# Efficiency analysis by combination of frontier methods: Evidence from unreplicated linear functional relationship model.

1. Introduction (*)In the stock market, it is challenging to identify the most efficient company as many of variables are related to measuring the companies' performance. The investors sometimes earn excess profits by exploiting any observable trends in stock price series. These days it is very difficult to identify the most efficient company by observing only the stock price. Many techniques are applied by investors to optimize their return and minimize the risk of their investment (Saad et al., 2011). Particularly in policy making, the efficiency measurement is important because it assists an efficient allotment of capital across versatile productive sectors in an economy. The investors get an accurate signal from the stock price if the market or company is efficient. In this way, efficiency helps to boost stock market liquidity and economic growth as well as stimulates long-term investment. Reversely, inefficiency creates higher costs and fluctuations in stock price (Hubbard, 2008).

In current years, the academic research on the performance of financial institutions has increasingly focused on frontier efficiency analysis. For performance evaluation, ample change occurred in the past two decades. Nowadays, performance evaluation is critical as a large number of variables (input and output) are involved in the measurement of the corporate performance (Adrienn, 2014). Performance analysis gives opportunities to investors, particularly private equity shareholders, to find the extra value for their non-financial performance (Patricia & Balazs, 2014).

There are many methods in the frontier analysis to evaluate performance such as parametric methods and non-parametric methods, stochastic method (Fenyves et al., 2015). The stochastic frontier analysis (SFA) model becomes the most frequently used procedure because it segregates statistical noise from the effect of inefficiency (Kumbhakar & Lovell, 2003). In spite of this, SFA model speculates a distinct probability distribution for the efficiency level. However, if the selection of input-output variables or decision making units is erroneous then the finding score will incorporate error (Coelli et al., 2005). The data envelopment analysis (DEA) model skips this sort of specification error and it does not need a prior postulation regarding the associate analytical type of an assumed likelihood distribution or the production function for efficiency (Dong et al., 2014). DEA does not allow random errors in the optimization which is its main drawback. Therefore, if any noise exists, this may exaggerate the common inefficiency. Consequently, two methods (DEA and SFA) have their advantages as well as drawbacks (Huang & Wang 2002).

Many researchers (e.g. Casu et al., 2004; Delis & Papanikolaou, 2009; Weill, 2004) find that the consistency of efficiency derived from DEA and SFA is not significant. For this reason, this study concentrates on finding the combination of the DEA and SFA efficiency scores which will be a new experiment in literature perspective. For the justification of model effectiveness this study analyzes the impact of profit risk (return on asset) on efficiency as theoretically we know that a most profitable company should be efficient. Moreover, Fernandes et al. (2018) and Altunbas et al. (2007) find that there is a strong connection between efficiency and profit risk; because inefficient financial firm tends to take less risk by investing and hold more capital. Fernandes et al. (2018) find that profit risk has a positive effect on the efficiency of peripheral European domestic banks. More precisely, profit risk can be well-defined as a proportion of net income over the total asset. However, the selected data may contain some error due to imputation of some missing value by maximum likelihood method or balance sheet data sometimes make some manipulation by the company. For this reason, this study concentrates to find error-free technical efficiency by applying the unreplicated linear functional relationship model (ULFR) that first introduced by Adcock in the year 1877 (Sprent, 1990).

This study is a new idea for the estimation of the financial firm's efficiency by using the combination of DEA and SFA by utilizing the unique data set especially in respect to stock market related input output variable's data set. The study provides a unique setting to calculate financial efficiency matric and finds the effect of profit risk on efficiency by using regression analysis and ULFR. This analysis will help to find technical efficiency sores that error-free and more effective. Moreover, these findings could provide useful and important signal in case of decision making for management.

Given the above, this study's aim is four-fold. First, DEA and SFA utilized to find technical efficiency. Second, the combination of DEA and SFA that is measured by averaging DEA and SFA scores to find technical efficiency. Third, examination of the influence of efficiency on profit risk to find the most efficient method. Finally, ULFR model will be applied to find error-free efficiency.

This paper is structured as follows. Section 2 describes the background of this study (review of literature), Section 3 presents the methodology of the study. Next, Section 4 is about result and discussion and Section 5 illustrates the limitation of the study. Finally, Section 6 presents the conclusion.

2. Review of literature

In many pieces of literature, various efficiency approaches have been applied to find banking efficiency. Only a relatively few studies have used two or more frontiers for estimating financial firm efficiency for the same data set. Aigner et al. (1977) suggest the parametric approach (SFA), Charnes et al. (1978) suggest the non-parametric (DEA) further developed to non-constant returns (NCR) by Banker et al. (1984).

Bauer (1990), Lovell (1993), Greene (1993), and Coelli et al. (2005) provide the extensive reviews and contributions for the two methods.

Resti (1997), Eisenbeis et al. (1997), and Huang & Wang (2002) extend comparative study on SFA and DEA in financial firms. In their studies, the two approaches provide relatively close mean efficiencies. Resti (1997) and Eisenbeis et al. (1997) find very high rank-order correlations between DEA and SFA.

