AN EFFICIENT PORTFOLIO FRONTIER OF

ISLAMIC BANKING FINANCING INSTRUMENTS1 (Indonesian Case : 2001 – 2007)

Rifki Ismal2

PhD Student, School of Government and International Affairs

Durham University (United Kingdom)

Phone : +44 (0) 7900411659

Email : rifki.ismal@durham.ac.uk

Abstract. Most of the Islamic banking financing goes to Murabahah followed by

Mudarabah, Musharakah and Istisna. It is found that the actual and expected rate

of return of Murabahah is notably the highest among others but it contains high

financing risk. Mudarabah also has a high rate of return but combining Mudarabah

with other instruments might produce a lower financing risk than Murabahah.

Considering all findings of the individual and portfolio performance, the efficient

portfolio frontier shows that combination of Murabahah and Mudarabah is the

best one upon certain range of financing risk and return.

Keywords: rate of return, NPF, FDR

1 This paper is the extension and modification version of the previous author’s paper: A Short Risk Return on Islmic Banking Financing Instruments. 2 The author address: School of Government and International Affairs, Al Qasimi Building, Elvet Hill Road, Durham University, Durham (DH1 3TU), United Kingdom (UK).

1

1. INTRODUCTION

Indonesian Islamic banking industry3 has been growing promisingly since

the establishment of the first Islamic bank in 1992. Up to end of 2007, there are

three Islamic Commercial Banks (BUS) followed by 25 Islamic Banking Unit

(UUS) and 114 Islamic Rural Banks (BPRS) integrating 683 offices around the

country (see table 1 below). In its development, Islamic banking industry has been

showing a healthy financial intermediary and prudential operation as shown by its

main banking indicators.

For example, Financing to Deposit Ratio (FDR) has been lying between

100%-120% annually since 2001 while in conventional banking it is around 60%

and Non Performing Financing (NPF) positions between 2%-4% while

conventional one records higher position at 8%. Others, like total asset, financing

and deposit have been growing annually for more than 60% on average4 (Bank

Indonesia, 2006:20-30).

Table 1. Selected Islamic Banking Indicators

BANKING INDICATORS 2000 2001 2002 2003 2004 2005 2006 2007Islamic Banks (unit) 2 2 2 2 3 3 3 3Islamic Banking Units (unit) 3 3 6 8 15 19 20 25Islamic Rural Banks (unit) 79 81 83 84 88 92 105 114Total Offices (unit) 146 182 229 337 443 550 567 683Total Asset (trillion Rp) 1.79 2.72 4.05 7.86 15.33 20.88 26.72 36.53Total Financing (trillion Rp) 1.27 2.05 3.28 5.53 11.49 15.23 19.53 27.94Total Deposit (trillion Rp) 1.03 1.81 2.92 5.72 11.86 15.58 20.67 25.65 Source : Bank Indonesia

As a fund manager, Islamic bank arranges financing instruments into a set

of portfolio financing taking into account its risk and return. This paper tries to

analyze the risk and return of the Islamic banking portfolio in order to construct

an efficient portfolio-financing that will give high return but low financing risk.

The paper firstly finds out expected return of the financing instruments, variance

of instruments etc under risk and return analysis. Complemented with the

correlation analysis among instruments, it tries to minimize financing risk and

3 Islamic banking industry consists of Islamic Commercial Banks (BUS), Islamic Banking Unit (UUS) and Islamic Rural Banks (BPRS). Islamic Banking Unit (UUS) is a special sharia banking unit in conventional bank (windows system or dual banking system) while Islamic Rural Banks (BPRS) names Islamic banks operated in suburb / rural areas. 4 As reported in Bank Indonesia annual report 2006.

2

maximize portfolio’s return by constructing an efficient portfolio frontier between

2001-2007 period.

2. THE MOST FAVORITE ISLAMIC FINANCING INSTRUMENTS

Islamic financing terminology recognizes three kinds of financing: (i)

Equity based financing, (ii) Debt based financing; (iii) Service based financing

(Obaidullah, 2005:17). In classical Islamic law, equity-based financing products

comprise of Mudarabah (trustee partnership), Musharakah (joint venture),

Muzara’ah (Harvest Yield Profit Sharing) and Musaqot (Plantation Management

Fee Based on Certain Portion of Yield) (Antonio, 1999:143-155). Whilst, Islamic

debt-based financing consist of Murabahah (mark up sale), Ijarah (leasing), Bay

Salam (deferred delivery sale), Bay Istisna (manufacture-sale), Istijrar (recurring

sale), and Qardh (benevolent loan). Lastly, Islamic banks also provide a range of

banking services such as Wakalah, (opening of letter of credit), Kafala (letter of

guarantee) and Hiwala (Obaidullah, 2005:113-115).

