Evaluating the performance of islamic banks using a modified monti-klein model

Sumarti, Novriana; Andirasdini, Indah G.; Ghaida, Nidya I.; Mukhaiyar, Utriweni Article Evaluating the performance of islamic banks using a modified monti-klein model Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Sumarti, Novriana; Andirasdini, Indah G.; Ghaida, Nidya I.; Mukhaiyar, Utriweni (2020) : Evaluating the performance of islamic banks using a modified monti-klein model, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 13, Iss. 3, pp. 1-21, https://doi.org/10.3390/jrfm13030043 This Version is available at: https://hdl.handle.net/10419/239137 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Risk and Financial Management Article Evaluating the Performance of Islamic Banks Using a Modified Monti-Klein Model Novriana Sumarti 1,*, Indah G. Andirasdini 2, Nidya I. Ghaida 3and Utriweni Mukhaiyar 1 1Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl Ganesha 10 Bandung, Jawa Barat 40132, Indonesia; [email protected] 2Master Program, Deparment of Mathematics, Institut Teknologi Bandung, Jl Ganesha 10 Bandung, Jawa Barat 40132, Indonesia; [email protected] 3Undergraduate Program, Deparment of Mathematics, Institut Teknologi Bandung, Jl Ganesha 10 Bandung, Jawa Barat 40132, Indonesia; [email protected] *Correspondence: [email protected] Received: 2 December 2019; Accepted: 26 February 2020; Published: 2 March 2020   Abstract: The development of Islamic banking continues to increase in many Muslim (majority) countries. Substituting interest with profit shares in the assets of a given Islamic bank as one of the bases of operation has many interesting implications, one of which is the need for more involved risk and return measures. In this paper, we take a balance sheet analysis-based approach to formulating profit in order to assess the performance of an Islamic bank. Then the implementation of this approach is demonstrated using data provided by Indonesia’s financial services authority, known as the OJK. We develop formulae for the calculation of profit share between funding and financing funds as well as the appropriate rates of return. The resulting figures are then used to construct statistical models for short-term forecasting of the volumes of funding fund from the depositors and financing fund for business people who need funds for their investment projects. The approach we develop is innovative for Islamic banks and would be a welcome addition to their performance assessment toolkit. One of the results of our model indicates an increasing pattern on the equivalent rates of returns for funding and financing funds every year, which is caused by the fact that the reported income from the financing fund seems to have been accumulated from the beginning until the end of year in the Islamic bank. Keywords: balance sheet; Islamic or Sharia banking; time series model; Monti-Klein bank profit analysis 1. Introduction 1.1. Overview The concept of an Islamic bank compels financial managers to adjust their strategies as their operations can no longer be based on borrowing and lending at a mark-up. More specifically, Islamic banks must seek out prospective projects and participate financially, establishing their stake and their right to a share of returns on said projects. One of the main implications of this is that a higher level of disclosure is expected as returns to investors are now a share of the fruits of a project instead of simply a number. While this also leads to a tighter relationship between the real and financial sides to the economy—as discussed in Siddiqi (2006) and Van Greuning and Iqbal (2009)—it naturally requires a more involved procedure for calculating the return (usually called nisbah) and risk of a project. Our intention is to delve into this aspect of Islamic banking, developing a return and risk measure for Islamic banks based on the Monti-Klein model of profit calculation as we shall elaborate. Aside from J. Risk Financial Manag. 2020,13, 43; doi:10.3390/jrfm13030043 www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2020,13, 43 2 of 21 standard performance evaluation, we demonstrate that these measures can be used to facilitate the construction of statistical models which can help assess the prospects of a given Islamic bank. 1.2. Literature Review Hassan and Aliyu (2018) provide a survey of studies comparing the profitability and returns of Islamic banks with conventional banks, demonstrating that these studies generally use regression and vector autoregression (VAR) models. One study of note is that of Zainol and Kassim (2010), who used the VAR framework to analyse market dynamics between conventional and Islamic banks in Malaysia. They found among other things that there is a negative relationship between the total deposit of Islamic banks and the interest rate of conventional banks. Doumpos et al. (2017) stated that there is no significant difference globally of the overall financial strength between Islamic and conventional banks. However, regionally, conventional banks outperform the Islamic banks in Asia and the Gulf Cooperation Council, but Islamic banks perform better in the Middle East, North Africa and Senegal region. Sumarti et al. (2017) shows that Islamic Banking growth in Indonesia has not given significant impact to Indonesia’s economic growth, even though the development of Islamic banks has been going for more than 20 years. As for the suggestion in calculation of risk, some of the more rigorous approaches follow Van Greuning and Iqbal (2008) in explicitly modeling risk based on balance sheet assets and liabilities. Examples include Fadhlurrahman and Sumarti (2016) and Sumarti et al. (2018), who use deterministic systems of equations to model the dynamics of balance sheet items to predict given the banks’ deposit and loan evolution. Bidabad and Allahyarifard (2019) as well as Rahman (2019), use this approach to model optimal asset mixes for Islamic banks. Our review of the literature therefore indicates that while time series analysis and dynamics modeling have been employed, our use of the Monti-Klein model is relatively novel and should provide both contributions and new directions for the development of Islamic banking’s performance evaluation methods. 