Ferrier & Lovell (1990) identify rank-order correlation that is approximate to zero (0.02). In contrast, the inefficiency scores measures from the DEA approach are more than two times greater than those calculated using SFA by Eisenbeis et al. (1997). Dong et al. (2014) find out SFA efficiency scores which are slightly higher than DEA efficiency scores. The findings of the SFA exercise discover lower mean inefficiency than those of the DEA (Delis, 2009). Huang & Wang (2002) estimate 22 Taiwanese commercial banks' economic efficiency for the period 1982 to 1997 by using SFA and DFA (distribution-free approach) as well as DEA. The result shows that the mean efficiency scores derived from the three methods (DEA, SFA, and DFA) are the same. On the other hand, the Spearman's rank correlation coefficients for SFA, DFA, and DEA efficiency measures are quite minor indicating that these techniques are not consistent in their efficiency rankings. Weill (2004) also investigates in European countries' (Italy, France, Germany, Switzerland and Spain) banking data to find the consistency of efficiency frontier techniques (DEA, SFA, and DFA). He describes that the efficiency rank order correlations among the methods are generally poor. More recently, Fernandes et al. (2018) have evaluated the efficiency of European peripheral domestic banks. They have made the linear regression analysis of bank-risk determinants and their performance over the period 2007 to 2014 and have found that profit risk and efficiency have a positive relation. Fah et al. (2007) utilized ULFR model to find error value from dependent and independent variables' simple linear regression: as conventional regression models are not suitable for global versus localized measure, perfect reference and bivariate case. They have found that coefficient of determination (COD) of ULFR better than COD of simple linear regression.

Ismail (2005) has concentrated on Malaysian commercial bank to find efficiency over the period 1994 to 200 and postulates that DEA technique shows higher efficiency scores than the parametric methods and scores are positively related to each other. Sufian et al. (2016) have found with DEA approach that banks from Asian countries are comparatively more efficient rather than external banks. Davies (2017) postulates that technical efficiency of Malaysian commercial banks is 71.33%. He suggests that domestic banks have been inefficient in controlling their costs due to their size.

Janang et al. (2013) with SFA approach have found that remuneration is positively linked to the efficiency of government-linked companies. Suhaimi et al. (2012) have confirmed that 7 banks are efficient among the 9 banks in Malaysia. Hasan et al. (2012) have found that Malaysian internal banks have the mean efficiency of 94% and the most efficient bank is RHBANK while the least efficient bank is PBK.

From the best of our knowledge, virtually nothing has been published to critically examine the impact of profit risk on technical efficiency (derived from DEA, SFA, and CDS) in the field of the financial sector of the Bursa Malaysia. Despite studying of efficiency by different method, no research shows the combination of both methods and finds the impact of efficiency and profit risk. Most importantly, no article is recognized that shows the error-free technical efficiency by applying ULFR model. In light of these knowledge gaps, this article proposes a model CDS that can measure efficiency more efficiently.

3. Research methodology

3.1. Data envelopment analysis

The data envelopment analysis is defined as a mathematical programming method that measures the efficiency of a firm or decision-making unit (DMU). It also measures the similar DMUs with the simple restriction that all DMUs lie below or on the efficiency frontier (Seiford & Thrall, 1990). The DEA method suggested by Charnes et al. (1987) and further developed to non-constant returns (NCR) explain how to design the production possibility set without guessing a production function from given a set data of input, output variables. The DEA approach is based on the MPI (Malmquist Productivity Index) to investigate how the productivity of each company changes through time. This is done by following an output-oriented DEA approach described by Fare et al. (1994). The best way to introduce DEA is via the ratio form. For each DMU needs to obtain a measure of the ratio of all outputs over all inputs, such as

[theta] = [[p.sub.i][y.sub.it]/[q.sub.i][x.sub.it]]

Where, [p.sub.i] is an Mx1 vector of output weights for [i.sup.th] firm and [q.sub.i] is a Kx1 vector of input weights of [i.sup.th] firm. To select optimal weights we specify the mathematical programming problem:

[mathematical expression not reproducible] (1)

Where, for each DMU (decision making unit) s is output observation, m is input observation, r is [s.sup.th] output, i is [m.sup.th] input, [y.sub.r1] is [r.sup.th] output for time period t, [x.sub.it] is [i.sup.th] input for time period t, n is DMU observation, j is [n.sup.th] DMU, [lambda] is no-negative scalar, [x.sub.ij] is [m.sup.th] input for [n.sup.th] DMU, [y.sub.ij] is [s.sup.th] output for [n.sup.th] DMU, [theta] is a scalar representing the value of efficiency score for each DMU. A firm is assumed to be technically efficient if it is impossible to increase output without altering input. To measure the technical efficiency, the software DEAP version 2.1 is used, though this study does not discuss about productivity except technical efficiency.

3.2. Stochastic frontier analysis

A firm is called efficient if it is able to attain its objectives, otherwise it is called inefficient. It is assumed that a firm's main goal is to minimize production cost that means any excess of inputs is to be avoided so that there is no unnecessary use of capitals. It is often considered, in the production theory, which firms are behaving efficiently in an economic response. The production theory is proposed by Cobb & Douglas (1928). They develop the production theory by using of labour, capital, production, value, and wages for the manufacturing firms. The firms are capable to effectively assign all supplies relative to the inputs, outputs and constraints executed by the framework of the production function. Moreover, the firms are able to effectively assign all supplies relative to whatever behavioural aims presented to the manufacturers (Fare et al., 1985).

