An Efficient Portfolio Frontier of Islamic Banking ...staff.ui.ac.id/system/files/users/rifki.ismal/material/durham... · An Efficient Portfolio Frontier of Islamic Banking Financing

An Efficient Portfolio Frontier

of Islamic Banking Financing

Instruments

(Case of Indonesia: 2001-2007)

Paper Presented in

International Workshop in Islamic Economics,

Banking and Finance

Joint Program of Durham University & Kyoto University

July 6th, 2008

Rifki Ismal

School of Government and International Affairs (SGIA)

Durham University

Outline of Presentation

Introduction about Indonesian Islamic Banking Industry.

Objective of the paper.

The Most Favorite Islamic Financing Instruments.

Risk Return Portfolio Theory.

Efficient Portfolio Theory.

Risk Return Analysis of Financing Instruments.

Single Financing Instruments.

Portfolio Financing Instruments.

An Efficient Portfolio Frontier.

Conclusion and Policy Recommendation

Introduction about Indonesian Islamic

Banking Industry

The industry has been growing promisingly since the establishment of the first Islamic bank in 1992.

Up to end of 2007, there are 3 Islamic Banks, 25 Islamic Banking Unit (UUS) and 114 Islamic Rural Banks (BPRS) with total 683 offices.

FDR is between 100%-120% (2001-2007) and NPF is around 2%-4%.

BANKING INDICATORS 2000 2001 2002 2003 2004 2005 2006 2007

Islamic Banks (unit) 2 2 2 2 3 3 3 3

Islamic Banking Units (unit) 3 3 6 8 15 19 20 25

Islamic Rural Banks (unit) 79 81 83 84 88 92 105 114

Total Offices (unit) 146 182 229 337 443 550 567 683

Total Asset (trillion Rp) 1.79 2.72 4.05 7.86 15.33 20.88 26.72 36.53

Total Financing (trillion Rp) 1.27 2.05 3.28 5.53 11.49 15.23 19.53 27.94

Total Deposit (trillion Rp) 1.03 1.81 2.92 5.72 11.86 15.58 20.67 25.65

Objective of The Paper

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 maximize portfolio’s return by

constructing an efficient portfolio frontier

between 2001-2007 period.

The Most Favorite Islamic Financing

Instruments

3 classical types of financing: (i) Equity financing, (ii) Debt financing; and (iii) Service financing.

Indonesia employs Musharakah and Mudarabah(equity financing); Murabahah, Bay Salam, Bay Istishna, Qard (debt financing); and Wakalah, Hiwalah, Kafalah (services). And Wadiah current account; Wadiah/Mudarabah saving deposit and Mudarabah time deposit.

During 2001-2007 Murabahah counts 68% of total financing, Mudarabah (19%), Musharakah (8%) and Bay Istisna (4%). Others like Bay Salam, Ijarah, Qard, Wakalah, etc are very small.

Therefore, the paper focuses to the four abovewithout ignoring that there are other insignificant instruments existing in the industry.

Risk Return Portfolio Theory

Used to analyse risk and return of an individual or group of

instruments by looking at their actual and expected rate of

return, probability of occurrence and market share.

N

i

iii rpRE1

)(

)(.....)()()()( 332211 nnp REwREwREwREwRE

Expected Return of Single Instrument

Exp (R) of > 1 Instrument

The difference between expected return and its actual one depicts the

variance of the instrument (σ) .

n

i

n

j

jijip wwRVar1 1

,)(

N

i

inni

i j

jijii RErpRErpwwRVar1

22

11

1

1

1

1

)]([(......)]([,)(

General Formula of Variance

Var of 1 instrument

Risk Return Portfolio Theory

It is determined by individual variance, weight & correlation value

Var of 3 insts

The low value of portfolio variance should indicate a low risk of the

combination although, individually, instrument might have a high

risk. Thus, we evaluate the instrument individually and in a group as

well.

Var of 2 insts),(2,)( 21212

2

21

2

1

2

1

2

1

rrCovwwwwwwRVari j

jijip

),(2),(2

),(2,)(

32323131

21213

2

32

2

21

2

1

3

1

3

1

rrCovwwrrCovww

rrCovwwwwwwwRVari j

jijip

),(2

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

),(2,)(

4343

4242323241413131

21214

2

43

2

32

2

21

2

1

4

1

4

1

rrCovww

rrCovwwrrCovwwrrCovwwrrCovww

rrCovwwwwwwwwRVari j

jijip

Var of 4 insts

21

212,1

),(

rrCov Coefficient of correlation

Efficient Portfolio Theory

Subject to &

An efficient portfolio frontier is the locus of all convex combination of

any two efficient portfolios. If we decide two prospective financing

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

is a constant, then a set of efficient portfolio Z is :

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

variance of return of all portfolios having the optimal expected return.

Then, we set an efficient portfolio p by solving :

n

i

n

j

pjiji RVarwwMin1 1

, )(

n

i

pii RErw1

)(

n

i

iw1

1

Z = γx + (1- γ)y =

nn yx

yx

y

)1(

...

