# Does Islamic Bank Strategy Mimic Interest Rate Finance Essay

Many scholars mentioned that Islamic banks which use profit and loss sharing principle seem to imitate the volatility of interest rate on delivering return to depositor instead of financial performance which affected by economic growth. Thereby, this research attempts to examine empirically the existence of Islamic bank's mimicking strategy in Indonesia using artificial neural networks (ANN) model.

This research conducted two examinations to discover strong evidence that interest instruments significantly dominate volatility of depositor return (RR).

Using N(7-3-1) architecture in first examination, we found that market interest rate (INTR) as proxy of interest instrument affects RR with only 51.43% importance level then followed by four other variables as proxies of economic growth. Since this result is not strong enough to answer the research question, second examination is required by adding two variables namely central bank interest rate (BIRT) and broad money (M2).

Using N(9-4-1) architecture, we found that interest instruments (BIRT and INTR) dominantly affect RR volatility with almost 98% importance level. These finding shows that existence of mimicking strategy has been empirically proven due to dominance of interest instrument on affecting RR volatility rather than economic growth instruments.

## 1. Introduction

Time deposit rate of return (RR) defines as how much money will be received regularly by depositor from their deposit in Islamic bank, which is equivalent with conventional bank interest rate per annum. The rates will be varied among the Islamic banks. Because, it is depend on predetermined loss and profit ratio that offered by the bank where it may be a function of the bank’s profit (Zoubi and Olson, 2008). In connection with macroeconomic turmoil, Bashir (2000) found that GDP and inflation rate determine the fluctuation of profitability and rate of return margin of Middle East Islamic banks.

The empirical literature in Islamic banking about mimicking strategy of deposit return volatility is very rare. We found that only a few such as Chong and Liu (2009) examined the relation between RR and interest rate of conventional bank. They found that changes in conventional bank deposit rate cause changes in RR. When RR deviates far above (below) the conventional bank deposit rate, it will be adjusted towards the long-term equilibrium level.

Nienhaus (1983) noticed that Islamic banks use interest rate as benchmarking rate to calculate their profit and loss sharing ratio. Haron (2004) however, found clear evidence that Islamic banks did benchmarking to interest rate for fixing their charges to users of fund as well as the rewards given to depositor.

From theoretical perspective, the Islamic bank must deliver return to depositors based on pre-determined profit and loss sharing (PLS) ratio. Under PLS principles, return will be received by depositor should be fluctuated depends on Islamic bank’s profitability which performance is affected by economic growth rather than imitating interest rate volatility. In contrast, conventional banks deliver interest to their depositors every month according to pre-determined rate. All the time, deposit account holders will receive the same amount every month as interest revenue.

In his paper, El-Gamal (1997) argued that the transactions in Islamic bank such as time deposit and saving deposit, are themselves not purely Islamic. Since, the return seems to be rewarded which typically has a high correlation with market interest rate, although it tends to be lower than the market rate (Bank Negara Malaysia, 1994).

Interestingly, during February 2001 to December 2009, Indonesian Islamic banks are able to generate higher deposit rate than conventional bank as shown in figure 1.

Figure 1: Comparison between one-month time deposit return and time deposit interest rate

(Source: Bank of Indonesia)

Regarding economic turmoil, Islamic banks face displaced commercial risk. This is the possibility of depositors shifting their fund to conventional bank due to uncompetitive return when unpleasant economic condition occurred (Iqbal et al., 2007). Kasri and Kasim (2009) found that shock in interest rate of conventional bank affect the number of deposit in Indonesian Islamic bank negatively. Consequently, Islamic banks need to maintain their return in order to compete with conventional bank. In practice, the effort to deliver competitive return is criticized due to mimicking interest rate volatility (Chong and Liu, 2009).

In this case, there are two opinions related with the above condition. Khan (1995) argued that mimicking interest rate based system is an alternative in the short run to be survived and hopefully, it will be gradually replaced with the system which in line with Islamic law in the future. On the contrary, Ahmad (1992) disagrees with that and wishes to do transformation on the economic system instantaneously to be an Islamic economic.