Additionally, Berger & Humphrey (1997) modified the production function model to concentrate on financial sector's efficiency. The efficiency of the financial sector means the efficient allocations of financial resources that are imperative to increase productivity. This shows that the economy has the upper hand to transfer the input of saving resources for more productive output. In order to measure statistical noise, Aigner et al. (1977) added symmetric error term to the deterministic frontier. The model expressed as:

[Y.sub.it] = [X.sub.it][beta] + ([V.sub.it]-[U.sub.it]), i = 1,2, ... N, t = 1,..., T (2)

Where, [Y.sub.it] is (the logarithm of) the production of the [i.sup.th] firm in the [t.sup.th] time period; [X.sub.it] is a kx1 vector of (transformations of the) input quantities of the [i.sup.th] firm in the [t.sup.th] time period; [V.sub.it] are random variables which are assumed to be iid N(0,[[sigma].sub.i.sup.2]); [beta] is an vector of unknown parameters.

[U.sub.it] = [U.sub.i][e.sup.-[eta](t-T)] (3)

Where, [U.sub.i] is the inefficiency level of the [i.sup.th] producer at time T and [eta] is an unknown parameter.

The term [TE.sub.it] is technical efficiency for the [i.sup.th] firm in the [t.sup.th] time period define by using stochastic frontier model (2) as follows (Battese & Coelli, 1988):

[TE.sub.it] = [e.sup.[-U.sub.it]] (4)

Here, [U.sub.it] is the stipulation of the inefficiency model in equation (3). The maximum-likelihood estimates are used to measure the parameters of the stochastic frontier model.

3.3. Empirical form of stochastic frontier model

The Cobb-Douglas stochastic frontier production model's functional form is defined as:

ln([ROE.sub.it]) = [[beta].sub.0] +[[beta].sub.1] ln([TV.sub.it]) + ln([DPS.sub.it]) + [[beta].sub.3] ln([MC.sub.it]) + [[beta].sub.4] ln([PV.sub.it]) + [[beta].sub.5] ln([FL.sub.it]) + ([V.sub.it] - [U.sub.it]) (5)

Where, the subscripts t and i represents the [t.sup.th] year and [i.sup.th] firm of the observations, and i = 1,2,....26; t = 1,2,...10; ROE, TV, DPS, MC, PV, FL are defined in the Table 2; "ln" represents the natural logarithm.

3.4. Combination of DEA and SFA (CDS)

The average of DEA and SFA efficiency scores is considered as the combination of DEA and SFA (CDS).

CDS = [Efficiency score of DEA + Efficiency score of SFA/2]

3.5. Linear regression

In this study, the linear regression model is utilized to investigate the impact of profit risk on efficiency score (derived from DEA, SFA and CDS) in the financial sector of Bursa Malaysia. So, the three models take the following forms:

Ef [(DEA).sub.i] = [[beta].sub.0] + [[beta].sub.1][Pr.sub.i] +[[epsilon].sub.i] (6)

Ef [(SFA).sub.i] = [[beta].sub.0] + [[beta].sub.1][Pr.sub.i] + [[epsilon].sub.i] (7)

Ef [(CDS).sub.i] = [[beta].sub.0] + [[beta].sub.1] [Pr.sub.i] + [[epsilon].sub.i] (8)

Where, Ef [(DEA).sub.i], Ef [(SFA).sub.i], Ef [(CDS).sub.i], are the average technical efficiency scores of the company i derived from DEA, SFA and CDS respectively; [Pr.sub.i] is the average profit risk of [i.sup.th] firm; [[beta].sub.0] is constant and represents the slope parameter; represents error term.

3.6. Unreplicated linear functional relationship model

Suppose that EF (CDS) and PR are two linearly related unobservable variables, then the functional form is

[Q.sub.i] = EF [(CDS).sub.i] = [[beta].sub.a] + [[beta].sub.f][PR.sub.i] (9)

and the two corresponding random variables are observed with error d and e, respectively as

[mathematical expression not reproducible] (10)

The following conditions are assumed:

[mathematical expression not reproducible] (11)

Hussin (1997) defined the model (9) and (10) as the unreplicated linear functional relationship (ULFR) model when there is only the variables EF(CDS) and PR. Where, [d.sub.i] and [e.sub.i] are random variables that are mutually independent and normally distributed. When the ratio of the error variance is known, that is [[[sigma].sup.2.sub.e]/ [[sigma].sup.2.sub.d] = [lambda], then the maximum likelihood estimators of parameters [[beta].sub.a], [[beta].sub.f], [[[sigma].sup.2.sub.d] and [PR.sub.i] are:

[mathematical expression not reproducible]

Where, [bar.Ef] = [[sigma][Ef.sub.i]/n], [bar.Pr] = [[sigma][Pr.sub.i]/n], [S.sub.yy] = [SIGMA] [([Ef.sub.i] - [bar.Ef]).sup.2], [S.sub.xx] = [SIGMA] [([Pr.sub.i] - [bar.Pr]).sup.2], [S.sub.xy] = [sigma] ([Pr.sub.i] - [bar.Pr])([Ef.sub.i] - [bar.Ef]).

And the coefficient of determination of ULFR ([R.sup.2].sub.f]) for any value of [lambda]:

[R.sup.2.sub.f] = [[SS.sub.r]/[S.sub.yy]],

Where, [SS.sub.r] = [[[??].sub.f] ([S.sub.yy] - [S.sub.xx]) + 2[[??].sub.f] [S.sub.xy]/1 + [[??].sup.2.sub.f]]

3.7. Data collection

There are 30 listed financial companies in Bursa Malaysia. This study concentrates on balance data of 26 listed companies. The sample is panel data which covers 26 financial companies listed in Bursa Malaysia over the period of 2007 to 2016. There are total 260 observations. Data are collected from Bloomberg. All the company names are shown in the Table 1.

