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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.

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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
Publication:Business and Economic Horizons
Geographic Code:9MALA
Date:Jan 1, 2019
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