However, among all of the classic financing instruments above, Indonesian

Islamic banking industry has only employed a limited number of financing

instruments. So far, there are Musharakah and Mudarabah (for equity based

financing); Murabahah, Bay Salam, Bay Istisna, Qardh (for debt based financing);

and finally Wakalah, Kafalah and Hiwalah (service based instruments). Whilst,

the depositors themselves invest their fund in form of current account (Wadiah);

saving deposit (Wadiah/Mudarabah) and time deposit (Mudarabah).

Looking at its characteristics, debt financing can be categorized as a

certain (well-determined) source of income for the bank, while equity financing is

the opposite one. Moreover, debt financing does not require much effort for

monitoring and coordinating compared with equity financing. No wonder that

Islamic banks all around the world emphasis its financing policy to be more on

debt financing than equity financing. For the case of Indonesia, economic

condition in aftermath of the 1997’s economic crisis, complicated equity financing

procedures, requirement of strong effort and experience to conduct long-term

investment and under developed Islamic financial market are reasons retaining

Islamic banks to concentrate on equity financing.

3

Period of 2001-2007 records Murabahah as the most favorite and usable

financing instruments in the industry. On average, it dominates 68% of total

financing followed by Mudarabah (19%), Musharakah (8%) and Bay Istisna (4%)

as displayed in table 2 below. Meanwhile, other financing instruments like Bay

Salam, Ijarah, Qard, Wakalah, etc take only small share of the industry. Therefore,

this paper focuses just to the four significant financing instruments above without

ignoring that there are other insignificant instruments existing in the industry. In

the following part, by using portfolio theory, historical data from 2001-2007 and

reliable information, the paper analyses the performance of the individual and

group of instrument(s) followed by some findings.

Table 2. Share of Financing Instrument in the Industry (%)

Year Musharakah Mudarabah Murabahah Istisna2001 3.12 24.36 64.92 7.612002 2.40 16.37 73.62 7.612003 3.37 15.20 75.32 6.112004 10.32 17.84 68.30 3.552005 12.48 19.93 65.42 2.182006 12.30 20.53 65.42 1.742007 14.66 21.04 62.81 1.49

Source : Bank Indonesia

3. RISK RETURN PORTFOLIO THEORY

Risk return portfolio theory is used to analyse an individual asset’s rate of

return, expected return, probability of occurrence and market share. Furthermore,

it detects risk of the individual instrument from the variance of its actual and

expected return. Other than individual instrument, the theory also captures the risk

of more than one instrument up into involving the entire instruments. By using

some technical calculation below, we will evaluate the performance of financing

instrument individually and in combination with other instruments, redesign the

financing strategy and know the role and domination of each financial instrument

in a set of portfolio.

Expected return of one and a set of financing instrument can simply be

formulated as:

(Single instrument)

(1)

∑=

=N

iiii rpRE

1)(

4

)(.....)()()()( 332211 nnp REwREwREwREwRE ++++= (>1 instrument)

(2)

Where pi represents the probability of an event (return) occurs and ri is the rate of

return (RoR) of the instrument. Although in Islamic financial theory the future

returns of equity financing is uncertain (not known) but in this case it is assumed

that the historical data is a good predictor for the probability of occurrence (pi)

above. For more than one instrument, every instrument will be given a weight

(wn), taken from its market value5 as formulated in equation 2. Hence, it gives a

proportionate treatment for all instruments in the set of financing portfolio.

Then, the difference between expected return and its actual one depicts the

variance of the instrument (σ) which takes the general formula as given in

equation 3 below. High variance of an instrument shows the inconsistency of the

return over its indicative pattern (expected RoR) and indicates a relatively high

degree of uncertainty (financing risk) over the observed period. Variance of one

instrument is shown in equation 4 below.

∑∑= =

=n

i

n

jjijip wwRVar

1 1,)( σ

(3)

∑∑∑== =

−=+−==N

iinni

i jjijii RErpRErpwwRVar

1

2211

1

1

1

1

)]([(......)]([,)( σ

(4)

),(2,)( 212122

212

1

2

1

2

1

rrCovwwwwwwRVari j

jijip ++== ∑∑= =

σσσ

(5)

),(2),(2

),(2,)(

32323131

212132

322

212

1

3

1

3

1

rrCovwwrrCovww

rrCovwwwwwwwRVari j

jijip

++

+++== ∑∑= =

σσσσ

(6)

5 Taken from the value of each instrument in the market (share in the market).

5

),(2),(2),(2),(2),(2

),(2,)(

4343

4242323241413131

212142

432

322

212

1

4

1

4

1

rrCovwwrrCovwwrrCovwwrrCovwwrrCovww

rrCovwwwwwwwwRVari j

jijip

+++++

++++==∑∑= =

σσσσσ

(7)

However, variance between two instruments as depicted in equation 5

explains that besides depending on individual variance, weight of each instrument

in the market and correlation value between them determines the significance of

the variance. The same formula also applies for variance of three financing

instruments (equation 6 and see appendix 1 for a proof) and four financing

instruments (equation 7 and see appendix 1 for a proof).

