Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

MODEL OF ASSET LIABILITY BALANCING AND OPTIMAL LIQUIDITY RESERVE IN ISLAMIC BANKING (Case of Indonesia 2000-2008)

Rifki Ismal1 PhD Student in Islamic Banking and Finance School of Government and International Affairs Durham University (United Kingdom) Phone : +44 (0) 7900411659 Email: [email protected]

Abstract. The paper firstly derives model of Islamic banking behavior in competitive banking sector and optimal liquidity reserve to find theoretical variables which determine the balance of asset and liability and optimal liquidity reserve. In fact, total Islamic deposit is driven by return sharing paid by Islamic banks to all depositors; income from operational financing; cost of banking activities and SBI rate. Whilst, total financing is also influenced by the same variables (but from bank’s point of view) and profit from non operational financing. And, profit from operational financing; investment in all financing and; revenue sharing over deposit collectively determine the optimal liquidity reserve. At the end, paper addresses some potential problems of liquidity mismatch which should be anticipated by Islamic banks, regulators and all stakeholders.

Keywords: Profit and Loss Sharing, SBI rate, Liquidity mismatch, Liquidity reserve

1

The author address: School of Government and International Affairs, Al Qasimi Building, Elvet Hill Road, Durham University, Durham (DH1 3TU), United Kingdom (UK).

1

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

As financial intermediary, bank basically receives depositors’ fund through its deposit instruments and lends it to entrepreneurs for profit so long as balancing liquidity in asset and liability. To fulfill demand of liquidity from its depositors, bank reserves some internal liquidity. This bank’s financial management is set to achieve its goal to maximize bank’s value as defined by its profitability and risk level (Greuning and Iqbal, 2008:64). Banking regulator on the other hand monitors bank’s revenues and costs associated with its lending activity and whether the bank fails (Repullo, 2005:47). 1. ASSET LIABILITY BALANCE MODELS 1. 1. Conventional Bank’s Behavior in Competitive Banking Sector Those banking activities and goals inspire the idea to develop banking behavior model in a competitive banking sector as the one formulated by Freixas and Rochet (1999:54-57) to balance bank’s asset and liability. First of all, the model assumes that bank is a risk neutral and price taker with profit maximization motive under a balance asset and liability side. Full information and optimal risk sharing are also assumed, implying a competitive bank’s deposit (Diamond and Dybvig, 2000:4). Initially, the model formulates bank’s profit as the output of total revenues from asset side minus total expenditures (costs) from liability side as in the following:

  rL L  rM  rD D  C ( D, L)

(1)

where π is bank’s profit; rL is return from loan interest; L is total bank’s loan; r is money market rate; rD is deposit interest; D is total bank’s deposit and; C is total cost representing bank’s technology in managing both deposit and loan. In particular, M is bank’s net position in money market and is given by this formula: M  (1   ) D  L

(2)

whilst α is compulsory reserve required by central bank. Therefore, π can be rewritten as:

 ( D, L)  (rL  r ) L  r (1   )  rD D  C ( D, L)

(3)

and maximum profit will be the first order condition of (3) as written below:

 C  C  (rL  r )  ( D, L) and  r (1   )  rD   ( D, L) L L D D

(4)

Thus, volume of loan and deposit should be adjusted in such a way that (r L-r) and [r(1-α)rD] equals its marginal cost. An increase in rD will decrease bank demand deposit and an increase in rL will move supply of loan up. If there are N different banks (n = 1,…N) with its typical 2

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

deposit (Dn) and loan (Ln), and total amount of securities (T-Bills) held, household function of saving and companies function of investment are formulated in equation (5), (6) and (7) below (Freixas and Rochet, 1999:55): N

S (rD )  B   D n (rL , rD , r )

(saving function of household)

(5)

(investment demanded by companies)

(6)

(inter bank market)

(7)

n 1

N

I (rL )   Ln (rL , rD , r ) n 1

N

N

n 1

n 1

 Ln (rL , rD , r )  (1   ) D n (rL , rD , r )

Equation 7 assumes that aggregate position in inter bank market is zero and r plays as controlled variable by central bank. Finally, by modifying equations (4) with assumption of constant marginal cost of intermediation (CL ≡ γL and CD ≡ γD) such that rL = r + γL and rD = r(1α) - γD and add them together into equation (5), (6) and (7), equilibrium equations with a bank’s maximum profit, optimal liquidity balance which fulfills investor expected utility2, are: S r (1   )   D  

I r   L  B 1

(8)

N

N

n 1

n 1

I r   L    Ln (rL , rD , r )  1    D n (rL , rD , r )

(9)

Equation 8 explains that liquidity in liability side of the bank is determined by reserve coefficient (α); or open market operation (B) on the equilibrium level of rL and rD (Freixas and Rochet, 1999:56). Whereas investment demanded by companies is influenced by bank’s cost of managing deposit and loan besides money market interest rate. Subsequently, equation 9 is also driven by set of interest (rL; rD; r) besides cost of managing loan, total deposit and liquidity reserve required by central bank. 1. 2. Islamic Bank’s Behavior in Competitive Banking Sector One way to measure asset liability mismatch is through cash flow of asset and liability beside the present value (Currie and Velandia, 2002: 7). Therefore, referring to Freixas and Rochet model of bank’s behavior above, the adjusted behavior model is derived for Islamic banking case. But before constructing it, sharia principles purify that conventional model in order to make it applicable for Islamic banking. Such principles are written below:

2

Fitting investor expected utility is as also taken into account in Diamond (2007:194).

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

1. Islamic banks change the term “loan” into “financing” to distinguish Islamic approach of utilizing deposit with conventional one. Regarding financing, sharia prohibits any transactions/business dealing with interest (riba), gambling (maysir), fraud (gharar), etc. Thus, Islamic modes of financing take form of either debt, equity or service financing. 2. Sharia jurisprudence adopts risk-return sharing concept for any profit and loss of financing. Then, interest on loan (rL) in conventional model is modified into return from financing (rf) as a consequence of risk-return sharing and the employment of profit and loss concept between Islamic banks and their business partners. 3. Similarly, interest rate from deposit (rD) in conventional model is turned out to be profit sharing ratio (rβ) in Islamic banking because of sharia jurisprudent above. 4. Because any return in form of interest is prohibited, sharia does not allow any remuneration for unutilized fund such as reserve requirement from central bank. Following Islamic banking principles, Indonesian Islamic banking industry has specific characteristics to be concerned as underlying assumptions and are written below: 1. There are two types of financing: (i) Operational Financing (F) composes of mostly Murabahah (61%) and Mudarabah (30%) and; (ii) Non Operational Financing (L) which is dominated by Ijarah (2%). Thus, Islamic banks receive a pre-determined short-term cash inflow (rf and rl) with a minimum probability of bearing looses3. Such financing is funded by saving and time deposit4 (79% of total deposit (D)) which is mostly short-term tenor5. Hence, banks know the withdrawal time and behavior of the deposits in order to manage a well scheduled financing. 2. Besides for financing, some liquidity is also subtracted from deposit for liquidity reserve that consists of reserve requirement (RR) stipulated by central bank and cash reserve. 3. Placement in Islamic money market and SWBI (both in M) is very liquid but not the ultimate target of bank’s financing. Deposit of non resident is very trivial and not significant to be considered in the model. 4. Islamic banks adopt revenue sharing scheme (rβ) rather than profit and loss sharing in the deposit contract. Technically, operational return is shared with depositors in the first stage