1.3. Outline We will dedicate Section 2to detailing our methodology in conducting this research and Section 3 to describing the data we use to implement the constructed models. Section 4contains our results on evaluation of balance sheets of banks and subsequent analysis. Section 5provides a summary of and our conclusions for this study including possible future directions for this strand of research. 2. Methodology 2.1. Overview In a financial report, the information presented in the financial statements should be understood, relevant, reliable and comparable. According to the Statement of Financial Accounting Standards (PSAK), the financial statement is written as a form of the balance sheet. Table 1shows the balance sheet of Islamic or Sharia bank, where the liabilities part or the source of fund is called Funding, and the assets part is called Financing. A formulation model on transforming the source of fund to become the application of fund theoretically in the balance sheet is rebuilt so we can calculate the equivalent rate of return for each source of fund. Using these calculated rates, the profit of a bank is estimated using Monti-Klein method, where some variables are modified in accordance with the balance sheet of Sharia banking. For the implementation of the model, in order to describe the situation and predict the near future, the statistical descriptive analysis is used to build time series models based on data of Sharia banks in Indonesia. The statistical descriptive analysis used is in the form of time series methods. Time series methods, utilizing a series of data listed in time order, are used to illustrate the relationship between the current value of an observed variable and its values at previous time steps. Using the regression method, the profit or loss of a bank is estimated based on basic components of the balance sheet. We construct J. Risk Financial Manag. 2020,13, 43 3 of 21 autoregression formulae based on the observation of the number of data lags and errors of regressions that are modeled, so we use Autoregressive Integrated Moving Average (ARIMA). It will be seen that we also need to implement seasonal factors in the time series in order to capture seasonal patterns in the data. The collected data is processed using statistical software, including R, which is one of the data analysis and simulation softwares that can provide visualization in accordance with the expected data processing. Table 1. The balance sheet of a Sharia bank. Financing (Assets) Funding (Liabilities) Murabahah (Mur), Istisna (Ist) Qard (Qrd), Ijarah (Ijr) Wadiah Savings (WS), Wadiah Accounts (WA) Mudarabah (Mud), Musharakah (Mus) Mudarabah Savings (MS), Mudarabah Accounts (MA), Mudarabah Certificate of Deposit (MD) 2.2. The Modified Monti-Klein The original Monti-Klein model as described by Freixas and Rochet (2008) is a constrained optimisation problem in which a monopolistic bank maximises its end of period net value by selecting the appropriate level of equity to raise as well as the rates it offers to depositors and prospective debtors. The main modification we make concerns how to calculate the bank’s rates which are different from conventional interest rates of deposits and loans. First, we take a look at the Islamic bank’s balance sheet. Originally, its exact composition varies depending on a particular bank’s business and market orientation. The funding structure of a bank directly affects its cost of operation and therefore determines a bank’s potential profit and level of risk. Harahap and Yusuf (2010) adds a third source of financing, a pool of funds for unrestricted investment, as it has features to distinguish it from conventional debt-based and equity-based financing. Specifically, it is a pool of funds raised through a Mudarabah Mutlaqah arrangement which basically makes it a dedicated investment account to be used at the bank’s discretion. The accounting equation is therefore now expressed as: Asset =Liability +Unrestricted Investment +Equity Next, the model of an Islamic bank balance sheet is constructed based on Muljono (2015) and Sumarti (2019), which is shown in Table 1. Let Dbe the size of the Islamic bank’s total pool of funds, which is called Funding. As per regulations, a part of it is deposited into a reserve fund Rwhile the rest Lis used to finance projects such that: D(t)=L(t)+R(t) (1) We shall refer to Las the financing funds; the term “financing” is used instead of “investment”. Islamic banks also offer simple zero-interest loans referred to as Qard, which is only used as a supplement of investment funds without generating any profit. Regulations also require a portion of the reserve funds Smust be held by the central bank and the remaining amount Mas the net position in the interbank market due to some fund placement and liabilities in other banks. We therefore have: R(t)=S(t)+M(t) (2) In accordance with the Monti-Klein model, funds (1) and (2) have associated returns and costs of financing. We introduce a cost function C(D,L) which represents a general cost of raising funds and putting them to use. This results in the following equation for a bank’s end of period net value, modified to reflect the circumstances of an Islamic bank: π=total revenue −total cost J. Risk Financial Manag. 2020,13, 43 4 of 21 π(D,L) = rLL(t) + rS(t) + rM(t)−rDD(t)−C(D,L). (3) where r reflects the rate of the interbank market, and equivalent rates of returns for funding rD and financing rLwill be formulated in Equations (9) and (12). As we have discussed above, Islamic banks can raise funds through various financial contracts. In practice, the main modes of fundraising are through Wadiah and Mudarabah contracts. These collectively come in five different categories: Wadiah savings ( D1 ), Wadiah accounts ( D2 ), Mudarabah savings ( D3 ), Mudarabah accounts ( D4 ) and Mudarabah certificate of deposit ( D5 ). Note that Wadiah are pure deposit contracts which cannot be utilized for financing without permission from the owner. There is no permission in D1 and there exists one in D2 , but the return of financing in D2 is usually in a form of uncertain bonuses, which is not discussed here. Therefore, we define the following: D(t) = D1(t) + D2(t) + D3(t) + D4(t) + D5(t). (4) In relation to the requirement that a portion of Dmust be held in reserve, Table 2demonstrates the portions of the