The same interpretation like variance of single instrument, the low value

of portfolio variance indicates a low risk of the instruments’ combination

although, as an individual, instrument in a group might have high risk. Therefore,

evaluating instrument individually and in a group is very essential to find a robust

portfolio combination with low risk and high return. And, in order to measure the

degree of correlation (Coefficient of Correlation or ρ), we adopt formula in

equation 8 below.

21

212,1

),(σσ

ρrrCov

=

(8)

4. EFFICIENT PORTFOLIO THEORY

An efficient portfolio is the portfolio of risky assets that gives the lowest

variance of return of all portfolios having the same expected return (Benninga,

2000:141). From the previous equation, we set an efficient portfolio p by solving:

∑∑= =

==n

i

n

jpjiji RVarwwMin

1 1, )(σ

(9)

6

subject to:

∑=

==n

ipii RErw

1

)(μ and

(10)

∑=

=n

iiw

1

1

Then, an efficient portfolio frontier is the locus of all convex combination

of any two efficient portfolios. If we decide, for example, two prospective

financing instruments: x and y such that x = (x1,…,xn) and y = (y1, …..,yn), and

assuming γ is a constant, then a set of efficient portfolio Z will defined as follows:

Z = γx + (1- γ)y = (11) ⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−+

−+−+

nn yx

yxy

)1(...

)1()1(x

22

11

γγ

γγγγ

By solving this problem, we will come up with a combination of

instrument x and y that has low variance and high return. If we name the efficient

portfolio frontier of x and y as {E(Rx), σ2x} and {E(Ry), σ2

y} and if Z = γx + (1-

γ)y then the variance and standard deviation of the efficient portfolio frontier will

be,

E(Rz) = γE(Rx) + (1-γ)E(Ry) (12)

σ2z = γ2σ2

x + (1- γ)2σ2y + 2γ(1- γ)Cov(x,y) (13)

5. RISK- RETURN ANALYSIS OF ISLAMIC FINANCING

INSTRUMENT.

a. Single Financing Instrument.

Actual Rate of Return and Probability of Occurrence

Implementing the above formulas with historical data from 2001 - 2007,

we firstly look at the return of individual instrument. Average annual rate of

actual return (RoR) of each instrument is depicted in the table 3 below and later

according to the assumption above, it will be used as a proxy to calculate the

expected rate of return.

7

Table 3. Average Annual RoR (%)

Year I II III IV2001 0.03 0.19 0.54 0.072002 0.01 0.10 0.45 0.052003 0.01 0.06 0.31 0.022004 0.07 0.11 0.41 0.022005 0.08 0.13 0.40 0.012006 0.08 0.13 0.43 0.012007 0.12 0.16 0.48 0.01

I = Musharakah; II = Mudarabah; III = Murabahah; IV = Istisna

Source: Bank Indonesia

Table 4. RoR’s Probability Distribution (%) Rate of Return

Interval I II III IV=< 0.02 42.35 5.88 1.18 65.88

0.03 - 0.05 17.65 14.12 1.18 18.820.06 - 0.08 11.76 21.18 4.71 9.410.09 - 0.11 9.41 11.76 1.18 4.71

0.12 =< 18.82 47.06 91.76 1.18

Probability of Occurance

I = Musharakah; II = Mudarabah; III = Murabahah; IV = Istisna Source: Bank Indonesia

It is seen from table 3 that return of Murabahah is the highest among other

instruments. The average annual return of it is 0.43%, greater than Mudarabah

(0.13%), Musharakah (0.06%) and Istisna (0.03%). Undoubtedly, it emerges as

most of the bank’s financing is in Murabahah which has a predictable return

followed by other instruments which requires more attention and efforts to be

successfully implemented.

For example, in order to gain high return from equity financing

(Mudarabah and Musharakah) in the post-economic crisis, Islamic banks should

do intensive monitoring, have full information, arrange cooperation with

enterprises, conduct a business commitment and trust6, etc (Bank Indonesia,

2006:25). Another reason is because of most of the deposit is placed in short term

time deposit, so Islamic bank precautionary and safely locates the fund also in

short term financing (Murabahah) to have a predictable short-term return and

control over the liquidity as well.

6 Business partner usually prefers banks to bear the business loss to themselves. So Musharakah is less preferred than Mudarabah/Murabahah and in general equity financing highly required business trust between Islamic banks and their counterparts.