Against all these backdrops, this research aims not to be involved with such controversy, agree or disagree opinion with the mimicking strategy. However, this paper attempts to investigate empirically the strong evidence of mimicking strategy existence in Indonesian Islamic bank by examining importance level of macroeconomic variables on affecting volatility of depositor return in the past ten years using artificial neural networks.

This research does not employ statistical technique such as logistic and regression analysis since those technique relies on the restrictive assumption of linear separability, multivariate normality and independence of the predictive variables (Ravi et al, 2008). Moody (1995) confirmed that macroeconomic variables are characterized as nonlinearities time series data that violate those assumptions, therefore Alyuda Neuro Intelligent software is employed to develop ANN model using back propagation as learning algorithm.

We expect that the result can give contribution to existing literature on explaining the existence of mimicking strategy in Islamic bank using ANN model.

The reminder of the paper deals with the following topics. Section 2 briefly explains the literature review of how macroeconomic variables affect Islamic bank profitability and theory of ANN. Section 3 discusses the results of employing the application. Section 4 concludes the paper.

## 2. Literature Review

2.1 Macroeconomic variables vs. Islamic bank profitability.

Some authors found empirically the determinants of macroeconomic variables on Islamic bank performance, which theoretically will determine return given to depositor afterwards. Interestingly, most of them mentioned that interest rate is the most significant variables on profitability or credit risk rather than economic growth variables such as money supply, exchange rate, stock indices, inflation rate, etc (see for example: Bashir (2000), Haron (2004) and Maximilian (2008)).

Economic growth variables determine bank’s profitability in following ways. Bourke (1989) mentioned that market expansion would produce ability to increase profits as represented by strong relationship between money supply and profit. Exchange rate, on the other hand, affects profits of Islamic bank not from trading in foreign exchange since it is prohibited, except through its impact on general product’s price fluctuation that affect business and market. Moreover, stock indices development leads to higher growth at the firm, industry and country level (Aburime, 2008) which will give more profit to Islamic bank from financing activities. Thus, Bashir (2000) mentioned that inflation may affect Islamic bank’s profits if revenue accrues of business is larger than arising of overhead cost due to inflation.

2.2 Artificial Neural Networks Model

ANN model is a branch of artificial intelligence that is able to solve problem especially in pattern classification and recognition. It is a computational model which the structure and function imitate biological neuron in the human brain. It consists of a group of artificial neurons, which are interconnected. Every single neuron processes information (receiving input and delivering output) using a special algorithm function.

Serju (2002) mentioned two advantages of ANN method compared with others to modeling the relationship between independent and dependent variables. First, they are universal approximators of function in that they can approximate whatever functional form best characterizes the time series. That means, ANN are considered to be data-driven rather than model-driven (Argyrou, 2006) because they are best suited for problems for which data are available but the underlying theoretical model is unknown (Zhang et. Al, 1998). It makes ANN superior to other statistical methods where ANN is able to deal with non-linear data and multi dimensional aspect. Second, ANN method has been proven to be better for long-term forecast horizons, but is often as good as statistical forecasting methods over shorter forecast horizons. This superiority will be used to measure the robustness of the model using in and out of sample forecasting.

As can be seen in figure 3, there is a neuron j, which has a certain number of inputs (x1,x2..xj) and single output (yj). Each input has a weight assigned to them (w1j, w2j,..wij). The weights are an indication of importance of the incoming signal to each input. The net value (uj) of the neuron is then calculated with the sum of all the input multiplied by their specific weight.

Figure 3: A Model of Neuron (source: NeuralystTM User's Guide)

Then, with reference to threshold value (tj) and activation function, the neuron (j) determines output value (yj) will be sent to. Activation function is a function used to transform the activation level of a unit (neuron) into an output signal. The activation function for output layer is generally linear. Meanwhile, the non-linear feature is introduced at the hidden transfer function. The most popular transfer function is sigmoid or logistic, nearly linear in the central part. Each neuron has its own unique threshold value (tj), if the net value (uj) is greater than the threshold (tj), the neuron (j) will send output (yj) to other neuron.