For this study, five inputs and an output have been selected. The input and output variables are selected based on Ismail et al. (2012) and other major studies on the efficiency of the financial sector. The five input variables are market capital, total volume, dividend per share, financial leverage, price to book ratio. The output variable is return on equity. The dividend per share is included to the study as it has relation with stock returns. On the other hand, it furnishes signaling effect to stock prices and previous empirical proof found dividend per share has anticipating power for stock returns (Campbell et al., 1988). The total volume is chosen as it has important signal tool and it is an instructive variable for stock returns. Moreover, the market capital effect appears to have a persistent explanation on stock returns (Fama & French, 1992; Ismail et al., 2012). The software package DEAP Version 2.1 and the software package FRONTIER 4.1 of Coelli (1996a, 1996b) were used in order to carry out the SFA and DEA estimations.

4. Result and discussion

Summary statistics of the data are shown in Table 2. Currency is measured in USD. Total market capital is shown in millions of USD. Dividends per share are also shown in USD. All the variables' maximum and minimum value are also shown in Table 2. The values of financial leverage, price to book ratio, return on asset and return on equity are in ratio form.

However, this section presents the estimated results of DEA, SFA, and CDS. A firm will be said technically efficient if it can reduce inputs used in producing given outputs. The efficiency score of value 1 states that a firm is on the best practice frontier. A value of less than 1 indicates inefficient use of resources.

4.1. Efficiency derived from DEA

The efficiency scores are presented in Figure 1. It is seen that the average technical efficiency of financial companies listed in Bursa Malaysia was 0.8999. This means that companies were less than 10% inefficient in using their existing resources. Moreover, Siew et al. (2017) found average efficiency score 0.5865 in the financial company listed in Malaysia. It is also obvious that companies LPI, ACSM, APX, JOH, ECML, and MAA were efficient for all time period. The result is approximately similar to Siew et al. (2017) which state that LPI, BURSA, ACSM, APX were fully efficient. The results also depict that MAY was the least efficient company with 70.28% efficiency. Moreover, the efficiency scores of HLG, ALLZ, and INS were approximately same as they were around 0.98. Among the banks in Malaysia, Sufian et al. (2016) found that RHB was the most efficient bank with the efficiency score 0.937 and the least efficient bank was WAH TAT bank (0.288). On the other hand, in this study BIMB bank (0.8455) was the most efficient bank and MAY bank (0.7028) was the least efficient bank. However, in this study the RHB bank's efficiency score was 0.739.

FIGURE 1. EFFICIENCY SCORE DERIVED FROM DEA Company name Efficiency MAY 0.7028 PBK 0.8253 CIMB 0.758 HLBK 0.7716 RHBBANK 0.739 HLFG 0.8348 AMM 0.7191 BIMB 0.8455 AHB 0.7788 LPI 1 STMB 0.9551 ALLZ 0.9863 MNRB 0.9648 MHBS 0.9697 PO 0.9588 MBS 0.8659 BURSA 0.9427 ACSM 1 INS 0.9982 RCE 0.9447 APX 1 JOH 1 ECML 1 HLG 0.9906 TAE 0.8452 MAA 1 Average 0.8999 Source: Data from historical data of Bloomberg terminal. Note: Table made from bar graph.

4.2. Efficiency derived from SFA

The average technical efficiency derived from SFA was 0.8809 which means that the financial companies listed in Bursa Malaysia were 12% efficiency behind to get maximum outputs from given inputs. The efficiency scores are presented in Figure 2.

FIGURE 2. EFFICIENCY SCORE DERIVED FROM SFA Company name Efficiency MAY 0.8357 PBK 0.9164 CIMB 0.8812 HLBK 0.8992 RHBBANK 0.8901 HLFG 0.9233 AMM 0.8452 BIMB 0.9279 AHB 0.8706 LPI 0.9145 STMB 0.9379 ALLZ 0.9502 MNRB 0.928 MHBS 0.8784 PO 0.7602 MBS 0.9358 BURSA 0.8618 ACSM 0.9638 INS 0.9367 RCE 0.9226 APX 0.8461 JOH 0.5857 ECML 0.8818 HLG 0.9347 TAE 0.8434 MAA 0.8309 Average 0.8809 Source: Data from historical data of Bloomberg terminal. Note: Table made from bar graph.

The company ACSM seemed to be more efficient in controlling efficiency, as its efficiency score stands at 0.9637. But, the company JOH was the least efficient company as its efficiency score was 0.5857. Hasan et al. (2012) applied the SFA approach for finding the efficiency of the domestic banks listed in Bursa Malaysia over the period 2005-2010. He found that PBK (0.918) was the least efficient bank and RHBBANK (0.986) was the most efficient bank. On the other hand, in this study efficiency scores of PBK and RHBBANK were 0.9164 and 0.8901 respectively. The result of Hasan et al. (2012) differs from our study as they used different inputs and outputs.

