Keywords

1 Introduction

Banks play a significant role in financial market as well as economies in every country [1]. Monitoring on the bank financial management is necessary to meet the target profit as well as control the liquidity. Thus, data analysis on financial statement is essential in financial planning [2]. Bank financial management considers multiple goals such as asset, liability, equity, earnings, profitability and optimum management item [3]. A trade-off point must be obtained among multiple goals in order to optimize the financial management [4]. Decision makers have to achieve an optimal solution that best fit their desire goals. Therefore, goal programming (GP) model has been presented to solve multiple goals in optimizing the financial management of banks [5, 6].

In bank financial management, there are some limitations and drawbacks identified based on the past studies. Firstly, there is no comprehensive study done on comparison among the banks for benchmarking using GP model. GP model is only constructed to optimize the financial management of a single bank without benchmarking on other banks. The comparison among the banks in financial management is important since it can determine the potential improvement according to the benchmark [7,8,9]. Besides that, subjective judgment in assigning weight of the goals is another drawback in optimizing the financial management of banks. The problem of reliability on respondents’ judgment or subjective weights may result in bias perspective and inconsistent issue [10]. Hence, this study aims to propose a two-stage GP model in optimizing the bank financial management. At the first stage, entropy method is proposed to determine the objective weight of each goal. At the second stage, a GP model is constructed to optimize the bank financial management with multiple goals based on the entropy weights and benchmark target value.

2 Literature Review

Kosmidou and Zopounidis [2] developed a GP model to examine the asset and liability of a Greek commercial bank. The authors utilized the financial statement in 1999 to develop an optimal asset and liability management for the following year. Several contradictory goals such as liquidity and returns were considered in the model. Different goals and constraints were taken into account as well as deviation variables to determine the favorable scenarios for future. In short, the proposed model aims to seek for a direction for bank’s future financial planning.

Naderi [3] denoted that company’s future risk can be predetermined with GP model. The optimal asset and liability management can be achieved through proper structure of bank’s balance sheet elements. The findings proved that the model managed to determine appropriate structure for the optimal management.

Halim et al. [5] developed a GP model to examine the achievement and improvement of six goals in bank financial management. Data for the main goals from 2010 to 2014 were obtained through annual statement. The results showed that all goals were achievable and four goals could be increased to higher aspiration level. Therefore, potential improvements on goal achievement can be identified with GP model.

Tektas [11] applied GP model in determining an efficient financial management for the bank with respect to different managerial strategies. Two Turkish commercial banks were investigated to improve the wellbeing of the banks. Different goals such as liquidity, asset and revenue were examined to determine the optimal financial management of the banks.

Arewa et al. [12] conducted a research in United Bank of Africa to investigate the financial management of the bank using GP model. Six goals such as assets, liabilities, equities, profits, earnings and optimum management item were examined to determine the deviation of each goal in optimizing the proportions of items in financial statement.

Viswanathan et al. [13] indicated that GP model is a useful tool for asset allocation and liability composition because it considers large amount of constraints to determine the optimal solution for the bank. The generated results managed to show a realistic and compatible composition for asset and liability.

Chen et al. [14] developed a GP model to analyze the financial management of a listed bank for the period of 2011–2015. Six goals such as assets, liabilities, equities, profits, earnings and optimum management item were examined in their studies. The results showed that all goals were achievable and three goals could be increased to new target value for further improvement.

In addition, GP model has also been utilized to solve multiple objective decision problem in portfolio optimization [15,16,17,18].

3 Data and Methodology

3.1 Data

This study investigates four listed banks in Malaysia, namely Public Bank Berhad (PBBANK), RHB Bank Berhad (RHBBANK), CIMB Group Holding Berhad (CIMB) and Malayan Banking Berhad (MAYBANK) from year 2012 to 2016. Asset, liability, equity, earning, profitability and optimum management item are the main goals in financial management of the banks [3, 5].

3.2 Proposed Two-Stage Goal Programming Model

A two-stage GP model is proposed to compare and optimize multiple goals in bank financial management. The proposed two-stage GP model comprises two stages as follows.

  • Stage 1:

    At the first stage, the weight of the goal is determined with entropy approach.

  • Stage 2:

    At the second stage, a GP model is constructed for each bank to optimize multiple goals based on the entropy weights obtained in the first stage. The potential improvement will be recommended based on the optimal solution obtained.

