for the two
subsamples: 2003-2006 on Notes: This estimation is based on the whole fund universe; the American, International, and Islamic
panel A and 2007-2010 subsets are compared to the PPF based on the whole fund universe; the percentages in parenthesis
on panel B correspond to the fraction of efficient funds or funds above average with respect to its subgroup
 Performance
Panel A: 2003-2006 Panel B: 2007-2010
Funds measurement
No of Efficient Average Funds above No of Efficient Average above of mutual funds
funds funds (%) average funds funds (%) average

Fund 14,509 2,792 73.10 5,934 22,531 3,969 46.32 7,176

universe (19.24%) (40.90%) (17.62%) (31.85%) 223
American 13,589 2,382 71.77 57,100 20,932 3,600 46.39 6,582
funds (17.53%) (42.02%) (17.20%) (31.44%)
International 843 354 91.48 404 1,504 330 69.32 380
funds (41.99%) (47.92%) (21.94%) (25.27%)
Islamic 77 41 93.69 52 95 37 62.88 37 Table VIII.
funds (53.25%) (67.53%) (38.95%) (38.95%) The estimation of
equation (3) for the two
Notes: This estimation is based on independent universes; the American, International, and Islamic subsamples: 2003-2006 on
subsets are compared to the PPF based on their own universe; the percentages in parenthesis panel A and 2007-2010 on
correspond to the fraction of efficient funds or funds above average with respect to its subgroup panel B

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 efficient funds are the same regardless
of the PPF specification for the post-crisis subsample. This is an extra robustness
check as this incorporates both specification 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 efficiency. In fact, Islamic funds appear
as efficient 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
efficiency 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. A DEA
performance index is employed to measure efficiency 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 definition, efficiency is always defined 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.
ARJ In summary, obtained results suggest that though Islamic funds are limited to a
25,3 smaller asset universe, they do not lose efficiency regardless of the specification of the
PPF. Islamic funds are the most efficient followed by International and then American
funds. Overall, these results are persistent for the percentage number of efficient funds,
the average performance index, and the percentage number of funds above average
performance. Also, these results are robust to different specifications of the DEA
224 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 inefficiencies remaining
within the efficient funds, it can be safely concluded that Islamic funds remain highly
efficient despite their investment limitations, and they show the smallest number of
inefficiencies 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 financial 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 efficiency and
average performance, Islamic funds remain the most efficient.
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 profit
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
identification of fully efficient funds, such funds should be considered for every investor’s
portfolio. All in all, Islamic mutual funds create a highly profitable 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.
 4. Given the inputs (x1, x2, . . . , xn), they are consider radial if they increase proportionally given Performance
an a . 0, such that the inputs increase as (ax1, ax2, . . . , axn) (Cooper et al., 2000).
measurement
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. of mutual funds
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 225
prevailing level of inputs.
7. Zawya is one of leading Middle Eastern business information firms. 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/benefit for higher momentums due to non-normality of returns.
9. See the introduction of Glawischnig and Sommersguter-Reichmann (2010).

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Corresponding author
M. Kabir Hassan can be contacted at: mhassan@uno.edu

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