4.3. Combination of DEA and SFA (CDS)

The technical efficiency scores derived from the combination of DEA and SFA are shown in Figure 3. The average technical efficiency was 0.8904, that means financial companies listed in Bursa Malaysia were 11% efficiency behind to get maximum outputs from given inputs. The company ACSM seemed to be more efficient in controlling efficiency, as the efficiency score stands at 0.9819. Whereas, the company MAY was the least efficient as its efficiency score is 0.7693. Average efficiency of companies ALLZ, INS and HLG were around 0.96. Among the 26 companies, 15 companies were less than 10% inefficient. However, only 2 companies were more than 20% less efficient.

FIGURE 3. EFFICIENCY SCORE DERIVED COMBINATION OF DEA AND SFA Company name Efficiency MAY 0.7693 PBK 0.8709 CIMB 0.8196 HLBK 0.8354 RHBBANK 0.8146 HLFG 0.8791 AMM 0.7822 BIMB 0.8867 AHB 0.8247 LPI 0.9573 STMB 0.9465 ALLZ 0.9683 MNRB 0.9464 MHBS 0.9241 PO 0.8595 MBS 0.9009 BURSA 0.9023 ACSM 0.9819 INS 0.9675 RCE 0.9337 APX 0.9231 JOH 0.7929 ECML 0.9409 HLG 0.9627 TAE 0.8443 MAA 0.9155 Average 0.8904 Source: Data from historical data of Bloomberg terminal. Note: Table made from bar graph.

4.4. Comparison of DEA, SFA and CDS efficiency scores

The empirical findings of efficiency scores are presented in Figure 4. It is clear that the DEA average efficiency score (0.8999) was greater than the SFA average efficiency score (0.8809). Moreover, CDS average efficiency was 0.8904 that is greater than SFA. However, such types of differences are not surprising because SFA allows DMUs to depart from the frontier due to inefficiency as well as statistical noise. But, DEA method cannot measure statistical noise. These results coincide with the results of Sufian et al. (2016), Ismail (2005), Isik & Hasan (2002). However, Dong et al. (2014) have found the opposite result in their study of cost efficiency of the Chinese banks.

In three methods, only DEA shows around similar efficiency scores. Furthermore, this study examined that there was a lesser difference among efficiency scores of financial companies estimated by DEA, SFA and CDS (SFA scores < CDS scores < DEA scores). The study suggests that the three models tend to have limited continuity in selecting the most efficient and the least efficient financial companies in terms of efficiency score.

4.5. Selection of most efficient method by regression analysis and ULFR

From Table 3, it is found that the relationship between efficiency and profit risk was statistically significant at the 5% level of significance by DEA and CDS since the p-value was less than 0.05.

This depicts that the profit risk positively affected the efficiency of the financial company listed in Bursa Malaysia. That means more profitable financial company or less leveraged company was higher efficient and would face a lesser cost of going insolvent over the period 2007 to 2016. Fernandes et al. (2018) applied the DEA method and also found that the profit risk positively affects the efficiency of European peripheral domestic banks. They found the coefficient score was 0.216. However, in this study, the relation between SFA and profit risk was insignificant (p-value was more than 0.05). Furthermore, its coefficient value was the lowest (0.273) among the three methods. The coefficient value of CDS was 0.54 and that was the highest among the three methods. The result postulates that 1% increase in profit risk can increase the efficiency by 0.54%. Finally, from the regression results of three models, it can be concluded that the best way to measure efficiency is CDS model. Moreover, the coefficient of determination value ([R.sup.2]) value was better in the CDS model than other methods.

The sixth column of Table 3 displays that the coefficient of determination for ULFR; it is seen that a strong relationship between profit risk and efficiency is derived from CDS. Among the three methods' COD value of ULFR, the highest value shows that CDS is more reliable than other two methods. Fah et al. (2007) found COD of ULFR (0.4408) and COD of simple linear regression (0.1231) in the study of causation with Malaysian road accident data; this explains that variability of dependent variable in ULFR is better than in the simple linear regression. Our study also shows that COD of ULFR (0.9994) is higher than COD of simple linear regression (0.292); this means that ULFR model in the measuring the relationship between profit risk and efficiency is better than linear regression.

4.6. Error-free efficiency scores of financial companies

The efficiency derived from CDS may contain measurement error as it is the method combining DEA and SFA models. Moreover, CDS may contain an error due to some missing values imputation. To remove error we applied ULFR model. From the column three of Table 4, it is seen the error-free efficiency derived from CDS. The amount of error was minimal for all the companies.

The highest amount of error that was less than 2%, in companies ACSM, LPI, INS, and BURSA. On the other hand, companies HLG, MNRB, RCE, MAY encountered less than 0.05% error. Fernandas et al. (2018) applied Double Bootstrapped Truncated Regression to obtain bias-corrected scores but they did not show bias-free each company scores. Hasan et al. (2012) applied the SFA approach for finding the efficiency of the domestic banks listed in Bursa Malaysia over the period 2005-2010 but did not find error-free efficiency. These error-removed efficiency score will help to identify the most efficient company (ACSM) and the least efficient company (MAY).

5. Research Limitations

Our study only concentrates on two most popular efficiency models (parametric and non-parametric). However, in the future study, other efficiency models such as DFA (Distribution Free Approach), Cobb-Douglas model (1995) could be used. Additionally, the analysis only focused on yearly data, and in future research this model can be justified with daily data.