3

Except for Mudarabah, Murabahah and Ijarah are relatively safe and perfectly liquid assets. Wadiah demand deposit (21% of total deposit) is assumed idle (excluded in bank’s financing). 5 56.96% of total deposit is short term. It also implies consumers’ consumption behavior. 4

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

before banks bear their cost of operation6 (C(D,F)) on it. Nonetheless, non operational return is not shared and directly becomes banks’ non operational profit (NOP) after squaring cost of financing looses (C(L)) which is usually lesser than C(D,F). Thus, depositors do not have to compensate any looses, instead they get a continuous return on their account. As such, Indonesian Islamic banking behavior in competitive banking sector is derived in set of models below:

  r f F  rM 1  r   C D, F   rl L  C ( L)

(10)

with the 1st [.] as operational profit and the 2nd [.] as non operational profit whilst, M is formulated as M  (1   ) D  F  L 

(11)

So, π can be rewritten as:

  r f F 1  r   1  r F  r 1    r 1   D  L1  r   C ( D, F )  rl L  C L 

(12)

and maximum profit is the first order condition of (12) as written below:  C  rf 1  r   1  r   ( D, F ) F F

(13)

 C  r 1     r 1     ( D, F ) D D

(14)

 C  rl  1  r   ( L) L L

(15)

The same as conventional model previously, the maximum profit is reached if Islamic bank can make operational return (after return sharing) equals marginal cost of financing; Islamic money market return plus operational return (after return sharing) equals marginal cost of deposit and; non operational return plus return sharing equals marginal cost of financing looses. Assuming there are N different Islamic banks (n = 1,…N) with its typical deposit (Dn) and financing schemes (Fn and Ln) without any government securities7 being held, saving function of household and investment demanded by companies are: N

S (r f )   D n (r f , r , r )

(saving function of household)

(16)

n 1

N

N

n 1

n 1

I (r , rl )   F n (r f , r , r )   Ln (rl , r )

6 7

(investment demanded by companies)

(17)

Including monitoring cost of operation. Sukuk Act was approved in May 2008 so government sukuk is still in early stage of development.

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

N

N

N

n 1

n 1

n 1

 F n (rf , r , r )   Ln (rl , r )  (1   ) D n (rf , r , r )

(inter bank money market)

Rifki Ismal

(18)

And, by modifying equations (13), (14) and (15) with assumption of constant marginal cost of intermediation (CF ≡ γF, CD ≡ γD and CL ≡ γL) such that: rf  1 

F

1  r  

;

r  1 

D

r (1   

;

and rl   L  (1  r )

(19)

and add them together into equation (16) in conjunction with (17) and (18), we come up with equilibrium equations with Islamic banking industry as in the afterwards:

  F  N n S 1   D (rf , r , r )   1  r    n1   

N

N

n1

n1

 F n (rf , r , r )   Ln (rl , r ) (1   )



I (r , rl ) (1   )

N   N D I 1  ;  L  (1  r )    F n (rf , r , r )   Ln (rl , r ) n1  r 1     n1

(20)

(21)

Model (20) informs that a balanced liquidity in liability side is a function of cost of financing; revenue sharing ratio; profit loss sharing (PLS) return from operational financing; liquidity reserve; total deposit; PLS return from money market and; non operational financing return. Whilst, model (21) informs a balanced liquidity in asset side is a function of cost of deposit; liquidity reserve; total financing; PLS from operational financing; revenue sharing ratio; PLS return from money market and; non operational financing return. 2. AN OPTIMAL LIQUIDITY RESERVE MODEL 2. 1. Conventional Model of an Optimal Liquidity Reserve Following model of bank’s behavior in competitive banking sector as a basis of constructing a balanced asset liability model, this part is going to focus solely on building liquidity reserve model. As mentioned early, liquidity reserve composes of cash reserve which is basically bank’s discretion and reserve requirement which is stipulated by central bank. Hence, total available fund for credit can be simplified as total deposit (D) minus total liquidity reserve (R) or D – R. Banks regularly withdraw money from liquidity reserve based on three conditions. First is because of regular liquidity demanded where banks take money as regularly predicted and calculated. Second is because of irregular liquidity demanded whereas besides taking money from liquidity reserve, banks borrow extra fund from money market or sell short term marketable 6

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

securities. Last but not the least is because of liquidity run. In addition to selling marketable securities, if it is still not enough, banks occupy external liquidity providers such as central bank emergency liquidity, government bailout, etc (Ismal, 2007: 15 – 21). Model of liquidity reserve is also taken from Freixas and Rochet (1999) which is a modification of Monti-Klein model. The idea starts from liquidity reserve which is taken from total deposit such that available deposit for credit is formulated as D – R as written early. Then, net amount of withdrawal under static framework at the end of the period is supposed to be a random variable ~ x . If the realization x of ~ x is greater than R, the bank has a liquidity shortage and it has to pay a penalty rp(x-R), proportional to the shortage. Assuming deposits are costless and risk neutral, bank’s expected profit is (Freixas and Rochet, 1999: 228):  ( R)  r D  R   rR  r E max 0, ~ x  R  L

p

(22)

Further assumption that if expected cost of liquidity shortages formula in [.] is a convex function and random variable ~ x has a continuous density function f(x), such shortages is differentiable. Hence, Freixas and Rochet denote C(R) as an expected cost such that: 

C ( R)  rp  ( x  R) f ( x)dx R

C ' ( R)  rp 



R

f ( x)dx  rp Pr oba~ x  R

C ' ' ( R )  rp f ( R )  0

(24) (25)

Hence, the maximum profit for bank is achieved when (see appendix A for proof):  ' ( R)  r  r   r Pr oba~ x  R = 0 L