)1(

)1(x

22

11

If we name the efficient portfolio frontier of x and y as {E(Rx), σ2x} and

{E(Ry), σ2y} 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) σ2

z = γ2 σ2x + (1- γ)2σ2y + 2γ(1- γ)

Cov(x,y)

Risk Return Analysis of Islamic Financing

Instruments (Single Instrument)

Average annual rate of actual return (RoR) of each instrument is

depicted below and later according to the assumption above, it will be

used as a proxy to calculate the expected rate of return

Year I II III IV

2001 0.03 0.19 0.54 0.07

2002 0.01 0.10 0.45 0.05

2003 0.01 0.06 0.31 0.02

2004 0.07 0.11 0.41 0.02

2005 0.08 0.13 0.40 0.01

2006 0.08 0.13 0.43 0.01

2007 0.12 0.16 0.48 0.01

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

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%)

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 18.82

0.06 - 0.08 11.76 21.18 4.71 9.41

0.09 - 0.11 9.41 11.76 1.18 4.71

0.12 =< 18.82 47.06 91.76 1.18

Probability of Occurance


More than 0.12% RoR of

Murabahah has probability of

occurrence 91.7% and

Mudarabah for 47%. But, less

than 0.02% RoR of Musharakah

tends to occur with 42.3% and

Istishna for 65.88%.



The previous result confirms the tendency of the banks to concentrate

most of their financing on Murabahah and Mudarabah. However,

developing Musharakah and Istishna is important especially Musharakah

could potentially produce higher profit.

Then, we get expected RoR and we can compare it with the actual RoR

of every instrument.

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

Dec-0

0

Jun-0

1

Dec-0

1

Jun-0

2

Dec-0

2

Jun-0

3

Dec-0

3

Jun-0

4

Dec-0

4

Jun-0

5

Dec-0

5

Jun-0

6

Dec-0

6

Jun-0

7

Dec-0

7

Actual RoR

Expected RoR

%

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

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

%

Actual & Expected RoR Murabahah

Actual & Expected RoR Mudarabah



0.000

0.050

0.100

0.150

0.200

0.250

Dec-0

0

Jun-0

1

Dec-0

1

Jun-0

2

Dec-0

2

Jun-0

3

Dec-0

3

Jun-0

4

Dec-0

4

Jun-0

5

Dec-0

5

Jun-0

6

Dec-0

6

Jun-0

7

Dec-0

7

Actual RoR

Expected RoR

%

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

0.180

0.200

Dec-0

0

Jun-0

1

Dec-0

1

Jun-0

2

Dec-0

2

Jun-0

3

Dec-0

3

Jun-0

4

Dec-0

4

Jun-0

5

Dec-0

5

Jun-0

6

Dec-0

6

Jun-0

7

Dec-0

7

Actual RoR

Expected RoR

%

Actual & Expected RoR Musharakah

Actual & Expected RoR

Istishna

Flow of business and realization of return is pooled and settled in the last month of the year.

With regard to managing liquidity, this pattern depicts cash inflow for banks from their depositors.

Murabahah’s RoR is well predicted compared to others.



Variance of Individual Instrument

All of instruments have been showing an increasing trend of variance since 2003 especially Mudarabah, except Istishna.

It indicates that financing instrument tends to be more risky year by year unexceptionally Murabahah and Mudarabah. Some internal and external economic problems explain this reality.

Intensive monitoring of the mostly occupied instruments and developing less attractive one (Istishna) should be considered.

Year I II III IV

2001 0.00032 0.00518 0.00285 0.00176

2002 0.00003 0.00123 0.00191 0.00053

2003 0.00004 0.00050 0.00064 0.00013

2004 0.00092 0.00159 0.00182 0.00011

2005 0.00094 0.00208 0.00146 0.00002

2006 0.00099 0.00248 0.00178 0.00001

2007 0.00198 0.00358 0.00170 0.00001



Instruments (2 Instruments)Firstly, we calculate weight from market share of instrument as

requirement to construct expected RoR of a portfolio (table below).

Murabahah and Mudarabah dominates the industry so gaining the bigger weight in the portfolio.

Plotting weight to each

instrument. On average

expected RoR with weight of

Murabahah is 0.26% whilst

Mudarabah is 0.01%.

Year I II III IV

2001 0.03 0.24 0.65 0.08

2002 0.02 0.16 0.74 0.08

2003 0.03 0.15 0.75 0.06

2004 0.10 0.18 0.68 0.04

2005 0.12 0.20 0.65 0.02

2006 0.12 0.21 0.65 0.02

2007 0.15 0.21 0.63 0.01


Year I II III IV Total

2001 0.0002 0.0202 0.3196 0.0004 0.3404

2002 0.0001 0.0058 0.3001 0.0006 0.3067

2003 0.0002 0.0017 0.2129 0.0005 0.2154

2004 0.0010 0.0068 0.2502 0.0003 0.2583

2005 0.0015 0.0097 0.2365 0.0002 0.2478

2006 0.0016 0.0113 0.2548 0.0001 0.2678

2007 0.0031 0.0144 0.2792 0.0001 0.2968



Instruments (2 Instruments)

Finally, we end up with portfolio of 2 instruments (table below).