constituents of Dthat are generally available for financing based on Sumarti (2019). For example, the weighted amount of Mudarabah savings that can be used as financing fund is 90% D3(t). We denote αito be the portion of a given Dithat may be used for financing. Table 2. Values of αfor each type of funding. Type of Funding Weight (α) Accounts 89% Savings 90% Certificate of Deposit (Mudarabah) 91% The financing fund Lis allocated to the following contracts: Murabahah ( L1 ), Istisna ( L2 ), Qard ( L3 ), Ijarah ( L4 ), Mudarabah ( L5 ) and Musharakah ( L6 ) contracts. There is also a defined ε which accounts for any discrepancies between the total amount available for financing 5 P i=1 αiDi(t) and the total value of the financing funds L(t). The financing fund L can be written as follows L(t) = L1(t) + L2(t) + L3(t) + L4(t) + L5(t) + L6(t) + ε(t). (5) The weighted deposit 5 P i=1 αiDi(t) is supposed to be entirely distributed into financing fund L(t) = 6 P j=1 Lj(t) . This can be true if 5 P i=1 αiDi(t) = L(t) , which is not always happening. We define DjL to be the real amount of funding being distributed to the financing Lj , j= 1, 2, . . . , 6, which can be written as follows: DjL(t) = Lj(t) L(t) 5 X i=1 αiDi(t). (6) We consider two possibilities on the discrepancy between two funds, L(t)and 5 P i=1 αiDi(t). Case 1. 5 X i=1 αiDi(t)≥L(t) J. Risk Financial Manag. 2020,13, 43 5 of 21 This means there is a remaining fund from the weighted deposit that is not applied to the financing fund. We assume this remaining fund is used in another project ε(t), so ε(t) = 5 X i=1 αiDi(t)−L(t). (7) Consequently, we observe that the financing fund is all sourced from the weighted deposit. DjL(t) = 5 X i=1 αiDi(t)−ε(t) = Lj(t). Case 2. 5 X i=1 αiDi(t)<L(t)or 5 P i=1 αiDi(t) L(t)<1 The weighted deposit is not enough to finance all financing fund L(t) and consequently ε(t) = 0. We assume the weighted Dis distributed evenly on all financing fund Lj(t) . Financing fund which is not sourced from the weighted deposit is obtained from the bank’s other source not considered in this research. The equations being constructed above define a given Islamic bank’s financing and funding funds and their financial constraints in accordance with the original Monti-Klein model. To complete the setup, we formulate the equivalent rates of return for all of the bank’s associated financial contracts. As explained before, Islamic banks obtain their income by participating in profitable projects. It requires data of financing income from the monthly income statement and other comprehensive income reported in the balance sheet. Let Ij(t) be income at time-tfrom j-th contract in financing fund. For example, I5(t) is the total income shared from the entrepreneurs in the Mudarabah contract at time-t. This shared income is distributed to all depositors in the funding funds in a certain proportion, which is defined as follows: PjL(t) = DjL(t) Lj(t)×Ij(t). (8) where PjL(t) is the profit share from financing fund Lj(t) , j= 1, 2, . . . , 6. For case 1 above, PjL(t) = Ij(t) . The equivalent rate of return rLfor the financing fund L(t)is simply defined as follows, rL(t) = 6 P j=1 PjL(t) L(t)(9) Profit shared 6 P j=1 PjL(t) will be distributed to the depositors for each funding fund and to the bank itself based on the profit shared proportion (nisbah). The gross profit share for i-th funding contract is defined as follows, for i=1, 2, . . . , 5. PiD(t) = αiDi(t) 5 P i=1 αiDi(t) × 6 X j=1 PjL(t). (10) The share proportion (nisbah) might be varied among Islamic banks. We used nisbah guidelines set by the Indonesian central bank, Bank Indonesia (BI), which is shown in Table 3. Here we assume the bonus for Wadiah contract is available and constant. Note that theoretically, the bonus is fluctuated depending on each bank policy. J. Risk Financial Manag. 2020,13, 43 6 of 21 Table 3. Share proportion (nisbah) of funding fund. Funding Contract Nisbah Ni Wadiah accounts (WA) 6% Wadiah savings (WS) 9% Mudarabah accounts (MA) 6% Mudarabah savings (MS) 21% Mudarabah deposit (MD) 45% The net profit share for the depositors of i-th funding fund PiNis defined as follows PiN(t) = Ni×PiD(t)(11) Here Ni is the nisbah for i-th contract. Consequently, the net profit share for the bank is ( 1 −Ni)PiD(t) . The equivalent rate rDis simply defined as the average of the rates of return of all deposits. rD(t) = 1 5 5 X i=1 PiN(t) Di(t)!. (12) In Equation (12) above, the net profit is divided by the deposit, not the weighted deposit, because the rate should be calculated with respect to the real amount written in depositors’ account balance. Now we calculate the bank’s profit or loss using Monti Klein model as in the Equation (3), which can be expressed as π(D,L) = rLLD(t) + rS(t) + rDBL(t)−rLBL(t)−rDD(t)−C(D,L). (13) where LD(t) = 6 P j=1 DjL(t) is total funding fund distributed to the financing fund. Rate ris the equivalent rate of return from the interbank market. We assume its value is the same as Central Bank’s monthly interest rate. The term is the total fund borrowed by the bank at the time t, and its value is collected from the balance sheet. The variable S(t) is the cash reserves, which in this case is securities owned by the bank at the time t. LBL(t) is total financing fund borrowed by other banks at time t. Management cost C(D , L) is taken from the reported profit and loss statement and other comprehensive incomes in the monthly report. 2.3. Regression Model Having constructed formulae for a given Islamic bank’s size of funding, financial assets, associated rates of return and profit, we use the resulting data to estimate ARIMA models for selected Islamic banks. The model finds a causal relationship between a variable of response (dependent) and a predictor variable (independent). The causal relationship is demonstrated by the correlation values describing the linear relationship between two random variables where the value is between − 1 and 1. Detailed explanation on time series models can be found in Wei (2006); Ruppert (2010) and Cryer and Chan (2018). If the regression equation with one independent variable involves a p-order autoregressive error structure (AR), meaning ptimes differencing process, the equation will be the form of Yt=α0+φ1Yt−1+. . . +φpYt−p+α1Xt+α2Xt−1+. . . +αpXt−p+εt(14) where α0 is a constant parameter, φ1 , . . . , φp are parameters respectively related to the response variable at time lags t− 1, . . . , t−p and α1 , α2 , . . . , αp are parameters respectively related to the predictor variable at time lags t,t−1, . . . ,t−p. For example, ARIMA (1,1,0) has the equation with the form of Yt=α0+φ1Yt−1+φ2Yt−2+α1Xt+α2Xt−1+α3Xt−2+εt. J. Risk Financial Manag. 