(23)

p

(26)

and the optimal liquidity reserve (R*) is found in the following relation:

r  r  Pr oba ~ x  R*  L rp





(27)

This implies that the optimal amount of liquidity reserve is the amount for which the marginal opportunity cost of holding reserves equals the expected cost of liquidity shortage or simply it equals to ratio of liquidity premium (rL – r) to the penalty interest rate rp (Freixas and Rochet, 1999: 228-229). Prisman, Slovin and Sushka further improve this model by introducing some randomness in the volume of fund collected or distributed by bank. Firstly they starts from demand function of loan as L = L(rL) and supply function of deposit as D = D(rD) such that the

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

amount of reserve is simply R = D(rD) - L(rL). With those assumptions, the expected profit function of bank becomes:

  rL L(rL )  rD D(rD )  rR  rp Emax 0, ~ x  R 

or (see appendix B for proof),

  rL  r LrL   r  rD D(rD )  rp E max 0, ~ x  R 

(28) (29)

And, we find the maximum expected profit with respected to loan rate is (Freixas and Rochet, 1999: 229-230):   rL  r L' rL   LrL   rp Pr oba~ x  R L' rL  = 0 rL

(30)

and with an elasticity of the demand for loan: rL L' rL  LrL 

L  

(31)

the optimal reserve (R*) is defined as (see appendix C for proof):  1 rL 1    r L  Pr oba ~ x  R*   rp





(32)

Equation 11 implies that the optimal reserve is determined by ratio of the difference between loan interest with respected to its elasticity and penalty interest rate. 2. 2. Islamic Liquidity Reserve Model of Indonesia The same as the way to derive Islamic banking behavior model, other characteristics and regulation in the Indonesian case are inserted and applied into liquidity reserve model. 1. As part of liquidity reserve (R), reserve requirement is stipulated by Bank Indonesia as 5% of the total Rupiah deposit and 3% of total foreign deposit. In addition to that 5% reserve requirement, the latest Bank Indonesia banking regulation number 6/21/2006 article 3 stipulates extra reserve requirements for Islamic banks with FDR below 80% but still have positive reserve requirement account. In fact, as most of the Islamic banks have FDR beyond 80% FDR (even above 100%), so the model does not take into account this extra reserve requirement. 2. However, if bank’s reserve requirement (RR) falls below the standard, central bank charges 125% of the daily Islamic money market indicative return for RR which falls below 5% but still positive. An additional 150% of that amount is further charged for RR which lies below

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

5% and the balance is negative (Bank Indonesia banking regulation number 6/21/2006 article 14). What is called penalty (rp) in the following Islamic model captures both charges (125% and an extra 150%). 3. Bank Indonesia does not pay any remuneration for RR (Bank Indonesia banking regulation number 6/21/2006 article 7). Therefore, the Islamic model eliminates r of R as in conventional model above. Considering those characteristics and regulations, the Indonesian Islamic banking expected profit allowing for penalty cost of less reserve requirement is much simpler than the conventional one and formulated as:

  rf F rf 1  r   rL LrL   rp E max 0, ~ x  R 

(33)

The maximum expected profit is then:   1  r F rf   rp Pr oba~ x  R F ' rf  = 0 rf

(34)

and with an elasticity of the demand for financing of:

rf F ' rf 

f 

F rf  the optimal reserve (R*) is defined as (see appendix D for proof):

(35)

1  r   rf  (36) Pr oba ~ x  R*  rp   f    Model (36) above implies that an optimal liquidity reserve is determined by bank’s return





over penalty rate ratio and rate of return of financing over financing elasticity ratio. Thus, some variables which have to be considered for econometric modeling afterward are rate of return of financing; elasticity of financing; penalty rate of an incompliance amount of reserve requirement; bank’s return from operational financing; realization of the return sharing paid by Islamic banks to depositors; and total Islamic bank’s financing. 3. ECONOMETRICS ANALYSIS Based on an optimal asset liability model and liquidity reserve model constructed above, a dynamic model (Autoregressive Distributed Lag – ARDL model) is employed to describe depositors and banks’ financing behaviors; identify what critical factors and condition determining asset-liability balance; analyze factors determining an optimal liquidity reserve and; find what policies to be taken to control and manage a balance asset-liability and liquidity

9

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

reserve. ARDL is used to the fact that dependent variable is often influenced by both lag of independent variable(s) and lag of itself because stakeholders and market players often include previous business performances and information in their investment decision (Studentmund, 2005: 173-175). The econometrics analysis starts from (1) Defining variable and model specification; (2) Constructing the models including testing them to fulfill the requirement of classical normal error term and Best (minimum variance), Linier, Unbiased Estimator (BLUE) of Gauss-Markov theory and finally; (3) Interpreting the result of the models. 3. 1. Definition of Variables and Model Specification All time series data in the models are using Bank Indonesia (BI) monthly data, from December 2000 into September 2008. As bank’s policy with regards to asset liability management and liquidity reserve is short to medium-term sight (Molle, 2008:1) and due to unavailability of long series data8, the models are built for short term analyses. A. Liability Model This model represents the liquidity behavior of Islamic banking depositors. In this model, dependent variable is total amount of Islamic deposit (SD) which composes of Wadiah saving deposit and Mudarabah time deposit. Independent variables, on the other side, are selected and tested referring to equation (20) and the most relevant and applicable ones are: 1. Total amount of return sharing paid by Islamic banks to all depositors (RPA). It lies as one of the depositors’ investment decisions to add/ withdraw liquidity to/from Islamic banks; 2. Total amount of income from operational financing (DFR). For depositors, this is indicator of business and banking performance in managing robust portfolio financing; 3. Total amount of cost of banking operation (CO) which covers all types of cost related to banking activities. Depositors use this to evaluate the cost efficiency of the industry and under controlled CO is indeed one of indicators of the good Islamic banking performance. 4. BI Certificate Rate (SBI). It is used as comparison with Islamic bank’s return. If the former is higher than the later, rational depositors9 might potentially convert from Islamic into conventional banks causing liquidity risk to Islamic banks (displaced commercial risk) and vice versa. 8 9

A complete data compilation starts from December 2000. Those who positions Islamic bank and conventional one indifferently.