6. Conclusion

The study has concentrated on three methods, SFA, DEA, and combination of DEA and SFA (CDS) to identify the most efficient method to measure technical efficiency on sample data of financial companies that are listed in Bursa Malaysia. This study is conscious that this is the sole empirical measure that uses market data of financial companies' listed in Bursa Malaysia to compare different efficiency frontier techniques. The empirical results have depicted that there were no consistency between the efficiency scores derived from DEA and SFA. More generally, the first consistency case has revealed that the average efficiency scores derived from SFA are slightly shorter than those of the DEA and CDS.

After that, this study has analysed the relationship between efficiency and profit risk to find the most efficient method as theoretically it is known that profitable company should be most efficient. The results of linear regression and ULFR have shown that CDS has the most significant relationship with profit risk by linear regression COD. In the data set, some missing data were imputed by the maximum likelihood method, for this reason the measurement can encounter some error. To find error-free efficiency we have applied ULFR model and found error-free efficiency. The most efficient company was ACSM and the least efficient company was MAY. Considering no consistency on different efficiency scores across the different methods, this study will help to measure the error-free efficiency by CDS model. This type of empirical analysis could be applied in many other sectors of stock market.

Acknowledgement

We are grateful for the financial support provided by the UTAR Research Fund (UTARRF) (Project Number: IPSR/RMC/UTARRF/2017-C1/M01), Universiti Tunku Abdul Rahman, Selangor, Malaysia for conducting this research. We also thankful to the Daffodil International University for supporting us.

References

Adrienn, H. (2014). Financing aspects of the hungarian general manufacturers in 2010-2012. Annals of the University of Oradea, Economic Science Series, 23(1), 905-911.

Aigner, D., Lovell, C., Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6, 21-37.

Altunbas,Y., Carbo, S., Gardener, E. P., Molyneux, P. (2007). Examining the relationships between capital, risk and efficiency in European banking. European Financial Management, 13(1), 49-70.

Banker, R., D., Charnes, A., Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-1092.

Battese, G. E., Coelli, T. J. (1988). Prediction of firm-level technical efficiencies with a geeneralised frontier production function and panel data, Journal of Econometrics, 38, 387-399.

Bauer, P. W., Berger, A. N., Ferrier, G. D., Humphrey, D. B. (1998). Consistency Conditions for Regulatory Analysis of Financial Institutions: A Comparison of Frontier Efficiency Methods, Journal of Economics and Business, 50(2), 85-114.

Berger, A. N., & Humphrey, D., B. (1997). Efficiency of financial institutions: International survey and directions for future research, European Journal of Operational Research, 98(2), 175-212.

Campbell, J. Y., Shiller, R. J. (1988). Stock Prices, Earnings, and Expected Dividends, The Journal of Finance, 43, 661-676.

Casu, B., Girardone, C., Molyneux, P. (2004). Productivity change in European banking: a comparison of parametric and non-parametric approaches, J. Bank. Finance, 28, 2521-2540.

Charnes, A., Cooper, W. W., Rousseau, J., Semple, J. (1987). Data Envelopment Analysis and Axiomatic Notions of Efficiency and Reference Sets, Research Report CCS 558, Centre for Cybernetic Studies. The University of Texas at Austin.

Cobb, C., Douglas, P. H. (1928). A theory of production, American Economic Review, 18, No. 1, 139-165.

Coelli, T., Rao, D. S. P., & Battese, G. E. (1998). An introduction to efficiency analysis. Boston: Kluwer Academic Publishers.

Coelli, T., Rao, D. S. P., O'Donnell, C. C., & Battese, G. E. (2005). An introduction to efficiency and productivity analysis. New York: Springer.

Coelli, T. J. (1996a). A guide to DEAP Version 2.1 A data envelopment analysis (computer) program (CEPA Working Paper). University of New England.

Coelli, T. J. (1996b). A guide to FRONTIER Version 4.1 A computer program for stochastic frontier production and cost function estimation (CEPA Working Paper). Department of Econometrics. University of New England.

Davies, N. O. (2017). Empirical analysis of commercial banks in Malaysia using data envelopment analysis (DEA) Model, International Journal of Banking and Finance Research, 3(1), 40-48.

Delis, M. D., & Papanikolaou, N. I. (2009). Determinants of bank efficiency: evidence from a semi-parametric methodology, Managerial Finance, 35(3), 260-275.

Dong, Y., Hamilton, R., & Tippett, M. (2014). Cost efficiency of the Chinese banking sector: A comparison of stochastic frontier analysis and data envelopment analysis, Economic Modelling, 36, 298-308.

Eisenbeis, R., Ferrier, G., & Kwan, S. (1999). The informativeness of stochastic frontier and programming frontier efficiency scores: Cost efficiency and other measures of bank holding company performance (Working Paper, 99-23), Federal Reserve Bank of Atlanta, December.

Fah, C. Y., Ghapor Hussin, A., & Rijal, O. M. (2007). An investigation of causation: The unreplicated linear functional relationship model. Journal of Applied Sciences, 7, 20-26.

Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns, The Journal of Finance, 47, 427-465.

Fare, R., Grosskopf, S., & Lovell, C. A. K. (1994). Production frontiers. New York: Cambridge University Press.

Fenyves, V., Tarnoczi, T., & Zsido, K. (2015). Financial performance evaluation of agricultural enterprises with DEA method, Procedia Economics and Finance, 32(15), 423-431.