2020,13, 43 7 of 21 The data also strongly suggests that there are seasonal effects, which makes it more appropriate to use a more generalised form of the ARIMA model. This form combines seasonal factors in a multiplicative and is denoted as ARIMA (p , d , q)×(P,D,Q)S where nonseasonal parameters p , d , q are respectively the order of AR, differencing process and MA, and parameters P , D , Q are respectively their related seasonal parameters; S is the number of time lags until the pattern repeats itself. For example, a yearly pattern data with ARIMA ( 1, 0, 0 )×(1, 0, 0)12 without a predictor variable has the equation with the form of Yt=α0+φ1Yt−1+α1Yt−12 +α2Yt−13 +εt. (15) In the implementation, the formulae and statistical models are used for forecasting. To this end, we use the first 43 months as training data and the remaining 5 months as validating data. Lastly, there is the issue of controlling for bank and/or asset size. The Indonesian central bank has established the Bank Umum Kelompok Usaha or Commercial Bank Group (BUKU) classification (to be elaborated upon in Section 3) for banks based on the size of their primary equity. More specifically, our sample comes from selecting a bank from each of the three (out of four) classification tiers. We then apply our tools of analysis to each in separation and compare the results. We consider ourselves justified in this approach as our main goal is to construct measures of performance that can better accommodate the idiosyncrasies of Islamic banks. 3. Data Implementation 3.1. Original Data In this research, data being used is publically available data from some prominent Islamic banks in Indonesia which can be obtained from the website of Indonesia’s financial services authority at www.ojk.go.id. The data consists of the banks’ monthly income statements during the period April 2015–March 2019. Banks in Indonesia are subject to the BUKU (Bank Umum Kelompok Usaha or Commercial Bank Group) classification as outlined in Bank Indonesia regulation No. 14/26/PBI/2012: BUKU 1, the first tier consists of banks with primary equities of less than one trillion IDR; BUKU 2 consists of banks with primary equities between one trillion IDR (inclusive) and five trillion IDR (exclusive); BUKU 3 consists of banks with primary equities between five trillion IDR (inclusive) and thirty trillion IDR (exclusive); and BUKU 4 consists of banks with primary equities above thirty trillion IDR (inclusive). Note that there are no BUKU 4-tier Islamic banks so our samples represent the first three tiers denoted Bank A for BUKU 1, Bank B for BUKU 2 and Bank C for BUKU 3. For the presentation in tables later in this section, we use a sample of full year coverage of years 2016, 2017 and 2018. Having examined the balance sheet of each bank, we provide an example of the balance sheet from Bank C for January 2016 whose primary equity was between 5 and 30 trillion IDR. Figures of other banks can be seen in Appendix A. Figure 1shows real data of funding and financing funds, which are both increasing, as well its financing income, which generally seems to increase gradually throughout the year and drop sharply towards the end. We suspect that this is because there are banks in Indonesia which are required to report their incomes in a cumulative manner such that income from one month carries over until the end of the financial year. However, it is also possible that the banks generally deal in short-term financing such as operational financing so it makes sense for their business activities to grow throughout the year. As we were unable to ascertain which one of these is the case, we have not controlled for cumulative income. Later, the pattern will result also in a yearly pattern of the equivalent rates of returns. It can be observed that Bank C primarily raises its funds through Mudarabah certificates of deposit (MD) and mainly invests its funds into Murabahah contract (Mur). Note that Bank C does not provide Istisna credit, which is basically a credit facility to preorder goods that need to be made or built first. J. Risk Financial Manag. 2020,13, 43 8 of 21 J. Risk Financial Manag. 2020, 13, 43 8 of 21 Figure 1. Funding (top left) and Financing (top right) funds; Financing income (bottom) from Bank C. Composition of funding and financing funds for all banks are shown respectively in Figure 2 and 3. In Figure 2, the amount of Mudarabah Deposit (MD) dominates significantly in A and B, which is about 80%. The amounts of other funds are much smaller, which are about 16% and lower. Furthermore, in Bank B, the amount of Mudarabah Account is zero starting from February 2006. In January 2006, there is no value for Mudarabah Deposit in Bank B, and it suddenly exists and dominates starting from February 2006. In Bank C, the composition of Mudarabah Deposit also dominates the balance sheet but the percentage is about 44.2% to 55% in a decreasing trend. There are two amounts, Mudarabah Saving and Wadiah Saving, which increase their percentages respectively from 25.2% to 28.8% and from 85% to 18.3%. Figure 2. Compositions of funding fund from Bank A (top left), B (top right) and C (bottom). Figure 1. Funding ( top left ) and Financing ( top right ) funds; Financing income ( bottom ) from Bank C. Composition of funding and financing funds for all banks are shown respectively in Figures 2and 3. In Figure 2, the amount of Mudarabah Deposit (MD) dominates significantly in A and B, which is about 80%. The amounts of other funds are much smaller, which are about 16% and lower. Furthermore, in Bank B, the amount of Mudarabah Account is zero starting from February 2006. In January 2006, there is no value for Mudarabah Deposit in Bank B, and it suddenly exists and dominates starting from February 2006. In Bank C, the composition of Mudarabah Deposit also dominates the balance sheet but the percentage is about 44.2% to 55% in a decreasing trend. There are two amounts, Mudarabah Saving and Wadiah Saving, which increase their percentages respectively from 25.2% to 28.8% and from 85% to 18.3%. J. Risk Financial Manag. 