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

5. Apart from those, it is also found that lag of total amount of Islamic deposit (SD) explains the dependent variable. It stands for depositors’ self assessment of their prior investment decision with Islamic banking. This will also convey liquidity behavior of depositors. As such, a liability model is written in equation (37) afterwards followed by a complete list of variables and their historical statistics listed in Table 1. Δ(SDt) = c + β1Δ(RPAt-2) + β2Δ(DFRt-5) + β3(COt-6) + β4Δ(SDt-12) - β5Δ(SBI t-6) + e

(37)

Table 1. Statistical Summary (million Rp)

Variable Islamic Deposit (SD) Return sharing paid by Islamic banks to all depositors (RPA) Income from operational financing (DFR) Profit from non operational financing (NOP) Bank Indonesia Certificate Rate (SBI)* Cost of Banking Operation (CO) Investment in operational financing (PDF)

Mean Median Std Deviation 9,516,425 8,284,236 7,651,059 378,994.3 225,045 368,079.5 862,379.9 462,660 879,958.9 246,766.9 101,618 286,458.0 11.083 9.875 3.3985 582,543 385,452 565,065.2 10,996,677 9,469,946 8,583,169

* In percentage per year

Some policy instruments such as liquidity reserve and SWBI rate are not taken into account in the liability model for two reasons. First, SWBI is central bank’s policy to manage industry’s liquidity which is a discretionary based and not directly expressing depositors’ liquidity behavior. Second, liquidity reserve, in particular reserve requirement rate is fixed (stipulated by central bank) to certain percentage of total deposit. Inserting these policy instruments in the model (to explain total deposit) will technically violate classical error term assumption. However, liquidity reserve will be accommodated specially in liquidity reserve model later on. B. Asset Model This model represents Islamic banking performance in managing liquidity. Dependent variable is total amount of investment in operational financing (PDF) which consists of debt based and equity based financing. Independent variables are selected and tested referring to equation (21) and the most relevant and applicable ones are: 1. Total amount of return sharing paid by Islamic banks to all depositors (RPA). Islamic banks count this variable in financing portfolio decision to sustain the existing depositors and attract new candidates. Under dual banking system, a competitive and attractive Islamic banking return is a must in order to make it competitive (Ismal, 2008a:12-13);

11

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

2. Total amount of income from operational financing (DFR). Undoubtedly DFR is one of the important variables to measure the result and robustness of bank’s portfolio financing; 3. Total amount of profit from non operational financing (NOP). It is bank’s additional income besides operational return. To support and reach an optimal financing performance, this variable can not be ignored; 4. Total amount of cost of banking operation (CO). From bank’s perspective, CO determines how much bank’s profit will be and how good it manages cost of banking activities. 5. Akin to liability model, lag of total amount of investment in operational financing (PDF) triggers the dependent variable as well. It makes sense since the output of the previous portfolio financing comes as one of important factors for the next portfolio financing. Finally, equation of asset model is written in the following while a complete list of variables and their historical statistics are included in Table 1 previously. Δ(PDFt) = c + β1Δ(RPAt-11) + β2Δ(DFRt-10) + β3(COt-6) + β4Δ(PDFt-1) + β5Δ(PDFt-2) + β6Δ(NOP) +e

(38)

As the model measures variables in their aggregate level, operational income (DFR) does not distinguish types of financing which contribute to DFR and return sharing paid by Islamic banks to all depositors (RPA) also does not distinguish owner of account holders. Further, due to characteristics of the Indonesian Islamic banking industry, Islamic banks’ cash flow from business sector can be assumed as fixed, continuous and pre-determined (certainty condition) because of the domination of debt based financing. Meanwhile, depositors’ income is not ultimately fixed to certain amount but still positive (because of return sharing scheme). But, after sharing revenue with depositors, Islamic bank’s profit can be positive or negative depending on how much its cost of banking operation is. Meanwhile, macroeconomic variables such as GDP, inflation rate, exchange rate, base money etc are assumed embodied in financing performances variables and not being treated in a special manner. One of the reasons is because the share of Islamic banking industry is only around 2% of the total banking industry so that including specifically those macroeconomic variables in the model are not really noteworthy. C. Liquidity Reserve Model This model shows an optimal liquidity reserve and variables that derive such an optimal and balance liquidity. Dependent variable is total amount of liquidity reserve (R). Independent 12

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

variables are selected and tested referring to equation (36) and the most relevant and applicable ones are in the following: 1. Total amount of investment in all kinds of financing (PF). This variable is part of elasticity of financing as written in equation (36) which influence the optimal liquidity reserve to be managed; 2. Total amount of profit from operational financing (OP). This variable is the main contributor of total return from financing and one indicator of how robust bank’s portfolio financing is and how attractive and competitive its revenue sharing to depositors will be. Depositors’ liquidity behavior (to inject or take money) submits to the performance of this variable. 3. Percentage of revenue sharing over deposit (RSD). It approaches (rβ) in equation (36) and acts as one deterministic variable of depositors’ investment decision with Islamic banks. 4. Total amount of liquidity reserve (R) which composes of reserve requirement (RR) and cash reserve. The position of liquidity reserve is decided by Islamic banks upon taking into account the performance of financing; pattern of liquidity demanded by depositors; penalty rate (rp) if reserve requirement falls below the stated level by central bank; opportunity cost of holding this non profitable account, etc. 5. Prior position of liquidity reserve. The same as in liability and asset model, this prior position stands as one of the bank’s considerations for the current and future liquidity reserve position. Then, the optimal liquidity reserve model is written afterwards followed by a complete list of variables and their historical statistics shown by Table 2. ΔRt = c - β1Δ(OPt-3) + β2Δ(PFt-2) - β3(RSD) + β2Δ(Rt-12) + e

(39)

Table 2. Statistical Summary (million Rp)

Variable Profit from operational financing (OP) Investment in all financing (PF) Revenue sharing over deposit (RSD)* Liquidity Reserve (LR)

Mean 825,576 13,673,828 4.029 653,115

Median Std Deviation 496,401 774,681 11,350,808 10,595,069 3.565 2.213 573,813 475,261

* In percentage per year

Table 2 informs that total financing faces an increasing trend as shown by a high value of mean and median. Fortunately, because of domination debt based financing, such an increasing trend gives benefit to depositors in form of growing profit from operational financing (OP) and

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

higher percentage of revenue sharing over deposit (RSD). These numbers point out a good management of financing. Nevertheless, the current business and economic situation bring some challenges to Islamic banks predominantly to arrange a robust level of liquidity reserve in line with their financing activities and to provide well-demanded liquidity to depositors. R in Table 1 shows a high median and standard deviation meaning that, despite successful financing management above, business activities are getting riskier than before and depositors’ liquidity behavior is getting more difficult to be predicted and anticipated. 3. 2. Construction of Models A. Stationary Test Before modeling, unit root test is conducted to check stationary of every variable. The basic idea of stationary can be explained by taking a simple AR (Autoregressive) (1) process: Yt  a0  a1Yt 1   t