8

In addition, as Islamic banking theory relies on the probability of success

in real sector, it is important to mapping the probability distribution of RoR per

instrument. Under interval classification of RoR listed in table 4, there are

interestingly two extreme probability distributions of RoR. A high rate of return

of Murabahah and Mudarabah (over 0.12%) occurs in a very high probability of

occurrence, which is 91.7% for Murabahah and 47% for Mudarabah. Whilst

unfortunately, low RoR of Musharakah and Istishna (less than 0.02%) occurs

dominantly with 42.3% (Musharakah) and 65.88% probability of occurrence.

Confirming previous result, this fact confirms the tendency of the banks to

concentrate most of their financing on Murabahah and Mudarabah. However,

because these four instruments are the only mostly used financing instruments in

the industry, more effort should also be given to develop the unutilized

instruments (Musharakah and Istishna) to make them equally contribute to the

whole business activities. Especially, activating Musharakah, as it is one of the

investment based instrument that potentially produce higher profit7 with some

degree of risk. Both Mudarabah and Musharakah entail a long-term investment

that can improve portfolio financing8, utilize economic capital and workers.

However focusing financing temporarily in Murabahah is not bad at all

considering the under developed Islamic banking industry and stage of public

acceptance regarding Islamic banking which is still not full (Ismal, 2008:5-10). By

advancing a lot of fund in Murabahah contract for a short-term period, Islamic

banks gain two advantages, firstly predicted and continuous short-term return and

secondly securing liquidity position against short-term withdrawal.

Expected Rate of Return

Applying equation 1, the concentration of the probability of occurrence

determines the value of individual instrument’s expected RoR as prevailed in

figure 1-4 in the following. From the figures, we find that RoR of all financing

instruments has a specific pattern with a peak point in the last month of every

year.

7 Higher share to depositors as well. 8 Ideally, the fund should be located mostly in long term financing (the essence of the Islamic type of financing) rather than just financing buying and selling in short term period.

9

Figure 1. Expected & Actual RoR of Musharakah

0.000

0.050

0.100

0.150

0.200

0.250

Dec

-00

Jun-

01

Dec

-01

Jun-

02

Dec

-02

Jun-

03

Dec

-03

Jun-

04

Dec

-04

Jun-

05

Dec

-05

Jun-

06

Dec

-06

Jun-

07

Dec

-07

Actual RoR Expected RoR

%

Source: Bank Indonesia

Figure 2. Expected & Actual of Mudarabah

0.000

0.0500.100

0.1500.200

0.250

0.3000.350

0.4000.450

0.500

Dec

-00

Jun-

01

Dec

-01

Jun-

02

Dec

-02

Jun-

03

Dec

-03

Jun-

04

Dec

-04

Jun-

05

Dec

-05

Jun-

06

Dec

-06

Jun-

07

Dec

-07

Actual RoR Expected RoR

%

Source: Bank Indonesia

Figure 3. Expected & Actual RoR of Murabahah

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

Dec-00

Jun-0

1

Dec-01

Jun-0

2

Dec-02

Jun-0

3

Dec-03

Jun-0

4

Dec-04

Jun-0

5

Dec-05

Jun-0

6

Dec-06

Jun-0

7

Dec-07

Actual RoR Expected RoR

%

Source : Bank Indonesia

10

Figure 4. Expected & Actual RoR of Istishna

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

0.180

0.200D

ec-0

0

Jun-

01

Dec

-01

Jun-

02

Dec

-02

Jun-

03

Dec

-03

Jun-

04

Dec

-04

Jun-

05

Dec

-05

Jun-

06

Dec

-06

Jun-

07

Dec

-07

Actual RoR Expected RoR

%

Source : Bank Indonesia

It means that flow of business and realization of return is pooled and

settled in the last month of the year and it occurs not only for equity based

financing but also for debt based financing. For the sake of managing liquidity,

this pattern should be taken into account as a factor that determines timing of cash

inflow against cash outflow from depositors to banks.

Another one, although actual RoR of Musharakah, Mudarabah and

Istishna financing is relatively high, its expected RoR is low meaning probability

of such a high return in the future is perhaps not promising. Exception might be

given to Mudarabah, which has a high-expected RoR compared to Musharakah

and Istishna implying that its future return can be well predicted. Istishna,

however, has been showing the same path like Murabahah particularly since 2005

(see figure 1-4 above).

Despite evaluating its pattern, from annual data listed in figure 5 below,

we know that expected RoR of Murabahah and Mudarabah dominate the

prospective financing of Islamic banking year by year. Average annual expected

RoR from 2001-2007 shows that Murabahah’s expected RoR records 0.39% while

Mudarabah 0.05% and continued by rest of the instruments with a much lower

valuea than Murabahah and Mudarabah.

11

Figure 5. Annual Expected RoR (%)

0% 20% 40% 60% 80% 100%

2001

2002

2003

2004

2005

2006

2007

Musharakah Mudarabah Murabahah Istishna

Source: Bank Indonesia

Finally, the set of realities above enlighten that equity based financing

(Mudarabah and Musharakah financing) do needs bank’s intensive financing

monitoring and cooperation to improve and reduce the uncertainty of the return

payment. Furthermore, the distribution of banks’ return to the depositors should

take into account the flow of the fund as mentioned above in order to prevent

banks from liquidity risk.