2020, 13, 43 8 of 21 Figure 1. Funding (top left) and Financing (top right) funds; Financing income (bottom) from Bank C. Composition of funding and financing funds for all banks are shown respectively in Figure 2 and 3. In Figure 2, the amount of Mudarabah Deposit (MD) dominates significantly in A and B, which is about 80%. The amounts of other funds are much smaller, which are about 16% and lower. Furthermore, in Bank B, the amount of Mudarabah Account is zero starting from February 2006. In January 2006, there is no value for Mudarabah Deposit in Bank B, and it suddenly exists and dominates starting from February 2006. In Bank C, the composition of Mudarabah Deposit also dominates the balance sheet but the percentage is about 44.2% to 55% in a decreasing trend. There are two amounts, Mudarabah Saving and Wadiah Saving, which increase their percentages respectively from 25.2% to 28.8% and from 85% to 18.3%. Figure 2. Compositions of funding fund from Bank A (top left), B (top right) and C (bottom). Figure 2. Compositions of funding fund from Bank A (top left), B (top right) and C (bottom). J. Risk Financial Manag. 2020,13, 43 15 of 21 Table 8. Forecast profit of Bank C in IDR trillion. Components November 2018 December 2018 January 2019 February 2019 Forecast 557.564 595.328 158.111 173.571 Observation 612.659 652.843 34.839 148.716 Deviation 55.095 57.515 123.272 24.855 Bottom bound 388.399 387.942 −66.048 −58.567 Upper bound 726.728 802.714 382.271 405.709 5. Discussion of Results 5.1. The Developed Methodology The methodology we have developed for the performance evaluation of Islamic banks is effective for two main reasons: firstly, it is more “asset-” or “business-centric” and hence more true to the essence of Islamic finance; secondly, it provides a more conceptually robust approach to calculating an Islamic bank’s net income. Regarding the first reason, our methodology forces the identification of an Islamic bank’s sources and uses of funding as well as their underlying contracts. This is significant because the various contracts have differing characteristics which can help in identifying the environment in which the bank is operating. An example of this is the classic “murabahah syndrome” in which Islamic banks will go against their stated preference for profit-sharing and instead prefer fixed-income contracts such as Murabahah. There could be a very good excuse for this such as a substantially high-risk environment, one of high information asymmetry or one in which there are few capable entrepreneurs, as analysed by Aggarwal and Yousef (2000). It is also possible that a bank’s management has low ability, especially in properly using Islamic financial contracts, for example, by using the wrong contracts for a given project. Therefore, our approach can also add another dimension to assessing the ability of an Islamic bank’s management. Regarding the second merit of our approach, forcing the identification of an Islamic bank’s sources and uses of funds helps as an extra mental check for scrutinising the bank’s balance sheets. In our case, we found a significant underreporting of profits/losses by Bank A which we have shown in Figure 5. Of course, we acknowledge that the merits of our methodology are contingent on the level of reporting required from Islamic banks. The reason is if Islamic banks report their balance sheet items based on conventional classes then our methodology cannot be employed. 5.2. The Estimated Models We begin with some comments on the balance sheet items before commenting on the results of the profit/loss ARIMA model taking into account seasonality. With regards to funding, it is sensible that all three banks depend most on Mudarabah certificates of deposit (MDs) for their financing capital as it provides them an actual investment horizon and the ability to share losses. Bank B seems to be rather curious in that it initially depended mainly on Mudarabah savings accounts (MSs) and then switched to MDs. With regards to the uses of funds, the common thread seems to be that the three Islamic banks prioritise channeling their funds into Murabahah and Musharakah contracts. Banks A and C behave similarly to retail banks and possibly commercial banks with a reliance on Murabahah contracts providing fixed income and a more definite investment horizon. It is rather surprising that the BUKU tier 2 bank B seems to involve a significantly greater share of its funds in Musharakah contracts and this could be worth investigating further. The greatest surprise would be that the BUKU tier 3 bank C prefers less risky contracts despite having the greatest amount of primary equity, such that it does not even provide Istisna contracts which can effectively be an alternative to Murabahah contracts as a source of fixed income. A bank might be default due to experiencing losses that are much larger than its equity. Figure 5 shows that Bank A, classified as BUKU tier 1, experienced high losses but then it could be saved. Banks B and C do not experience the losses, and the banks make good profit every month. However, the maximum profits of Bank B and Bank C are respectively never IDR 5 trillion and IDR 30 trillion, J. Risk Financial Manag. 2020,13, 43 16 of 21 which are the upper limits of their BUKU classification. So they will not be upgraded into higher classes (BUKU tier 3 and BUKU tier 4 classes, respectively) in the near future. The constructed time series models using regression give good correlation between the funding fund and the Monti-Klein (MK) profit. Even though the reported income of financing fund shows an increasing pattern throughout the year and then drops at the end of the year, MK profit of Bank A does not obtain the same pattern. The operational cost is high for months and it reaches its maximum in December 2016. These values will be detected as the innovational outliers that give impact on their consecutive data. Consequently, the constructed regression model without outlier identification has small values of RMSE and R-squared, but the R-squared is still significantly greater than 50%. The regression model modified with outlier identification can give much improvement to be 94% of R-squared. Unfortunately, much effort on outlier identification to sophisticate the model does not impact on higher performance on the forecasting process. This phenomenon also occurs in other regression models of Banks B and C which do not have very extreme outliers in their data. We can refer this phenomenon to the Parsimony principle, which means an obtained model should require the smallest number of parameters or less complicated features that will adequately represent the time series. We can conclude that the first regression models perform more satisfactorily in the forecasting process, which is usually the main objective of constructing time series models. However, we have to be careful when using the model in forecasting the performance of a bank a long way ahead in the future, for example, more than two years, when the original data is obtained from a 4–5 year period. 