(40)

where Yt-1 is lag independent variable which might contain a constant and trend; a is a constant and; ε is assumed to be a white noise (Enders, 1995: 70). If |a1|≥1, Yt is a non stationary series meaning it has a trend; does not have constant mean and; the variance is time variant. So, the hypothesis of stationary can be evaluated by testing whether absolute value of a1 is strictly less than one. Two common tests used in this stage are Augmented Dickey-Fuller (ADF) and Phillip and Perron (PP). ADF re-estimates (24) by subtracting Yt-1 (Lutkepohl and Kratzig, 2004:54): p 1

Yt  Yt 1   a j Yt  j   t

(41)

j 1

where α = -a, null and alternative hypothesis of H0: α = 0 and H1: α < 0; with tα< α/(se(α)). The basic idea of ADF is to correct high order serial correlation by adding lagged difference terms in the right hand side of the equation. Meanwhile, Phillips and Perron (PP) use nonparametric statistical methods to take care of the serial correlation in the error terms without adding lagged difference terms (Gujarati, 2004: 818). The result of stationary test is depicted in table 3 and 4 in the following.

14

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Table 3. Stationary Test of Asset Liability Variables Variable Name SD RPA DFR CO SBI NOP PDF

Augmented Dickey-Fuller Level 1st Difference -4.333 -8.848*** -3.135** -11.514*** -2.918** -10.389*** -4.490*** -1.5133 -4.0432*** 2.6570* -10.0658*** 2.565 -2.322

Rifki Ismal

Table 4. Stationary Test of Liquidity Reserve Variables

Phillip and Perron Level 1st Difference 5.216 -8.947*** -3.152** -12.511*** -2.847* -13.824*** -4.323*** -1.1988 -3.9050*** -2.5584 -13.8509*** 4.402 -5.332***

Note: *,**,*** refers to stastical significance of 10%, 5% and 1%

Variable Name OP PF RSD R

Augmented Dickey-Fuller Phillip and Perron Level 1st Difference Level 1st Difference -2.461 -10.542*** -2.388 -11.992*** 6.064 -6.682*** 6.355 -6.734*** -4.0511*** -4.0511*** 5.85 0.059 5.87 -11.276***

Note: *** refers to stastical significance of 1%

Table 3 reveals that SD and PDF (dependent variables) are not stationary in level but integrated in order 1 (1st difference). Meanwhile, RPA, DFR, NOP and SBI (independent variables) are all stationary (1% statistical significance) in order 1 (1st difference) except CO which has been stationary in level. Meanwhile, table 4 reveals that R is stationary in order 1 as well followed by other variables (OP, PF and R). Nonetheless, return sharing paid by Islamic banks to depositors (RSD) is already stationary in level or I(0). Thus, the model will integrates all variables in order 1 except CO to find the robust asset and liability models whilst liquidity reserve model will integrate all variables in their 1st different except RSD to find the robust liquidity reserve models. B. Correlation and Causality Test To asses how strong the linear relation between dependent and independent variables and the causality direction of it, correlation coefficient test and granger causality test are used. Correlation coefficient formula is:

r1, 2 

[( X  X )( X  X )] (X  X ) (X  X ) 1

1i

2i

2

2

1i

1

2i

(42) 2

2

with r value ranges between -1 ≤ r ≤ 1. Basically it detects correlation of two variables without explaining causality or direction of the correlation (if exists). Then, if two variables has a perfect positive linear correlation, r = 1; it they have a perfect negative linear correlation, r = -1; and if there is no linear correlation, r = 0. Whilst, granger causality specifically detects how much current dependent variable (Yt) can be explained by past value of it (Yt-n) and lag value of independent variables (Xt-n). Mathematically, granger causality function is (Gujarati, 2004: 697):

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

n

n

i 1

j 1

Yt    i X t  i    jYt  j u1t

n

n

i 1

j 1

Rifki Ismal

and X t   i X t  i    jYt  j  u2t

(43)

Yt is said to be granger cause by Xt if the latter explain the former as well as lag of the former and vice versa. The assesment of both tests for variables of liability and asset is afterwards. Table 5. Coefficient of Correlation

Variable Name SD PDF

Value of Coefficient of Correlation RPA DFR CO SBI NOP 0.6960 0.7486 0.6547 -0.5904 0.7284 0.7763 0.6788 0.7996

Table 6. Granger Causality Test Null Hypothesis RPA does not Granger Cause D(SD) DFR does not Granger Cause D(SD) CO does not Granger Cause D(SD) SBI does not Granger Cause D(SD) RPA does not Granger Cause PDF NOP does not Granger Cause PDF DFR does not Granger Cause PDF CO does not Granger Cause PDF

F-Stat 9.4232 10.0581 23.0428 13.7086 8.8568 11.0188 7.7144 4.4769

P-value 0.0028 0.00211 0.0000 0.0003 0.0037 0.0013 0.0067 0.0372

Conclusion Not Accepted Not Accepted Not Accepted Not Accepted Not Accepted Not Accepted Not Accepted Not Accepted

Coefficient of correlation shows that SD has more than 50% indication of a perfect positive linear correlation with RPA, DFR and CO (Table 5) and perfect negative linear correlation with SBI. Like SD, PDF has the same indication even with a higher magnitude than SD. This result indicates that all of these variables have strong correlation compared to other variables considered in equation (20) and (21) and the value of SD and PDF associates with the value of RPA, DFR, CO and SBI (for SD) and RPA, DFR, CO and NOP (for PDF). This correlation is further examined by granger causality test in Table 6 to see the direction of it. Granger causality explains that RPA, DFR, CO, SBI are indeed explaining SD whilst RPA, DFR, CO (from bank’s perspective) and NOP are cooperatively explaining PDF. This outcome strengthens the decision to choose SD and PDF as dependent variables and to be explained by RPA, DFR, CO, SBI (for SD) as well as RPA, DFR, CO, NOP (for PDF). However, assessment for liquidity reserve variables is shown by table 7 and 8. Table 7. Coefficient of Correlation

Coeff of Correlation Variable Name OP PF RSD R 0.738 0.9981 0.1829

Table 8. Granger Causality Test

Null Hypothesis OP does not Granger Cause D(R) PF does not Granger Cause D(R) RSD does not Granger Cause D(R)

F-Stat 23.0317 35.6202 9.1028

P-value 6.7E - 6 5.4E - 8 0.0033

Conclusion Not Accepted Not Accepted Not Accepted

Coefficient correlation shows that R has more than 50% indication of a perfect positive linear correlation with both OP and RSD and greater indication with PF (Table 7). R and OP denotes coefficient of correlation of 0.74, R and RSD records 0.18, while R and PF depicts the strongest