Variance of Financing Instruments

By using equation 4, the variance of the individual instrument informs an

interesting message with respected to risk of financing. All of financing

instruments have been showing an increasing trend of variance since 2003 except

Istishna. It is coming from two conditions (1) A bigger gap between actual and

expected RoR and (2) A high probability of occurrence as mentioned previously.

Mudarabah has the biggest variance of all instruments driven by its wide gap

between actual and expected RoR followed by big probability of gap occurrence.

After Mudarabah is Murabahah that has the least gap between actual and expected

RoR but contains a high probability of gap occurrence, followed by Musharakah

the third one. Finally is Istishna which has the lowest variance of all but low

probability of gap occurrence. It is because Istishna is not the most occupied

instrument (see table 5 below).

12

Table 5. Annual Variance per Instrument Year I II III IV2001 0.00032 0.00518 0.00285 0.001762002 0.00003 0.00123 0.00191 0.000532003 0.00004 0.00050 0.00064 0.000132004 0.00092 0.00159 0.00182 0.000112005 0.00094 0.00208 0.00146 0.000022006 0.00099 0.00248 0.00178 0.000012007 0.00198 0.00358 0.00170 0.00001

I = Musharakah; II = Mudarabah; III = Murabahah; IV = Istisna Source: Bank Indonesia

This realism informs that although Murabahah and Mudarabah are

promising financing instruments, both of them have a high risk of financing.

Meanwhile, Musharakah and Istishna, the less prospective instruments due to their

low probability of high return, become the least choice of financing priority for

Islamic banks, as they are not profitable and having high risk (especially

Musharakah).

In relation with bank’s financing policy, they have to be aware of this

finding particularly because most of their financing is in Murabahah. Islamic

banks have to keep maintaining a high level of Murabahah’s return especially in

line with its expected return otherwise risk financing emerged and affecting the

performance of their asset (Bank Indonesia, 2006:24). For other financing

instruments, the banks had better increase their financing allocation, improve

monitoring and coordination with entrepreneurs. It will hopefully boost the actual

and expected RoR. Finally, these efforts will increase banks’ return and lessen

instrument’s variance (risk of financing simultaneously).

b. Portfolio of Financing Instrument.

Market Share and Weighted Expected RoR

After evaluating individual performances above, we come up with

analyzing combination of instruments (set of portfolio) by using equation 2 above.

First of all, we find out the weight of every financing instrument in the industry

taken from its share in the total industry’s financing. That weight is listed in table

6 below. Referring to the fact that the leader of financing instruments are

Murabahah and Mudarabah, no wonder that portion of these two instruments

13

captures the biggest part the whole industry. Weight of Murabahah is the first one,

followed by Mudarabah and the rest of the financing instruments.

Table 6. Weight of Each Instrument

Year I II III IV2001 0.03 0.24 0.65 0.082002 0.02 0.16 0.74 0.082003 0.03 0.15 0.75 0.062004 0.10 0.18 0.68 0.042005 0.12 0.20 0.65 0.022006 0.12 0.21 0.65 0.022007 0.15 0.21 0.63 0.01

I = Musharakah; II = Mudarabah; III = Murabahah; IV = Istisna Source: Bank Indonesia Table 7. Expected RoR of the Portfolio

Year I II III IV Total2001 0.0002 0.0202 0.3196 0.0004 0.34042002 0.0001 0.0058 0.3001 0.0006 0.30672003 0.0002 0.0017 0.2129 0.0005 0.21542004 0.0010 0.0068 0.2502 0.0003 0.25832005 0.0015 0.0097 0.2365 0.0002 0.24782006 0.0016 0.0113 0.2548 0.0001 0.26782007 0.0031 0.0144 0.2792 0.0001 0.2968

I = Musharakah; II = Mudarabah; III = Murabahah; IV = Istisna Source: Bank Indonesia

Secondly, by using weight above, we construct the value of individual

instrument’s expected RoR due to its share in the industry and it is depicted in

table 7 above. Again, because RoR of Murabahah and Mudarabah is the highest

among others completed by their high portion in the industry, the value of RoR of

both instruments leads the result. On average, weighted expected RoR of

Murabahah counts for 0.26% and Mudarabah for 0.01% and the rest are below

0.001%.

Finally, it is also seen in table 7 that a combination of weighted expected

RoR for all financing instruments reaches the highest point in 2001 and 2007. One

reason, it is because there has been an indication of the decreasing market share

(weight) of Istisna since 2001 while on the other side, there is an increasing

market share of both Musharakah and Mudarabah up into 2007 (see table 6).