In this research, a single neuron is not useful to solve the problems. We need to combine some neurons into multilayer structured which so called neural networks to have the power for answering pattern classification and recognition problems. This research employs single layer feed-forward network with backpropagation as learning rule, which is the most common neural network currently in use. In figure 4, we can see the 4-3-1 network architecture (in abbreviated form, N(4-3-1)) which consists of one input layer with 4 neurodes, one hidden layer with 3 neurodes and one output layer with 1 neurode. Every neuron in the layer works with the way as explained previously.

Figure 4: A Single Layer Feed-forward Network (source: NeuralystTM User's Guide)

The input layer is a layer that directly connected to outside information. All data in the input layer will be feed-forward to hidden layer as the next layer. The hidden layer will perform as feature detectors of such signals and release them to output layer. Finally, the output layer is considered as a collector of the features detected and producer of the response. In the networks, the output is function of the linear combination of hidden unit’s activation; each one is a non-linear function of the weighted sum of inputs.

Azadeh et al. (2007) explained the mathematical model of ANN as following.

y = f(x,θ) + ε…(1)

Where x is the vector of explanatory variables, ε is the random error component and θ is weights vector (parameters). Eq. [2] is the unknown function for estimation and prediction from the available data. The model can be found as followings:

y = f [ύ0+ (λj+xiwij) ύj] …(2)

where:

y = network output

f = output layer activation function

ύ0= output bias

m= number of hidden units

h= hidden layer activation function

λj= hidden unit biases (j = 1,. . . ,m)

n= number of input units

xi= inputs vector (i = 1,. . . ,n)

wij= weight from input unit i to hidden unit j

ύj= weights from hidden unit j to output (j = 1,. . . ,m)

## 3. Methodology

To answer the problem, we used a macroeconomics model of bankruptcy and ANN to see how a firm responses on macroeconomic fluctuation which is reflected on financial performance.

3.1 Data

This research initially uses five macroeconomic variables as independent variables to develop ANN model on determining RR volatility as dependent variables. We extend previous research in Indonesian Islamic bank conducted by Maximilian et.al (2008) that also employed ANN model to asses’ credit risk. We used the same five variables except for GDP and M2 with following reason. We change the GDP with INTR due to the purpose of this research as used by Chong and Liu (2009). Thus, we modify M2 variables to M1 in this first examination due to interest free consideration on money supply variables used.

The five variables consist of average of one-month time deposit interest rate (INTR), narrow money (M1), exchange rate (EXCH), Jakarta stock indices (STIN), and inflation rate (INFR). We expect that this ANN model will provide strong evidence that INTR will significantly dominate RR volatility instead of other variables. Otherwise, the second ANN model will be constructed.

In the second model, we add two variables, which consist of central bank interest rate (BIRT) and broad money (M2) to answer the research question. We expect that addition of BIRT will enhance dominance of interest instrument in the model. Meanwhile, addition of M2 is pre-assumed to enhance dominance of economic growth instruments as used by Haron (2004).

Additionally, M1 is money supply, which only consists of currency in the hands of the public, demand deposit, other checkable deposit and traveler checks. Meanwhile, M2 is the sum of M1, saving and small time deposit at all financial institution, overnight repurchase agreement issued by all commercial banks. Batten and Thornton (1983) noticed that M1 and M2 explain the variation of American gross national product (GNP) during 1960-1983 for 48% and 26% respectively. However, money supply plays a key role to linking banking sector and real sector, (Qin et al., 2005).

At the end, we use average of one-month time deposit rate of return of Indonesian Islamic bank (RR) as independent variables in both models. For doing so, we collect all monthly data from central bank (Bank of Indonesia) for 120 periods from January 2000 to December 2009. We summarize the research framework as can be seen in figure 5.