16

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

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among others with 0.99. This is evidence that these four variables have strong correlation compared to other variables considered in equation (36) and the value of R associates with the value of OP, RSD and PF. Investigation with granger causality strengthens the idea further. As shown in Table 8, granger causality indicates that R is explained by its independent variables (OP, PF and RSD) with the strongest influence from PF followed by OP and RSD respectively. This finding means that the decision to locate R as dependent variable to be explained by OP, PF and RSD as independent variable and lag of R is very reasonable and statistically significant. It is because causality relationship goes from OP, PF and RSD to R and not vice versa. The subsequent section explains the result of the regression between SD, PDF, R and their independent variables as well as presenting the significant lag period of every independent variable to enlighten dependent variables. C. Regression Result The estimated models of liability, asset and liquidity reserve are depicted in Table 9, 10 and 11 in the following. All regressions have fit the requirement of classical normal error term such as autocorrelation test, heteroskedasticity test, multicolinearity test including Ramsey Reset test for correctly specified equation. The coefficient of individual and overall variables has also been robust with Gauss-Markov requirement of BLUE. Table 9. Estimated Liability Model

Table 10. Estimated Asset Model

Dependent Variable: D(SD) Dependent Variable: D(PDF) Independent Variable Coefficient t-statistic Independent Variable Coefficient t-statistic 40100.35 1.3398 Constant -2315.9 -0.0352 Constant D(RPA(-11)) 0.3791 3.8413 D(RPA(-2)) 0.3128 2.4681 D(DFR(-10)) 0.1126 2.1434 D(DFR(-5)) 0.1949 3.3934 0.1648 3.2298 D(SBI(-6)) -265342 -3.2773 CO(-6) D(NOP) 1.0961 5.1099 CO(-6) 0.2864 3.8209 D(PDF(-1)) 0.3166 3.6793 D(SD(-12)) 0.5076 3.1504 D(PDF(-2)) 0.3138 4.0625 Diagnostic Analysis Value P-value Diagnostic Analysis Value P-value R-squared 0.3921 R-squared 0.6764 Residual Sum of Square 8.30E+12 Residual Sum of Square 3.56E+12 Akaike Info Criterion 28.3967 Akaike Info Criterion 27.5608 F-Statistics 9.1614 0.0000 F-Statistics 24.7405 0.0000 Jarque Bera 2.3720 0.3054 Jarque Bera 2.0763 0.3541 LM test 0.4089 0.6659 LM test 1.5314 0.2234 ARCH LM test 1.6952 0.1969 ARCH LM test 0.0017 0.9669 Ramsey RESET 0.6673 0.4167 Ramsey RESET 0.2057 0.6515

First of all, the liability model reveals that lag 2 periods of banks’ marginal return sharing paid by Islamic banks to all depositors (ΔRPAt-2); lag 5 periods of marginal income from 17

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

Rifki Ismal

operational financing (ΔDFRt-5); lag 6 periods of marginal SBI rate (ΔSBIt-6); lag 6 periods of cost of banking operation (COt-6) and; lag 12 periods of marginal Islamic deposit (ΔSDt-12) jointly determine current marginal Islamic deposit (ΔSDt). Since 41.4% of total deposit is in form of 1-month time deposit, depositors tend to consider lag 2 periods of return sharing paid by Islamic banks to all depositors (short term) in deciding their next deposit placement. So long with it, the performance of Islamic banks in managing the fund as reflected in income from operational financing and cost of banking operation is also evaluated semi annually (lag 5 and 6 periods) due to the pattern of business cycles in the country. Lag 6 periods of SBI rate is also part of depositors’ consideration because signal of monetary policy is exercised by them semi annually. Finally, how much benefit gained by depositors as a result of placing fund in Islamic deposit for a year (lag 12 periods) guides their further placement of fund. Meanwhile, the second model, asset model shows that lag 11 periods of return sharing paid by Islamic banks to all depositors (ΔRPAt-11); lag 10 periods of marginal income from operational financing (ΔDFRt-10); lag of 6 periods of cost of banking operation (COt-6); marginal profit from non operational financing (ΔNOP) and; lag 1 and 2 periods of marginal investment in operational financing (ΔPDFt-1 and ΔPDFt-2) cooperatively explain the current marginal investment in operational financing (ΔPDFt). For Islamic banks, lag 11 periods of return sharing paid by Islamic banks to all depositors delivers at least two important messages: (i) The robustness of their previous portfolio financing policies and; (ii) The benchmark to pay at least the same return to depositors in the next payment periods. These two messages underpin how much the next marginal bank’s financing will be. Later, the last 10 periods of income from operational financing also comes into calculation because both 61% Murabahah and 30% Mudarabah10 financing are short term tenor. Next, the previous cost of banking operation (lag 6 periods) positions as a pointer for Islamic banks to keep improving cost efficiency to gain a better (higher) profit. However, profit from non operational financing is taken into account in the current basis because Ijarah return in this basis is the most relevant one to be considered. Finally, how much investment in operational financing in the last 1 and 2 periods, guides banks’ next financing policy.

10

Statistical data informs that 73.6% of financing goes to small and medium enterprise (SME) which is retail financing for short term period.

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

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Finally, the last model, estimated model of liquidity reserve expresses that lag 3 periods of marginal profit from operational financing (ΔOPt-3); lag 2 periods of marginal investment in all financing (ΔPFt-2) and; lag 9 periods of percentage revenue sharing over deposit (RSDt-9) mutually determine marginal liquidity reserve in the current period (ΔRt). Therefore, there is no variable influencing liquidity reserve in its current level. Rather, the most influential period is the prior (lag) period of every variable. Table 11. Estimated Liquidity Reserve Model Dependent Variable: D(R) Independent Variable Coefficient t-statistic Constant 13182.39 2.5588 D(OP(-3)) -0.0146 -3.0008 D(PF(-2)) 0.0100 2.0032 RSD(-9) -2212.85 -2.2014 D(R(-12)) 0.8568 8.0721 Diagnostic Analysis Value P-value R-squared 0.5242 Residual Sum of Square 2.95E+10 Akaike Info Criterion 22.7330 F-Statistics 21.9357 0.0000 Jarque Bera 0.7315 0.6936 LM Test 2.6846 0.1057 ARCH LM test 2.2985 0.1182 Ramsey RESET 1.4110 0.2388