Fare, R., Grosskopf, S., Norris, M., & Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries, The American Economic Review, 84(1), 66-83.

Fernandes, F. D. S., Stasinakis, C., & Bardarova, V. (2018). Two-stage DEA-truncated regression: Application in banking efficiency and financial development, Expert Systems with Applications, 96, 284-301.

Ferrier, G., & Lovell, C. A. K. (1990). Measuring cost efficiency in banking: Econometric and linear programming evidence, Journal of Econometrics, 46, 229-245.

Greene, W. H. (1993). The econometric approach to efficiency analysis, in Fried, H. O., Lovell, C. A. K., & Schmidt, S. S. (Eds.), The measurement of productive efficiency (pp. 68-119), New York: Oxford University Press.

Hasan, M. Z., Kamil, A. A., Mustafa, A., & Baten, M. A. (2012). A Cobb Douglas stochastic frontier model on measuring domestic bank efficiency in Malaysia, PLoS ONE, 7(8), 1-5.

Huang, T. H., & Wang, M. H. (2002). Comparison of economic efficiency estimation methods: Parametric and non-parametric techniques, Manchester School, 70, 682-709.

Hubbard, R. G. (2008). Money, the financial system, and the economy. 6th ed. US: Pearson Education.

Isik, I., & Hassan, M. K. (2002). Cost and profit efficiency of the Turkish banking industry: An empirical investigation, The Financial Review, 37(2), 257-280.

Ismail, M. K. A., Rahman, N. M. N. A., Salamudin, N., & Kamaruddin, B. H. (2012). DEA portfolio selection in Malaysian stock market. International Conference on Innovation, Management and Technology Research, ICIMTR2012, Malacca, pp. 739-743.

Ismail, M. (2005). A study of efficiency and competitive Behaviour of commercial Banks in Malaysia (Doctoral thesis), Retrieved from UMI Dissertation Publishing, UMI Number U584012.

Janang, J. T., Suhaimi, R., & Salamudin, N. (2013). Directors incentive and technical efficiency of government linked companies in Malaysia: A stochastic frontier analysis, BEIAC 2013-2013 IEEE Business Engineering and Industrial Applications Colloquium, (February 2016), pp. 50-55.

Katib, M., Nasser, & Mathews, K. (2000). A non-parametric approach to efficiency measurement in the Malaysian banking sector, The Singapore Economic Review, 44, 89-114.

Kumbhakar, S. C., & Lovell, C. K. (2003). Stochastic frontier analysis. Cambridge University Press.

Lovell, C. A. K. (1993). Production frontiers and productive efficiency. In Fried, H. O., Lovell, C. A., Schmidt S. S. (Eds.), The measurement of productive efficiency (pp. 3-67). New York: Oxford University Press.

PatrAcia, B. N., & Balazs, F. (2014). Returns of private equity comparative analyses of the returns of venture capital and buyout funds in Europe and in the US. Annals of the University of Oradea: Economic Science, 23(1), 820-827.

Pereira De Souza, M. V., Diallo, M., Castro Souza, R., & Baidya, T. K. N. (2010). The cost efficiency of the Brazilian electricity distribution utilities: a comparison of Bayesian SFA and DEA models. Mathematical Problems in Engineering, 2010, 1-19.

Resti, A. (1997). Evaluating the cost-efficiency of the Italian banking system: What can be learned from the joint application of parametric and non-parametric techniques, Journal of Banking and Finance, 21, 221-250.

Saad, M. N., Idris, H., & Edzalina, N. (2011). Efficiency of life insurance companies in Malaysia and Brunei: a comparative analysis, International Journal of Humanities and Social Science, 1(3), 111-122.

Sealey, C. W. J., & Lindley, J. T. (1977). Inputs, outputs, and a theory of production and cost at semi-parametric methodology, Managerial Finance, 35(3), 260-275.

Seiford, L. M., & Thrall, R. M. (1990). Recent developments in DEA: the mathematical programming approach to frontier analysis, Journal of Econometrics, 46, 7-38.

Siew, L. W., Fai, L. K., & Hoe, L. W. (2017). An empirical investigation on the efficiency of financial companies in Malaysia with data envelopment analysis model, American Journal of Information Science and Computer Engineering, 3(3), 32-38.

Sprent, P. (1990). Some history of functional and structural relationships, Contemporary Mathematics, 112, 3-15.

Sufian, F. (2004). The efficiency effects of bank mergers and acquisitions in developing economy: Evidence from Malaysia, International Journal of Applied Econometrics and Quantitative Studies, 1(4), 53-74.

Sufian, F. (2016). Determinants of efficiency in the Malaysian banking sector: Evidence from semi-parametric data envelopment analysis method, Studies in Microeconomics, 4(2), 151-172.

Sufian, F., & Habibullah, M. S. (2014). Banks' total factor productivity growth in a developing economy: Does globalisation matter?, Journal of International Development. 26(6), 821-852.

Sufian, F., & Majid, M. A. (2006). Banks' efficiency and stock prices in emerging markets: Evidence from Malaysia. Journal of Asia-Pacific Business, 7(4), 35-53.

Sufian, F., Kamarudin, F., & Nassir, A. M. (2016). Determinants of efficiency in the Malaysian banking sector: Does bank origins matter?. Intellectual Economics, 10(1), 38-54.