Figure 5. Research framework

## 4. Results of employing Alyuda Neurointelligence

The followings are the step-by-step explanation of software utilization for this research based on work of Argyrou (2006). We need three steps to examine relationship between independent and dependent variables as follow:

1. Data preparation

2. Importance level examination of independent variables

3. Robustness evaluation of the networks

4.1 First Examination

4.1.1 Data Preparation

The input to Alyuda resembles a spreadsheet. At the beginning, all data must be clean from data anomalies, because such anomalies can degrade the neural network performance. By clicking “analyzed” menu on “data” button, the application will help to remove data anomalies. According to user manual, data anomalies are categorized into two conditions: (1) missing values and (2) outliers. In particular, missing values are values that are not known, resulting in blank cells in the input columns. On the other hand, outliers are extreme values that differ from the most data. Therefore, a value that lies outside this range is considered to be an outlier and will be removed.

Then, the RR column was set up as output or target variables while the respective variables are categorized as input variables and then designated as numerical data. The data are partitioned into training, validation and testing set. In the “data” button, there is a “data partitioning” menu which can be used for doing data partition. The result of data analysis can be seen in table 1. This examination uses 120 time series data where 117 data of them are accepted for neural network training. In data partition, we use random method which consists of 81 data as training set, 8 data as validation set, and 18 data as test set.

## No

## Data Analysis Results

1

7 columns and 120 rows analyzed

2

7 columns and 117 rows accepted for ANN training and 3 rows disabled

3

6 numeric columns are EXCH, STIN, M1, INFR, INTR and RR

4

1 data/time column is MONTH

5

Output column is RR

6

Data partition method is random

7

Data partition results

a. 81 records to training set (69.23%)

b. 8 records to validation set (15.38%)

c. 18 records to test set (15.38%)

8

data anomalies are 3 numeric outliers

Table 1. Data Analysis result for the first examination

The next step is to normalizing the input data to make it suitable for neural-network processing. The normalization simply converts the input data into a new version before a neural network is trained. Normalizing function can be found in “preprocessed” menu, which is included in “data” button. Bishop (1995) offers the following three reasons for input data normalization: First, to ensure that the size of input data reflects their relative importance in determining the required output. Second, to enable the random initialization of weights before neural network training and third, different variables may have different units of measurements; hence, their typical values may differ significantly.

All the input columns are normalized in the same way, because they all include numerical values. The result of data pre-processing step can be found in table 2.

## No

## Data Pre-processing Results

1

Columns before preprocessing are 7; MONTH, EXCH, STIN, M1, INFR, INTR and RR

2

Columns after preprocessing are 8 ; MONTH Sin, MONTH cos, EXCH, STIN, M1, INFR, INTR and RR

3

Input column scaling range is [-1..1]

4

Output column scaling range is [0..1]

5

Numeric columns scaling parameter

a. EXCH: 0.00043 b. STIN: 0.000838 c. M1: 0.000004 d. INFR: 0.686563

e. INTR: 0.210084 f. RR: 0.153292

Table 2. Data pre-processing result for first examination

4.1.2 Importance level examination of independent variables

Before Alyuda provides importance level information of each independent variable, we need to find the best architecture of ANN. Theoretically, the choice of the best neural network architecture is based on the following criteria:

1. It has the smallest training error

2. It has the smallest test error

3. It has the smallest difference between training and testing error

4. It has the simplest structure.

Using Alyuda, we run the exhaustive search to find the best possible architecture for the models using r-squared as fitness criteria and 20.000 iterations to avoid over fitting. In the “network” button, the application provides “search architecture” menu to find the best architecture. This process takes considerable time because it searches for the best network architecture among all possible alternatives in the specified range.

The searching process choose N(7-3-1) as networks architecture with 0.78224 of r-squared value after 20.000 iterations. The chosen networks consist of one input layer with 7 active neurons while 2 neurons as date which plays no role in training or testing the neural networks, one hidden layer with 3 neurodes and one output layer with 1 neurod.

Next step is to train the networks to provide the information. However, we need to select three configurations before training. First, the logistic activation function is selected for all the neurodes regardless of the layer on which they reside. Second, the sum of squared errors is selected to minimize the output error function. This is summation of squared differences between the actual value and model’s output. For completeness, we restate that the neural network output falls in the range from 0 to 1, because of the logistic activation function. These steps are provided in “network properties” menu, which is also included in “network” button.