Further, the model finds positive direction between the current marginal liquidity reserve with the last 2 periods of marginal investment in all financing and last year marginal liquidity reserve. Meanwhile, negative direction occurs between current marginal liquidity reserve with the last 3 periods of marginal profit from operational financing and the last 9 periods of percentage revenue sharing over deposit. In fact, it tells that the decision of an optimal liquidity reserve must go in the same direction (positive) with total investment in all financing and prior (annual) record of the liquidity reserve. When Islamic banks extended higher investment in the last two periods than the previous one, they have to prepare extra liquidity reserve to anticipate financing failure, unexpected liquidity withdrawal from depositors, etc. The same case with the last 12 periods of liquidity reserve, if it was high meaning they have to locate extra liquidity lately. One main reason is because of yearly demand of business activities as indicated by annual pattern of currency in circulation (Ismal, 2009:11). However, Islamic banks have to hold extra liquidity reserve in the opposite direction with profit from operational financing. It is because if Islamic banks face any business loss leading to 19

Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

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lower profit from operational financing and percentage revenue sharing over deposit, they have to prepare some additional liquidity reserve to anticipate liquidity withdrawal from return oriented (rational) depositors. Such depositors have two accounts (Islamic bank’s account and conventional bank’s account) and will switch their deposit to the one who pays higher return. 4. INTERPRETATIONS OF MODELS A. Liability Model Liability side as sources of fund for Islamic banks has specific liquidity behavior pointing out depositors’ behaviors towards investing fund in Islamic banks. Amongst others, depositors’ ultimate formative factor is SBI rate. It is depositors’ benchmark return in comparison with the one offered by Islamic banks (Ismal, 2008b:4). Hence, in order to be competitive and to convince depositors to put more fund, revenue sharing should be set competitively and match depositors’ expected return (SBI rate). After SBI rate, how much benefit gained by depositors from depositing money in Islamic deposit is their second consideration. It connotes not only monetary benefit (revenue, bonus, etc) but also non monetary benefit such as banking services, facilities, etc. Depositors’ satisfaction in general plays the key important role in directing their further placement. Thirdly is specifically related to how much return sharing paid by Islamic banks to all depositors in short term period. The higher Islamic banks earn profit, the better the depositors’ perception and more funds from depositors will be injected (Chapra, 1985:110). And because depositors’ interest still focuses in 1-month Mudarabah time deposit11 with expectation of a short term return, revenue sharing paid by banks in the last 1-2 months time is very crucial. This behavior is caused by (a) Transaction motive (non investment motive) of depositing money in Islamic banks (b) Fragile economic condition which may potentially ask depositors to withdraw some cash (c) Some big corporations still rely one conventional bank for long term placement of deposit. Next is cost of banking operation. Through multiplier effect, it effects depositors’ decision. A high FDR tends to lead more cost of banking operation. Depositors perceive it as more return sharing will be potentially paid so that they add more deposit. The last influential factor is income from operational financing. Compared with all former variables, depositors less considers this variable specifically. Nonetheless, if they hear/know from media, etc that their 11

One month Mudarabah time deposit captures 56.8% of the 46% total Mudarabah time deposit.

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

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Islamic bank earns high income from operational financing, they will be happy to place more fund and vice versa. B. Asset Model Following depositors’ liquidity behavior, asset side describes Islamic banks liquidity behavior. First of all, one of the purposes of Islamic banks to manage liquidity is how to optimize profit from non operational financing. It is because this variable is not only the source of income which is not shared with depositors but also an adjustable rate can be implemented to Ijarah contract responding to the volatile economic condition. If it tends to be more prospective, higher marginal financing will be advanced by the banks. The next factor is return sharing paid by Islamic banks to all depositors. The importance of this factor is related to the attractiveness, competitiveness and ability of Islamic banks to match depositors’ return expectation. Third variable is the general result of the previous decision of bank’s investment in operational financing. This factor evaluates the successfulness or failure of last financing policy and to be improved in the next financing decision. Hence, it captures setting up the robust portfolio financing adjustable to current economics/business condition. The fourth important factor is valuing the performance of its business partners and the prospect of the project being financed. Selecting the business partners, analyzing business proposal and building good cooperation with business partners will result in a sustainable and higher profit being produced. How good the previous record and how prospective the future business condition underlies Islamic banking’s next financing decision. That factor actually links with cost of banking operation, the fifth one. If bank’s financing is expansive, cost of it might also up accordingly. However, if that expansion produces return as expected, Islamic banks might not doubt release more financing because banks might create more revenue by increasing cost (Hassan, 2003: 4). In order to fulfill the expectation of depositors, achieving more revenue with additional cost of operation is a consequence of Islamic banks to be competitive and attractive. C. Liquidity Reserve Model The model delivers some important messages with respected to factors determining an optimal position of liquidity reserve. First of all, liquidity reserve mainly depends on return sharing paid by Islamic banks to all depositors. Because of the potential of displaced commercial risk, once return sharing is paid lower than before, Islamic banks might prepare extra liquidity

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

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reserve. Secondly is the previous position of liquidity reserve. Islamic banks submit to this factor because it contains regular demand of liquidity by business sector. Thirdly refers to prior investment in operational financing. If it moves up, liquidity reserve is also up anticipating either regular or irregular liquidity withdrawal. One reason, expansion of operational financing is caused by an increasing trend of deposit which requires Islamic banks to reserve higher position of liquidity than before (Ismal, 2008a: 2). Lastly, is profit from operational financing. Dependency of current liquidity reserve position with this factor mimics dependency of liquidity reserve with return sharing paid by Islamic banks to depositors. Once profit from operational financing falls, it will suggest Islamic banks to prepare extra liquidity since payment of return sharing to depositors will be falling as well. 5. MODEL RESULT WITH REGARDS TO LIQUIDITY RISK This quantitative analysis stresses some important liquidity behaviors as well as the potential of liquidity risk to be considered by Islamic banks. Those are: 1. Depositors’ liquidity behavior is mostly influenced by the current economic/business condition. Unpleasant economic condition with increasing trend of interest rate (SBI rate) tends to persuade them to switch deposit from Islamic into conventional banks. Having an economic stability is extremely critical to mitigate this intention. 2. Depositors’ decision to inject or withdraw money depends on performance of Islamic banks to conduct a robust portfolio financing. They hope to get a positive, sustainable and competitive return. Meanwhile, Islamic banks’ financing contract can not guarantee such depositors’ expectation due to the nature of sharia contracts. Therefore, excess liquidity in Islamic banks might occur if business is in downturn (limited fund can be extended) and it can also lead to inability of banks to pay promising return to depositors. However, fortunately, equity and debt financing are found so far very resilience during unpleasant economic condition with low probability of loss (Ismal, 2008c:5-8). 3. Moreover, there is a different performance evaluation period between depositors and Islamic banks. Depositors evaluate Islamic banks based on banks’ payment of short term (lag 2 periods) revenue sharing but on the other hand, Islamic banks release financing in consideration of (longer) historical revenue sharing payments (lag 11 periods) to depositors. If depositors’ return expectation is suddenly high, it might not be accommodated subsequently by the banks. Paying a well-calculated and well-determined revenue sharing