Entropy Method (First Stage)

Objective weight is emphasized owing to subjective weighting from the decision makers are based on their opinions and preferences. Therefore, the subjective judgment might be imprecise or inconsistent. Entropy method determines the objective weight of each goal [19, 20]. From the past studies, entropy weight has been integrated with TOPSIS model in multiple-criteria decision making (MCDM) problems [1, 4, 10, 19,20,21]. In this study, entropy method is proposed to determine the weights of the goals as follows.

Step 1: Form the decision matrix based on the total performance rating of all banks under each criterion. The rows indicate alternatives for \(i = 1,2,3, \ldots ,n\) whereas columns refer to criteria for \(j = 1,2,3, \ldots ,m\).

$$Y = \left[ {\begin{array}{*{20}c} {y_{11} } & \cdots & \cdots & {y_{1m} } \\ \vdots & \ddots & {} & \vdots \\ \vdots & {} & \ddots & \vdots \\ {y_{n1} } & \cdots & \cdots & {y_{nm} } \\ \end{array} } \right]$$

Step 2: Form a new normalized matrix (\(Z\)) by normalizing the decision matrix based on Eq. (1).

$$z_{ij} = \frac{{y_{ij} }}{{\sum\nolimits_{i = 1}^{n} {y_{ij} } }}$$
(1)
$$Z = \left[ {\begin{array}{*{20}c} {z_{11} } & \ldots & \ldots & {z_{1m} } \\ \vdots & \ddots & {} & \vdots \\ \vdots & {} & \ddots & \vdots \\ {z_{n1} } & \ldots & \ldots & {z_{nm} } \\ \end{array} } \right]$$

Step 3: Determine the entropy value (\(\mathop e\nolimits_{j}\)).

$$e_{j} = - k\sum\limits_{i = 1}^{n} {z_{ij} \ln z_{ij} } \,{\text{where}}\,k = \frac{1}{\ln n}$$
(2)

A higher entropy value proposes less useful information about the criteria, hence a smaller weight will be assigned and vice versa [20].

Step 4: Obtain the degree of divergence (\(d_{j}\)) of the intrinsic information involved by each criterion.

$$d_{j} = 1 - e_{j}$$
(3)

Step 5: Determine the objective weight of each criterion.

$$w_{j} = \frac{{d_{j} }}{{\sum\nolimits_{k = 1}^{m} {d_{k} } }}$$
(4)

Goal Programming Model (Second Stage)

At the second stage, a GP model is constructed for each bank to optimize multiple goals based on the entropy weights and benchmark target value. GP model is designed owing to the difficulty in solving multiple objectives especially in achieving contradict goals for a company. GP model is able to deal with multiple goals simultaneously while obtaining the optimal solution that satisfied all the restrictions on the decision variables [17, 22, 23]. The GP model is shown as follows:

$${\text{Minimize}}\,z = w_{1} G_{1} + w_{2} G_{2} + \cdots + w_{j} G_{j} \,{\text{where}}\,j = 1,2,3, \ldots ,m.$$
(5)

Subject to

$$\sum\limits_{c = 1}^{h} {(a_{jc} x_{c} + d_{j}^{ - } - d_{j}^{ + } ) = g_{j} }$$
(6)
$$x_{c} ,d_{j}^{ - } ,d_{j}^{ + } \ge 0$$

where

\(z\):

total deviation;

\(w_{j}\):

entropy weights for \(j = 1,2,3, \ldots ,m\);

\(d_{j}^{ - }\):

negative deviation variable (underachievement) for \(j = 1,2,3, \ldots ,m\);

\(d_{j}^{ + }\):

positive deviation variable (overachievement) for \(j = 1,2,3, \ldots ,m\);

\(x_{c}\):

amount of financial statement for \(c = 1,2,3, \ldots ,h\);

\(a_{jc}\):

weight of financial statement for \(c = 1,2,3, \ldots ,h\);

\(g_{j}\):

target value for \(j = 1,2,3, \ldots ,m.\)

This study aims to optimize multiple goals as follows.

G1:

Maximize asset (\(d_{1}^{ - }\)),

G2:

Minimize liability (\(d_{2}^{ + }\)),

G3:

Maximize equity (\(d_{3}^{ - }\)),

G4:

Maximize profitability (\(d_{4}^{ - }\)),

G5:

Maximize earnings (\(d_{5}^{ - }\)),

G6:

Maximize optimum management item (\(d_{6}^{ - }\)).