Then, the networks are trained with specific condition. Using “train” button, we can scroll down the “option” menu to decide the training parameter. This step uses some specific condition to avoid over fitting such as; choosing backpropagation algorithm and afterward the learning and momentum rates are set at 0.1. The training stops when the model’s mean squared error reduces by less than 0.000001 or the model completes 20,000 iterations, whichever condition occurs first. When this step completed, the networks will provide the importance level information of each independent variable on explaining the fluctuation of RR.

4.1.3 Robustness evaluation of the networks

Before we use the information from previous step, we need to investigate robustness of the N(7-3-1) network architecture on modeling the relationship between independent and dependent variables.

The networks are tested against the testing set by clicking “test” button. Thus, Alyuda showed that the performance of N(7-3-1) is very good through value of correlation (r), R2, mean of absolute error (AE) and mean of absolute relative error (ARE). The details can be found in table 3.

## Parameter

## Value

Correlation (r)

0.885143

R2

0.731673

Mean of AE

0.544927

Mean of ARE

0.069602

Table 3. Performance of networks

According to Alyuda manual, the value of correlation (r) and R2 generally are the indicator of multiple correlations between independent or predictor variables and dependent or predicted variable. The coefficients of r can range from -1 to +1. The closer r is to 1, the stronger the positive linear relationship between both variables. In contrast, the closer r is to -1, the stronger the negative linear relationship will be. Therefore, when r is near 0, it means that there is no linear relationship between both variables. Meanwhile, R2 is a statistical ratio that compares model forecasting accuracy with accuracy of the simplest model that just uses mean of all target values as the forecast for all records. The closer this ratio to 1 the better the model is. Small positive values near zero indicate poor model. However, negative values indicate models that are worse than the simple mean-based model.

Additionally, based on mean value of AE and ARE, we can examine the deviation of the predicted output value from the desired one, since AE and ARE are error values that show the "quality" of the model. ARE is calculated by dividing the difference between actual and desired output values by the module of desired output value. It means that the smaller the network error is, the better the network had been trained.

Another way to test robustness of the network model is through an examination on prediction vs. actual graph using in-sample data as can be seen in figure 6. In this figure, we can see the performance of the model is very good. The quality is shown by the predicted line, which located very close to the actual line.

Figure 6. Actual vs. prediction graph for first ANN Model.

This robust network reveals that, as shown in table 4, INTR and M1 are the most significant variables on RR fluctuation with 51.43% and 31.71% importance level, respectively. Afterwards STIN, EXCH, and INFR contribute with 12.76%, 3.62% and 0.46%, respectively.

## No

## Independent Variables

## Importance (%)

1

INTR

51.433336

2

M1

31.71058

3

STIN

12.763219

4

EXCH

3.625164

5

INFR

0.467701

6

MONTH

0

Table 4. Percentage of contribution of independent variables

Since the networks do not provide strong evidence that interest instrument dominantly affects RR volatility (only 51.43%), therefore this research should conducts second examination.

4.2 Second Examination

In general, the second examination has the same treatment and using the same criteria as in the previous one, especially in the step of data preparation. As we can see in table 5, the details of data analysis are briefly shown.

## No

## Data Analysis Results

1

9 columns and 120 rows analyzed

2

9 columns and 117 rows accepted for ANN training and 3 rows disabled

3

6 numeric columns are EXCH, STIN, M1, M2, INFR, INTR, BIRT and RR

4

1 data/time column is MONTH

5

Output column is RR

6

Data partition method is random

7

Data partition results

a. 81 records to training set (69.23%)

b. 8 records to validation set (15.38%)

c. 18 records to test set (15.38%)

8

data anomalies are 3 numeric outliers

Table 5. Data analysis result

In this examination, there are 7 independent variables which BIRT and M2 are intentionally added to build the second model. Moreover, in table 7 we can see the result of data pre-processing step.