Banks do not prefer utilizing Istisna to others, probably due to its low demand in

the business sector and small margin available to be charged by banks.

14

Another reason is because of the impact of world oil price problem in

2004-2005 leading to an increase in domestic inflation and volatile Rupiah

exchange rate. That situation forced the government to adjust the domestic fuel

price, causing domestic price to go up, to save the government budget (Ismal,

2006:14-20). Unfortunately, this shock affected the whole economy

unexceptionally the performance of Islamic financing instruments.

Variance Portfolio of Two Financing Instruments

After calculating expected RoR of a portfolio financing, we construct the

variance of two instruments by using equation 5. The result is plotted in the

following table 8. Analyzing variance of two financing instruments describes

interesting facts. Firstly, Mudarabah that has the highest individual variance does

not show the high variance if being combined with other instruments (except

Murabahah). But, secondly, whatever partner of Murabahah, it produces high

variance especially if Murabahah is combined with Mudarabah. And lastly,

combination of Istishna and Musharakah does not cause any significant variance

(risk of financing).

Table 8. Variance of Instrument in Pairs

Year I & II I & III I & IV II & III II & IV III & IV2001 0.0003 0.0015 0.0000 0.0178 0.0006 0.00342002 0.0000 0.0011 0.0000 0.0042 0.0001 0.00172003 0.0000 0.0004 0.0000 0.0008 0.0000 0.00042004 0.0002 0.0022 0.0000 0.0044 0.0001 0.00102005 0.0002 0.0019 0.0000 0.0040 0.0001 0.00072006 0.0002 0.0021 0.0000 0.0046 0.0001 0.00082007 0.0003 0.0015 0.0000 0.0023 0.0002 0.0007I = Musharakah; II = Mudarabah; III = Murabahah; IV = Istisna

Source: Bank Indonesia

Following variance analysis of pair instrument, by looking at the value of

correlation coefficient, (using equation 8), it proves that strong correlation of two

instruments happens only between (1) Murabahah and Musharakah; (2)

Murabahah and Mudarabah; and (3) Murabahah and Istisna as shown by table 9

below.

15

Table 9. Coefficient of Correlation Year I & II I & III I & IV II & III II & IV III & IV2001 1.6287 6.9426 1.1874 13.4137 2.0912 10.00272002 1.6486 6.6210 1.1503 8.4875 1.4594 5.82012003 0.6647 2.6941 0.3083 2.9559 0.4260 1.89282004 2.0957 7.2740 1.1520 8.5298 1.3460 4.67092005 1.8671 6.4105 1.8200 7.2316 2.0500 7.07652006 1.6030 6.1101 1.8653 6.6014 2.0216 7.69032007 0.5408 2.2729 0.6667 2.1910 0.6446 2.7141

I = Musharakah; II = Mudarabah; III = Murabahah; IV = Istisna Source : Bank Indonesia

Combining together information from variance and coefficient of

correlation of two instruments, we know that the performance of Murabahah

influences other instrument in a portfolio. Meaning, if a bank takes for example

portfolio financing of only two instruments that one of them is Murabahah, the

result or performance of Murabahah will strongly determine the result of the

whole portfolio. Mudarabah on the other hand, despite having a high financing

risk (high individual variance), does not dominate the whole result of a portfolio.

Meaning, if a bank, for example, makes a portfolio of financing that includes

Mudarabah, the result or performance of the portfolio will be shared between

Mudarabah and its partner instrument, hopefully with low portfolio variance as

indicated early.

Variance Portfolio of More than Two Financing Instruments

A set of portfolio consisting of three and four instruments by using

equation 6 and 7 is plotted in table 10 afterwards. Continuing the former

discovery, the existence of Murabahah in a set of portfolio causes the variance to

go up. The influence of Murabahah dictates the portfolio and it is seen

predominantly in the combination of (1) Musharakah, Mudarabah and

Murabahah; (2) Musharakah, Murabahah and Istisna; and (3) Mudarabah,

Murabahah and Istisna. Even, when the whole instruments are put together in one

portfolio, Murabahah’s domination raises the portfolio’s variance.

16

Table 10. Variance of Three and Four Instruments Year I, II & III I, II & IV I, III & IV II, III & IV I, II, III & IV2001 0.0181 0.0006 0.0037 0.0203 0.02062002 0.0043 0.0001 0.0018 0.0049 0.00502003 0.0008 0.0000 0.0004 0.0008 0.00082004 0.0059 0.0002 0.0023 0.0045 0.00602005 0.0054 0.0002 0.0019 0.0040 0.00542006 0.0060 0.0003 0.0021 0.0046 0.00612007 0.0032 0.0003 0.0015 0.0023 0.0032

I = Musharakah; II = Mudarabah; III = Murabahah; IV = Istisna Source : Bank Indonesia

Nevertheless, portfolio variance of all instruments tends to go down

recently. It occurs when the banks try to increase the market share of Mudarabah

and Musharakah. And, it seems that the prospective performance of Mudarabah

with a high-expected RoR and low portfolio variance has contributed to the

decreasing trend of portfolio of four instruments. Therefore, it is important for

Islamic banks to expand share of Mudarabah financing in the portfolio besides

Murabahah.