LINGO software is employed to solve the proposed two-stage GP model. According to the optimal solution of GP model, the goal has been achieved if the respective deviation variable is zero [5]. The potential improvement can be determined for each bank according to the deviation from the target value. LINGO software has been applied in various studies to solve the optimization problem [24,25,26,27,28,29,30,31].

4 Results

Table 1 presents the weight of multiple goals as described in the first stage of the proposed model.

Table 1 Weight of multiple goals
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As shown in Table 1, the highest weight of the goal is earnings (0.1973), followed by profit (0.1949), equity (0.1587), optimum management item (0.1503), asset (0.1497) and lastly liability (0.1490). Based on the Entropy method, the decision makers can identify the importance of the goals based on past financial data as data driven decision analysis instead of obtaining subjective judgment.

Tables 2, 3, 4 and 5 present the optimal value and goal achievement for CIMB, MAYBANK, PBBANK and RHBBANK respectively according to the optimal solution of GP model.

Table 2 Optimal solution of CIMB (RM Trillion)
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Table 3 Optimal solution of MAYBANK (RM Trillion)
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Table 4 Optimal solution of PBBANK (RM Trillion)
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Table 5 Optimal solution of RHBBANK (RM Trillion)
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According to Table 2, CIMB is able to achieve four goals for asset, equity, earnings and optimum management item because of zero values for negative deviation respectively. This implies that CIMB is able to meet or overachieve the target values for these goals. For liability and profitability goals, \(d_{2}^{ + }\) and \(d_{4}^{ - }\) are non-zero. Therefore, these two goals are not achieved for CIMB. From the findings, the target value of equity and earnings can be revised for continuous improvement. The target value of equity and earnings can be improved by RM 0.0212 trillion and RM 0.0086 trillion respectively based on the positive deviation. As shown in Table 3, the goal achievements for MAYBANK are same as CIMB, which are asset, equity, earnings and optimum management item. The target value of asset and equity can be improved by RM 0.0011 trillion and RM 0.0158 trillion respectively for MAYBANK in future.

From the results in Table 4, PBBANK is able to achieve four goals as well except liability and earnings. In addition, the target value of asset, equity and profit can be improved by RM 0.0024 trillion, RM 0.0120 trillion and RM 0.0100 trillion respectively over the next five years for continuous improvement. For RHBBANK, \(d_{1}^{ - }\), \(d_{3}^{ - }\), \(d_{5}^{ - }\) and \(d_{6}^{ - }\) are zero as presented in Table 5. This implies that the asset, equity, earnings and optimum management item are achieved by RHBBANK. Moreover, the target value of asset can be improved by 1.8838 × 10–3 based on the optimal solution.

Table 6 shows the potential improvement for each bank according to the deviation from the benchmark target value.

Table 6 Potential improvement according to the deviation from the benchmark target value
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As shown in Table 6, the potential improvement can be determined in order to achieve the benchmark target value. Three goals namely, asset, equity and optimum management item are achieved by all banks. However, liability goal is unachievable by all banks because the positive deviation from the benchmark target value is non-zero. CIMB, MAYBANK, PBBANK and RHBBANK should minimize their total liability by RM 1.8674 trillion, RM 1.8739 trillion, RM 1.8791 trillion and RM 1.8905 trillion respectively to meet the benchmark target value of RM 0.9709 trillion. For profitability, only PBBANK can achieve the goal due to zero deviation from the benchmark target value. CIMB, MAYBANK and RHBBANK should decrease RM 0.0086 trillion, RM 0.0022 trillion and RM 0.0037 trillion respectively to meet the benchmark target value of RM 0.0335 trillion.

5 Conclusion

A two-stage GP model is proposed to compare and optimize multiple goals in financial management of the banks in Malaysia. The weight of each goal is determined using entropy method at the first stage. The findings indicate that CIMB, MAYBANK, PBBANK and RHBBANK can achieve the goal for asset, equity and optimum management item. Furthermore, the target value of asset, equity, earning and profit can be increased according to the optimal solution of the proposed model. The significance of this study is to determine the potential improvement on liability, profit as well as earnings in bank financial management.