6. Conclusions Revisiting the calculation of profit share using formulas based on theoretical procedures can create an insight review of the balance sheet analysis. Losses on the main components of a balance sheet made by a bank can be identified whether the periodical report mentions these losses or not. The equivalent rates of return for each contract can be made as a tool for the decision making process on defining a new campaign of the bank in order to increase the amount of targeted contract in the near future. Making a decision on the best statistical model using regression time series requires appropriate experience in providing good candidates of ARIMA models before the best model is decided upon. The model can be made to forecast values of the near future situation in the form of 95% confident interval. However, the forecast values cannot capture potential extreme fluctuation in the future, so the time series model is not recommended to forecast data for a much later period. Author Contributions: Conceptualization, N.S.; Methodology, N.S., I.G.A. and N.I.G.; Software, I.G.A. and U.M.; Validation, N.S., I.G.A. and U.M.; Formal analysis and investigation, N.S. and U.M.; Resources and data curation, I.G.A. and N.I.G.; Writing—original draft preparation, I.G.A.; Writing—review and editing, visualization and supervision, N.S. All authors have read and agreed to the published version of the manuscript. Funding: The beginning of this research was funded by 2017 ITB Research Grant. Acknowledgments: The authors thank Lukman Arbi and anonymous reviewers of this manuscript for the recommendations and constructive comments. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Figures A1 and A2 respectively show the funding and financing funds and also the financing income of Bank A and B. The reported profit of all banks is in Figure A3. J. Risk Financial Manag. 2020,13, 43 17 of 21 J. Risk Financial Manag. 2020, 13, 43 16 of 21 regression model modified with outlier identification can give much improvement to be 94% of Rsquared. Unfortunately, much effort on outlier identification to sophisticate the model does not impact on higher performance on the forecasting process. This phenomenon also occurs in other regression models of Banks B and C which do not have very extreme outliers in their data. We can refer this phenomenon to the Parsimony principle, which means an obtained model should require the smallest number of parameters or less complicated features that will adequately represent the time series. We can conclude that the first regression models perform more satisfactorily in the forecasting process, which is usually the main objective of constructing time series models. However, we have to be careful when using the model in forecasting the performance of a bank a long way ahead in the future, for example, more than two years, when the original data is obtained from a 4–5 year period. 6. Conclusions Revisiting the calculation of profit share using formulas based on theoretical procedures can create an insight review of the balance sheet analysis. Losses on the main components of a balance sheet made by a bank can be identified whether the periodical report mentions these losses or not. The equivalent rates of return for each contract can be made as a tool for the decision making process on defining a new campaign of the bank in order to increase the amount of targeted contract in the near future. Making a decision on the best statistical model using regression time series requires appropriate experience in providing good candidates of ARIMA models before the best model is decided upon. The model can be made to forecast values of the near future situation in the form of 95% confident interval. However, the forecast values cannot capture potential extreme fluctuation in the future, so the time series model is not recommended to forecast data for a much later period. Author Contributions: Conceptualization, N.S.; Methodology, N.S., I.G.A. and N.I.G.; Software, I.G.A. and U.M.; Validation, N.S., I.G.A. and U.M.; Formal analysis and investigation, N.S. and U.M.; Resources and data curation, I.G.A. and N.I.G.; Writing—original draft preparation, I.G.A.; Writing—review and editing, visualization and supervision, N.S. All authors have read and agreed to the published version of the manuscript. Funding: The beginning of this research was funded by 2017 ITB Research Grant. Acknowledgments: The authors thank Lukman Arbi and anonymous reviewers of this manuscript for the recommendations and constructive comments. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Figures A1 and A2 respectively show the funding and financing funds and also the financing income of Bank A and B. The reported profit of all banks is in Figure A3. (a) (b) J. Risk Financial Manag. 2020, 13, 43 17 of 21 (c) Figure A1. (a) Funding fund, (b) Financing fund, (c) Financing income from Bank A. (a) (b) (c) Figure A2. (a) Funding fund, (b) Financing fund, (c) Financing income from Bank B. Figure A3. Reported operational profit of Banks A, B and C. Figure A1. (a) Funding fund, (b) Financing fund, (c) Financing income from Bank A. J. Risk Financial Manag. 2020, 13, 43 17 of 21 (c) Figure A1. (a) Funding fund, (b) Financing fund, (c) Financing income from Bank A. (a) (b) (c) Figure A2. (a) Funding fund, (b) Financing fund, (c) Financing income from Bank B. Figure A3. Reported operational profit of Banks A, B and C. Figure A2. (a) Funding fund, (b) Financing fund, (c) Financing income from Bank B. J. Risk Financial Manag. 