6. AN EFFICIENT PORTFOLIO FINANCING FRONTIER

The final step of this paper is constructing an efficient portfolio financing

frontier benchmarking from the previous findings. Considering the prospective

performance of Murabahah and Mudarabah, we use these instruments (Murabahah

to be instrument x and Mudarabah to be instrument y) in the portfolio frontier and

find the efficient portfolio frontier that produces high-expected RoR and low

financing risk with certain set of portfolio portion (γ). By solving equation 9-13

above particularly assuming set of γ ranging from 0 into 1.05 with 0.075 different

interval value such that,

Z = γx + (1-γ)y = (14)

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−+

−+−+

nn yx

yxy

)05.11(05.1...

)075.01(075.0)01(0x

22

11

we find the portfolio frontier as shown in figure 6 below. Given the range that we

set, the portfolio frontier starts from point A into point C with a turning point in B.

17

Finally, according to the definition of efficient portfolio frontier mentioned early,

the line that indicates the efficient portfolio frontier is the one from point B into C

as seen in thick line of figure 6 below. Meanwhile, the line between point A and B

is not the efficient one.

Figure 6. An Efficient Portfolio Frontier

00.05

0.10.15

0.20.25

0.30.35

0.40.45

0.02 0.04 0.06 0.08 0.1 0.12Portfolio's Standard Deviation (%)

Portfolio's Mean Return (%)

B

C

A

Just for an illustration, point B has an expected RoR of 0.21% and

standard deviation of 0.10% from γ = 0.525. Whilst point C, as the highest

possible outcome of the Mudarabah and Murabahah combination, has the value of

expected RoR of 0.39% and standard deviation of 0.04% by setting γ = 0.

Therefore, the efficient combination of Mudarabah and Murabahah financing

instruments is ranging in this interval value (point B – point C).

7. CONCLUSION

Indonesian Islamic banking allocates most of the fund into Murabahah

financing, followed by Mudarabah, Musharakah and Istisna. The actual and

expected RoR of Murabahah is noted the highest among others and followed by

high financing risk in a portfolio. Mudarabah, the second favorite financing

instrument, has a little bit lower RoR but if it is combined with other instruments,

its financing risk is lower than Murabahah. Considering all aspect of individual

and portfolio performance, the efficient portfolio frontier tells that Islamic banks

in the country can optimize their portfolio financing by not only concentrating

financing on Murabahah itself but also Mudarabah with specific range of

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allocation. Nonetheless, as Musharakah and Istishna are not fully employed,

developing much effort to improve the performance of Musharakah is also

recommended in order to maximize all financing instruments existed in the

industry.

REFERENCES

Bank Indonesia (2006), Islamic Banking Annual Report, Jakarta, March 2006. Bank Indonesia (2000-2007), Islamic Banking Monthly Statistics Report, Jakarta, 2000-2007. Elton E and M Gruber (1997), Modern portfolio Theory, 1950 to date, Journal of Banking and Finance number 21, 1997, pp. 1743-1759. G M Constantinides and A G Malliaris Portfolio Theory (1995), in R A Jarrow Handbooks in Operations Research and Management Science, Vol 9. 1995. Markowitx H M (1991), Foundations of Portfolio Theory, Journal of Finance, 46, pp. 469-478. Copeland TE, JF Weston and K Shastri (2005), Financial Theory and Corporate Policy, Addison Wesley, Forth Edition, 2005. Obaidullah, Mohammed (2005). "Islamic Financial Services". Islamic Economic and Research Center, King Abdul Aziz, University Jeddah, Saudi Arabia, May 2005. Antonio, Syaefi (1999). “Sharia Bank for Bankers and Practitioners”. Bank Indonesia and Tazkia Institute, 1st Edition, Jakarta, December 1999. Ismal, Rifki (2008). The Potential of Liquidity Risk in Islamic Banking. Unpublished Academic Paper, Durham University, United Kingdom, February, 2008. Ismal, Rifki (2006). Indonesian Bond Market: Redemption in August – December 2005. Presented paper in HKMA seminar in Bond Market, March 28th, 2006, Hong Kong. Benninga, Simon (2000), Financial Modeling, The MIT Press Cambridge, Massachusetts London, England, Second Edition, 2000.

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APPENDIX 1

Below is the derivation process from general formula of variance into

variance of certain level requested.