Year I & II I & III I & IV II & III II & IV III & IV

2001 0.0003 0.0015 0.0000 0.0178 0.0006 0.0034

2002 0.0000 0.0011 0.0000 0.0042 0.0001 0.0017

2003 0.0000 0.0004 0.0000 0.0008 0.0000 0.0004

2004 0.0002 0.0022 0.0000 0.0044 0.0001 0.0010

2005 0.0002 0.0019 0.0000 0.0040 0.0001 0.0007

2006 0.0002 0.0021 0.0000 0.0046 0.0001 0.0008

2007 0.0003 0.0015 0.0000 0.0023 0.0002 0.0007


Mudarabah that has the highest individual variance does not show the high variance if being combined with other instruments (except Murabahah).

Whatever partner of Murabahah, it produces high variance especially if Murabahah is combined with Mudarabah (4th column).

Combination of Istishna and Musharakah does not cause any significant variance (risk of financing).


Instruments (2 Instruments)Following portfolio of 2 instruments, coefficient of correlation

confirms other facts (table below) :

Strong correlation happens between (1) Murabahah and Musharakah; (2) Murabahah and Mudarabah; and (3) Murabahah and Istisna.

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.

If a bank makes a portfolio of financing that includes Mudarabah, the result or performance of the portfolio will be shared between Mudarabah and its partner instrument .

Year I & II I & III I & IV II & III II & IV III & IV

2001 1.6287 6.9426 1.1874 13.4137 2.0912 10.0027

2002 1.6486 6.6210 1.1503 8.4875 1.4594 5.8201

2003 0.6647 2.6941 0.3083 2.9559 0.4260 1.8928

2004 2.0957 7.2740 1.1520 8.5298 1.3460 4.6709

2005 1.8671 6.4105 1.8200 7.2316 2.0500 7.0765

2006 1.6030 6.1101 1.8653 6.6014 2.0216 7.6903

2007 0.5408 2.2729 0.6667 2.1910 0.6446 2.7141



Instruments (3 and 4 Instruments)

Portfolio of 3 instruments is displayed in table below.

The existence of Murabahah in a set of portfolio causes the variance to

go up, except in combination of the 3rd column (I, III, IV).

Even, when the whole instruments are put together in one portfolio,

Murabahah’s domination raises the portfolio’s variance (5th column) .

But, 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. Noted Mudarabah has low variance in a portfolio.

Year I, II & III I, II & IV I, III & IV II, III & IV I, II, III & IV

2001 0.0181 0.0006 0.0037 0.0203 0.0206

2002 0.0043 0.0001 0.0018 0.0049 0.0050

2003 0.0008 0.0000 0.0004 0.0008 0.0008

2004 0.0059 0.0002 0.0023 0.0045 0.0060

2005 0.0054 0.0002 0.0019 0.0040 0.0054

2006 0.0060 0.0003 0.0021 0.0046 0.0061

2007 0.0032 0.0003 0.0015 0.0023 0.0032



•As the dominant of Murabahah (x) and Mudarabah (y),

we adopt them to construct the portfolio frontier and find

the efficient one having high-expected RoR and low

financing risk.

•Assuming set of γ ranging from 0 into 1.05 with 0.075

interval, so :

Z = γx + (1-γ)y =

nn yx

yx

y

)05.11(05.1

...

)075.01(075.0

)01(0x

22

11


The portfolio frontier starts from point A into point C with a turning

point in B. The line that indicates the efficient portfolio frontier is

from point B into C (thick line).

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

standard deviation of 0.10% (γ = 0.525). Whilst point C has the value

of expected RoR of 0.39% and standard deviation of 0.04% (γ = 0).

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.02 0.04 0.06 0.08 0.1 0.12

Portfolio's Standard Deviation (%)

Portfolio's Mean Return (%)

B

C

A

Conclusion and Policy Recommendation

Most of financing go to Murabahah financing, followed by

Mudarabah, Musharakah and Istisna.

The actual and expected RoR of Murabahah is noted the highest

among others but 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 can optimize

their portfolio financing by not only concentrating financing on

Murabahah itself but also Mudarabah with specific range of

allocation.

Nevertheless, as Musharakah and Istishna are not fully employed,

developing much effort to improve the performance of Musharakah

and istishna is also recommended in order to maximize all

financing instruments existed in the industry.

Documents

An Efficient Portfolio Frontier of Islamic Banking ...staff.ui.ac.id/system/files/users/rifki.ismal/material/durham... · An Efficient Portfolio Frontier of Islamic Banking Financing