2020,13, 43 18 of 21 J. Risk Financial Manag. 2020, 13, 43 17 of 21 (c) Figure A1. (a) Funding fund, (b) Financing fund, (c) Financing income from Bank A. (a) (b) (c) Figure A2. (a) Funding fund, (b) Financing fund, (c) Financing income from Bank B. Figure A3. Reported operational profit of Banks A, B and C. Figure A3. Reported operational profit of Banks A, B and C. Appendix B Figures A4 and A5 are calculated rates of returns from funding and financing funds of Banks A and B. J. Risk Financial Manag. 2020, 13, 43 18 of 21 Appendix B Figures A4 and A5 are calculated rates of returns from funding and financing funds of Banks A and B. Figure A4. Rates of return for Funding (left) and financing (right) funds from Bank A. Figure A5. Rates of return for Funding (left) and financing (right) funds from Bank B. Appendix C Having revised the regression models by considering outliers, the following models are called Models-2 for Banks B and C, respectively. (22) (18) 112 13 11213 (35) (39) (42) (19) (29) (40) 1 0.945 1.5264 0.0226 1.4424 ( 62396 26413 (1 0.945 1.5264 1.4424 ) 25368.4 14193.4 29916.4 13430 27023.3 4909.8 98 tt t t t tt tt t tt tttt YY Y X Y I I YY Y IIIIII −− − −− − =− + − + − + −+ + ++−+−−+ (36) (25) (23) (24) (9) (21) (41) (38) (28) (32) 67.1 8104.9 17788.4 9738.8 ) 28794.8 41152.3 29069.8 14963.7 6243.2 28802 tt tt t t t ttt II II I I I III − −−−++−−− (21) (22) 11213 11213 (20) (15) (9) (27) 1 1.5 4.8644 7.2966 0.0077 (233020.5 113938.7 (1 1.5 4.8644 7.2966 ) 175427.6 98878.4 ) 536206.7 150430.2 tt t t t tt tt t tt t t YY Y Y X I I YY Y II II −− − −− − =+ − − + − −− + −++− where 1 0  =  (k) , is outlier, ,others. t k I Figure A6 shows the estimated profits for Banks A, B and C. Tables A1–A3 are the obtained figures for the forecasting process using Models-2. Finally, Figure A7 describes the comparison among MK profit and forecast profits from Models-1 and from Models-2. Figure A4. Rates of return for Funding (left) and financing (right) funds from Bank A. J. Risk Financial Manag. 2020, 13, 43 18 of 21 Appendix B Figures A4 and A5 are calculated rates of returns from funding and financing funds of Banks A and B. Figure A4. Rates of return for Funding (left) and financing (right) funds from Bank A. Figure A5. Rates of return for Funding (left) and financing (right) funds from Bank B. Appendix C Having revised the regression models by considering outliers, the following models are called Models-2 for Banks B and C, respectively. (22) (18) 112 13 11213 (35) (39) (42) (19) (29) (40) 1 0.945 1.5264 0.0226 1.4424 ( 62396 26413 (1 0.945 1.5264 1.4424 ) 25368.4 14193.4 29916.4 13430 27023.3 4909.8 98 tt t t t tt tt t tt tttt YY Y X Y I I YY Y IIIIII −− − −− − =− + − + − + −+ + ++−+−−+ (36) (25) (23) (24) (9) (21) (41) (38) (28) (32) 67.1 8104.9 17788.4 9738.8 ) 28794.8 41152.3 29069.8 14963.7 6243.2 28802 tt tt t t t ttt II II I I I III − −−−++−−− (21) (22) 11213 11213 (20) (15) (9) (27) 1 1.5 4.8644 7.2966 0.0077 (233020.5 113938.7 (1 1.5 4.8644 7.2966 ) 175427.6 98878.4 ) 536206.7 150430.2 tt t t t tt tt t tt t t YY Y Y X I I YY Y II II −− − −− − =+ − − + − −− + −++− where 1 0  =  (k) , is outlier, ,others. t k I Figure A6 shows the estimated profits for Banks A, B and C. Tables A1–A3 are the obtained figures for the forecasting process using Models-2. Finally, Figure A7 describes the comparison among MK profit and forecast profits from Models-1 and from Models-2. Figure A5. Rates of return for Funding (left) and financing (right) funds from Bank B. Appendix C Having revised the regression models by considering outliers, the following models are called Models-2 for Banks B and C, respectively. Yt=0.945Yt−1−1.5264Yt−12 +0.0226Xt−1.4424Yt−13 +1 (1−0.945Yt−1+1.5264Yt−12+1.4424Yt−13)(−62396It(22)+26413It(18) +25368.4It(35)+14193.4It(39)−29916.4It(42)+13430It(19)−27023.3It(29)−4909.8It(40)+9867.1It(36)−8104.9It(25) −17788.4It(23)−9738.8It(24))−28794.8It(9)+41152.3It(21)+29069.8It(41)−14963.7It(38)−6243.2It(28)−28802It(32) J. Risk Financial Manag. 2020,13, 43 19 of 21 Yt=1.5Yt−1+4.8644Yt−12 −7.2966Yt−13 −0.0077Xt+1 (1−1.5Yt−1−4.8644Yt−12+7.2966Yt−13)(233020.5It(21)−113938.7It(22) −175427.6It(20)+98878.4It(15)) + 536206.7It(9)−150430.2It(27) where It(k)=       1, kis outlier, 0, others. Figure A6 shows the estimated profits for Banks A, B and C. Tables A1–A3 are the obtained figures for the forecasting process using Models-2. Finally, Figure A7 describes the comparison among MK profit and forecast profits from Models-1 and from Models-2. J. Risk Financial Manag. 2020, 13, 43 19 of 21 Figure A6. Estimated profits of Models-2 for each bank. Table A1. Models-2 forecast profit for Bank A in IDR million. Components Nov 2018 Dec 2018 Jan 2019 Feb 2019 Forecast 58.118 63.512 65.712 180.770 Observation 65.262 186.007 9.290 16.798 Deviation 7.144 122.495 56.422 163.972 Bottom bound −553.322 −540.570 −531.477 −409.147 Upper bound 669.558 667.593 662.901 770.686 Table A2. Models-2 forecast profit for Bank B in IDR million. Components Nov 2018 Dec 2018 Jan 2019 Feb 2019 Forecast 143.863 150.044 156.225 162.406 Observation 119.179 128.613 19.289 40.900 Deviation 24.684 21.431 136.936 121.506 Bottom bound 54.508 20.479 −8.343 −35.170 Upper bound 233.218 279.610 320793 359.982 Figure A6. Estimated profits of Models-2 for each bank. J. Risk Financial Manag. 2020,13, 43 20 of 21 Table A1. Models-2 forecast profit for Bank A in IDR trillion. Components November 2018 December 2018 January 2019 February 2019 Forecast 58.118 63.512 65.712 180.770 Observation 65.262 186.007 9.290 16.798 Deviation 7.144 122.495 56.422 163.972 Bottom bound −553.322 −540.570 −531.477 −409.147 Upper bound 669.558 667.593 662.901 770.686 Table A2. Models-2 forecast profit for Bank B in IDR trillion. Components November 2018 December 2018 January 2019 February 2019 Forecast 143.863 150.044 156.225 162.406 Observation 119.179 128.613 19.289 40.900 Deviation 24.684 21.431 136.936 121.506 Bottom bound 54.508 20.479 −8.343 −35.170 Upper bound 233.218 279.610 320793 359.982 Table A3. Models-2 forecast profit of Bank C in IDR trillion. Components November 2018 December 2018 January 2019 February 2019 Forecast 593.269 611.977 630.685 649.393 Observation 612.659 652.843 34.839 148.716 Deviation 19.39 40.866 595.846 500.677 Bottom bound 174.667 15.357 −122.134 −251.282 Upper bound 1011.871 1208.597 1383.505 1550.068 J. Risk Financial Manag. 