## No

## Data Pre-processing Results

1

Columns before preprocessing are 9; MONTH, EXCH, STIN, M1, M2, INFR, INTR, BIRT and RR

2

Columns after preprocessing are 10; MONTH sin, MONTH cos, EXCH, STIN, M1, M2, INFR, INTR, BIRT and RR

3

Input column scaling range is [-1..1]

4

Output column scaling range is [0..1]

5

Numeric columns scaling parameter

a. EXCH: 0.00043 b. STIN: 0.000838 c. M1: 0.000004 d. M2: 0.000001

e. INFR: 0.686563 f. INTR: 0.210084 g. BIRT: 0.178412 h. RR: 0.153292.

Table 6. Data pre-processing results

4.2.1 Importance level examination of independent variables

Using the same parameters for designing the network as used in the first examination, Alyuda provide N(9-4-1) network architecture to examine relationship between independent and dependent variables. In this step, the process stopped after 20.000 iterations with value of r-squared is 0.757851.

After the network has been designed, we trained the network using the same parameter as in the first examination to provide information about the importance level of each macroeconomic variable on affecting the RR volatility.

4.2.2 Robustness evaluation of the networks

Before we use the information, we need to investigate the robustness of the networks. Therefore, the network architecture and training result should be tested. Using the same configuration as used in first examination, we found the quality of networks is very reliable through the value of correlation (r), R2 , mean value of AE and mean value of ARE in table 7.

## Parameter

## Value

Correlation (r)

0.858535

R2

0.643134

Mean of AE

0.51796

Mean of ARE

0.07277

Table 7. Performance of networks

Furthermore, through actual vs. prediction graph using in-sample data as we can see in figure 7 that the network performs very well as indicated by prediction line which has similar pattern with actual line.

Figure 7. Actual vs. Prediction graph for Second ANN Model.

Finally, we can examine the importance level of each variable as shown in table 8. Accordingly, we can see that ANN put both INTR and BIRT as the most significant variable on RR volatility with almost 98% importance level.

## No

## Independent Variables

## Importance (%)

## 1

## INTR

## 71.70672

## 2

## BIRT

## 25.56138

## 3

## M1

## 1.380907

## 4

## M2

## 0.704832

## 5

## EXCH

## 0.513852

## 6

## STIN

## 0.103915

## 7

## INFR

## 0.028393

Table 8. Percentage of contribution of independent variables

## 4. Conclusion

Haron (1983) found that Islamic banks benchmark interest rate through adjustment of both financing and deposit rate. In Indonesia, the efforts are conducted in following ways; first, the banks grant some of their profit to adjust RR given to depositor for benchmarking with market deposit interest rate. Second, the banks use central bank interest rate in financing process to immediately adjust their financing rate to be benchmarked with market credit rate. Using central bank interest rate as benchmark will help them to be adapted with conventional bank faster than waiting newly forming market rate after central bank changes the rate. Subsequently, the bank will be able to deliver competitive deposit return without sacrificing their profit.

The first way could be the reason why INTR contributes only 51% in the first model. In the model, ANN has only INTR as input to learn how it affects RR despite four other macroeconomic growth variables. This is describing 51% possibility of the bank to do granting procedure to depositor during the sample period. Which mean that there is 49% possibility when the banks deliver return based on actual profit. As shown in figure 1 that Indonesian Islamic banks have three periods when they can provide better return than INTR. Therefore, we think that 51% of level importance is acceptable.

On the other hand, the second way helps us to explain why addition of BIRT increases the contribution of INTR about 20% in the second ANN model. ANN might learn the inter-relation of BIRT and INTR on RR volatility through the financing process where the banks use BIRT to increase profit and then adjust RR to follow INTR changes. Therefore, this addition describes the mimicking strategy through financing process. Unfortunately, we cannot provide empirical evidence for this argument since the software has no feature to describe internal process of networks learning which learn inter-relationship between independent variables in hidden layer of the networks. Future work is needed to find this empirical evidence using other application.

However, this research has successfully found the empirical evidence of mimicking strategy existence in Indonesian Islamic banks through the dominance of interest instrument on affecting RR volatility.

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