General formula :

∑∑= =

=N

i

N

jjijip wwRVar

1 1,)( σ

(8)

For two financing instruments :

jjjjp wwwwRVar ,,)( 2211 σσ +=

2222212112121111 ,,,, σσσσ wwwwwwww +++=

(9)

),(2 212122

212

1 rrCovwwww ++= σσ

For three financing instruments :

jjjjjjp wwwwwwRVar σσσσσσ 332211)( ++=

22222121131312121111 σσσσσσσσσσ wwwwwwwwww ++++=

3333323231312323 σσσσσσσσ wwwwwwww ++++

),(2),(2 3131212132

322

212

1 rrCovwwrrCovwwwww ++++= σσσ

(10)

),(2 3232 rrCovww+

For four financing instruments:

jjjjjjjjp wwwwwwwwRVar σσσσσσσσ 44332211)( +++=

21211414131312121111 σσσσσσσσσσ wwwwwwwwww ++++=

32323131242423232222 σσσσσσσσσσ wwwwwwwwww +++++

43434242414134343333 σσσσσσσσσσ wwwwwwwwww +++++

4444 σσww+

),(2),(2 3131212142

432

322

212

1 rrCovwwrrCovwwwwww +++++= σσσσ

),(2),(2),(2 424232324141 rrCovwwrrCovwwrrCovww +++

(11)

),(2 4343 rrCovww+

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Glossary of Arabic Words

Mudarabah : A form of partnership where one party provides the funds while the other provides expertise and management. The latter is referred to as the Mudarib. Any profits accrued are shared between the two parties on a pre-agreed basis, while loss is borne by the provider(s) of the capital. Murabahah : Literally it means a sale on mutually agreed profit. Technically, it is a contract of sale in which the seller declares his cost and the profit. As a financing technique, it can involve a request by the client to the bank to purchase a certain item for him. The bank does that for a definite profit over the cost which is stipulated in advance. Musharakah : Musharakah means a relationship established under a contract by the mutual consent of the parties for sharing of profits and losses in the joint business. It is an agreement under which the Islamic bank provides funds which are mixed with the funds of the business enterprise and others. All providers of capital are entitled to participate in management, but not necessarily required to do so. The profit is distributed among the partners in pre-agreed ratios, while the loss is borne by every partner strictly in proportion to respective capital contributions. Qard (Loan of fungible objects) : The literal meaning of Qard is ‘to cut’. It is so called because the property is really cut off when it is given to the borrower. Legally, Qard means to give anything having value in the ownership of the other by way of virtue so that the latter could avail of the same for his benefit with the condition that same or similar amount of that thing would be paid back on demand or at the settled time. It is that loan which a person gives to another as a help, charity or advance for a certain time. The repayment of loan is obligatory. Bay Salam : Salam means a contract in which advance payment is made for goods to be delivered later on. The seller undertakes to supply some specific goods to the buyer at a future date in exchange of an advance price fully paid at the time of contract. It is necessary that the quality of the commodity intended to be purchased is fully specified leaving no ambiguity leading to dispute. Bay Salam covers almost everything which is capable of being definitely described as to quantity, quality and workmanship. Bay Istishna : It is a contractual agreement for manufacturing goods and commodities, allowing cash payment in advance and future delivery or a future payment and future delivery. A manufacturer or builder agrees to produce or build a well described good or building at a given price on a given date in the future. Price can be paid in installments, step by step as agreed between the parties. Istishna can be used for providing the facility of financing the manufacture or construction of houses, plants, projects, and building of bridges, roads and highways.

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Ijarah : Letting on lease. Sale of a definite usufruct of any asset in exchange of definite reward. It refers to a contract of land leased at a fixed rent payable in cash and also to a mode of financing adopted by Islamic banks. It is an arrangement under which the Islamic banks lease equipments, buildings or other facilities to a client, against an agreed rental. Kafalah (Suretyship) : Literally, Kafalah means responsibility, amenability or suretyship, Legally in Kafalah a third party become surety for the payment of debt. It is a pledge given to a creditor that the debtor will pay the debt, fine etc. Suretyship in Islamic law is the creation of an additional liability with regard to the claim, not to the debt or the assumption only of a liability and not of the debt. Hiwalah : Literally, it means transfer; legally, it is an agreement by which a debtor is freed from a debt by another becoming responsible for it, or the transfer of a claim of a debt by shifting the responsibility from one person to another – contract of assignment of debt. It also refers to the document by which the transfer takes place. Ijarah Muntahia Bittamleek : A mode of financing, by way of Hire-purchase, adopted by Islamic banks. It is a contract under which the Islamic bank finances equipment, building or other facilities for the client against an agreed rental together with a unilateral undertaking by the bank or the client that at the end of the lease period, the ownership in the asset would be transferred to the lessee. Wakalah : A contract of agency in which one person appoints someone else to perform a certain task on his behalf, usually against a certain fee.

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