Suhaimi, R., Abdullah, A., Nee, C. F., & Ibrahim, N. A. (2012). Profit efficiency and competitiveness of commercial banks in Malaysia, World Academy of Science, Engineering and Technology, 66, 627-630.

Weill, L. (2004). Measuring cost efficiency in European banking: a comparison of frontier techniques. J. Prod. Anal, 21, 133-152.

Omar Sharif, (1) Md Zobaer Hasan, (2) Chang Yun Fah, (1) Mahboobeh Zangeneh Sirdari (1)

(1) Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Malaysia

(2) School of Science, Monash University, Malaysia

corresponding e-mail: omarsharif[at]1utar(dot)my

address: Universiti Tunku Abdul Rahman, 43000 Kajang, Selangor, Malaysia

(*) The article was prepared in the framework of state budget scientific research work "Cyber security in the fight against bank fraud: protection of financial services consumers and growth of financial and economic security of Ukraine" (Registration No. 0118U003574) and "Improving the National System of Counteraction to Legalizing Funds Acquired in a Criminal Way in the Context of Increasing the Financial and Economic Security of the State" (Registration No. 0117U002251).

DOI: http://dx.doi.org/10.15208/beh.2019.7

TABLE 1. COMPANIES LISTED IN BURSA MALAYSIA COMPANY NAME SHORT NAME IN THE BLOOMBERG TICKER BURSA MALAYSIA NUMBER (MK EQUITY) Malayan Banking Bhd MAYBANK MAY Public Bank Bhd PBBANK PBK CIMB Group Holdings Bhd CIMB CIMB Hong Leong Bank Bhd HLBANK HLBK RHB Bank Bhd RHBBANK RHBBANK Hong Leong Financial Group HLFG HLFG AMMB Holdings Bhd AMBANK AMM BIMB Holdings Bhd BIMB BIMB Affin Holdings Bhd AFFIN AHB LPI Capital Bhd LPI LPI Syarikat Takaful Malaysia TAKAFUL STMB Allianz Malaysia Bhd ALLIANZ ALLZ MNRB Holdings Bhd MNRB MNRB Manulife Holdings Bhd MANULFE MHBS Pacific & Orient Bhd P&O PO Malaysia Building Society MBSB MBS Bursa Malaysia Bhd BURSA BURSA Aeon Credit Service (M) Bhd AEONCR ACSM INSAS Bhd INSAS INS RCE Capital Bhd RCECAP RCE Apex Equity Holdings Bhd APEX APX Johan Holdings Bhd JOHAN JOH ECM Libra Financial Group Bhd ECM ECML Hong Leong Capital Bhd HLCAP HLG TA Enterprise Bhd TA TAE MAA Group Bhd MAA MAA Source: Bloomberg terminal and Bursa Malaysia. TABLE 2. SUMMARY STATISTICS OF INPUT AND OUTPUT VARIABLES VARIABLES MINIMUM MAXIMUM MEAN STD. DEVIATION ROA -5.24 26.13 2.6349 3.31450 ROE -27.74 54.75 12.9440 10.27505 TV 770400.0 3761712400 459870978.71 726230640.93 DPS 0.00 1.34 .0481 0.09293 MC 18.09 26844.15 2868.5974 5378.04424 PB 0.18 9.60 1.4813 1.23367 FL 1.01 32.19 8.4594 6.39369 Source: Bloomberg Terminal. TABLE 3. RELATIONSHIP BETWEEN EFFICIENCY (derived from DEA, SFA and CDS) and profit risk MODEL CONSTANT ([[beta].sub.0]) COEFFICIENTS ([[beta].sub.1]) S.E DEA -1.765 0.461 (*) 4.317 CDS -10.591 0.54 (*) 6.687 SFA 0.307 0.273 6.386 MODEL [R.sup.2] [R.sub.f.sup.2] p-value DEA 0.2130 0.9983 0.018 CDS 0.2920 0.9994 0.004 SFA 0.0750 0.9991 0.177 Source: SPSS and Microsoft Excel. Note: (*) - 5% significant. TABLE 4. ERROR-FREE EFFICIENCY SCORES DERIVED FROM CDS COMPANY NAME (short form) EFFICIENCY DERIVED ERROR-FREE EFFICIENCY FROM CDS ACSM 0.9819 0.9910 LPI 0.9573 0.9768 INS 0.9675 0.9760 ALLZ 0.9683 0.9668 HLG 0.9627 0.9625 MNRB 0.9464 0.9457 STMB 0.9465 0.9441 ECML 0.9409 0.9401 RCE 0.9337 0.9389 APX 0.9231 0.9304 BURSA 0.9023 0.9238 MHBS 0.9241 0.9208 MAA 0.9155 0.9183 MBS 0.9009 0.8973 BIMB 0.8867 0.8816 HLFG 0.8791 0.8740 PBK 0.8709 0.8675 PO 0.8595 0.8568 TAE 0.8443 0.8455 HLBK 0.8354 0.8312 AHB 0.8247 0.8199 CIMB 0.8196 0.8155 RHBBANK 0.8146 0.8098 JOH 0.7929 0.7823 AMM 0.7822 0.7781 MAY 0.7693 0.7648

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Author: | Sharif, Omar; Hasan, Md Zobaer; Fah, Chang Yun; Sirdari, Mahboobeh Zangeneh |
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Publication: | Business and Economic Horizons |

Geographic Code: | 9MALA |

Date: | Jan 1, 2019 |

Words: | 7056 |

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