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

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ratio to avoid withdrawal risk and bankruptcy should be implemented in this case (Ismal, 2008b: 10-12). 4. Under the same case, depositors look at the performance of banks’ business partners (through income from operational financing) in the last 5 periods but Islamic banks value their business partners’ performance in a longer one (lag 10 periods) to set up their financing policy. This might invite a different business return perspective leading to liquidity mismatch between asset and liability side. With any degree of maturity mismatch, banks will be vulnerable to changes in liquidity preferences (Rajan and Bird, 2001: 9). 5. It is very imperative for Islamic banks to set an optimal level of liquidity reserve and in order to do that they have to incessantly improve the performance of the asset side (portfolio financing management) and fully understand depositors’ liquidity behaviors. 6. CLOSING REMARKS Conventional banking model of liability, asset and liquidity reserve inspire the construction of the Islamic ones. With regards to liquidity management, liability and asset models address the significant role of variables: return sharing to depositors; SBI rate; income from operational financing; cost of banking operation and; profit from non operational financing. Meanwhile an optimal liquidity reserve should consider variables of return sharing to depositor; profit from operational financing and; total investment in all financing. At the end, three models highlight some potential liquidity risk problems which have to be anticipated and followed up by Islamic banks, regulators and all stakeholders.

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BIBLIOGRAPHY Freixas, Xavier and Rochet, Jean-Charles (1998). Microeconomics of Banking. The MIT Press, 3rd Printing, London, England, 1998. Greuning, Hennie Van and Iqbal, Zamir (2008). Risk Analysis for Islamic Banks. The World Bank Publisher, Washington DS, USA, 2008. Currie, Elizabeth and Velandia, Antonio (2002). “Risk Management of Contingent Liabilities Within a Sovereign Asset Liability Framework”. World Bank working paper series number 174069, January, 2002. Molle, Dalle John (2008). “Asset and Liability Management- A Modern Perspective on Interest Rate and Liquidity Risk Management”. Paper of Kaplan Financial : Treasury and Capital Market. Kaplan City Campus 51 Cuppage Road #02-01 Singapore, October 2-3, 2008. Diamond, Dauglas W and Dybvig, Philip H (2000). “Bank Runs, Deposit Insurance, and Liquidity”. Federal Reserve Bank of Minneapolis Quarterly Review, Volume 24 No. 1, Winter, 2000, p 6. Diamond, Daughlas (2007). “Banks and Liquidity Creation: A Simple Exposition of The Diamond-Dybvig Model”. Federal Reserve Bank of Richmond Quarterly Review, Volume 93 No. 2, Spring 2007, p 194. Repullo, Rafael (2005). “Liquidity, Risk Taking and The Lender of Last Resort”. International Journal of Central Banking (CEMFI), Volume 1 No. 2, September 2005. p 48. Rajan, Ramkishen S and Bird, Graham (2001). “Banks, Maturity Mismatches and Liquidity Crises: A Simple Model”. Center for International Economics Studies, Discussion Paper No. 0132, Adelaide University, July 2001, p 9. Lutkepohl, Helmut and Kratzig, Markus (2004). Applied Time Series Econometrics. Cambridge University Press, 2004, p 54. Enders, Walter (1995). Applied Econometric Time Series. John Wiley & Son, 1st Edition, Canada, 1995, p 70. Chapra, Muhammad Umer (1985). Toward Just a Monetary System. The Islamic Foundation, Leicester, UK, 1985, p 110 – 111. Kabir, Hassan (2003). “Cost, Profit and X-Efficiency of Islamic Banks in Pakistan, Iran and Sudan”. Proceeding Conference on Islamic Banking: Risk Management, Regulation and Supervision, organized by Bank Indonesia, Ministry of Finance Indonesia and IDB, Jakarta, September 30th – October 2nd, 2003.

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Ismal, Rifki (2008a). “The Potential of Liquidity Risk in Islamic Banking”. Academic Paper Presented in Ustinov College Finance Seminar, Durham University, United Kingdom, May 3rd, 2008. Ismal, Rifki (2008b). “Withdrawal Risk, Bankruptcy and Revenue Sharing Equilibrium Ratio in Islamic Banks”. Unpublished Academic Paper, Durham University, United Kingdom, December 5th, 2008. Ismal, Rifki (2008c). “Islamic Banks Portfolio Risk Measurement”. Unpublished Academic Paper, Durham University, United Kingdom, November 3rd, 2008.

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Model of Asset Liability Balancing and Optimal Liquidity Reserve in Islamic Banking

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Appendix A

 ( R)  rL D  R   rR  rp E max 0, ~ x  R 

 ( R)  rL D  rL R  rR  rp E max 0, ~ x  R  ~  ' ( R)  r  r  r Pr obax  R  = 0 L

p

r  r  Pr oba ~ x  R*  L rp





so that, such that, finally, (proven)

Appendix B

  rL L(rL )  rD D(rD )  rR  rp Emax 0, ~ x  R 

or,   rL L(rL )  rD D(rD )  r DrD   LrL   rp Emax 0, ~ x  R  ~   rL L(rL )  rD D(rD )  rD rD   rL rL   rp E max 0, x  R    r  r Lr   r  r D(r )  r E max 0, ~ x  R  L

L

D

D

so that, finally it becomes, (proven)

p

Appendix C   rL  r L' rL   LrL   rp Pr oba~ x  R L' rL  = 0 rL rL L' rL   rL ' rL   LrL   rp Pr oba~ x  R L' rL  = 0

LrL  rL  rp Pr oba~ x  R  r  L' rL 

so that, then,

by multiplying with

rL r L' rL  and knowing  L   L LrL  rL

 1 rL 1    r L  x  R*   We comes up with the optimal reserve (R*) as Pr oba ~ rp





(proven)

Appendix D   1  r F rf   rp Pr oba~ x  R F ' rf  = 0 rf

1  r F (rf ) Pr oba~ x  R  rp F ' (rf )

then,

by multiplying with

rf rf

and knowing  f  

1  r   rf x  R*  We comes up with the optimal reserve (R*) as Pr oba ~ rp    f





rf F ' ( rf ) F ( rf )

  (proven)  

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