2020, 13, 43 20 of 21 Table A3. Models-2 forecast profit of Bank C in IDR million. Components Nov 2018 Dec 2018 Jan 2019 Feb 2019 Forecast 593.269 611.977 630.685 649.393 Observation 612.659 652.843 34.839 148.716 Deviation 19.39 40.866 595.846 500.677 Bottom bound 174.667 15.357 −122.134 −251.282 Upper bound 1.011.871 1.208.597 1.383.505 1.550.068 Figure A7. Comparison of profits of MK calculation (observed data), Models-1 and Models-2 for Banks A, B and C. References (Aggarwal and Yousef 2000) Aggarwal, Rajesh K., and Tarik Yousef. 2000. Islamic Banks and Investment Financing. Journal of Money, Credit and Banking 32: 93–120. (Bidabad and Allahyarifard 2019) Bidabad, Bijan, and Mahmoud Allahyarifard. 2019. Assets and liabilities management in Islamic banking. International Journal of Islamic Banking and Finance Research 3: 32–43. (Chang et al. 1987) Chang, Ih, George C Tiao, and Chung Chen. 1987. Estimation of Time Series Parameters in the Presence of Outliers. American Statistical Association and the American Society for Quality Control 30: 193– 95. (Cryer and Chan 2018) Cryer, Jonathan D., and Kung-Sik Chan. 2018. Time Series Analysis. New York: Springer. (Doumpos et al. 2017) Doumpos, Michael, Iftekhar Hasan, and Fotios Pasiouras. 2017. Bank overall financial strength: Islamic versus conventional banks. Economic Modelling 64: 513–23. (Fadhlurrahman and Sumarti 2016) Fadhlurrahman, Akmal, and Novriana Sumarti. 2016. Implementation of the dynamical system of the deposit and loan growth based on the Lotka-Volterra model and the improved model. AIP Conf. Proc. 1723: 030007. doi:10.1063/1.4945065 (Freixas and Rochet 2008) Freixas, Xavier, and Jean-Charles Rochet. 2008. Microeconomics of Banking, 2nd ed. Cambridge: MIT Press. (Harahap and Yusuf 2010) Harahap, Sofyan S., and Muhammad Yusuf. 2010. Akuntansi Perbankan Syariah (Sharia Banking Accounting). Jakarta: LPFE Usakti. (Hassan and Aliyu 2018) Hassan, M.K., and S. Aliyu. 2018. A contemporary survey of Islamic banking literature. Journal of Financial Stability 34: 12–43. (Muljono 2015) Muljono, Djoko. 2015. Buku Pintar Akutansi Perbankan dan Lembaga Keuangan Syariah (Accounting Guide Book of Islamic Banking and Financial Institutions). Yogyakarta: Penerbit Andi. (Rahman 2019) Rahman, M. 2019. Islamic banks with mutuality and neutrality: A balance-sheet-based theoretical framework. The Quarterly Review of Economics and Finance 74: 3–8. (Ruppert 2010) Ruppert, David. 2010. Statistic and data analysis for Financial Engineering: Liner Regression with ARMA Errors. New York: Springer. Figure A7. Comparison of profits of MK calculation (observed data), Models-1 and Models-2 for Banks A, B and C. References Aggarwal, Rajesh K., and Tarik Yousef. 2000. Islamic Banks and Investment Financing. Journal of Money, Credit and Banking 32: 93–120. [CrossRef] Bidabad, Bijan, and Mahmoud Allahyarifard. 2019. Assets and liabilities management in Islamic banking. International Journal of Islamic Banking and Finance Research 3: 32–43. Chang, Ih, George C Tiao, and Chung Chen. 1987. Estimation of Time Series Parameters in the Presence of Outliers. American Statistical Association and the American Society for Quality Control 30: 193–95. [CrossRef] J. Risk Financial Manag. 2020,13, 43 21 of 21 Cryer, Jonathan D., and Kung-Sik Chan. 2018. Time Series Analysis. New York: Springer. Doumpos, Michael, Iftekhar Hasan, and Fotios Pasiouras. 2017. Bank overall financial strength: Islamic versus conventional banks. Economic Modelling 64: 513–23. [CrossRef] Fadhlurrahman, Akmal, and Novriana Sumarti. 2016. Implementation of the dynamical system of the deposit and loan growth based on the Lotka-Volterra model and the improved model. AIP Conf. Proc. 1723: 030007. [CrossRef] Freixas, Xavier, and Jean-Charles Rochet. 2008. Microeconomics of Banking, 2nd ed. Cambridge: MIT Press. Harahap, Sofyan S., and Muhammad Yusuf. 2010. Akuntansi Perbankan Syariah (Sharia Banking Accounting). Jakarta: LPFE Usakti. Hassan, M.K., and S. Aliyu. 2018. A contemporary survey of Islamic banking literature. Journal of Financial Stability 34: 12–43. [CrossRef] Muljono, Djoko. 2015. Buku Pintar Akutansi Perbankan dan Lembaga Keuangan Syariah (Accounting Guide Book of Islamic Banking and Financial Institutions). Yogyakarta: Penerbit Andi. Rahman, M. 2019. Islamic banks with mutuality and neutrality: A balance-sheet-based theoretical framework. The Quarterly Review of Economics and Finance 74: 3–8. [CrossRef] Ruppert, David. 2010. Statistic and Data Analysis for Financial Engineering: Liner Regression with ARMA Errors. New York: Springer. Siddiqi, Mohammad N. 2006. Islamic Banking and Finance in theory and practice: A Survey of state of the art. Islamic Economic Studies 13: 2–48. Sumarti, Novriana. 2019. Islamic Financial Mathematics. Bandung: Bandung Institute of Technology, ITB Press. Sumarti, Novriana, Milati M. Hayati, Ni-Luh P.A. Cahyani, Robby R. Wahyudi, Dwi P. Tristanti, and Reny Meylani. 2017. Has the growth of Islamic banking had impact to economic growth in Indonesia? Paper presented at the 4th IEEE International Conference on Engineering Technologies and Applied Sciences (ICETAS), Salmabad, Bahrain, November 29–December 1. Sumarti, Novriana, Akmal Fadhlurrahman, Hanifa R Widyani, and Iman Gunadi. 2018. The Dynamical System of the Deposit and Loan Volumes of a Commercial Bank Containing Interbank Lending and Saving Factors. Southeast Asian Bulletin of Mathematics 42: 757–72. Van Greuning, Hennie, and Zamir Iqbal. 2008. Risk Analysis for Islamic Banks. Washington: The World Bank. Van Greuning, Hennie, and Zamir Iqbal. 2009. Balance Sheet Analysis: Islamic vs. Conventional. New Horizon, pp. 16–17. Available online: http://www.islamic-banking.com/resources/7/NewHorizon%20Previouse% 20Issues/NewHorizon_JanMar09.pdf (accessed on 1 September 2018). Wei, William W.S. 2006. Time series Analysis Univariate and Multivariate Methods, 2nd ed. Boston: Pearson Education, Inc. Zainol, Zairy, and Salina H Kassim. 2010. An analysis of Islamic Bank’s exposure to rate of return Risk. Journal of Economics Cooperation and Development 31: 59–84. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).